Lower Hybrid Current Drive Experiments on the Encore Tokamak - CaltechTHESIS

AA A A AAA

ran styrofoam wanna

magnetic
- stirrer

Figure 5-18. Schematic of experimental arrangement used for the
calorimetric tests to check power flow through the antenna.

Alcohol was chosen as the base for the liquid load medium in order to match the

impedance of the antenna dielectric and increase the dimensions of the evanescent region.

The wave-guide material has a dielectric constant of € = 30. A mixture of 95% alcohol

5-29

and 5% water has a similar dielectric constant at radio frequencies.*’ By comparison,
distilled water has € = 80. The loss tangent must be increased to the point that the e-
folding distance for the RF power is a fraction of the load dimensions. The e-folding
distance should, in fact, be a fraction of the e-folding distance of the evanescent wave-
guide end-field. Utilizing data from King** it is seen that dissolving salt in the amount of
10gm/liter in the dielectric load increases the conductivity into the range 6 = 1 Si/m. For
this concentration the real part of the dielectric constant is essentially unchanged. The

increased conductivity gives a loss tangent of

S=— 31. (5.21)
WE

The resulting e-folding distance for our parameters is of the order of a few centimeters,
while the wavelength for plane waves in the fluid (~ 12 cm) is only slightly increased.

An indication of the effectiveness of the load is given by the drop in reflected
power to 10 dB or more below forward power upon immersion of the antenna end.

Styrofoam was placed between the polyethylene bucket and magnetic stirrer
because the stirrer became warm after running. The mechanical energy of stirring was
negligible for the duration of the experiment and the pre-experiment temperature was
stable to a tenth of a degree centigrade. The end of the antenna was covered with a thin
sheet of plastic to prevent salt water from soaking into the wave-guide dielectric. The
antenna and RF load were placed remote from personnel behind a metal door, and fire
extinguishers were available. Temperature measurements were made both with an alcohol
thermometer located at the bottom of the bucket and with an IR thermometer. These two
measurements were in agreement. All seals were made air tight with RTV to prevent

evaporative cooling. The heat capacity of the NaCl, Hj0, polyethylene bucket,

thermometer and stir-bar were included. Collectively, however, the heat capacity of these
materials is an order of magnitude less than that of the alcohol.

Only one wave-guide was powered. The forward RF power was measured by a
directional coupler hooked directly to the antenna. The coupler insertion loss of 0.2 dB
was noted. The power reflected back into the non-powered wave-guides was measured

and was negligible.

5-30

Average RF power levels of 233 watts incident to the antenna were used. The
experiment was run twice, with RF on times of 120 and 180 seconds. The results for the
two trials agree within 1%. The result is that the thermal energy measured in the load is
66% of the RF energy input to the antenna. The missing energy is 34% of the RF energy
input to the antenna and could be accounted for by losses in the antenna structure. A 1-
dB loss in the antenna as suggested by the earlier tests would account for 17% of the
input RF energy. A 1.8-dB loss in the antenna would be required to account for the entire
34%,

There are two principle sources of error, both of which tend to make the antenna
appear to have more loss. RF power that is not damped in the load, but escapes as
radiation will not heat the load. Second, the antenna has a large thermal mass and is
essentially at room temperature. Since the antenna has thermal contact with the load it
can act as a heat sink. Since the evanescent waves are damped close to the antenna, this
heat sink is all the more important.

In conclusion, antenna losses of 1.0 tol.8 dB need to be invoked to explain the
calorimeter data. Considering the possible errors, a 1.0-dB loss per pass, as was

suggested by the earlier bench test, seems reasonable.

RF Power Supply

A 4-channel, 450 MHz power supply with a combined output of 50 kW was
designed and built.°? A schematic of the RF supply is shown in Figure (5-19), and a
picture of the operational unit is shown in Figure (5-20). A considerable amount of time
was spent debugging problems with the RF supply. Kapton bypass capacitors in the
Eimac RF amplifier cavities occasionally failed accompanied by big arcs, so a fast
protection circuit utilizing ignitrons was installed to quickly crowbar the HV supply in
the event of an arc. The high voltage connections to the final amplifiers had to be well
shielded. To stabilize the amplifier chain, numerous isolators as well as substantial
shielding were installed in the low power sections. It was found necessary to pay

particular attention to isolating and shielding the low power stages from the high power

stages.

5-31

50mW

otorola
+21 dB MHW 720

+ 13 dB + 2.5kV
WWW-5
180°
Hybrid
——_— |
50W
LWW VW
Quadrature Quadrature
Hybrid Hybrid

To Grill Antenna

Figure 5-19. Schematic of the 50kW RF power supply. The
phase shifters and isolators were obtained from Micon Inc.*°, the
RF tubes and cavities from Varian Eimac*!, and the hybrids from
Merrimac.” The output directional couplers and additional
isolation to stabilize the amplifier chain is not shown.

5-32

The output power and sometimes the phase of RF amplifiers depend upon the
amount of reflected power. To make the phase and power of the RF supply immune to
the cabling, antenna structures and changing plasma conditions, high power ferrite
isolators where purchased and installed on the outputs of the final amplifiers.*? These
devices dump reflected power to dummy loads so that the final amplifiers see a constant
and almost negligible amount of reflected power. In the event of sustained large reflection,
the isolator dummy loads included temperature sensors capable of detecting thermal
overload and shutting down the RF supply. Output and reflected power could be

monitored with high power directional couplers on the output of the final amplifiers.

Figure 5-20. The four channel RF power supply used for the
LHCD experiments. On the table are directional couplers for
measuring forward and reflected power (long blue devices).

5-33

Quadrature hybrid modules employed in the low power sections of the amplifier
chains gave nominal output phasing at 0, 90, 180 and 270 degrees. Due to the phase
shifts inherent in the antenna, other phases were required. Phasing was accomplished
with the addition of phase shift modules. Cable delays in the low power sections were
also occasionally employed. At 450MHz, the wavelength in air is about 67cm. The
wavelength is roughly 2/3 of the vacuum value in the coax dielectric. These distances
make cable phasing a very reasonable alternative.

The OSHA average continuous exposure limit for RF radiation at frequencies from
10MHz to 100GHz is 10mW/cm?. Using a Narda-8611 survey meter with the 0.3-
26GHz probe, no average exposure was measurable on the lowest scale (0.1mW average
power) near any of the equipment. Window ports on the tokamak were checked as well
as the antenna structure, cabling and RF supply. Conditions involving plasma as well as
no plasma were checked. With a spectrum analyzer and a loop of area 1 cm’ on the end
of coax, instantaneous levels as high as roughly 7 mW/cm’ were observed very close to
the air cooling intakes on the final RF output cavities. Since the duty factor was generally
0.04 or less, the average power was considerably less. A small fluorescent lamp was
often carried around to detect any gross RF leakage, but none was ever seen.

The passive RF hardware was not immune to failure. In one incident, an audible
"ticking" sound was heard coincident with the repetitive RF bursts. The sound turned
out to be a spark on the RF connector of one of the high-power directional couplers. The

connector was defective and was repaired.

RF Plasma Probes

Considerable amounts of data were collected with the use of plasma probes, which
were scanned across minor cross sections of the Encore plasma. In this section aspects of
the construction of these probes is given, and their function is discussed.

Basic construction of the plasma probes involves telescoping cylinders of
stainless steel and alumina with a central conductor of tungsten wire. The construction

aims to produce coax protected by an outer cylinder of alumina as shown in Figure (5-21).

5-34

. alumina sheath
0.059” OD x 0.039” ID

stainless steel outer conductor
0.035” OD x 0.026” ID

alumina dielectric
0.024” OD x 0.012” ID

tungsten inner conductor
0.010” OD

Figure 5-21. Cut away view of end of RF plasma probe, not to
scale. The alumina sheath is 25cm long. The exposed tungsten is
treated with a tesla coil to remove sharp edges.

Tungsten wire and alumina are chosen for their resistance to sputtering. Alumina
has one of the lowest sputtering yields of any known material.4 The sputtering
threshold for tungsten is 33eV*° and is considerably greater than a typical plasma
temperature in Encore (~10eV). Of the elemental metals, only rhenium at 3S5eV has a
higher sputtering threshold. Plasma in Encore typically involves atomic or molecular
species that are not fully ionized. As such, the plasma temperature is clamped close to
the ionization potential of the tokamak fill gas. For argon this is 15.8eV and for hydrogen
is 13.6eV.

The exposed portion of the tungsten wire is bent over at 90° and in the plasma is
oriented parallel to the toroidal magnetic field. See Figure (5-22). The reason for this is as

follows. From equation (4.78)
2 2
Pg (5.22)
kj rv, Ss
Except at the plasma edge, the ratio -P/S is a large positive number. This implies that

i, >>A,. Thus LH wave phase variations along the toroidal field are slower than

5-35

perpendicular to the toroidal field. Increases of probe area to increase sensitivity should

therefore be along the toroidal field rather than perpendicular to it.

Figure 5-22. Schematic layout of the grill antenna and RF plasma
probes. The probes can be scanned over the two-dimensional
minor cross section.“® In addition, the probes can be moved to
any port around the tokamak. On Encore there are 20 ports
around the outer circumference, located every 18°.

The central conductor of the RF plasma probes is floating. Capacitive coupling
allows high frequencies to pass unimpeded down 50-ohm cable to a power detector, often
a spectrum analyzer. As discussed in the LH theory section, LH waves in Encore are
electrostatic. Wave energy is carried primarily by particle motion rather than by electric
or magnetic fields. The electrostatic field is generated by ion density fluctuations
oscillating along k. The electrons circle around k without producing a density gradient.
What the probe sees is an ion density varying at 450MHz.

According to elementary gas-kinetic theory, the number of particles of a given

species T crossing per unit area per unit time (from one side only) is”
T=—nvy, (5.23)

where V is the mean particle speed. For comparable electron and ion temperatures, the

mean speed of the electrons is much greater. The mean electron current greatly exceeds

the mean ion current and the floating probe potential is negative. From (5.23) the ion

5-36

current is proportional to the ion density, which includes a component fluctuating at
450MHz. Since the mean floating potential does not change, the plasma sheath
surrounding the probe does not change and the frequency response is limited only by the
capacitance of the probe. Since the capacitance is likely of the order of one picofarad, the
frequency response is probably limited to something like

1 1
RC (50ohms)(107” farad)

= 20GHz. (5.24)

If the ion density fluctuations become large enough, the assumption that the plasma
sheath remains unaffected may become false. It is assumed, however, that the signal level
detected varies monotonically with the wave power. In this case, the location of the LH

wave power in the scanned minor cross section can be unambiguously identified.

Two-Sided DC Probe

Some data was taken with a Two-sided current collecting probe shown in Figure
(7-23). The purpose of this probe was to discriminate direction of electrons moving at
high speed along the toroidal field. Each of the two exposed pieces of tungsten wire
intercepts toroidal magnetic field lines from a direction opposite that of the other. The
wires are biased negatively so that they collect ion saturation current. When bombarded
by fast tail electrons, electrons are collected despite the negative bias. This flow of
electrons can dwarf the ion saturation current. Hence, toroidally accelerated electrons can
be detected and their direction ascertained. By varying the probe bias, some information
regarding the electron energy can be obtained. The electron cyclotron radius is given by

T,
re 34.0 cm. (5.25)

gauss

For Beauss=1300 gauss and T,=100eV, equation (5.25) returns r° =0.026cm. This is
about 0.010" and too small for an electron to "hop" around the alumina separating the two
tungsten wires. On the other hand, for argon ions with T=3eV, 1" =1.2cm and ions

could pass around the alumina shield separating the two wires.

5-37

0.101” OD

+ at

0.020” OD le <«____ double bore
tungsten wire alumina tubing

4.3mm 1.5mm

Figure 7-23. Schematic of the end of a two-sided current
collecting probe used to determine tail-electron direction. In the
plasma, the two tungsten wires lie in the same horizontal plane
and are oriented perpendicular to the toroidal-field. In this
manner, each tungsten wire intercepts hot tail electrons from a
single toroidal direction.

Phase Measurements

The inherent phase delays in the individual waveguides must be measured so that
the grill antenna can be properly phased to launch (as nearly as possible) unidirectional
LH waves. Phase delay in cabling and passive components such as directional couplers
must also be known. Calculations for these quantities cannot be considered reliable.

Initially, phase measurements were attempted with small electric-dipole probes
maneuvered in front of the grill antenna. Reproducibility was a problem. The electric
probes were particularly sensitive to motions and positions of objects in the vicinity.
The exact position of the probe was important. The measured phase could vary by up to
+ 20° depending on the position. In order to measure the phase at the end of one of the
central waveguides, a cable connected to the dipole antenna crossed in front of other
waveguides, altering the boundary conditions.

A magnetic-coupled loop antenna proved to be much more reliable, and was

totally insensitive to motion of nearby objects. More importantly, it was insensitive to

5-38

the exact position of the loop. In addition, the cable connected to the loop could be made
to approach the open end of the waveguide without crossing in front of other waveguides.
Further reproducibility was obtained by enclosing the magnetic pick-up loop as well as
the end of the grill antenna in a box of RF absorbing foam.

Originally, a pair of mixers and a local oscillator was used to display a sinusoidal
waveform on an oscilloscope, from which the phase could be measured. Later, a vector
voltmeter was used to obtain more precise measurements. The vector voltmeter
measurement scheme was capable of determining phase to +5°. A schematic of the
phase measurement arrangement is shown in Figure (5-24). The phase shifts of cabling
and directional couplers could be determined by adding them between the RF source and

antenna and noting the additional phase lag.

50-ohm termination

Pm 2
a |
a ‘e] a RF absorbing
in A a eee

: g foam

aay in

directional
coupler

Figure 5-24. Set up for determining phase delay in the individual
waveguides of the grill antenna.

5-39

The vector voltmeter could not be used for checking the phase of the high-power RF
system due to the pulsed output. Measurements of the RF supply phase were made

with the oscilloscope system.

' R. J. Briggs et al., "Transport of energy to the lower hybrid resonance in an
inhomogeneous plasma,” Phys. Rev. Lett., 29, (1972), p. 852

2 Pp. Lallia, "A LHR slow wave launching structure suited for large toroidal
experiments," 1974 Topical RF Conference, Texas, p. C3-1

3M. Brambilla, "Slow-wave launching at the lower hybrid frequency using a
phased waveguide array," Nuc. Fus., 16, (1976), p. 47

4 §. Bernabi et al., "A theoretical and experimental study of plasma-wave
coupling and propagation using phased waveguide arrays and electrostatic
structures," PPPL-1288, Sept. 1976, Princeton U., Plasma Physics Laboratory,
Princeton, NJ

> V. Krapchev et al., "Waveguide array excitation of lower hybrid fields in a
tokamak plasma," Nuc. Fus., 18, (1978), p. 519

6 O. N. Scherbinin et al., "effect of wall corrugations on the lower hybrid wave
spectrum of a waveguide array,” Nuc. Fus., 19, (1979), p. 1675

7 V. B. Krapchev et al., "Non-linear coupling of lower-hybrid waves at the edge
of tokamak plasmas," Phys. Rev. Lett., 46, (1981), p. 1398

8 J. Rodney et al., "Multipactor in the Brambilla grill," Proc. of the IEEE, 70,
(1982), p. 203

° F. Gardiol, "Open-Ended Waveguides: Principles and Applications,” in
Advances _in Electronics and Electron Physics, vol. 63, (1985), p. 139

10 J. Preinhaelter, "Optimization of the muti-junction grill for lower hybrid
current drive," Nuc. Fus., 29, (1989), p. 1729

'! Pp. Lallia, "A LHR slow wave launching structure suited for large toroidal
experiments," 1974 Topical RF Conference, Texas, p. C3-1

12 Fields and Waves in Communication Electronics, Ramo, Whinnery and Van
Duzer, (1965) John Wiley & Sons, p. 289

13, R. E. Collins, Field Theory of Guided Waves, 2nd edition, (1991) IEEE Press, p.
483

'4 Fields and Waves in Communication Electronics, Ramo, Whinnery and Van
Duzer, (1965) John Wiley & Sons, p. 421

'S Eccoflo HiK free flowing dielectric powders, dissipation factor 0.0007, density
2.70 gm/cc, € = 12, Emerson & Cuming, Inc., Canton, MA 02021

'®© Stycast 35D, dielectric casting resin, dissipation factor 0.002, Emerson &
Cuming, Inc., Canton, MA 02021

'T F, Sporleder and H. Unger, Waveguide tapers, transitions and couplers,
(1979) Institution of Electrical Engineers, London, p. 2

'8 R. A. Waldron, "The theory of reflections in a tapered waveguide," The Radio
and Electronic Engineer, Oct. 1966, p. 245

' F. Sporleder and H. Unger, Waveguide tapers, transitions and couplers,
(1979) Institution of Electrical Engineers, London, p. 2

20 Montgomery, Dicke and Purcell, principles of Microwave Circuits, (1948)
McGraw-Hill, p. 168

21 Stycast HiK 500F, high temperature, high dielectric constant stock,

dissipation factor < 0.002, dielectric strength > 300 volts/mil, Emerson &
Cuming, Inc., Canton, MA 02021

5-40

22 Stycast HiK cement, dissipation factor 0.01, © = 20, Emerson & Cuming, Inc.,
Canton, MA 02021

23 Robert E. Collin, Field Theory of Guided Waves, Ist edition, McGraw-Hill, NY,
(1960), p. 266

°4 Robert E. Collin, Field Theory of Guided Waves, Ist edition, McGraw-Hill, NY,
(1960), p. 270

25 Fields and Waves _in Communication Electronics, Ramo, Whinnery and Van
Duzer, (1965) John Wiley & Sons, table 8.09, p. 444a

26 G. W. Pierce, Phys. Rev., 2, (1985), p. 99, (claim 12 kV/3.5mm)

27 UG 496/U, Amphenol 82-92

28 J. R. Whinnery et al., "Coaxial-Line Discontinuities," Proc. of the LR.E.,
(November 1944), p. 695

29 "Combat-BN Coatings" available from Carborundum Corporation, 168
Creekside Drive, Amherst, NY 14228

30 V. Krapchev and A. Bers, “Wave-guide Array Excitation of Lower Hybrid
Fields in a Tokamak Plasma,” Nuc. Fus., 18, 1978, p. 519

31M. Brambilla, “Slow Wave Launching at the Lower Hybrid Frequency using a
Phased Wave-guide Array,” Nuc. Fus., 16, 1976, p. 47

32 V. Krapchev et al., "Waveguide array excitation of lower hybrid fields in a
tokamak plasma," Nuc. Fus., 18, (1978), p. 519

33, Pp. Lallia, "A LHR slow wave launching structure suited for large toroidal
experiments,” 1974 Topical RF Conference, Texas, p. C3-1

34 “Dielectric Materials Chart,” Emerson & Cuming, Inc., Canton, MA 02021, 1975
35 Fields and Waves _in Communication Electronics, Ramo, Whinnery and Van
Duzer, (1965), John Wiley & Sons, p. 289

36 Fields and Waves in Communication Electronics, Ramo, Whinnery and Van
Duzer, (1965), John Wiley & Sons, p. 426, 444a

37 Antennas in Matter, R. King and G. smith, MIT Press 1981, p. 740

38 Antennas in Matter, R. King and G. smith, MIT Press 1981, p. 741

3° The basic construction was largely carried out by Frank Cosso. The author of
this thesis was extensively involved in the debugging required to make the RF
supply operational.

40 Micon Inc., Ferrite Control Div., 1105 Industrial Parkway, Bricktown, New
Jersey 08723

41 Varian, Eimac Division, 301 Industrial Way, San Carlos, California 94070

42 Merrimac Industries, Inc., 41 Fairfield Place, West Caldwell, NJ 07006

43, R. O. Collado et al., "Specification of high-power ferrite circulators,” in
Microwaves & RF, November, (1987), p. 107

“4 Brian Chapman, Glow Discharge Processes. John Wiley & Sons, NY, (1980),
p.379, p. 396

45 Brian Chapman, Glow Discharge Processes, John Wiley & Sons, NY, (1980),
p.394

46 E. Fredrickson, "An experimental and theoretical investigation of a finite
beta modified drift wave," Thesis, Caltech (1985), p. 5

47 |. H. Hutchinson,_principles of Plasma Diagnostics, Cambridge University
Press, NY, (1987), p. 51

6-1

6 Data from Ohmic Plasmas

The Encore tokamak produces repetitive and highly reproducible ohmically
generated target plasma for LHCD. The plasma is well characterized and the magnetic
field and density can be easily varied. LH waves were launched with the solid dielectric
antenna into plasmas with a variety of plasma parameters in order to verify LH
accessibility, propagation angle and antenna phasing asymmetry. High power LH waves

were launched in attempts to generate significant changes in plasma current.

Low Power Measurements

Early measurements verified that proper antenna phasing can launch directional
plasma waves and verified the propagation-angle dependence on the toroidal magnetic
field expected of lower-hybrid waves. The antenna utilized was the first antenna model
discussed in chapter 5, which is shown in Figure (5-2) at the far left. This antenna had
identical phase delays for all four ports and setting the phase was particularly simple.
The RF power supply is shown schematically in Figure (6-1) and automatically generates

the directional quadrature phasing.

0.5 watt
amplifier

- Quadrature
Hybrid

_ Hybrid
Junction

To Grill
Antenna

450 MHz
oscillator

Le Quadrature.
Hybrid

Figure 6-1. Low power (2-watt) RF supply for launching signal-
level LH waves with quadrature phasing from a 4-port grill

antenna.

6-2

The experimental arrangement is shown in Figure (6-2). Two linear RF-probes operating
in the tokamak mid-plane are located on either side of the grill antenna. The probes scan

parallel to major radii of the torus.

Probe 1

Grill
Antenna

Probe 2

Figure 6-2. Experimental arrangement for launching and
detecting signal level LH waves in Encore.

The grill antenna excited a cavity mode in the torus that could obscure the plasma
wave signal. Using a "boxcar" sampling device to look for the LH wave during a specific
portion of the plasma shot was found necessary. The detection electronics is shown
schematically in Figure (6-3). Capacitive coupling prevented DC probe voltages from
damaging the RF electronics. The low pass filter eliminated any constant RF signal such

as RF broadcast from other installations.

probe | probe 2

capacitive

— 4 coupling
bandpass spectrum
filter -—j amplifier } analyzer
high pass
X-Y recorder 4 boxcar |-4 aler,

Figure 6-3. Schematic of electronics used for signal level
detection of lower hybrid waves in Encore.

6-3

Data showing directionality is given in Figure (6-4). The toroidal magnetic field
was 345 gauss, allowing deep penetration of the LH waves. The coils generating the
vertical magnetic field on Encore were often configured to simultaneously produce a
radial-horizontal magnetic field to null out magnetic errors in the toroidal magnetic field.
It was found necessary to keep the vertical and radial-horizontal coil currents identical to
obtain reproducibility. The probes are not unidirectional. LH waves impinging from
either toroidal direction or from multiple toroidal revolutions in the same direction are
detected. LH wave damping is necessary to demonstrate the directionality. Better than

10dB of directionality was noted in the probe measurements.

Probe |!

Major Radius (cm)-

38
Outer
Wall

Figure 6-4. RF-voltage versus position in major radius for the
two probes located on either side of the grill antenna. With
quadrature phasing better than 10dB directionality was noted.

The propagation angle of LH waves with respect to the toroidal magnetic field is
given by equation (4.89). The angle is inversely proportional to the magnitude of the
magnetic field and independent of plasma density. The LH waves are launched from the
grill antenna located on the tokamak outer wall. Faster penetration into the torus is
expected for lower magnetic fields. This is indeed seen in the probe measurements,

providing confirmation that LH waves are being launched and observed. See Figure (6-

5).

6-4

690 gauss «= <"S"" ce /\

ee powpeet

520 gauss- “~~ [ \

ad ~ 1,
we mee need

350 gauss ~~~ 7

38 Outer
Wall

Figure 6-5. RF-voltage versus position in major radius for three
different toroidal magnetic fields. The location of the peaks
moves as expected for LH wave propagation.

Set-Up for Measurements with the Solid Dielectric Antenna

Considerable data was taken using the solid dielectric antenna and an X-Y probe
capable of scanning a square inscribed in the minor cross section of Encore. The
arrangement of the antenna and X-Y probe on the tokamak is shown schematically in
Figure (6-6). The probe and antenna are separated by 45 degrees in the toroidal direction.
The grill antenna was phased to launch LH waves preferentially in the counter clockwise
direction, which is the direction in which electrons are accelerated by the ohmic supply.
Data taken on the side of the antenna to which LH waves are preferentially launched are
denoted "downstream" data. To obtain data on the "upstream" side of the antenna, the
positions of the antenna and probe were swapped, using the same two ports. The RF
power to the four channels was 260, 240, 250, and 270 watts, for a combined total of

1.2kW. The tokamak was filled with argon to a pressure of 5.0x10° torr. The vertical

magnetic field was varied to maximize the plasma current and its stability.

6-5

Top View

“Up Stream”

of the Antenna
van an Ae £4

Probe Located
“Down Stream’

LH Antenna
(quadrature phased for
counter clockwise launch)

Figure 6-6. Experimental arrangement of the antenna and X-Y
probe. To obtain the "upstream" data, the positions of the
antenna and probe were reversed, using the same two ports.

The orientation of the data plots is described in Figure (6-7). The grill antenna is
installed in a port on the outer wall. Consequently, plasma waves are generated near the
outer wall and then propagate to other locations in the minor cross section. Accessibility
limits the depth of penetration, and the LH propagation angle affects the rate of
penetration into the plasma. The physical size of the scanned square was measured as
16cm by 16cm. The diagonal of this square is 22.6cm and is close to the diameter of the

minor cross section (24cm).

top
near Vs near
inner YW outer

wall wall

bottom

Figure 0-7. Description of the orientation of the X-Y data plots.

6-6

The electronics used to collect the data is shown in Figure (6-8). Due to the large
plasma wave power utilized, the set up is somewhat simplified from that required for
signal level measurements. The spectrum analyzer was tuned to 450MHz by inputting
the oscillator signal driving the high power RF supply. The computer controls the
position of the probe which stops at 32 by 32 positions per scan to take data.

coupling
capacitor
- To Plasma Probe

30dB

Spectrum
Analyzer

Buffer
Amplifier
Transient
Digitizer

To Computer

Figure 6-8. Electronics used in taking the two-dimensional data
arrays of plasma wave power.

The data is displayed with a color-coding for relative RF power level. The scale
is two and one-third dB per color and there are ten colors. The color code is displayed in
Figure (6-9). Any data outside of the 23.3dB range is aliased into the nearest color range.
Care was taken to avoid aliasing into the top green bin through proper choice of the

reference level.

Figure 6-9. Color code for the X-Y data plots. The scale is 2 and
1/3 dB per color. Power increases from left to right. Green
colors represent large RF power.

6-7

Data from the Solid Dielectric Antenna

Due to the antenna phasing, LH waves are preferentially launched in the counter-
clockwise direction as seen from above. When the RF-probe is located slightly counter-
clockwise from the antenna it is considered "downstream." Two matrices of data where
taken. One matrix is with the RF-probe located downstream of the antenna, the other
with the RF-probe located upstream of the antenna.

Plasma currents utilized were 0.25, 0.50, 0.75. 1.00, 1.25, 1.50, 1.75, and 2.00
kilo-amps. Toroidal magnetic fields utilized were 345, 518, 690, 863, 1040, 1210 and
1360 gauss, measured at the axis of the minor cross section. The individual matrices
involve all possible combinations of plasma current and toroidal magnetic field. Rows
are associated with specific plasma current; columns are associated with specific toroidal
magnetic field. Higher rows are associated with higher plasma current. Columns further
to the right are associated with larger toroidal magnetic field.

Plasma density is roughly proportional to plasma current in Encore. Figure (6-10)
shows data of this nature.’ This means that in the matrix of plotted data, plasma density
can be assumed to be greater in higher rows. Plasma current increases monotonically
with the ohmic power. Since argon plasma in Encore is not fully ionized, it is reasonable
to expect that the degree of ionization and thus plasma density will increase
monotonically with ohmic power and thus with plasma current.

4.0E+12

T T.
y = 1.21E+12x - 6.50E+11 J
3.0E+12 4
Plasma

Density 2.0E+12
(cm-3)

1.0E+12

0.0E+00 VA

0.0 1.0 2.0 3.0 4.0

Plasma Current (kA)

Figure 6-10. Data showing that plasma density in Encore is

roughly proportional to plasma current.

6-8

Plasma in Encore at large minor radius where the grill antenna is located is not
always "smooth." The RF power reflected from the antenna is seen to drop when plasma
is present. The drop in reflected power is not steady but can show quite a bit of temporal
structure. The reflected power from one channel of the grill antenna is shown in Figure
(6-11). The plasma parameters were 345-gauss and 250-amps. Similar but less dramatic
oscillations were noted at 1 kilo-amp and 518-gauss. The structure of the plasma changes
with changes in the plasma current and toroidal field. These structure changes in turn
affect the antenna/plasma coupling. The oscillations shown in Figure (6-11) are probably

due to naturally occurring drift waves in the plasma.”

Figure 6-11. Oscillations in the reflected power from one
channel of the grill-antenna. The plasma parameters are 250-amp
current and 345-gauss toroidal field. The vertical scale is 10dB
per division. The horizontal scale is one millisecond per division.

The matrices of data are shown on the following three pages. For reference, the

plasma current and toroidal magnetic field vary across the matrices as in Table (6.1).

6-9

345G 518G 690G 863G 1040G 1210G 1360G

2.00 kA O O C 0 O O C]
1.75 kA O O U U O O O
1.50 kA O O O U O 0 O
1.25 kA U O U 0] O O U
1.00 kA O U O O U Q O
0.75 kA UL LJ O O U 0] a
0.50 kA O] O O O O O Oj
0.25 kA O O O O O C] O

Table 6.1. Plasma current and the magnetic field on the toroidal
axis for the arrays of plots shown on the following pages.

6-10

2.00

pth IS Ete ben

Te t0aS Nyt ie oe

b=. Rae Fe tess Bree Seem Te rece Spt FAs Bn
Tet te Brice sewn 2 =

ee

0.25

Fesoas Beh

345 518 690 863 1040
MAGNETIC FIELD (GAUSS)

Figure 6-12a. Downstream data.

PLASMA CURRENT (kA)

6-11

2.00

Tpt tec Fr=3so vg Tee

1.75

Tents Spree ve Serle See ve

Tyres By teat oe

1.50

1.25

Fest ae Cyt tee wp

1.00

Thee Spt2Bse oe Tpthes By Wwe

0.75

Terere Shae we

0.50

ah
Terese Gress up Tp ress Bethy

Se 8Is Byte

1040
MAGNETIC FIELD (GAUSS)

Figure 6-12b. Upstream data.

PLASMA CURRENT (kA)

Verification of LH Wave Accessibility

In Figure (4-7) the Ny, accessibility limit is plotted versus the major radius for

various toroidal magnetic fields, assuming a line average plasma density of 2x10’? cm

Graphs specifically applicable to the matrices of data are given below. The major radius
is measured from the center of the minor cross section. Thus R=0 corresponds to the
center of the minor cross section. Each curve corresponds to a particular toroidal
magnetic field. The toroidal fields on axis are 345, 518, 690, 863, 1040, 1210, and 1360
gauss. For a given major radius, the curves are monotonically lower in value as the
magnetic field is increased.

The 1/R dependence of the toroidal magnetic field upon the major radius is
included in the calculations. The plasma density profile in Encore is known to be flatter
than parabolic.> A semi-circle plasma density profile is assumed. The line average
density is obtained from the data in Figure (6-10). The linear fit in Figure (6-10) does not
have a zero intercept, and there is no data below one kiloamp. The line average densities
for plasma currents below one kiloamp were estimated from an extrapolation of the
lowest data point linearly to zero. The line average densities used are 1.77, 1.47, and

1.17x10" cm®?, and 8.6, 5.6, 4.2, 2.8, and 1.4x10'! cm”.

The shaded regions designate the Nj range launched by the grill antenna. The
spectrum peaks at Nj = 10 (see Figure (5-15)). Nj values equal to the accessibility limit
mode convert to the fast wave and propagate back out of the plasma. Nj values less than
or equal to the accessibility limit are consequently prevented from penetrating further into
the plasma. The shaded area above the center of the graph represents launched LH wave
power that is capable of propagating to the center of the plasma.

The right-hand side of the plots corresponds to the outer wall of the tokamak from
which the LH waves are launched. Under conditions of low toroidal magnetic field and
high plasma current, it would be possible for LH waves launched near the outer wall to
propagate around the periphery of the plasma and appear near the inner wall. The inner
wall of the tokamak corresponds to the left-hand side of the plots. Accessibility is

marginally improved near the inner wall due to the larger magnetic field at that location.

6-13

I, =0.25kA I, =0.50kA
15 15
a) 10 re 10 —_ “
ral = 345G ~
i " ve
w a i ae AA
Bf eee MIE Lb \
os - Oo 51f nm
a oo er — a / A a Z, = SSN =z Oe
1360 G 1360
-12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12 -12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12
Major Radius (measured from 38cm) Major Radius (measured from 38cm)
Ip =0.75kKA I, =1.00kA
15 15 a
peer 345 A
345 G ae \ \
10 ae \-] Be 10 eee
Le ose VES EN
OYA Pe = iz pers
1360 G
0 0 ,
-12 -10 -8 -6 -4 -2 02 4 6 8 10 12 -12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12
Major Radius (measured from 38cm) Major Radius (measured from 38cm)
Ip =1.25kA I, =1.50kA
20 — 25
~ 345 G ~_
a A 59 345G —
re 10 al |B VA rt
v1 -_ A] / pe
4 Vere “ ee
= [PI . —_ fe en aa
2 eee eG a 5 a
1360 G
0 0 J

“12-10-86 -42024 68 O01 -12-10-8 -6 -4 202 46 8 012

Major Radius (measured from 38cm) Major Radius (measured from 38cm)

6-14

Ip =1.75kA I, =2.00kA
25 30
_ 345 G pet | m5 —.
"B20 345G ot ‘
a 20
=) Is} ee By =) _ \
8 10 va eo oa uN & of “ae —™
gr —— — | a] a: -
1360 G a rae
0 |
-12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12 2 -10 -8 -6 -4 -20 2 4 6 8 1012
Major Radius (measured from 38cm) Major Radius (measured from 38cm)

Figure 6-13. The accessibility limit Ny, as a function of the major
radius, for various magnetic fields. The magnetic field
monotonically increases from the uppermost to the lowest curve.
The magnetic fields on axis are 345G, 518G, 690G, 863G,
1040G, 1210G, and 1360G respectively. The shaded region
indicates a typical launch spectrum for quadrature phasing of the
final LH antenna. A line average plasma density of
2.0x10'cem™ is assumed.

For the lowest toroidal field (uppermost curve in each plot), only the lowest
plasma current (0.25kA) shows good accessibility. This predicts that the left-hand
column of plots will show little if any green regions near R=0, except possibly for the
plot at the bottom. This is the case. In fact many plots in the left-hand column contain
large amounts of blue, which represents the lowest power bin.

Accessibility is best for the largest magnetic fields, which corresponds to the right
hand columns of the data matrices. Accessibility is also best for the lowest plasma
currents, which corresponds to the lower rows of plots in the data matrices. In the
downstream data matrix, most of the data plots with substantial amounts of green area
(corresponding to large plasma wave power) occur in the right-hand columns or lower
TOWS.

There are some data plots at 518 gauss and one at 690 gauss that have some

regions of green pixels, despite also having substantial plasma currents of at least 1kA.

These are plasmas with a large poloidal field to toroidal field ratio, and thus larger

6-15

rotational transform. The Nj spectrum will alter upon significant poloidal propagation.’
Provided that the poloidal propagation is rapid compared to wave damping, Ni changes
should occur and accessibility would be impacted. Accessibility is so poor for the lowest
magnetic field that little power can even enter the plasma, and thus have a chance for
subsequent Nj changes.

Larger Nj at launch are preferable for improved accessibility. For a four-port grill
antenna that would require narrower waveguides. That in turn would limit the total RF
power available. Limiting factors include waveguide electrical breakdown, multipacting
behavior and pondermotive forces upon the nearby plasma. The remedy is to have more
waveguides. This dramatically increases the control of the launched Nj spectrum,
provided the ability to continuously vary the phasing to the waveguides is included.

In attempts to drive plasma current with LH waves launched into ohmic plasmas,
it was consistently noted that AI, was largest for smaller plasma current. This is entirely

consistent with the improved accessibility at low plasma current.

LH Propagation Angle

The launched LH waves propagate at a specific angle with respect to the toroidal
magnetic field. Even if the waves are accessible to the plasma interior, if they propagate
inwards along too shallow a path, the power may be damped long before reaching the
plasma interior. The propagation angle is given in equation (4.89) and depends only on
the frequency (which is fixed) and the magnetic field. The values are given in Table
(6.2). Also given in the chart is an estimate of the maximum inward deviation of a LH
wave on a single pass between the antenna and probe. It is assumed that the LH wave is
launched near the outer wall, and that the toroidal separation of the antenna and probe is
45°. The major radius of the outer wall is 50cm, and 45° represents a portion of the
circumference measuring 39.3cm. The inward deviation is calculated as

AR = 39.30M X ® ian - (6.1)

6-16

B, (gauss) 345 518 690 863 1040 1210 1360
@ (degrees) 25° 17° 13° 11° 9° ge 7
AR (cm) 17.1 117 89 75 62 55 48

Table 6.2. Resonance cone angle and inward deviation versus
magnetic field on axis.

The data plots represent a physical dimension of 16cm on a side. The minor
diameter is 24cm. Hence, there is a gap of the order of 4cm between the outer wall and
the right-hand side of the plots.

Consider the second row from the bottom where accessibility is good. The data
plots show a clear indication that the penetration of the green areas into the plasma from
the right-hand side varies in a monotonic fashion with the magnetic field. The ~
penetration is greatest for lower magnetic field. The plot with the largest number of
green pixels is the one with 518-gauss and 500-amp plasma current. This set of
parameters enjoys both good accessibility and fast penetration due to a large propagation
angle.

The lowest row appears anomalous in that although accessibility is excellent and
for some magnetic fields the penetration should be rapid, few green areas appear. The
plasma current for this row is 250-amps. From equation (3.17) the maximum confined
electron velocity for a plasma current of 250-amps is 1.4x10° cm/sec. This corresponds
to an electron-energy of only 5.6 eV. Electrons more energetic than 5.6 eV are not
confined by the poloidal field. Since the ionization potential of argon is 15.8eV, electron
temperatures in Encore are clamped near this value. The lowest row of data plots
represents anomalous plasmas in that they are poorly confined.

For maximum magnetic field and plasma current between 1kA-1.5kA, significant
penetration appears despite the small propagation angle. There is good accessibility for
these plots. If LH wave damping were small, an additional toroidal revolution would add
additional deviation of up to 38cm. This deviation is so large that the power could appear
anywhere in the minor cross section. Because the plots appear to show wave power
creeping in from the right-hand side, significant contribution to the data from more than

one toroidal-propagation would be unlikely. Plasma turbulence may play arole.

6-17

Directionality due to Antenna Phasing

The phase of waveguides is such that the antenna launches power preferentially in
what is called the "downstream" direction in the data. If the upstream and downstream
data matrices are compared, it is immediately evident that significantly larger plasma
wave power is launched downstream compared to upstream. This demonstrates that the
quadrature phasing of the antenna produces an asymmetry in the Nj spectrum just as it is
supposed to do. Phasing appears to work in these ohmic plasmas.

Looking at the upstream data, few plots show yellow or green areas representing
significant power. In most instances, where significant power is found upstream, even
more power is detected downstream. This is evidence for the stability of the
measurements and the stability of the calibration. The only plots to buck this trend lie on
the third row at the three highest magnetic fields. In this case one has once again the
issue that the penetration appears excessive given the propagation angle. This
phenomenon has been noted at high magnetic field with plasma current between 0.75 and
1.5 kiloamp.

The RF-probe will detect power propagating from either toroidal direction. The
fact that so little power is seen upstream compared to downstream is strong evidence that
wave damping is sufficient to curtail contribution from paths of the order of one toroidal

revolution.

Attempts to Drive Large Plasma Current

The LH grill antenna was phased to launch waves primarily in the direction of the
ohmic accelerated electrons. The forward and reflected power in kilowatts to the four
waveguides during plasma launch for this experiment is as follows:

Channel 0 1 2 3
Reflected 0.6 1.1 2.1 0.1
Forward 40 40 3.3 3.0

There was some difficulty with channel two during this period.

The tokamak was filled to a pressure of 3.0x10° torr of hydrogen. Target plasma

with approximately 1kA ohmic current was used. The associated loop voltage was

6-18

recorded as 2.5 volts giving an ohmic power of 2.5kW. However, the calibration of the
loop voltage was later called into question. Judging from recorded data for other
plasmas, it is highly unlikely that the ohmic power could have exceeded 10kW. The
10.5kW of RF power coupled to the plasma is comparable to if not greater than the ohmic
power. In this case the plasma absorbs 73% of the RF power and only 27% is reflected.
In other cases more than 75% of the power was absorbed. The toroidal field was set to
1360 gauss on axis. A pulsed vertical magnetic field was used. The data is shown in
Figure (6-14). Plasma current is increased by as much as 300 amps, and the loop voltage
is decreased roughly 0.4 volts (16%) upon application of RF. Other settings of the
plasma parameters were tested. However, no other plasma conditions, antenna phasing,
or power settings resulted in a larger current increase by as much as a factor of 2. When
the phase shifters in the RF supply were slowly adjusted, the current increase could be
made to decrease, but not increase. This suggests that the phasing was properly adjusted

and that the current drive effects are phase sensitive.

Figure 6-14. LHCD results in hydrogen. The top trace registers
the vertical magnetic field. The second trace down is the loop
voltage with and without RF, 0.5V per division. The third trace
down is the plasma current with and without RF, 0.5kA per
division. The bottom trace registers the RF timing. Horizontal
scale is Imsec per division. The loop voltage is decreased, and
the plasma current increased with application of RF. The traces

involve superposition of many plasma shots.

6-19

The overall efficiency for current drive in Encore is of the order of

Lnps _ 300amps
P 10500 watts

watts

= 0.03 amps / watt. (6.2)

For comparison, a LHCD experiment on PLT maintained a plasma current of 183kA with
a RF power of 40kW.> The overall efficiency is

Lamps _ 183000amps
P 40000 watts

watts

= 4.6 amps / watt. (6.3)

It is known that the current drive efficiency scales inversely with the plasma density®

2 |
amps/m oo —

(6.4)

watts/m 7

The PLT experiment involved a plasma density of 2.2x10"" cm™?. Experiments on Encore

involved comparable or lower plasma density, so the current drive efficiency should not
be less due to density effects. Many successful LHCD demonstrations at other
institutions involved grill antennas comprised of four waveguides. Some other
phenomenon is hindering lower hybrid current drive on Encore. It will be argued in
chapter 8 that the cause of the poor current drive efficiency is related to the so-called
"density limit" problem.

Similar experiments were performed with the tokamak filled with argon to a

pressure of 3.5x10° torr. The results are shown in Figure (6-15). In this case, little if any

effect is seen on the plasma current or loop voltage upon application of RF.

Noticeable effects in argon were evident at lower plasma current. See Figure (6-
16). In this instance roughly 80 amps are driven on top of a 400-amp ohmic plasma
current. The ohmic power involved is only 2kW.

The question arises as to why LHCD in argon appears weaker than in hydrogen.
It was checked that the LH cone angle and the LH accessibility criteria are essentially

unaffected by the change in ion mass, for the plasma parameters used.

6-20

Figure 6-15. LHCD results in argon. The top trace registers the
vertical magnetic field. The second trace down is the loop
voltage with and without RF, 0.5V per division. The third trace
down is the plasma current with and without RF, 0.5kA per
division. The bottom trace registers the RF timing. Horizontal
scale is lmsec per division. The traces involve superposition of
many plasma shots.

Figure 6-16. Plasma current and loop voltage changes upon RF
application to an argon plasma. In all four photos, the top trace is
the RF marker. The upper photos are the plasma current, 200
amps per division. The lower photos are the loop voltages, 0.5

volts per division, 5-volt total signal.

6-21

One difference, however, involves the mass density. For a given pressure, argon
is twenty times as dense as diatomic hydrogen, and argon has twenty times as many total
electrons per unit volume (bound and free) as hydrogen. This means that argon has
twenty times the stopping power for high-energy electrons compared to hydrogen. The
lower density in hydrogen has the effect of making it easier to produce high-energy
electrons. In fact, when running the tokamak with hydrogen, care must be taken to avoid
unnecessary x-ray exposure. X-rays are generated when the high-energy electrons collide
with the chamber walls.

There are two possible effects. One is that LHCD generates high-energy
electrons. The collisional lifetime of LHCD generated high-energy electrons is longer in
hydrogen. The second effect is that the spectral gap between the N) spectrum at launch
and the high-energy tail of the thermal electron distribution is smaller if the thermal
electron distribution extends to higher energies. In hydrogen the thermal distribution
extends to higher energies and the spectral gap is thus smaller versus in argon.

Interpretation of loop voltage drops and current increases in ohmic plasmas is
subject to some degree of controversy. It could be argued, for instance, that plasma wave
heating would be expected to decrease plasma resistance. This lower resistance would
cause the ohmic supply to drive more current for a given loop voltage.’ Other groups
have demonstrated that LHCD works, and in chapter 7 LHCD will be demonstrated in
non-ohmic plasma. What is unique and interesting in these measurements is the

extremely low current drive efficiency.

Generation of Plasma Waves at Other Frequencies

With the 2-watt RF-supply energizing the solid dielectric antenna, it was observed
that the signal from a plasma probe was symmetrically broadened. This data is shown in
Figure (6-17). The probe and antenna were separated by 67.5 degrees toroidally. The

tokamak was filled with argon to a pressure of 3x10” torr. The toroidal field on axis was

1040 gauss. The plasma current was one kiloamp. The antenna was phased to launch LH

waves preferentially in the direction of the probe.

6-22

Figure 6-17. At left is the 2-watt input signal to the antenna. At
right is the symmetrically broadened signal measured with a
plasma probe. The horizontal scale is 5MHz per division. The
vertical scale is 10dB per division.

At high power, a different behavior was noted. The plasma probe detected a band
of lower frequencies than the input signal. The data is shown in Figure (6-18). In this

case the tokamak was filled with hydrogen to a pressure of 4x10” torr. The toroidal field

is 1040 gauss, and the plasma current one kiloamp. The antenna is located 45 degrees
clockwise from the probe in the toroidal direction (as viewed from above). The antenna
is quadrature phased to preferentially launch LH waves counter-clockwise. The
ohmically accelerated electrons also travel counter-clockwise. The power to the antenna

was 2kW per channel.

Figure 6-18. The antenna power is 2kW per channel. At left is
the input signal to the antenna. At right is the non-symmetrically
broadened signal measured with a plasma probe. The horizontal
scale is 5OMHz per division. The vertical scale is 10dB per
division.

Measurements show that under similar conditions, the spectrum of lower

frequency waves generated is broadest for hydrogen, intermediate for helium, and

6-23

narrowest for argon. This data is shown in Figure (6-19). The toroidal magnetic field is

1310 gauss. The plasma current peaks at roughly 1.5 kA.

Figure 6-19. Observed spectrum of waves for various gas fill. At
left is 5x10° torr hydrogen. The center trace is 4x10” torr

helium. At right is 4x10° argon. Horizontal scale is 5|0MHz per
division. Vertical scale is 10dB per division.

The plasma probe utilized was the X-Y probe. Scans were made of the minor
cross section for various frequencies noted in Figure (6-18). The plasma current and the
timing of the plots are shown in Figure (6-20). A 400MHz scan was taken at the marker
shown in Figure (6-20). A 417MHz scan was taken 0.34msec later. A 433MHz scan was
taken 0.67msec after the marker. A 450MHz scan was taken 1.0msec after the marker.

The resulting contour plots are shown in Figure (6-21).

Figure 6-20. Timing of the contour plot data. Second trace from
the top is the spectrum analyzer signal, SOMHZ per division.
Third trace is the timing marker for the 400MHz scan. Lowest
curve is the plasma current, 1kA per division. For the lower two
curves the horizontal scale is one millisecond per division.

6-24

400MHz 417MHz

ad

=,
Nee maah)

Figure 6-21. Contour plots of detected power at various
frequencies as noted. The right-hand side of the plots
corresponds to the outer wall where the LH waves are launched
by the grill antenna.

Figure (6-21) shows that the lower frequency waves are concentrated at the
plasma periphery near the outer wall. The lower the frequency, the more the plasma
wave power is restricted to the outer edge of the plots. These waves are likely associated

with parametric instability at the plasma edge.*®

Summary
Experiments on Encore show that LH waves launched by several grill antennas

including the solid dielectric antenna behave as one would expect. Accessibility depends

upon both the magnetic field and the plasma density and affects the maximum depth of

6-25

penetration. The LH propagation angle depends upon the magnetic field and affects the
rate of penetration. The directionality of the launched waves depends upon the antenna
phasing. The solid dielectric antenna launches directional LH waves into Encore that are
accessible to the center of the plasma and do indeed propagate there.

LHCD effects are observed in Encore. The changes in plasma current observed
are larger at smaller plasma current (and thus smaller density) as one would expect from
accessibility considerations. However, the lower hybrid current drive efficiency in
Encore is low by orders of magnitude compared to LHCD experiments on other
tokamaks. This cannot be explained as due to problems with accessibility, propagation
angle or the directionality of the launched spectrum.

During high power LHCD experiments, a spectrum of waves with frequencies
lower than that of the launched waves is detected. These waves appear to be

concentrated at the plasma periphery.

' Eric Fredrickson obtained the data indicating linearity. The author obtained the microwave measurement
yielding the density calibration.

* See for instance "An Experimental and Theoretical Investigation of a Finite Beta Modified Drift Wave,”
Eric Fredrickson, thesis, California Institute of Technology, Pasadena, CA, (1985).

3 Bric Fredrickson, private communication

* See the discussion at the end of chapter 4.

> F.C. Jobes et al., Phys. Rev. Lett., (1985), 55, p. 1295

°N. J. Fisch, "Theory of current drive in plasmas," Rev. Mod. Phys., (1987), 59, p. 214

™N. J. Fisch, "Theory of current drive in plasmas,” Rev. Mod. Phys., (1987), 59, p. 212

® Paul Bellan, private communication

7-1
7 Data from RF-Sustained Plasmas

The small LH current drive efficiency on Encore is explained in chapter 8 as
related to the so-called "density limit." Despite this problem, significant amounts of
LHCD current could be generated in Encore. It was found possible to sustain plasma
discharges without the aid of the ohmic heating system. This chapter reviews the

experiments of this nature.

Magenetic-Error-Field Current-Drive

Current drive experiments in ohmic discharges can be difficult to interpret.
Changes in plasma current may be directly due to current drive or they may instead be
due to plasma heating which increases the conductivity of the plasma, thus increasing the
ohmic plasma current. For ohmic discharges it was found that plasma current is
increased for antenna phasing to launch N; parallel to the ohmically accelerated electrons,
which in Encore is counterclockwise as viewed from above. The plasma current
increases Al, are of the order of a few hundred amps at most, which is small considering
that the RF power is a considerable fraction of the ohmic power.

It is desirable to eliminate the effects of the ohmic EMF in order to study the LH-
wave/plasma interaction. To this end RF was applied to afterglow plasmas in Encore for
which the ohmic input is disconnected and the plasma current and loop-voltage decay on
a L/R time scale. The idea is to use the ohmic drive to break down the plasma, and then
sustain a RF-current driven discharge beyond the ohmic decay period. Referring to
Figure (3-6), amplifier "B" operating in the closing switch mode to sustain the plasma is
not utilized. Only amplifier "A," operating in an opening switch mode, is used to
partially ionize the tokamak fill gas. In the opening switch mode a quick high-voltage
spike is produced as the current in the triode amplifier is disconnected. After amplifier
"A" disconnects, the ohmic supply is no longer engaged.

Initial experiments along this line appeared to yield no plasma beyond the ohmic
decay zone. The antenna was phased to launch lower hybrid waves parallel to the ohmic

electron drift and one expected that the decay of ohmic plasma current would reverse or

plateau as the RF current drive was established. Close examination of the Ip trace

7-2

showed, however, that not only was the plasma current decaying to zero but was in fact
overshooting to a negative value which was maintained for the duration of the RF pulse.
This negative overshoot was small, on the order of 10-20 amps and thus difficult to see

except on an expanded current scale. See Figure (7-1).

Figure 7-1. Example of a RF sustained plasma in Encore. Upper
trace is the "B" amplifier current. Next is the loop voltage
(1V/div). Next is a reference pulse coincident with application of
RF. The forth trace is the plasma current (100A/div). Note the
spike in the loop voltage trace when the ohmic supply ionizes the
fill gas, and at the termination of RF.

Initial suspicion was that the Rogowsky circuits were picking up RF interference
and giving a rectified output. The current was proven to be real in the following way.

An optical emission diagnostic showed emission coincident with the RF pulse.
Looking at the plasma in the tokamak through a window port when the RF was turned on,
a bright flash could be seen in place of the subdued blue glow of the short ohmic pulses.
The RF pulse duration was increased to eight milliseconds, considerably longer than the
one millisecond ohmic afterglow. The plasma light emission seen upon application of RF
matched the Rogowsky signal in duration. At the very least, the RF was maintaining
plasma breakdown.

The loop voltage due to the ohmic afterglow plasma decayed to zero value dur ing

the RF discharge and then exhibited a negative spike coincident with the end of the RF

7-3

pulse. This negative spike is consistent with the back EMF one would expect due to a
decaying reverse (negative) plasma current as shown by the Rogowsky diagnostic. The
loop voltage diagnostic is so simple, it is difficult to imagine it giving a misleading result.

Thus, because of the optical, Rogowsky and loop voltage diagnostics, there can be
no doubt that during application of RF a current carrying plasma is maintained devoid of
ohmic input. However, the direction of the current was opposite to what one would
expect based on LHCD theory and the antenna phasing.

Perhaps the phasing is backwards to what it is presumed to be. Upon reversing
the phasing so as to flip the Nj spectrum at launch to the other direction, exactly the same
reverse plasma current is obtained. In fact, for no phasing at all, that is, a symmetrical
N, distribution launched by a single waveguide, the same result is obtained. Application
of RF gives negative plasma current regardless of antenna phasing. The tokamak/RF-
antenna system has a handedness. The amount of current driven is linearly proportional

to the applied RF power. See Figure (7-2).

40 I I I l
y =7.117x - 4.360 12 = 0.998

Plasma Cunrentt (amps)

10 —

0.0 1.0 2.0 3.0 4.0 5.0

Power (kW)

Figure 7-2. I}

outer waveguides is powered. The current is proportional to the
power, and appears to have a threshold just below 1 kW.

versus RF power in kilowatts. Only one of the

7-4

What gives the handedness? What property of the system gives the direction of
the RF discharge current? To answer this question a great number of aspects of the
tokamak were varied in an attempt to alter the magnitude, and possibly change the
direction of the RF discharge plasma current If".

The polarity of the ohmic target plasma current was reversed without effect on

I". Moving the antenna in and out with respect to the chamber wall affected the amount
but not the direction of I;". The antenna was moved to different ports around the torus
without effect on I}*. Thus, local chamber wall features are not responsible.

All four ports of the grill antenna were powered one at a time and each gave an
identical result, reverse plasma current. The antenna was flipped upside down and the
same experiment repeated without change in the result. Thus the non-powered
waveguides or other construction features of the grill antenna can be eliminated.

Varying the vertical magnetic field Byer direction and magnitude could affect the
amount of current to some degree but not its direction. This result also eliminates the
vertical component of the earth's magnetic field. The horizontal component of the earth's
field does not give a net direction to the torus. Encore is a low magnetic field tokamak

and it is not out of the question that the earth's magnetic field could have an effect.
Reversing the toroidal field B, had absolutely no effect on If’. The iron core
transformer for the ohmic drive on Encore was partially pulled apart with no detectable
affect on I}". The position of the filaments used to provide electrons for breakdown was
varied without effect.

The vertical field coils were hooked up to generate a radial horizontal magnetic

field By. The RF plasma current was found to be a strong function of this horizontal field

and the direction of i could be reversed for certain values and direction of By. Data
was taken, It versus By, for both directions of the toroidal field B, and the results are

shown in Figures (7-3) and (7-4). Note that the direction of By needed to zero or reverse

i depends on the direction of B,- It is the combination of By and By that gives the

handedness. A small horizontal radial field superposed on the large toroidal field simply

7-5

leads to a small change in direction of the toroidal field, causing the field lines to spiral in

or out depending on the directions of By and B,.

4 Applied By (+ amps)

—_
B,
40
Pr
20
RF
I, 0

(amps)
-20 /
. poy

1000-5 0 5 10 1520

Horizontal Field Coil Current (amps)

Figure 7-3. RF induced plasma current I} versus the current in a
set of coils generating a radial horizontal magnetic field in the
Encore tokamak. It is increasingly difficult to obtain an ohmic
breakdown for increasingly negative coil current.

The data is consistent with the following picture. An inherent radial horizontal
magnetic "error" field By" in the Encore tokamak causes the magnetic field lines to

spiral in a horizontal plane. Suppose that the lower hybrid antenna generates electron
beams in both directions, localized near the chamber wall. The electron beam spiraling

out toward the chamber wall will be attenuated with respect to the electron beam

7-6

spiraling inwards toward the chamber center. Thus a net current I; is produced. See

Figure (7-5).

4 Applied B y (+ amps)

B,
40
Foo
, \
Iv 0
(amps) a
-20 -15 -10 -5 0 5 10

Horizontal Field Coil Current (amps)

Figure 7-4. RF induced plasma current I}" versus the current in a
set of coils generating a radial horizontal magnetic field in the
Encore tokamak. The direction of the toroidal field is opposite to
that in Figure 7-3. It is increasingly difficult to obtain an ohmic
breakdown for increasingly positive coil current.

If the horizontal error field Bi" is due to the toroidal field currents, then upon
reversing B,, By; also will also reverse and the direction of the spiral is unchanged.

This explains the insensitivity of I;* to the toroidal field direction. It also explains why

the direction of the applied correction By necessary to zero or reverse iv changes with

the direction of B, as shown in Figures (7-3) and (7-4).

Toroidal Magnetic
Field Line with
Horizontal Spiral

Ww A

LH Generated LH Generated .
Current Propagating Current Propagating
into the Outer Wall into the Interior of the

Minor Cross Section
LH Antenna

Figure 7-5. Schematic of the proposed theory explaining the
production of net toroidal current with a symmetric LH antenna
phasing. Spiraling of the toroidal field lines in a horizontal plane
(highly exaggerated in the figure) breaks the symmetry. LH
current generated near the outer wall of the torus propagates in
both toroidal directions. Current spiraling outward to the
chamber wall is rapidly attenuated with respect to current
propagating into the interior of the minor cross section.

If the antenna is generating beams in opposite directions then perhaps plasma
exists even when By is applied to zero I$’. Optical emission shows that a plasma exists

for the condition I}" = 0. However, optical emission is less for this case than when a net

current exists. A toroidal current is, of course, necessary for plasma confinement,

7-8

Further bolstering the spiral theory is the data shown in Figures (7-6) and (7-7)

where the necessary By to zero is is shown to be proportional to the toroidal field. This
confirms that the inherent horizontal radial error field is due to toroidal field coil currents.
The discrepancy at low toroidal field is an indication that smaller contributions to the
horizontal error field not due to toroidal field coil errors exist. One possible source for
this is the iron core transformer for the ohmic supply on Encore. This transformer has a

small gap at the tokamak center point to lower the inductance for impedance matching

purposes.

{ Applied By

<——
B,
65 a
rT
5 —
B,,coilcurrent 4-4
for 1° =0 }
(amps )
274 ~_
IJ og
0 q ' '
0 100 200 300 400

Toroidal Field Coil Current (amps)

Figure 7-6. Current in the coils which produce a radial horizontal

magnetic field necessary to achieve I> =0 versus current in the
toroidal field windings.

4 Applied B y

B,

7 4
6-4

B,,coilcurrent . |

for I;* =0
(amps)
3-5
2-54
1-4
0 t ‘ q
0 100 200 300 400

Toroidal Field Coil Current (amps)

Figure 7-7. Current in the coils which produce a radial horizontal

magnetic field necessary to achieve I,’ =0 versus current in the
toroidal field windings.

With the toroidal field on, one cannot simply stick a magnetic probe into the
machine to measure the inherent horizontal error field. Inferring from the applied By
necessary to correct the error and zero I>", the error is of the order of a few gauss. The
effect of the error is simply to slightly alter the direction of the toroidal field lines
(~ 1300gauss) and this simply cannot be seen with a handheld probe. However, the
direction of the inherent error field can be deduced from the correction field necessary to

eliminate it. When this is done the direction of the magnetic field line spiral thus inferred

agrees with that necessary to produce the observed direction of IF.

7-10

Three gauss out of 1300 represents a deviation in angle of 2.3 milliradians. After
traversing one circumference of the tokamak (major radius 38cm), the deviation in
position will be of the order of half a centimeter. Since the minor radius is 12cm, an
electron beam generated at the outer portion of the tokamak could expect to remain in the
chamber for something of the order of 48 passes before colliding with the inner wall.

It might be mentioned at this point how one can decide the direction of a magnetic
field. A useful picture is shown in Figure (7-8). The north pole is that from which
magnetic field lines emerge. Since north poles point north, the earth's North Pole is thus
technically a magnetic south pole. It is known that cosmic ray primaries (positively
charged ions) are bent to the east as they approach the earth.' Given their positive
charge, this is only possible if the magnetic field of the earth in space points to the north.
In the Northern Hemisphere the earth's magnetic field points north and down. Knowing
this, any magnetic probe may be quickly calibrated as to direction, by simply looking at
the earth's field. The absolute direction of a magnetic field rarely needs to be known.
The handedness of the spiraling field lines is insensitive to the convention used for the
direction of the magnetic field. If both the horizontal error field and the toroidal field are
assumed to point in the opposite direction, the field lines still spiral with the same

handedness.

. earth north
(magnetic south pole) _

S earth south
\_ (magnetic north pole) /

Figure 7-8. Accepted convention for the direction of magnetic
field lines produced by two common sources.

7-11

There are several ways to see how the toroidal field coils on Encore could
produce such a horizontal radial magnetic error field. To minimize errors and to avoid
encircling the ohmic transformer, the return current lead for the coils doubles back
underneath the input lead which is located underneath the coils. As can be seen in Figure
(7-9), the currents in the input lead sections do not entirely match the return current
because of the pancake coils. Because these connection leads are underneath the toroidal
coils a horizontal error will exist in the tokamak chamber. Another source of horizontal
error is due to coil tilt. A consistent tilt of the pancake coils about a vertical axis will also
result in horizontally spiraling field lines. By properly adjusting the tilt of the coils on
Encore it was later found possible to eliminate the horizontal error so that I = 0 for By

=0.

input lead

_S S\ a
return current

Figure 7-9. One source of the horizontal magnetic error field
involves the return current lead. There is no local cancellation of
the return current lead at the positions of the toroidal field coils.

In general, localized horizontal radial magnetic error fields in tokamaks can be
measured only by electron beam studies in which the beam spiraling can be detected.”
Average global magnetic error fields can be detected by the EMF induced in a toroidal
loop when the toroidal magnetic field is pulsed. Typical practice is simply to apply a
correcting By that is adjusted to maximize the plasma parameters.’ Encore, being a high
rep-rate, probe-compatible tokamak, usually contains low temperature collisional plasma
not fully ionized. For this reason, it is not sensitive to small horizontal errors.
Collisional current carriers in a typical Encore discharge simply do not have a long
enough mean free path to sample the slight spiraling. However, higher velocity RF

generated electrons are not so collisional. At 100eV, the mean free path of an electron is

7-12

of the order of a dozen circumferences of the torus, plenty of distance for the horizontal
spiral to have effect.

In Figure (7-10) RF-sustained plasma current is demonstrated in both toroidal
directions by manipulation of the radial horizontal magnetic error field. An ohmic target
plasma comprised of argon is used. A single waveguide is powered with 3.9kW. The

RF-current is sustained for more than 8 milliseconds, limited only by the RF power

supply.

Figure 7-10. Photos demonstrating RF-sustained plasma current.
In all photos, the top trace is the plasma current, 500A/div. upper
photo, SOA/div. lower photos. The second trace from the top is
the optical emission signal. The third trace is the ohmic primary.
The fourth trace is the RF marker. The bottom trace is the loop
voltage, SV/div. top photo, 2V/div. lower photos. For the bottom
right photo, a radial horizontal magnetic field of 6.5 gauss was
applied to reverse the spiraling of the toroidal field lines.

7-13

Effects Due to Phasing

The RF current drive discussed in the previous section produced net current from
a symmetric Nj spectrum by creating an asymmetry in the magnetic paths available to the
opposing beams. This section discusses experiments in which the magnetic error fields
were eliminated and quadrature phasing was utilized to generate non-symmetric Nj
distributions at launch. Very little net RF current was generated in this manner. Some
possible reasons for this are discussed.

The vertical field correction coils on Encore were reconnected in a parallel
configuration that allowed independent application of a correcting radial horizontal
magnetic field By as well as a vertical magnetic field By. For ohmically generated
plasma, it was standard to use a pulsed vertical magnetic field supply. This was replaced
with a DC current supply to prevent confusion due to transient behavior. By was
generated by a DC current supply as well.

With a single channel of the antenna powered the launched LH spectrum should
be symmetrical as shown in Figure (5-16f). With a 7.4kW to a single port and no
magnetic correction applied, the RF driven current was -23 amps.’ The settings of the

correction coils necessary to achieve I*" =0 could then be measured. The necessary

values of the correction coil currents to achieve If’ =0 varied with time. Some factors
that might influence this were examined.

Fourteen magnetic socket screws were removed form the torus without effect. A
magnetic optics table recently placed near the torus was moved without effect. Pieces of
iron placed on top of the torus leaning against the iron core of the ohmic transformer had
no effect. Pieces of iron placed near the outer mid-plane of the torus could completely
reverse the direction of I$’ depending upon their position. Lifting the torus slightly with
respect to the various magnetic coils had no effect. Moving the iron core of the ohmic
transformer back and forth had no effect. Moving around the toroidal magnetic field
current leads had no effect. Rotating the torus with respect to the iron core several
centimeters had no effect. A small hand magnet held near the torus had a detectable
effect on If*. Increasing the gap in the iron core transformer had a definite effect as

shown in Figure (7-1 1).

—t— B, clockwise

en Caneel 5) , counter clockwise

(looking from above)

B,, coil
current 3 tS

to obtain ,
I; =0

(amps) | =a

0 5 10 15 20

Gap in Iron Core (cm)

Figure 7-11. The current in the By correction coils necessary to
make I; =0 for various gaps in the iron core transformer of the

ohmic supply. Data is presented for both polarities of the toroidal
field.

An attempt was made to disengage the ohmic supply as much as possible by
removing the movable portion of the ohmic transformer core completely. Breakdown of
the plasma was found to be still possible. However, the initial ohmic loop voltage was
then found to decay on a very long time scale in the presence of RF sustained plasma.

The iron core transformer was restored to its original configuration.

For comparison, ie generated by each of the four channels of the antenna was
examined and the results are shown in table (7-A). No magnetic correction By or By was
applied for these measurements. The power to channel #1 was slightly less than that of
the other channels due to problems with the amplifier chain. In any event, the powers are

not equalized and this will cause degradation to the directionality of the Ni spectrum.

Channel #1 was less efficient in driving plasma current than the other channels for

7-15

unknown reasons. It is possible that there is an air gap in the coax paraffin or ceramic
dielectric for that channel. Also of interest, the interior waveguides (#1 & #2) have
significantly higher reflection coefficients from the plasma than the exterior waveguides.
Altering the power to individual channels was not simple. Continuously variable
attenuators were not included in the amplifier chains. In retrospect, optimum Nj
directionality probably requires fine adjustment of power to each waveguide, so that the

plasma-coupled power can be equalized for all four channels.

Channel Fwd. Power(kW) Ref. Power (kW) If" (amps)
#0 5.1 10% -15
#1 4.3 23% -8
#2 5.1 23% -16
#3 4.1 4% -15

Table 7-A. Comparison of the performance of each individual
waveguide in generating RF driven plasma current with no
magnetic correction fields By or By.

With one channel of the antenna powered, By was carefully adjusted so as to
achieve If" =0. The current in the By coils necessary to null out the RF driven plasma
current was determined to be 3.1 amps. In this condition it was found that I$’ =0 was
insensitive to the vertical magnetic correction field By. This makes sense from the
symmetry of the situation. The fast electron beams are generated equidistant from the top
and bottom of the chamber. The vertical field will induce a vertically oriented helix
rather than a horizontal spiral. No direction is favored by creating such a path for the two
beams.

All four ports of the antenna were then energized with quadrature phasing.
According to Figure (5-16c) this should give a fairly unidirectional N), spectrum at
launch. Numerical integration shows that 76% of the power should launch in one
direction, and 24% in the opposite direction. The amount of current driven was 3 amps.
The horizontal magnetic correction field was varied so as to maximize the RF driven

current and as much as 60 amps was obtained. See Figure (7-12).

7-16

70

60

50
40 al

s Af
54
20 7

i 10 7

(amps) 40 VA

0 12 3 4 5 6 7 8 9 10 11 12 13

Current inthe B,, Coils (amps)

Figure 7-12. RF driven plasma current versus the current in the
horizontal magnetic correction field coils. The antenna is
quadrature phased. At 3.1 amps the error field is nullified but
only 3 amps are obtained. 60 amps are obtained at the maximum
current used.

Next, the vertical magnetic field was adjusted so as to maximize the RF driven current.
100 amps of plasma current were obtained in this manner. Finally, the argon fill pressure
was varied to obtain an even larger plasma current of 144 amps as shown in Figure (7-
13). The largest RF-driven plasma current obtained by such procedures was 158 amps.

A typical result is shown in Figure (7-14).

7-17

150

125
ao

RF
I, 100
(amps)
75
50 ] t q

Pressure (10° torr)

Figure 7-13. RF driven plasma current versus the argon fill
pressure. A peak of roughly 144 amps is obtained at a pressure
of 2.5x10° torr.

Figure 5-14a, Magnetic error field assisted LHCD result. Upper
trace is the plasma current (50 amps/division). Lower trace is the
RF-on reference. Horizontal scale is 1 msec per division.

7-18

Figure 5-14b. Magnetic error field assisted LHCD result. Upper
trace is the plasma optical radiation output. Middle trace is the
loop voltage (2V/division). Lower trace is the RF-on reference.
Horizontal scale is 1 msec per division.

On the chance that there was an error in the method of setting the waveguide
phasing, many other phasings were experimented with. None was found to produce as
much plasma current as quadrature phasing (90° shift per waveguide). In particular,
experiments with zero phase shifts (all waveguides have the same phase) produced a
maximum net plasma current of 100 amps. 180° phase shift produced a maximum net
plasma current with other parameters optimized of 75 amps. These results suggest that
the phasing was as measured.

It is interesting to note that the vertical magnetic field which maximizes If" for 0°
phase shift per waveguide is only slightly less than for quadrature phasing (coil current
3.4 amps versus 3.8 amps). For 180° phase shift If" is maximized for a vertical field coil
current of 3.75 amp. The vertical field induced helix negates a drift that is proportional to
the electron toroidal velocity. This suggests that the typical toroidal electron velocities in
the RF driven current are similar independent of phasing. This is despite the fact that Nj
at launch is dramatically different according to the calculations shown in Figure (5-16).

Regardless of the Ny) spectrum at launch, in bridging the "spectral gap" to reach thermal

7-19

10eV electrons, presumably similar spectra composed of large Ny values are created after
launch.

The failure of phasing by itself to produce a unidirectional plasma current can at
least partly be attributed to the poor directionality of a four-waveguide system. Ideal
calculations indicate a 0.76 - 0.24 directionality. More waveguides are needed to
improve upon this. Failure to equalize the plasma-coupled power from the four
waveguides will only further deteriorate the ideal calculations. Another factor may
involve the nature of the target plasma to which the RF is applied. The RF generated
plasma is not homogeneous. Plasma density is likely highest where the RF generated
electron beams exist. The antenna is not presented with uniform plasma with a steep
density gradient in the major radius direction. If the four waveguides are not presented
with LH cutoffs located at similar distances, then further degradation in directionality is
sure to result. If the distance to the cutoff is significant compared to the separation
between waveguide centers, the N) spectrum will be altered from the ideal calculations.
Factors that might play a role in this include the field curvature in the fringing fields as

well as superposition of fields from neighboring waveguides.

Correlation of Reflected Power

The RF power reflected from the plasma varies slightly as a function of time.
Presumably this is due to the turbulent nature of the plasma. Simultaneous data was
taken of the reflected power versus time from the two outermost waveguides. These two
waveguides have the largest separation. The question was whether or not the variation in
reflected power versus time from the two waveguides would be correlated or not. Lack
of correlation would be evidence that due to plasma turbulence, the waveguides are not
each exposed to identical launch plasma. This in turn would offer evidence of a possible
mechanism for disruption of the calculated Ni spectrum. The data is shown in Figure (7-

15). The reflected power levels appear to be correlated.

7-20

Figure 7-15. Reflected power of the two outermost waveguides
versus time. A RF sustained discharge in hydrogen with
I>’ =30 amps is used. The horizontal scale is 0.2 msec per
division. The vertical scale is 2dB per division. The upper traces
are one waveguide, and the lower traces, the other.

Microwave Density Measurement

A microwave density diagnostic on Encore was capable of measuring line average
density. A measurement was taken during LHCD and the data is shown in Figure (7-16).
The measurements were calibrated against ohmically generated plasma that reached a

peak current of 3 kA. Line average density in Encore is proportional to the plasma

ohmic

current and is roughly 2x10’? em? for I, =2kA. Thus the calibration data involves a

line average density of about 3x10'* cm®. This line average density corresponds to 1.3

fringes in the microwave data. The LHCD data shows I, ~100 amps. The microwave
data shows about 0.3 fringes. Thus the line average density in the RF sustained plasma is
of the order of 7x10'' cm®. This is well above the cutoff (P=0) for the slow mode which

is 2.5x10? cm”.

Figure 7-16. Microwave density diagnostic data. At left is the
LHCD data. Upper trace is plasma current (500A/division).
Middle trace is the microwave fringe data. Lower trace is the RF
reference. At right is ohmic plasma calibration data. Upper
trace is microwave fringe data. Lower trace is plasma current
(2kA/division). Horizontal scale is 0.5 msec per division for both

photographs.

7-21

Dependence on the Toroidal Magnetic Field

The effect of B, on the maximum I)’ was looked at. Except for By, which was
varied, the parameters are the same as for the record If’. Quadrature phasing was used.
By was adjusted for each B, so as to maximize Is. By for maximizing [*” was found to
be independent of B,. In tokamak mode, the vertical magnetic field balances the "hoop"

force of the toroidal current and there is no B, dependence to By. The result of the

experiment is shown in Figure (7-17).

At lower magnetic fields, the net RF driven plasma current falls off. It is likely
that this is due to problems with accessibility. Figure (4-7) shows that accessibility for a
typical quadrature phase launch spectrum becomes hindered for magnetic fields below
929 gauss (300 amps coil current). Below this value the accessibility limit curve lies
entirely within the launch spectrum for quadrature phasing. Remarkably, this is exactly

where iv begins to drop in Figure (7-17).

200
150 4
RF /
I, 100
(amps)
50
0 q
0 100 200 300 400

Toroidal Magnetic Field Coil Current (amps)

Figure 7-17. Maximized net RF driven plasma current versus the
toroidal magnetic field coil current. Below 300 amps there is a
monotonic fall in plasma current.

7-22

Ion Mass Dependence

The atomic species used for the fill gas in Encore was varied to see what effect if
any it would have on If". Presumably the fill gas would affect primarily the ion mass
value. This in turn would affect the ion plasma frequency and the ion cyclotron
frequency. When an effect seemed to be apparent, the experiment was pushed to the

point that six different fill gases had been tried. The gases utilized are listed in table (7-
B).

Atomic Species Mass(amu) Jon Gauge Factor
Hydrogen 1.0 2.3
Deuterium 2.0 2.7
Helium 4.0 6.9
Nitrogen 14.0 1

Neon 20.2 3.3

Argon 39.9 0.89

Table 7-B. Fill gases used in the ion mass dependence
experiment. The "ion gauge factor" is the calibration factor for
correct reading of ion-gauge pressure based upon the ease of
ionization of the various gases.

The gas fill pressure was kept at approximately 3x10° torr for all of the gases.

The toroidal field was maximized to provide the best possible accessibility. The
horizontal error field was adjusted to maximize I}* for argon fill, and held constant for
all of the data. The result of the experiment is shown in Figure (7-18). Larger values of
I> but very similar mass dependence were obtained by adjusting the vertical field
independently in each case so as to maximize the RF driven current.

Since the "ion gauge factor" (related to the ease of ionization) as listed in table (7-
B) does not have a monotonic relationship with the atomic mass, it is difficult to imagine
that this factor plays a major role in the phenomena.

The LHCD density limit to be described in chapter 8 depends upon many
variables including the value of the ion mass. The equation for the density limit can be

written as°

wo = TOON sitar’ i. ma (7.1)

7-23

The units of niimit are cm”. The parameter y is defined by
Cay, 7.2
k, Y Vihermal ( )

Where Vihema 18 the electron thermal velocity. It characterizes the degree of upshift in k,
occurring in the plasma, enabling a resonant interaction between the launched LH waves

and the slower thermal distribution of electrons. The parameters B, and Bj; are

temperature enhancement factors and multiply the electron and ion temperatures

respectively. Bb. exceeds unity when the fast electrons providing the current drive have a

total energy comparable to the bulk, and characterizes the change in the electron

distribution due to the LH waves. {; exceeds unity when there is ion heating, and

characterizes the change in the ion distribution due to the LH waves.
Taking values pertinent to Encore (B=1300 gauss, Tj=3eV, T.=10eV,
@ = 2-450 x10°sec"'), and choosing y = 8, = 8, = 1, the results shown in Figure (7-19)

are obtained. For Encore parameters, the density limit is totally insensitive to the values

of T., T;, and Bj. The monotonic relationship is preserved for other choices of y and Be.

25

20

0 T T —T
0 10 20 30 40

Ion Mass (amu)

Figure 7-18. Dependence of the amount of RF driven plasma
current on the type of gas used to fill the tokamak. There is a

monotonic increase in I}* with atomic weight. The sharp rise in

the dependence rolls off above the mass of helium.

7-24

It is difficult to create plasma in Encore with line average density less than 10'*
cm” with the ohmic heating system. Ohmic breakdown cannot be achieved with line

average densities of the order of 2x10!! cm?. Densities of the order of 2x10'! em? occur

very close to the edge of the plasma. It is quite plausible that as the density limit is
increased, greater penetration of the LH waves is achieved causing the RF driven plasma

current to increase.

2.25E+11 |
Ls
2.20E+11 -
Density
Limit
(cm™)
2.15E+11 7
2.10E+11 1 t

0 10 20 30 40

Ion Mass (amu)

Figure 7-19. Dependence of the LHCD density limit in Encore
on ion mass. There is a monotonic relationship with larger ion
mass associated with a larger density limit. The sharp rise in the
dependence rolls off above the mass of helium.

RF Tokamak

An attempt was made to eliminate the use of the Encore ohmic supply for the
purpose of ionizing target plasma for LHCD. To replace the ohmic supply, a tungsten
filament was installed on the tokamak. This filament was biased to 400 volts and emitted
a current of 50-75 milliamperes. Using 180° phase shifts with 2.3kW per channel,

Is* =+65amps were obtained, the sign depending upon the direction of By enhancement.

See Figures (7-20a) and (7-20b). The maximized I}" was found to be insensitive to the

filament voltage over the range of 100-500 volts. Without ohmic generation of target

7-25

plasma, the tokamak loop voltage signal is due entirely to the rise and fall of the RF
driven current. The RF driven plasma current appeared to jump between discrete levels
of approximately 20, 40 and 60 amps as By was varied. Unlike the RF sustained plasma
generated from ohmic target plasma, these plasmas showed large sensitivity to By.
Varying the vertical magnetic field could alter the polarity of If", much as Bu did for the
ohmic initiated RF plasmas.

Encore was now operating in a pure RF mode. The ohmic supply makes quite a
bit of noise, whereas the RF system makes virtually none. In the pure RF mode, silent

blue flashes of light appeared in the tokamak window ports coincident with RF

application.

Figure 7-20a. LHCD without an ohmic target plasma. Phasing is
180° shift per waveguide. Upper trace is plasma current (20
amps per division). Lower trace is the loop voltage (1 volt per
division). Horizontal scale is | msec per division.

7-26

Figure 7-20b. Same as Figure 7-20a, but By adjusted to
maximize the RF driven current in the opposite direction. Upper
trace is plasma current (20 amps per division). Lower trace is the
loop voltage (1 volt per division). Horizontal scale is 1 msec per
division.

In Figures (7-20) the symmetry between the forward and reverse driven plasma
current for symmetric 180° phasing of the antenna is good. In Figure (7-21a) similar
results are shown for quadrature phasing to enhance the positive current. There is now a
notable asymmetry. Repeating this experiment with quadrature phasing to enhance the
negative current does not retain the asymmetry however. See Figure (7-21b). The
conclusion is once again that the effects of phasing in RF sustained plasma appears to be

weak.

Figure 7-21a. By and By adjusted to maximize reverse If" (left)

and forward I;* (right). Phasing is quadrature for forward
direction. :

7-27

Figure 7-21b. By and By adjusted to maximize reverse I} (left)

and forward I* (right). Phasing is quadrature for reverse
direction.

When the ohmic supply is used to break down the target plasma, there is a bright
flash of light. Due to the persistence of vision, the RF sustained plasma cannot be seen
independently with the naked eye. Without the ohmic breakdown, the RF sustained
plasma became instantly visible. There is a background glow from the volume inside of
the vacuum chamber. Superimposed is a very bright narrow beam that would move
around in response to changes in By and By. With no vertical field the glow was

concentrated at the top of the vacuum chamber as shown in Figure (7-22).

Figure 7-22. Glow from a RF produced plasma in Encore. The
glow is concentrated at the top of the vacuum chamber. The
toroidal magnetic field polarity is such that the guiding center
drifts for electrons are directed upwards.

From equation (3.12) the vertical confinement in a tokamak can be written as

7-28

\Sz| < (7.3)

The electron toroidal velocity can be associated with a parallel energy according to

(2B, |
Vie = —t = 5.93 x10" JE) cm/sec. (7.4)

The poloidal cyclotron frequency (denominator of equation (7.3)) can be written as

qB,

=3.5x10°—™ sec, (7.5)

IL,

cm

where the formula for the magnetic field a distance rem from a straight wire carrying a

current lamps has been used. Combining (7.3), (7.4) and (7.5) yields

\Sz]< 34 foe cm. (7.6)

amps
It will be shown in the double-sided probe measurements that the energy of the tail

electrons in the "beam" exceeds 100 eV. Taking values of rem=lom, lamps= 65amps and

Tev=100eV returns [Sz| <5cm. 100eV is a lower bound. Confinement is worse for larger

energies. Since the minor radius of Encore is only 12cm, these RF discharges do not
appear to be confined in the conventional tokamak sense.

In the absence of sufficient poloidal current to provide confinement, drifts due to
the magnetic field curvature and gradient force the electrons and ions out of the tokamak.
The VB and curvature-B drifts in a tokamak are oriented in the vertical direction.
Collectively these two drifts are sometimes referred to as the guiding center drifts.
Electrons drift one direction (up or down), and the ions the other. The resulting vertical
electric field causes an E XB drift in the major radius direction. The formula for the
gradient and curvature drift is’

* mv? BxV(B/2) im Bx < (vi)

2 t
+— -—_+*—__.. 7.7

The first term in equation (7.7) is the magnetic field gradient drift, and the second term is

the field curvature or centripetal drift. Equation (7.7) can be approximated as

7-29

__m lip Bix ~ Ban , MY; (7.8)
° qB, 4 * Be 20 nor qB, Rinajor

where fminor is the minor radius of Encore, Rimajor 1s the major radius, Bmax is the toroidal
field at the inner wall, Bmin is the toroidal field at the outer wall, and B, is the toroidal
field on axis. Using the values for maximum toroidal field (1300 gauss on axis),

assuming 100eV to calculate v; and assuming T.=10eV to compute v7, obtains

v, =4.1x10° cm/sec. The second "centripetal" term in equation (7.7) dominates. The
speed of an electron accelerated to 100eV in the toroidal direction is
Vy =5.9x 10°cm/sec. The ratio of these two quantities is

Vz — 9.0007. (7.9)

Vo
This represents a small angle. The vertical displacement per toroidal revolution is of the
order of 0.2 centimeter. The fact that the luminous "beam" appears at the top of the
tokamak is puzzling. It would seem unlikely that it could drift up there from an initial
location coincident with the end of the LH grill antenna without creating luminosity in
the intervening region as well. Even for electrons accelerated to Nj = 10 (v; = 0.1c),
equation (7.8) returns an angle of 0.003 radians. The vertical displacement per toroidal
revolution is 0.8 cm. What is perhaps more likely, the beam is generated along the
toroidal field lines nearest the filament which supplies the electrons for the breakdown.
What is surprising is that these field lines pass some distance from the end of the LH grill
antenna, probably of the order of the minor radius when the filament is located on a top
or bottom port.

With the addition of a vertical magnetic field By, the vertically oriented helical
path of the beam could be observed through an optical window mounted on a port located
at the outer mid-plane as shown in Figure (7-23). With the filament emitting electrons

but with no applied RF, no luminosity whatsoever was visible in the torus.

7-30

Figure 7-23. Helical path of RF-driven plasma current in
Encore. For this photo a vertical magnetic field was applied.
The optical window is located on a side port of Encore.

Note that the luminous beam is quite narrow from top to bottom. The launching
LH antenna is 7cm tall. The window port in Figure (7-23) is roughly 17cm tall.
Estimating from photos, the luminous beam is about 0.6cm thick. This could be
explained if the filament dimensions set the beam size.

It was determined that indeed the filament was the source of the luminous beams.
In Figure (7-22) the guiding center drifts for electrons are directed upwards and the
filament was located at the top of the torus. For other locations of the filament, the
luminous beam would appear in different locations as expected. The beam location near

the top of the torus explains the sensitivity of If" to the vertical magnetic field. By

adjusting By the symmetrically generated beams suffer differential attenuation against the

7-31

top of the chamber and the polarity of If* can be altered. This is analogous to the

horizontal spiraling phenomena for obtaining net current discovered earlier.
In Figure (7-23) the luminosity appears to decay over the ten or so revolutions

visible in the tokamak. The energy of an electron that can travel this distance in 2.5x10°

torr argon before coming to rest can be estimated. With a major radius of 38cm, ten

revolutions corresponds to a distance of 2400cm. It can be determined that room

temperature argon at a pressure of 2.5x10° torr has a density of 5.5x10"'' gm/cc. The

CSDA (Continuous Slowing Down Approximation) range is a very close approximation
to the average path length traveled by a charged particle as it slows down to rest. The
CSDA range is obtained by integrating the reciprocal of the total stopping power with
respect to energy. The path will generally not be straight and the "projected" range is the
average depth measured along the initial direction to which a charged particle will
penetrate in the course of slowing down. However, the CSDA range is a measure of the
greatest possible depth of penetration. Tables of CSDA range for electrons in argon are

available.* The data for argon are plotted in Figure (7-24).

0.01
Py = 1,093x!-723
0.001 r? = 1.000
0.0001
CSDA Range =
(g/cm?) 7
1E-05
1E-06
Zz
1E-07
0.0001 0.001 0.01 0.1
Energy (MeV)

Figure 7-24. The CSDA range for electrons in argon according
to reference &.

7-32

Using a distance of 2400cm and a density of 5.5x10"'' gm/cc, it is determined that the

CSDA range must be 1.3x10°’ gm/cm?. From Figure (7-24) this corresponds to an energy

of about 100eV.

From Figure (5-15) it can be seen that the grill antenna with quadrature phasing
generates an N) spectrum at launch from roughly 5-to-15. Electrons accelerated to
velocities corresponding to N)=15 have a parallel energy of 1140eV, while those
accelerated to correspond to Ni=5 have energies of 10.3keV. Electrons with a parallel
energy of 100ev correspond to N)=51. If these electrons are produced or sustained by a
LH wave interaction, then the spectral gap has been bridged. Ifa toroidal "cavity mode"
were responsible then the beam would not extinguish in luminosity moving away from
the top of the torus.

The LH wave interaction with the electron beam may persist as the electron beam
makes many revolutions of the torus. The electrons may continuously lose energy to the
argon atoms, but continuously gain some back from the LH waves. The RF sustained
plasma may be most concentrated at the top of the torus where the filament is located.
The beam may lose luminosity simply because it propagates out of the region at the top
of the chamber where the plasma necessary to support LH waves is most concentrated.

There happened to be a very narrow window port on top of Encore and pictures
were taken through it of the luminous beam from above. See Figure (7-25). For these

photos, the vertical field was adjusted to maximize I**. As By was adjusted, the position

of the luminous beam would move in major radius as expected. As in the picture taken
from the side, the dimensions of the beam were quite narrow compared to the dimensions
of the launching LH antenna. The beam is located at the top of the tokamak and very

close to the window port.

7-33

Figure 7-25. Luminous "beam" of RF driven plasma current as
seen through a window port located on top of the tokamak. The
beam progressively moves from right to left going down the
photos. By is varied to cause this motion.

X-Y Probe Measurements of Error Fields

The spiral nature of the magnetic field in Encore was observed in a more direct
fashion. A tiny filament was mounted on the end of an alumina probe and inserted
horizontally into the vacuum chamber from the outer mid-plane. The filament location
was approximately 6-7cm from the outer wall of the vacuum chamber. The vacuum level
in the chamber was of the order of 2x10° torr. The filament was heated and biased 20-
volts negative to produce an emission current of 1.4 microamps. The toroidal magnetic

field current was set to 395 amps producing a field on axis of approximately 1360 gauss.

7-34

The direction of the toroidal field is set clockwise as viewed from above.’ The two-sided
current probe described in chapter 5 was used to detect the current launched along the
toroidal field lines. Only one side of the probe was utilized. The orientation of the plots
is described in Figure (7-26). The probe measurements are shown in Figure (7-27). It

appears in these Figures that the filament is emitting from two distinct locations.

near GY near
inner outer
wall YY, wall

bottom

Figure 7-26. Orientation of the X-Y plots. The right-hand edge
is nearest the outer wall, the left-hand edge is nearest the inner

wall.
I= -6.5 amps I= 0 amps I= 4.0 amps
a =
I= 5.0 amps I= 6.5 amps

Figure 7-27. Electron current (dark patches) detected with one
side of the two-sided probe. The scanned area is a square
inscribing the circular cross section of the vacuum chamber. The
left side of the square is nearest the inner wall. The currents
listed are those in the radial-horizontal correction field coils, No

current was placed in the vertical field coils.

7-35

The vertical and radial components of the toroidal magnetic field of Encore
cannot be simply measured with a handheld magnetic probe. Since the toroidal field is so
large compared to the components of interest, small changes in the probe angle would
cause large changes in the probe measurement.

Probe measurements show that positive current in the radial-horizontal correction
field coils generates a magnetic field directed radially outward. Since this corrects the
radial drift seen in Figure (7-27), the radial field inherent to Encore is directed inward.
Since the uncorrected drift as visualized in Figure (7-27) is toward the inner wall and the
toroidal field is oriented clockwise (as seen from above), the current collecting probe
must face the filament on the "downstream" side of the filament in terms of the toroidal
field. In other words, the toroidal field lines must point from the filament to the current
collecting side of the double probe, rather than the other way around.

The vertical component of earth's magnetic fields points downward in the
Northern Hemisphere and is of the order of a half gauss.'° In the absence of a vertical
component from the toroidal field coils, the toroidal field would spiral slightly
downward. The current collecting side of the double-probe faces the filament on the
"downstream" side and yet upward drifts are seen in Figure (7-27). The inherent vertical
field of Encore must be either directed upward or else must be insufficient to overcome
the electron curvature and gradient-B drifts.

For the given polarity of the toroidal magnetic field, the gradient-B and curvature-
B drifts for the electrons are upward, independent of toroidal direction. In Figure (7-27)
upward drifts are seen. The vertical height of the scanned area was determined to be
15.9cm. In Figure (7-27) for the case of [=Samps, the vertical shift of the spiraling
electron beam per revolution is roughly 1.0cm. The maximum guiding center drift
velocity occurs when the 20eV energy of the source electrons goes entirely into vj. For

this case equation (7.8) gives a vertical drift velocity of 8x10* cm/sec. Electrons with
E)=20eV have a toroidal velocity of 2.65x10° cm/sec. The ratio of these two speeds is

0.0003. The maximum vertical displacement per revolution due to the guiding center
drifts is then about 0.07cm. The fact that the measured drift exceeds the maximum
possible guiding center drift implies that there is an inherent vertical magnetic field due

to the toroidal field coils and/or the horizontal field coils. The polarity of the vertical

7-36

field must be upwards in order to enhance the guiding center drifts. A lower bound to the
magnitude necessary is that which accounts for a 0.93cm drift per revolution. The
relevant equation is

By. 27R = 0.93cm. (7.10)
B,

It may be estimated from Figure (7-27) that the location in major radius of the emitting
filament is the axis of the chamber (38cm) plus 3.2cm. The toroidal field on axis is 1360
gauss and at the location of the filament would be 1254 gauss. Solving equation (7.10)
for By returns 4.5 gauss. This is the net vertical error field. Subtracting the downward
0.5 gauss due to the earth's magnetic field means that the vertical field due to Encore
when 5 amps are placed in the horizontal coils is of the order of 5.0 gauss (at the
measured location).'' This is a lower bound since the electron source does not produce a
beam that is mono-energetic in parallel energy.

Ideally one would place the electron source on an X-Y probe so that the field
error could be mapped as a function of position in the minor cross section of the torus.
Errors are not necessarily evenly distributed in the toroidal direction. For instance on
Encore, the iron core of the ohmic transformer induces localized field errors. Errors
accumulated in complete revolutions of the torus should be examined. Apparatus for

such measurements has been described.”

Energetic Electrons in RF Sustained Plasma

Hot electron measurements similar to those described in the previous section were
made in RF-sustained plasma. An ohmic target plasma was utilized. The scanned area
was a square, but rather than being inscribed in the minor cross section, it was displaced
3.8cm outward in major radius. This was done because many hot electrons were found
near the outer wall where the end of the grill antenna is located.

The toroidal field was set to circulate counterclockwise which is opposite to the
direction of the previous section. The inherent radial, horizontal, magnetic field is
consequently now directed outward. The magnitude of the toroidal field was 1300 gauss

on axis. The "two sided" X-Y scanning probe was located 157.5° counterclockwise from

the orill antenna as seen from above the tokamak. The experimental arrangement is

7-37

shown in Figure (7-28). The two probes were biased 100 volts negative so that detected
electron current must occur from energetic electrons. The two probes are labeled "1" and

"2," probe "2" facing into the toroidal field.

inherent radial
magnetic error
field

applied radial
magnetic field

grill
antenna

X-Y Probe
(two sided)

Figure 7-28. Experimental arrangement as seen from above the
tokamak.

4.9 kW power was delivered to a single channel of the four port grill antenna
(one of the two interior waveguides). The tokamak was filled with argon to a pressure of
2.5x10° torr.

The data is presented in the form of two-dimensional color-coded plots. Ten
colors represent the current ranges and the color code is given in Figure (7-29). Blue and
black represent negative ranges where ion current dominates. Shades of green represent

the most intense regions of hot electrons.

Figure 7-29. Color code for the data plots. The scale is linear
with lowest to highest going from left to right. The upper bound
of the lowest color is -7.4mV (across the input resistance of the
amplifier). The upper bounds of the next eight colors in mV are
2.6, 12.6, 22.6, 32.6, 42.6, 52.6, 62.6 and 72.6. The lower bound
of the largest color is 72.6mV.

In Figure (7-30) data for the case with no correcting radial horizontal magnetic
field and no vertical field is given. The location of the most intense hot electrons is near
the outer wall where the mouth of the grill antenna is located. From Figure (7-28) it can

be seen that the uncorrected spiraling of the toroidal field lines should push the hot

7-38

electrons nearer the outer wall for probe "2" and away from the outer wall for probe "1."
This is born out by the shifts in the outer border of the green regions in Figure (7-30).
For the direction of the toroidal field, the gradient-B and curvature-B drifts are downward
for electrons, independent of toroidal direction. The green regions in both plots of Figure

(7-30) are shifted downward from center.

Figure 7-30. Color-coded plots of hot electrons. No correcting
horizontal or vertical magnetic field is employed. The left plot is
from probe "1" and the right plot is from probe "2." The outer
wall of the tokamak is very near the right side of the plots, and
the inner wall is nearest the left side.

In Figure (7-31), the results of applying a strong radial-horizontal magnetic field
to more than reverse the horizontal error field is shown. I" is reversed as a consequence.

This time electrons impinging on probe "2" have spiraled into the interior of the tokamak,
while electrons that would have impinged on probe "1" have spiraled toward the outer

wall to such a degree that practically no green regions are evident.

7-39

Figure 7-31. 13 amps are applied to the radial-horizontal
magnetic field coils to reverse the direction of If". The applied
radial magnetic field is roughly 7.1 gauss. The left plot is from
probe "1" and the right plot is from probe "2." The outer wall of

the tokamak is very near the right side of the plots, and the inner
wall is nearest the left side.

In Figure 7-32, the applied radial-horizontal field is adjusted to make If" =0.

The right-hand boundaries of the green regions of denser hot electrons are comparable

distances from the outer wall.

Figure 7-31. Approximately 4.5 amps are place in the radial-
horizontal magnetic field coils to achieve If" =0. The left plot is

from probe "1" and the right plot is from probe "2." The outer
wall of the tokamak is very near the right side of the plots, and
the inner wall is nearest the left side.

In Figure (7-33) no correcting radial-horizontal magnetic field is applied.
However, +4.8 amps are applied to the vertical field coils. Probe measurements indicate
that this produces a field that points upwards with a magnitude of approximately 4.3
gauss. This was found to help the ohmic breakdown. The gradient and curvature-B drifts

7-40

for electrons are downward. The easier ohmic breakdown is consistent with the fact that
the ohmic supply drives electrons counterclockwise (as seen from above), and the
addition of the upward vertical field causes these accelerated electrons to spirals upwards
counteracting the downward drifts. Since no correcting radial-horizontal magnetic field
is applied, electrons impinging on probe "2" should be closer to the outer wall than those
impinging on probe "1." In Figure (7-33) this appears to be the case judging form the
right-most boundaries of the green regions. Electrons impinging on probe "2" (second
plot in Figure (7-33)) travel in the same direction as the ohmic electrons and appear well
confined. Electrons impinging on probe "1" (first plot in Figure (7-33)) appear less well
confined. In this case the electrons spiral downward due to the vertical field and also

drift downward due to the gradient and curvature-B drifts.

Figure 7-33. Approximately 4.8 amps are placed in the vertical
magnetic field coils creating a toroidal field that spirals upward.
No radial-horizontal field is applied. The left plot is from probe
"1" and the right plot is from probe "2." The outer wall of the
tokamak is very near the right side of the plots, and the inner wall
is nearest the left side.

Fast Wave Launch

In the previous section it was noted that a considerable fraction of the detected hot
electrons were found very close to the end of the grill antenna. It could be conjectured
that the evanescent fields between the end of the grill antenna and the slow wave cutoff
could accelerate electrons passing by. From Figure (5-16f) the Nj spectrum for a single
waveguide is much broader than for quadrature phasing, but is still concentrated below
Ny = 36. Acceleration is more likely if the initial toroidal velocity of the electron is

resonant with an Nj in the spectrum. For Nj = 36 the resonant electron would have an

7-41

energy of 198eV. In Figure (5-15f) some miniscule amount of power is available as high
as Ni; = 72. For Nj = 72 the resonant electron would have an energy of about 50eV. Such
energies are unlikely to be produced by the filament source but could possibly be
generated in the ohmic target plasma. It is also possible that electrons of these energies
generated by Landau damping of LH waves could subsequently be accelerated by the
evanescent region, thus enhancing the current drive.

There is an interesting way to test these ideas. If the grill antenna is rotated 90°,
then the electric field of the TEj9 mode is no longer parallel] to the toroidal field but
perpendicular to it. In this configuration it would be impossible for the evanescent fields
to accelerate electrons passing by in the toroidal direction. From equation (4.137) the
electric field perpendicular to both the toroidal magnetic field and the density gradient is
the appropriate polarization for launching fast waves. Fast waves have been launched
and well characterized in toroidal plasmas.'? Experimental results agree with predictions
from the cold-plasma dispersion relation. Fast waves can also drive current in toroidal
plasmas.'*'*'® The current drive efficiencies for the slow and fast mode are comparable.

From equation (4.128) the cutoff for the fast mode is at a slightly higher plasma
density than for the slow mode (equation (4.124)). If distance from the cutoff were any
concern, matters would be worse for the launch of fast waves.

The orientation of the antenna for fast wave launch is toroidally symmetric. For
the LH case with a single powered waveguide, toroidal symmetry is compromised due to
the presence of the uneven number of non-powered waveguides.

For the experiment, 4.9 kW was applied to a single waveguide, the third from the

top. The torus was filled with argon to a pressure of 2.5x10° torr. The toroidal field was

set to 1300 gauss on axis with polarity such that circulation was clockwise. For this
polarity the guiding center drifts for electrons are upwards. The radial-horizontal
magnetic error field is directed inwards. No radial-horizontal correction field was
applied. The preferred direction for accelerated electrons (spirals into the chamber rather
than out toward the outer wall) is clockwise.

When RF power was applied, 20 amps of plasma current were driven. For a

single waveguide the current drive efficiency is comparable to that from the launch of

slow waves. The larger density required to reach cutoff was not a serious impediment.

7-42

The direction of the net electron flow was clockwise as expected from the spiraling of the
field lines. To obtain the 20 amp current a downward directed vertical-magnetic-field of
approximately 2.4 gauss was applied.'’ The resulting downward spiral for electrons
propagating in the clockwise direction counteracts the upward guiding center drifts.

Hot electron measurements were made as described in the previous section. The
measured square was shifted 3.8 centimeters outward from being inscribed in the minor
cross section to capture hot electrons near the outer wall where the end of the grill
antenna is located. The antenna was located 135; clockwise from the X-Y probe as seen

from above. The color code is as previously described. The results are shown in Figure

(7-34).

Figure 7-34. Plots of hot electrons with fast wave launch. The
left plot records hot electrons accelerated clockwise in the torus.
The right plot records hot electrons accelerated counter-
clockwise in the torus.

Hot electrons were detected traveling in both directions. Orienting the antenna
electric field parallel to the toroidal electric field is not a requirement to generate hot
electrons. Electrons traveling in the preferred clockwise direction are vertically well
confined in Figure (7-34). Electrons travelling in the counterclockwise direction follow
magnetic field lines that spiral upwards in addition to drifting upwards due to the guiding
center drifts. Figure (7-34) demonstrates this behavior.

If" varied with the combination of radial and vertical magnetic field settings. By

altering the combination of radial and vertical fields slightly, a current of 26 amps was

obtained.

7-43

A radial-horizontal magnetic field was applied so as to reverse the preferred
direction for accelerated electrons. Now electrons traveling in the counterclockwise
direction spiral inwards rather than toward the outer wall. With the aid of an upward
directed vertical field of about 4 gauss, a current of 20 amps in the opposite direct was
obtained. This is the same magnitude of current obtained in the previous case.

In summary, several important observations can be made. Significantly
increasing the cutoff density does not seem to affect the current drive efficiency. This
suggests that proximity to the cutoff is adequate for both slow and fast waves. Rotating
the antenna electric field perpendicular to the toroidal direction does not hinder the
generation of fast toroidal electrons. Nor does it affect the basic current drive efficiency.
This suggests that the evanescent fields at the end of the grill antenna prior to the cutoff

location are not a major source of the hot electrons observed.

Role of the Vertical Magnetic Field

In Figure (7-33) apparent vertical confinement is achieved with an applied
vertical magnetic field of 4.3 gauss directed upward. It was previously estimated that the
toroidal field coils cause a vertical error of roughly 5.0 gauss directed upward when the
toroidal field circulates clockwise as seen from above, and the field on axis is 1360 gauss.
With the toroidal field now circulating counterclockwise as seen from above, and with
the field on axis being 1300 gauss, this 5.0 gauss error would be reduced proportionally
to 4.8 gauss and point downwards. The vertical component of the earth's magnetic field
is about 0.5 gauss directed downward. Combining these would predict that there was a
net vertical magnetic field of roughly 1.0 gauss directed downwards. However, the
electron drifts are also downward for this toroidal field polarity. Hence the net vertical
magnetic field must be directed upwards to explain the confinement seen with probe #2
in Figure (7-33). The magnitude of the discrepancy is not large. It is possible that the
vertical error field changed in magnitude, or that only a portion of it was due to the
toroidal field coils and thus changed polartity when the toroidal field was reversed.

The probe bias of -100 volts requires that detected electrons be more energetic

than 100eV. From the estimate of the CSDA range given earlier, one would anticipate

that the energy of the electrons creating the luminous beam would not be too much larger

7-44

than 100eV. One might estimate the necessary vertical field by equating the vertical
pitch of the toroidal magnetic field to the ratio of the vertical drift velocity and the
toroidal velocity. For electrons moving very fast along the toroidal field lines, the second

"centripetal" term of equation (7.7) dominates. The relationship becomes

B Vv m Vo

vertical, _ _* z—drift, — €

B, Vo q.B, R

, (7.11)

major

Using 100eV as the appropriate electron parallel energy, one can solve equation (7.11)
for the necessary net vertical magnetic field. The result is 0.9 gauss, a very modest
magnetic field. For 2.6 keV electrons corresponding Ni = 10, the necessary field would
be 4.5 gauss.

Equation (7.10) implies that larger vertical fields are necessary to confine more
energetic electrons. Large vertical fields are incompatible with the ohmically generated
target plasma and would present a problem. When the vertical field is used to confine the
hot electrons, there is a juggling problem because the confinement is energy selective.
Not all energies will be properly confined.

The arguments of the previous paragraph apply to very low current densities. It
must not be forgotten, however, that Encore is a tokamak. Even for currents as smail as
20 amps, it is the current density that determines the poloidal magnetic field, which in
turn provides conventional tokamak confinement. The dark green "beam" in the first plot
of Figure (7-34) has a diameter of the order of 1.5 cm. Were the beam to contain the bulk
of the 20 amps, the poloidal magnetic field at the edge of the beam would be of the order
of 5 gauss. From equation (3.12), however, a strict vertical confinement of 1.5cm for
100eV electrons requires a poloidal field of 280 gauss. It seems difficult to explain the
confinement of the hot electron beams in a conventional tokamak sense. However,
another factor to consider include the fact that current is driven in both directions in
separate "beams." It is only the net current that is measured. The current in the beam
could be much larger than 20 amps.

In true tokamak operation, the purpose of the vertical field is not to combat
guiding center drifts at all, but rather to combat the tendency of the toroidal current to

expand in major radius. The poloidal magnetic field confines the plasma. The tendency

7-45

for the toroidal current to expand can be seen as follows. Lengths of current traveling in

opposite directions on opposite sides of the torus repel each other.
It should be noted that IS" does not monotonically increase with increases in the

vertical magnetic field. There is always a peak observed in I} as the vertical field is
varied. Sometimes the peak is rather weak.

The issue of confinement in these unusual low-current RF-sustained discharges
requires further study. It appears as though the vertical magnetic field provides enhanced
confinement for the hot electrons. The fact that there is insufficient plasma current to
provide conventional tokamak confinement will be explained in the next chapter as due

to the density limit.

Toroidal Field Scan

Hot electron plots were recorded as a function of toroidal magnetic field. If the
location of the hot electrons varied with the toroidal field in a manner analogous to that of
lower hybrid waves, it would act as a confirmation that LHCD was taking place. It was
earlier argued that the sudden decrease in I} as the toroidal field is decreased agrees
remarkably well with the theory of accessibility of LH waves. This is strong evidence for
LHCD. In this section, comparison will be made with the LH cone angle.

The toroidal magnetic field was set to circulate counterclockwise, so the inherent
radial error field is directed outwards as seen from above. The grill antenna was located
157.5 degrees clockwise from the X-Y probe. For this orientation, the toroidal field lines
spiral toward the outer wall travelling from the antenna to the X-Y two-sided probe. The

tokamak was filled with argon to a pressure of 2.5x10™ torr. The probe bias was -100

volts as before. The color code is given in Figure (7-29). 3.9kW was applied to one of
the interior waveguides. Data was taken using the probe closest to the antenna. To avoid
any confusion, no vertical or radial-horizontal magnetic field was applied. The data is

shown in Figure (7-35).

7-46

1360 gauss 1210 gauss 1040 gauss

863 gauss 690 gauss 518 gauss

Figure 7-35. Plots of hot electrons for various magnetic fields.
The outer wall of the tokamak is very near the right side of the
plots, and the inner wall is nearest the left side.

In Figure (7-35) the areas of intense hot electrons, colored green, suddenly begin
to disappear by 863 gauss. A possible explanation for this behavior is that accessibility
of the antenna launch spectrum becomes significantly compromised at a toroidal field of
863 gauss. The N| spectrum for a single waveguide is given in Figure (5-16f). The
spectrum is peaked at N) = 0, and falls monotonically to zero by roughly N) = 32. The
slope of the curve in Figure (5-16f) is steepest in the region 8 accessibility limit moves above N) = 8 there will be a rapid drop in accessible power.
Most of the power involves Nj < 20.

Microwave density measurements were made during a RF sustained discharge
and the measurement is shown in Figure (6-13). The measured line average plasma
density was 7x10'' cm™. Evidence has been presented that RF discharges tend to form
concentrated beams, so the peak plasma density may be significantly higher than the line
average density. At the stated fill pressure there are roughly 8 x10'' argon atoms per

cubic centimeter, and single ionization will produce a plasma density of the order of

7-47

8x10" cm. For sake of argument assume a plasma density of 8.6x10"cm®?
corresponding to the 1.5kA graph in Figure (6-13). What this figure shows is that the
accessibility limit for a toroidal field on axis of 863 gauss has reached Nj = 10 and
accessibility is beginning to become a problem for a single waveguide spectrum. Any
further decrease in the toroidal field will rapidly hinder accessibility.

The lower hybrid "cone" angle is the angle with respect to the local magnetic field
at which LH waves propagate. From equation (4.89), the tangent of the LH cone angle

for Encore parameters is given by @/@,, and is independent of the plasma density. In

Figure (7-36) the LH "cone" angle is given as a function of magnetic field for 450 MHz.

17.5
15-4
12.5-
LH Cone Angle
(degrees) 10-
7.54
5 T T T
500 750 1000 1250 1500

Toroidal Field On-Axis (gauss)

Figure 7-36. The propagation angle of lower hybrid waves with
respect to the local magnetic field. At lower magnetic fields the
angle is considerably larger.

Possibly because accessibility decreases the amount of LH power injected as the
magnetic field is decreased, the amount of current represented by the dark and light green
areas in Figure (7-35) decreases as the magnetic field is reduced. The question is whether
the distribution of the current protrudes further from the outer wall (near the right-hand

side of the plots) as the magnetic field is decreased and the LH cone angle increased. The

distance from the grill antenna to the X-Y probe is 104cm. Due to the very small plasma

7-48

current the poloidal field is negligible compared to the toroidal field and twisting of the
field lines can be ignored. The maximum displacement of the LH wave front across the
minor cross section is given by multiplying the propagation angle in radians by the

distance. These values are given in the following table.

Baxis(gauss) Angle (degrees) Displacement (cm)
6.7

1360 . 12
1210 7.6 14
1040 8.8 16
863 10.6 19
690 13.1 24
518 17.3 32

The minor diameter of Encore is 26cm. The square containing the data is roughly
16cm in width. There is roughly a 5cm gap from the center of the edges of the square to
the chamber wall. For the three lowest magnetic fields, the LH waves have opportunity
to deliver energy and form hot electrons at the left-hand boundary of the plots. Since the
magnetic field lines spiral towards the outer chamber wall travelling from the antenna to
the X-Y probe, hot electrons cannot reach the left hand boundaries of the plots by
propagating along the toroidal field for multiple revolutions of the torus. Inspection of
Figure (7-35) shows that indeed areas of green exist near the left-hand boundaries for the
three cases featuring the lowest magnetic fields. For the three highest magnetic fields the
angle is insufficient to produce hot electrons at the left-hand edge of the plots. In Figure
(7-35) no areas of green exist near the left-hand edge for the three cases featuring the
largest magnetic fields.

Computing the horizontal centroid of the current and plotting this versus the
propagation angle is more quantitative. This is done in Figure (7-37).'® The results show
that indeed the centroid of the current moves further into the chamber as the LH angle

increases. The results are consistent with LHCD.

7-49

30

20-4
Current
Centroid

(# of pixels) o
oO
104
o0 oO
0 t T T
0 5 10 15 20

LH Propagation Angle (degrees)

Figure 7-37. Graph of the horizontal centroid of the hot electron
current versus the LH propagation angle. The plots are 32x32

pixels.

Effect of Initial Conditions

Under most circumstances, the initial conditions of the ohmic target plasma were
not noticed to have an impact on the plasma current I;* in RF sustained discharges. For
instance, when RF sustained plasma current was first discovered in Encore, the polarity
of the ohmic plasma was reversed without effect on the direction of If’ and with little
effect on its magnitude. However, it must be admitted that for most experiments great
care was taken to insure that the initial conditions were identical, and these effects were
not looked for. In the following instance a dependence on the conditions of the ohmic
target plasma was documented.

The configuration of the tokamak is shown in Figure (7-38). The toroidal field
was set to circulate clockwise as seen from above. The toroidal field was 1311 gauss on
axis. The inherent radial magnetic error field is directed radially inward for this toroidal
field polarity. An over correction was made to the radial magnetic error field. The

applied correcting field was directed radially outward and was of a magnitude to

completely reverse [°° (roughly Sgauss). For this configuration, the preferred direction

7-50

for electrons accelerated near the outer wall is counter clockwise. Electrons accelerated
in the counterclockwise direction will spiral into the chamber, rather than outward toward
the nearby wall. The ohmic system on Encore also accelerates electrons in the
counterclockwise direction. The plasma current was maximized for a vertical magnetic
field of 3.3 gauss directed upward, and this field was used to take the data..

The tokamak was filled with argon to a pressure of 2.5x10° torr. All four

waveguides were energized with identical phase. According to Figure (5-16a) this
produces a very narrow N| spectrum centered on zero, with virtually all of the power

satisfying N, <8, although some miniscule amount of power is available at Nj values as

high as 36. The RF power to the four waveguides in kilowatts was 4.7, 2.7, 4.7 and 3.7

respectively. The imbalance will broaden the Nj spectrum somewhat.

applied radial
magnetic field

Direction of
_~ ohmicly driven
electrons

inherent radial
/_.~ Magnetic error
field

Figure 7-38. Configuration of the tokamak for the experiment
showing an effect of initial ohmic plasma level on the RF-
sustained plasma current. RF driven electrons representing the
net RF current travel counterclockwise as do ohmic driven
electrons.

The If" data is shown in Figure (7-39). Two different settings of the ohmic

plasma setting were utilized (1.6 and 2.8). With the 2.8 setting, larger ohmic current was
produced, taking longer to decay. The larger initial ohmic current is associated with the

smaller RF-sustained plasma current (70 amps versus 100 amps). The ohmic and RF-

sustained current have identical polarity.

7-51

Figure 7-39. Plasma current versus time for two different
settings of the ohmic amplifier. The larger initial ohmic current

is associated with the smaller If". Horizontal scale is 1msec per
division. Vertical scale is 50amps per division. Lower trace

tracks the RF.

The loop voltage is shown in Figure (7-40). With no RF, the loop voltage quickly
decays to zero. With RF, the loop voltage never decays to zero during the RF-sustained
plasma, but instead appears to even plateau for the lower ohmic setting. There is a large
spike in the loop voltage when the RF is turned off and the plasma current decays. This

data is reproducible and several photographs of the same data were made.

7-52

Figure 7-40. Loop voltage versus time for two different settings
of the ohmic amplifier. Loop voltage is also shown for the lower
ohmic setting without RF. The loop voltage takes longer to
decay with the larger initial ohmic current. There is a large spike
in the loop voltage when the RF sustained current decays.
Horizontal scale is Imsec per division. Vertical scale is 200mV
per division. Lower trace tracks the RF.

A possible explanation for why the larger ohmic plasma current results in smaller
RF-sustained plasma current involves the distribution in the minor cross section of the
plasma electrons to be accelerated by LHCD. It is not known if the target electrons are
primarily thermal electrons or tail electrons. Experiments by others have shown that LH
waves launched parallel to ohmically driven electrons contribute to much greater

increases in plasma current than LH waves launched the other direction, suggesting that
thermal electrons are not the target electrons.’ Whichever, if the target electrons are
primarily formed at larger major radius, then I** will be larger due to the fact that the
path length before spiraling into the inner wall is larger. It is possible that the smaller
ohmic setting causes the bulk of the target electrons to be formed at larger major radius.
It would be possible to check this with probe measurements.

The loop voltage maintains a low but non-zero value during the RF-sustained
discharge. Three possible explanations are discussed in the following.

One possibility is that the RF induced plasma conductivity is such that the L/R

decay time is long compared to duration of the RF plasma. Since the RF is on long

before the loop voltage decays to the almost constant level of roughly 100mV, one would

7-53

have to argue that the conductivity took a few milliseconds to develop. The inductance

of Encore is of the order of one micro-henry.”

A typical ohmic discharge in Encore
might have a plasma current of 1kA and a loop voltage of 8 volts for a resistance of the
order of 8 milli-ohms. The L/R time is of the order of 0.1milli-second. In order to
achieve an L/R time on the order of 10 milliseconds or larger, the resistance of the
plasma would have to be of the order of 0.1 milli-ohm or less.

Another possibility is that the RF-sustained plasma is slowly decaying. If the
decay rate is one amp per millisecond, which is certainly possible in Figure (7-39), then

the loop voltage would be

di

a / =L = (10 henry )x (10° amp / sec) =ImV. (7.12)

loop

In order to get a loop voltage of 100 mV as in Figure (7-38), the decay rate would have to
be 100 amps per millisecond, and this is ruled out in Figure (7-39).

Yet another possibility is that the spiraling RF-driven electron beam impinges the
tokamak chamber inner wall at a location that is not 180 degrees from the gap in the torus
across which the loop voltage is measured. The roughly 100 amp plasma current must
then flow in the aluminum chamber wall. In order to drop 100 mV, a resistance of the
order of one milli-ohm across some portion of the torus is necessary. Although this
seems plausible, there is the question of why the two differing plasma currents end up

with virtually identical loop voltages.

Summary

Low current (< 160 amp) discharges were maintained in Encore by application of
RF with the grill antenna. Net plasma current is obtained not by antenna phasing but
rather with the aid of subsidiary magnetic fields that induce spiraling of the toroidal field
lines. When the electron acceleration is near the plasma periphery, the spiraling presents
an asymmetry that favors one toroidal direction over the other. It is not known why the
antenna phasing failed to produce significant asymmetry in the plasma current. The
highly inhomogeneous nature of the unusual plasma may play a role.

The decrease in plasma current at low toroidal field strength appears to closely

coincide with the onset of LH accessibility problems. This is strong evidence that LHCD

7-54

is involved. The dependence of the amount of plasma current on the ion mass correlates
with the ion mass scaling of the density limit discussed in chapter 8. There is some
evidence that the hot electrons produced distribute themselves in correspondence to the
LH propagation angle.

Fast wave launch produces similar plasma current, so acceleration of electrons by
the antenna evanescent fields prior to the plasma mode cutoff can be ruled out. The fast
wave cutoff is at a higher density than for the slow mode. Hence, proximity to the cutoff
is not an impediment to LHCD.

With the use of a miniature electron source and a probe capable of scanning the
minor cross section and detecting the electrons, the field errors in Encore can be observed
and quantified. Electrons with energies above 100eV have been observed in RF
sustained discharges. These beams of electrons are not confined in the conventional
tokamak sense due to the low poloidal magnetic field. The vertical field plays an
important role in the propagation of the low current beams. The behavior of the hot
electrons confirms the spiral nature of the toroidal field lines. Encore has been operated
in a purely RF mode without the use of an ohmic target plasma. When RF sustained
discharges utilize an ohmic target plasma, the nature of the target plasma can sometimes

affect the RF driven current level.

' This was an important discovery in the early study of cosmic rays. See I. Asimov, Understanding
Physics, Dorset Press, (1988), volume II, p. 218

> Pete Politzer, tokamak designer, GA Technologies, Inc., San Diego, CA, private communication

} Hiroyuki Ikezi, GA Technologies, Inc., San Diego, CA, private communication

4 The convention for current direction is based upon the normal ohmic current direction in Encore being
positive.

> Obtained from the operating manual for the Varian Ratiomatic Ion Gauge used to measure pressure in
Encore. Essentially it measures the difficulty in ionization by a 150-volt electron beam.

°L. H. Sverdrup and P. M. Bellan, "Cause of the Lower-Hybrid Current-Drive Density Limit,” Phys. Rev.
Lett., 59, (1987), p. 1197, equation (6).

7 George Schmidt, Physics of High Temperature Plasmas, second edition, 1979 Academic Press, p. 23,
equation 2-102

® See http://physics.nist.gov/PhysRefData/Star/Text/contents.html or Stopping Powers for Electrons and
Positrons, M. J. Berger et al., ICRU Report #37, International Commission on Radiation Units and
Measurements, Bethesda, MD, (1984), ISBN 0-913394-31-9, p.82

” The switch used to energize the toroidal field is in the "up" position to achieve this polarity. Placing the
switch in the "down" position produces a toroidal field that is counterclockwise as viewed from above the
tokamak. The calibration for gauss on axis is 3.45 times the coil current in amps.

” http://www.ngdc.noaa.gov/cgi-bin/seg/gmag/igrfpg.pl

Probe measurements demonstrate that at the center of the minor cross section, the horizontal coils

produce a negligible vertical field component.

7-55

2 D. M. Bellan, "Simple system for mapping magnetic field errors in tori," Rev. Sci. Instrum., 58, (1987), p.
148

RC. Platt and R. McWilliams, "Excitation of fast waves near the mean gyrofrequency,” Phys. Rev. Lett.,
57, (1986), p. 2276

'4 J Goree et al., "Fast-wave current drive in a toroidal plasma,” Phys. Rev. Lett., 55, (1985), p. 1669

'S S_C. Chiu et al., "Theory of fast wave current drive for tokamak plasmas," Nuc. Fus., 29, (1989), p. 2175
'6 DP. P. Sheehan, R. McWilliams et al., "Fast-wave current drive above the slow-wave density limit,” Phys.
Rev. Lett., 64, (1990), p. 1258

'T The value of 2.4 gauss is a measured value near the center of the torus and includes the earth’s magnetic
field but not any vertical field errors due to the toroidal field or the radial-horizontal field. The applied
field near the outer wall of the tokamak is of the order of 64% of the center value. Application of the
radial-horizontal field alters the vertical field slightly.

'8 The background level appears to be yellow. The red colors represent less current than the yellow
background. The presence of the red shades may indicate enhanced ion current due to higher plasma
density. The green shades represent electron current above the background level. In any event, the
computed centroid uses the green shaded areas only. The dark green areas were weighted per the given
current range despite the fact that dark green may include saturated pixels.

“NJ. Fisch, "Theory of current drive in plasmas," Rev. Mod. Phys., 59, (1987), p. 213

” See the text prior to equation (3.20). The iron core transformer is neglected for this estimate. It is
assumed that the ohmic windings are open circuits.

8-1

8 Lower Hybrid Current Drive Density Limit

Introduction

In the early days of lower hybrid current drive experiments, there were numerous
reports of success. Many groups built coupling antennas and associated power supplies.
When they flipped the switch, large currents were driven in tokamak plasmas.’ This did
not happen in the LHCD experiments on Encore. Eventually currents as large as 150
amps were driven in Encore, but considering the available RF power of 40 kW, the
efficiency was well below that observed in other experiments, as described in chapter 2.

The "successful" LHCD experiments noted that the current drive efficiency
plummeted at some plasma density. As described in chapter 2, the current drive
efficiency is supposed to drop with increasing plasma density, being proportional to the
inverse of the density. However, the "density limit" encountered in experiments across
the world was a more precipitous phenomena, and nobody knew what the explanation
was. The density limit varied from tokamak to tokamak. Encore is an unusual tokamak,
having a very low magnetic field and highly collisional plasma. Data shows that plasma
density in Encore is proportional to the plasma current.” It is therefore not possible to
have significant plasma current without a significant concomitant plasma density. Was it
possible that the density limit for Encore was such that any significant plasma current
would raise the plasma density above the limit? The density limit was shown to depend
on the frequency, with higher frequencies corresponding to higher density limits.
Experiments on Encore utilized a frequency of 450MHz, which is possibly the lowest
frequency employed in any experiment.

Many possible explanations for poor current drive efficiency on Encore were
examined. Directional couplers on the RF power supply output enabled demonstration of
large output power. As described in chapter 5, the antenna was found to effectively
couple large RF power to a dummy load. The antenna and RF power supplies function
properly.

In chapter 4 it is argued that the cutoff coincides with such a low plasma density

that it occurs very close to the antenna waveguides. Hence coupling of the antenna to the

plasma should not be a problem. In chapter 7 it ig shown that RE generated plasma could

8-2

be sustained in Encore. This demonstrates that the antenna is capable of coupling
significant amounts of power to the plasma.

In chapter 4 it is argued that for large enough toroidal magnetic field, accessibility
is not a problem. In chapter 6 data from ohmicly generated plasmas confirms these
calculations. Therefore, accessibility is not a problem.

In chapter 3 the L/R time constant of Encore was demonstrated to be short enough
so as not to hide significant changes in plasma current. The Rogowski current diagnostic
was shown to have a fast time response. If lower hybrid waves generated significant
amounts of plasma current, then either the loop voltage diagnostic or the Rogowsky
current diagnostic would see it.

It was in writing up the physics of lower hybrid waves and calculating the various
parameters as they related to Encore experiments that the idea for what might cause the
density limit occurred. The question was posed, "under what conditions can the launched
lower hybrid waves mode convert to the ion plasma mode in Encore?" The ion plasma
modes are heavily Landau-damped and useful for heating, but not current drive.

Mode conversion from the lower hybrid mode to the ion plasma mode occurs
before the lower hybrid resonance layer defined by (4.112) is reached. The mode
conversion layer is defined by equation (4.119). For the low field conditions of Encore

where @;,,; = @ceMci, equation (4.119) is essentially independent of magnetic field and ion

mass. For the Encore parameters Tj = 3 eV, T, = 10 eV, f = 450MHz, B = 1.3kG
equation (4.119) yields N; = 130. Waves with Nj = 130 will mode convert to ion plasma
waves. The antenna used in the Encore experiments will not launch significant power at
N; = 130. However, Nj = 130 corresponds to the thermal velocity of 15.2eV electrons
and lies in the "spectral gap" between the phase velocities of launched LH waves

(N,=10 corresponding to 2.6 keV electrons) and the thermal electrons at 10eV in
Encore (corresponding toN , ~ 240). See Figure (8-1). It is not known how the spectral

gap is bridged in current drive experiments although decay waves and Nj non-
conservation in toroidal geometry are possibilities. The presumption is that by some
means, waves with N; values corresponding to electrons in the thermal distribution must

be generated. If in bridging the spectral gap the Ny spectrum must slide in a continuous

8-3

fashion from values corresponding to high phase velocity to those corresponding to
thermal velocities, then if the mode conversion lies in the spectral gap, no waves will
make it past this road block. So the idea is that the density limit occurs when the

undesirable mode conversion to an ion plasma wave moves into the "spectral gap.”

N, =10
se, LH spectrum
at launch

plasma f (v.)

0 “spectral gap”

Figure 8-1. Schematic of the plasma electron velocity
distribution along the toroidal magnetic field juxtaposed with the
lower hybrid wave Nj spectrum at launch. In order for Landau
damping to occur, there must be a phase matching where

N, =c/v,,. The "spectral gap" is the region between f (v,.) and
the launch Nj spectrum.

In attempts to explain the density limit, difficult theories involving parametric
decay were looked at.* Other theories were more like ad hoc rules designed to cover all
known cases. In contrast, the proposed theory is simple and appealing, and unlike other
theories, offers a physical explanation that fits the data well. The issue of exactly how
the spectral gap is bridged is not addressed.

The following paper published in Physical Review Letters presents the above-
mentioned theory.° In the paper a comparison is made between the theory and
experimental results from many other tokamaks. Compelling agreement is

demonstrated.

' For instance see papers on LHCD in the proceedings of the fifth topical conference on "Radio Frequency
Plasma Heating," February 21-23, 1983, U. of Wisconsin-Madison.

> Data from Eric Fredrickson

3M. J. Mayberry et al., Phys. Rev. Lett., 55, 829 (1985)

*C.S. Liu, V. S. Chan et al., "Density Threshold for Parametric Instability of Lower Hybrid Waves in a
Tokamak,"” GA Technologies, Inc., San Diego, CA

° J. G. Wegrowe et al., "The density Limit in lower-Hybrid Current Drive," Comment on Plasma Physics
and Controlled Fusion, 8, 211, (1984)

° The idea behind the theory presented in the paper is due to the author of this thesis. The paper, however,

was largely written by Paul Bellan.

VOLUME 59, NUMBER I1 PHYSICAL REVIEW LETTERS 14 SEPTEMBER 1987

Cause of the Lower-Hybrid Current-Drive Density Limit

L. H. Sverdrup and P. M. Bellan

California Institute of Technology, Pasadena, California 91125
(Received 13 April 1987)

We derive a simple model which predicts the observed lower-hybrid current-drive density limit for all
major experiments to within a factor of 2. The model is based on (i) the experimentally observed upshift
in ky and Gi) the ky dependence of the mode coalescence condition of the linear model conversion of a

lower-hybrid wave into a hot-plasma wave.

PACS numbers: 52.40.Db, 52.25.Sw, 52.50.Gj, 52.55.Fa

Fisch! predicted in 1978 that de toroidal currents
could be driven in tokamaks by the injection of suitably
phased lower-hybrid waves. Prior to 1978, lower-hybrid
experiments had been designed to provide ion heating via
the linear mode conversion process predicted by Stix? to
occur at the lower-hybrid layer where @ =a@jp. Initial at-
tempts to reconfigure these heating experiments so as to
produce current drive were unsuccessful, until Yamamo-
to et al.> demonstrated on the JFT-2 tokamak that
current could be driven provided that the plasma density
was reduced substantially from the values typically used
in the heating experiments (i.e., the density was reduced
so that w > 2). The JFT-2 results have been subse-
quently reproduced and extended in a large number of
devices,*”'® and it has always been found that current
drive works only up to a (rather low) “density limit”
where mode conversion would not be expected since
@ > 2a. Experiments indicate that the density limit in-

Wegrowe and Engelmann”® postulated a density-limit
mechanism based on the wave interacting with hot ions,
but (as we will show) their model predicts the density
limit to have a strong singularity, inconsistent -with ex-
perimental observations.

We present here a new and very simple model which
predicts within a factor of 2 the observed density limits
of all major current-drive experiments. This model is
based upon (i) the dependence on parallei wave number
ky of the coalescence of the two modes involved in linear
mode conversion of a lower-hybrid wave into a hot-
plasma wave and (ii) the upshift in ky that is associated
with the filling of the spectral gap in current drive. Be-
fore deriving the model, let us briefly review (i) and (ii).

ky dependence of mode coalescence.—Stix’ showed
that when hot-plasma effects are included, the lower-
hybrid dispersion relation becomes

ane 4 2 2. me
creases with'® w and!? m;. The density limit is not pre- kientkies tkre=0, ()
. . ae 7 19
dicted in Fisch’s theory. Tonon and Moulin,’” and | where
2 2
Opi Ope _ op, __ 13 of. ur, Opi UT,
ep=lo-—yt—y. al yo HO TG Op Ty t3-Z TF I- (2)
@ Dee (0) 4 Dce Wee @

Equation (1) is quadratic in Kk, giving two modes,

J =l—e, + (eh 4k pene) 71/2eu,

(3)

which are plotted in Fig. 1. The small-&, mode is the
launched lower-hybrid wave (cold mode) which propa-
gates from the plasma periphery towards the lower-
hybrid layer (where €, =O); in the vicinity of this layer
the cold mode converts? linearly to the large-k, hot-
plasma mode which propagates back towards the peri-
phery and is strongly damped. It was originally as-
sumed? that mode conversion occurred at the lower-
hybrid layer where €, =0 (or equivalently @ =a), but
it was later noted?!.”? that the mode conversion actually
occurs at the point where the two modes described by
Eq. (3) coalesce, i-e., where
ky = 63/46 et.

(4)

Examination of Fig. | shows that the location of mode
coalescence is at a lower density than the lower-hybrid

© !987 The American Physical Society

I layer, and Eq. (4) shows that this location depends on a

large number of parameters.
Upshift of ky.—There is a well-known?>* problem

MODE COALESCENCE

lep=

density
FIG. 1. Plot of k2 vs density. Note that the location of
mode coalescence occurs at lower density (Ref. 21) than the

location of the lower-hybrid layer.

1197

VOLUME 59, NUMBER 11

PHYSICAL REVIEW LETTERS

14 SEPTEMBER 1987

concerning the use of Fisch’s theory to explain the results
of current-drive experiments. According to Fisch's
theory, lower-hybrid waves drive current by imparting
momentum to electrons in the tail of the distribution
function. These electrons can interact with the wave be-
cause their velocity u satisfies the resonance condition
u=q/ky. Yet, in all experiments!‘ the parallel refrac-
tive index launched is typically ny=ck\/@=1.5-10 so
that, in order for electrons to be resonant with the wave,
they must have 3x10°ments the electron temperature has ranged from 50 to
2000 eV (3x 108 < uz, <1.3x10°). Thus, except for the
hottest of these plasmas, there ought to be essentially
zero electrons capable of resonantly interacting with the
wave. What seems to happen is that the wave creates its
own tail by pulling electrons from the bulk out to high
velocities via parallel-wave-partial resonant interaction.
In order to do this, at least some component of the
launched wave ky spectrum must interact resonantly
with electrons in the bulk, and so a spectral component
must develop which has a parallel phase velocity much
lower than the launched value. In effect, ky has been
shifted up for some fraction of the launched wave power
(the remainder is, of course, unshifted and interacts with
the newly created tail electrons to give current drive as
predicted by Fisch). Various mechanisms for the upshift
have been proposed, such as toroidal-poloidal”* and pon-
deromotive** effects. It has also been suggested”? that
there is no upshift, but that the antenna spectrum in-
cludes enough of 2 large-ky component to pull electrons
from the bulk to high velocities.

We will not attempt here to decide which (if any) of
the above mechanisms cause the k, upshift. Instead, we

2 2

Ope 2 | 3 w* me T;
7 [2 [2 a t3Bi~z

T,

Me

@ ce mM;

All the major current-drive experiments had T7;/T,
=0.3—1; however, there was a fairly large range of fre-
quencies, magnetic fields, and observed density limits.
Figure 2 plots Eq. (6) for hydrogen (solid lines) and for
deuterium (dashed lines) and also shows the experimen-
tally measured normalized density limits of a large num-
ber of experiments. Here we have chosen y =f, = 8; =!
as plausible values which give a good fit to the observa-
tions [note, that according to Eq. (6), equally plausible
values of y=1.4, B,=B;=2 would give the same re-
sults]. Figure 2 also plots Eq. (6) for argon which was
used in the Caltech Encore plasma.?> Table I presents
the same information but with nonnormalized parame-
ters; hydrogen gas is assumed, unless specified otherwise,
and for case where 7; and/or T, were unspecified, an es-
timate of 7;/T, =0.3 was used to calculate the predicted
density limit.

It is clear from Fig. 2 and Table I that Eq. (6) pre-
dicts the experimental observations for a wide variety of

1198

al
+ ar) .
m Dee

will simply accept the upshift as an experimentally ob-
served fact; i.e., experiment has shown that ky is shifted
up for part of the launched power in such a way that

ky=/yur,, (5)
where y= 1-2.

We postulate that the density limit occurs when the k,
predicted by Eq. (5)—i.e., the ky interacting with the
bulk—is of such a value to satisfy Eq. (4). When this
occurs, (i) mode conversion takes place for the upshifted
ky component which thus becomes strongly attenuated
by perpendicular? damping processes, and so cannot pull
electrons from the bulk to the tail by parallel-
wave-particle resonance, so that (ii) there are no tail
electrons to resonantly interact with the unshifted (i.e.,
high phase velocity) component of the incoming wave,
and so (iii) there is no current drive. We emphasize
that, for the upshifted k, component, mode conversion
takes place even though w > ap.

Proceeding with the mathematical derivation, we
define x =w}./w*, so that €,=—x, €, =1—Ax, where
A=m,/m;— w/o, and &,=—xauz/o? where a
= 3 B.04/w3.+3(m./m;)*B;Ti/Te. (Here, we have in-
troduced the temperature enhancement factors B,,8;
which multiply the bulk temperatures 7,,7;. These
enhancement factors take into account the fact that the
total energy in rf-produced suprathermal tails can, de-
pending on rf power levels, be comparable to the energy
of the bulk; in particular, B, will exceed unity when the
fast electrons providing current drive have a total energy
comparable to the bulk,* while B; will exceed unity when
there is ion heating.2°) Using Eq. (5) in Eq. (4), we find
x =1/(Qa'/2+2), or in terms of the original variables

(6)

parameters. Several®:!3!6 experiments were carefully
controlled so as to determine the dependence on just one
parameter. Equation (6) is consistent with the observa-
tions of these experiments: in particular, Eq. (6) is con-
sistent with the dependence on @ observed in Versator !®
and Petula-B,!':!8 the dependence on B observed in FT,®
and the dependence on m; observed in ASDEX.?

From Eq. (6) and Fig. 2 it is seen that there are essen-
tially two regimes of interest: (i) a low-field region (slope
on left-hand side of Fig. 2) where the density limit is in-
dependent of and proportional to B?, and (ii) a high-
field region (flat portion of curve in Fig. 2) where the
density limit is independent of B and is instead deter-
mined by 7;/T., , and m;. The change from regime (i)
to regime (ii) occurs at @~ Wgm(2T;/T.)'?, where
gm = (0; Wee) 2 is the geometric mean frequency.

It is worthwhile to compare our model to that pro-

posed by Wegrowe and Engelmann”? (the Tonon and

VOLUME 59, NUMBER 11 PHYSICAL REVIEW LETTERS 14 SEPTEMBER 1987
T T T
© weca
2000 F- . Wegrowe and Engelmann model, H,T;/T. = 1/3
‘Or7
1500 F ASDEX “ @ WEGA
2 fe) wee ee D,: T/T. = 1/3
“pe Ar 7a Oo.
PLT
w? /ASDEX

1000 | / @pp-Ti _o FE 6OKG D,T/Te=1 4
fq "07" @ PETULA 1300MHz a eee .

// VERSATOR 800 MHz 8] FT 80kG

! @WwT2
| O FT40kG H,T./T. = 1/3
500 4
a! YPETULA 3.7GHz @@ JT-60 H,T;/T. =1
ENCORE ALCATOR-C
ib VERSATOR 2.45GHz
0 I i l j
0 3000 6000 9000 12000
Woe
we

FIG. 2. Density limit predicted by Eq. (6) vs experiments: The solid line is Eq. (6) for hydrogen and the dashed line is for deu-
terium. For experiments, solid circles indicate hydrogen, open circles indicate deuterium, and the triangle indicates argon (all refer-
ences in Table I). For comparison, the dotted line shows the Wegrowe and Engeimann model (Ref. 20) [Eq. (7) in text] for hydro-

gen, 7;/Te= +.

TABLE I. Comparison of observed density limit with prediction of Eq. (6).

B Ti

f Te Nodserved Eg. (6)
(MHz) (kG) (eV) (eV) (0? cm 73) (10! cm 73)
JFT-2 (D gas)** 750 14 250 6 9
Versator‘ 800 10 120 350 7 5
Versator® 2450 10 120 350 10 12
PLT (D gas)#> 800 30 10 11
WT-2°> 915 11 50 200 7 7
Alcator-Cf 4600 100 100 180
FT (D gas)&™i 2450 40 45 94
FT (D gas) 8h 2450 60 75 103
FT (D gas) 8h 2450 80 60 100
FT hi 2450 80 55 48
WEGAi 800 22.5 12 5
WEGA (D gas) 800 22.5 18 if
T7(D gas)! 900 19 17 14
Petula-B* 1300 28 1000 18 14
Petula-B! 3700 28 1000 80 73
JIPP-TIE™! 750 i4 8 6
ASDEX® 1300 22 20 15
ASDEX (D gas)* 1300 22 30 27
JT-60° 2000 45 20 34
Encore (Ar gas)? 450 1.5 5 10 I 0.3

*Reference 3.
Reference 14.
“Reference 16.
Reference 5.
“Reference 6.
‘Reference 15.
8Reference 8.

Reference 9.

iReference 20.
iReference 10.
Reference 11.
'Reference 18.
™Reference 12.
"Reference 13.
Reference 17,

PReference 25.

1199

VOLUME 59, NUMBER 11

PHYSICAL REVIEW LETTERS

14 SEPTEMBER 1987

Moulin model!? is essentially the same as the one in Ref.
20). We consider the standard case where there is one
ion species and Z=1. Expressing Eq. (12a) of Ref. 20
in our notation gives the Wegrowe and Engelmann den-
sity limit as

Of {92 me Ty mew? |

7 ?
wo? zé mi Te Mi We

(7)

where 92/z is an adjustable parameter,”° the value of
which is given in Ref. 20 to be ¢7/z¢=2. It is easily
seen that the right-hand side of Eq. (7) becomes singular
when 7;/Te =(@?/@2n—1)/2; this singular behavior is
also shown in Fig. 2, where Eq. (7) has been plotted as a
dotted line for the typical case of hydrogen, T;/T. = +.

Finally, let us consider the predictions of our model
for typical fusion-reactor parameters. With 7, =Ti,
average atomic mass ~2.5, f=8 GHz, and y=,
=; =1, Eq. (6) gives density limits of 4x 10'4 cm ~? for
B=6 T, and 8x10!'4 cm ~? for B=10 T.

In summary, we have described how the combination
of (i) the experimentally observed upshift of ky to
ky=o/yur, and (ii) the k; dependence of linear mode
conversion (of lower-hybrid waves into hot-plasma
modes) accounts for the lower-hybrid current-drive limit.

This work was supported by National Science Founda-
tion Grant No. ECS-8414541.

(a)Present address: Western Research Corporation, San
Diego, CA 92121.

IN, J. Fisch, Phys. Rev. Lett. 41, 873 (1978).

27. H. Stix, Phys. Rev. Lett. 15, 878 (1965).

3T, Yamamoto et al., Phys. Rev. Lett. 45, 716 (1980).

45. C. Luckhardt et al., Phys. Rev. Lett. 48, 152 (1982).

5S, Bernabei et al., Phys. Rev. Lett. 49, 1255 (1982).

1200

6M. Nakamura er al, J. Phys. Soc. Jpn. 51, 3696 (1982);
S. Tanaka et al., in Proceedings of the Tenth International
Conference on Plasma Physics and Controlled Nuclear Fusion
Research, London, 1984 (International Atomic Energy Agen-
cy, Vienna, 1985), Vol. 1, p. 623.

™M. Porkolab et al., in Proceedings of the Tenth Interna-
tional Conference on Plasma Physics and Controlled Nuclear
Fusion Research, London, 1984 (International Atomic Energy
Agency, Vienna, 1985), Vol. 1, p. 463.

8A. Santini, in Proceedings of the IAEA Technical Commit-
tee Meeting on Non-Inductive Current Drive in Tokamaks,
Abington, Oxon, England, 1983, Culham Laboratory Report
No. CLM-CD, 1983 (unpublished), p. 278; see also Table I in
J.-G. Wegrowe and F. Engelmann, Comments Plasma Phys.
Controlled Fusion 8, 211 (1984).

9F. Alladio et al., Nucl. Fusion 24, 725 (1984).

10V. V. Alikkaev et al., in Proceedings of the IAEA Technical
Committee Meeting on Non-Inductive Current Drive in
Tokamaks, Abington, Oxon, England, 1983, Culham Laborato-
ry Report No. CLM-CD, 1983 (unpublished).

IC, Gormezano et al., in Ref. 7, p. 503.

12K. Toi et al., in Ref. 7, p. 523.

131, Leuterer et al., in Ref. 7, p. 597.

14M. Porkolab, IEEE Trans. Plasma Sci. PS-12, 107 (1984).

15M. Porkolab et a/., Phys. Rev. Lett. 53, 450 (1984).

16M. J. Mayberry er al., Phys. Rev. Lett. $5, 829 (1985).

17M. Yoshikawa et al., in Proceedings of the Eleventh Inter-
national Conference on Plasma Physics and Controlled Nu-
clear Fusion Research, Kyoto, Japan, 1986 (to be published),
paper A-i-1.

I8F. Parlange et al., in Ref. 7, p. 557.

19G. Tonon and D. Moulin, in Ref. 7, p. 557.

20Wegrowe and Engelmann, Ref. 8.

21V. Krapchev and A. Bers, Phys. Fluids 21, 2123 (1978).

22P. Bonoli, IEEE Trans. Plasma Sci. PS-12, 95 (1984).

23S, Succi et al., in Ref. 7, p. 549.

24E. Canobbio and R. Croci, in Ref. 7, p. 567.

25L. H. Sverdrup and P. M. Bellan, Bull. Am. Phys. Soc. 31,
1578 (1986).

9-1

9 Summary and Conclusions

Launching lower hybrid waves in tokamak plasma to drive toroidal current is a
complicated endeavor. There are numerous interesting aspects worthy of investigation,
but only a few can be pursued. It is therefore no surprise that many questions have
arisen during this undertaking, and that not all of them have been answered.

An example of what has been ignored includes the plasma structure. Encore
plasma has a complicated structure of its own. The grill antenna is not simply butted
against the smooth surface of homogeneous and isotropic plasma. There is turbulence and
various modes such as drift waves. Ripples and "sausages" of plasma dance past the
antenna. With high RF power, pondermotive forces push on the plasma near the mouths
of the antenna waveguides. Whether by Doppler shifts, parametric decay or other
processes, the launched LH waves generate new waves at other frequencies.

Despite the seeming chaos, relatively simple and appealing theories describe much
of what takes place. The cold plasma dielectric tensor predicts the lower hybrid mode
accessibility and propagation angle. The LH propagation angle depends simply on the
toroidal magnetic field and this is observed. LH wave accessibility is simply related to a
combination of the plasma density and magnetic field. This behavior is observed. The
changes in plasma current seen are most dramatic at low plasma current where
accessibility is best. Quadrature phasing does produce a directional spectrum of launched
LH waves.

In order for the fast waves launched by the grill antenna to interact with the much
slower thermal electrons, some LH wave power must dramatically "slow down" and
increase in parallel refractive index (N)). Theoretically this can occur through sufficient
poloidal propagation but this may or may not be the dominant mechanism. No one has
ever proved that LHCD was ineffective due to lack of a mechanism for slowing down LH
waves. Virtually all reported experiments launch an N) spectrum that is too fast to damp
on thermal electrons. Virtually all reported experiments also drive plasma current with
efficiency on the order of amps per watt. This was not the experience on Encore.

When it became evident that the current drive efficiency on Encore was

abnormally low, a plethora of questions arose. Did the antenna function properly? Was

9-2

RF power measured correctly? Was the end of the antenna close enough to the cutoff for
the slow mode? Was the phasing of the antenna correct? Was the L/R time constant of
the tokamak short enough to see a large RF driven current? All of these questions were
answered in the affirmative.

The density limit phenomenon was well publicized, but not understood. It
described a condition in which current drive efficiency would plummet. Difficult theories
such as parametric decay were proposed to explain the phenomenon. Instead it was
shown in chapter 8 that a very simple and appealing theory invoking the "warm" plasma
dielectric tensor explained everything. Adding temperature to the cold dielectric tensor
allows the description of plasma heating with lower hybrid waves. A key connection was
realized. When LH waves dramatically slow down, they can, under some conditions,
mode convert to an ion plasma wave and heat the plasma. If this occurs before the LH
waves have slowed sufficiently to reach the tail of the electron distribution, current drive
can be blocked. The conditions for the mode conversion to the ion plasma wave depend
upon the plasma density, as well as many other variables. A mysterious phenomenon
became simply explained by the algebra of the plasma dielectric tensor. If LHCD is
incorporated into a future energy producing tokamak, attention will be directed to the
location in parallel refractive index of the mode conversion to the ion plasma wave.

An equally mysterious phenomenon was encountered when low current (< 160
amp) discharges were observed in Encore by application of RF with the grill antenna.
Antenna phasing did not specify the direction of the current. Many factors were
explored that also proved to play no role in the direction of the current, until the truth
was stumbled upon.

The direction of the plasma current was obtained not by antenna phasing but
rather by the unintentional spiraling of the toroidal magnetic field lines. When the
electron acceleration is near the plasma periphery, the spiraling presents an asymmetry
that favors one toroidal direction over the other. It is not known why the antenna
phasing failed to produce significant asymmetry in the plasma current. The highly
inhomogeneous nature of the unusual low current discharges may play a role.

Energetic electron tails produced by LHCD are less collisional than less energetic

electrons. The increased mean free path of these energetic electrons allows them to spiral

9-3

along the toroidal field lines for greater distances before suffering collisional redirection.
They thus have more time to sample magnetic field errors. If an energy producing
tokamak is ever built incorporating LHCD, significant attention will be paid to minimizing
field errors.

With the use of a miniature electron source and a probe capable of scanning the
minor cross section and detecting the electrons, the field errors in Encore were observed
and quantified. The behavior of the hot electrons confirms the spiral nature of the
toroidal field lines.

Encore has been operated in a purely RF mode without the use of an ohmic target
plasma. Electrons with energies above 100eV were observed in these RF-sustained
discharges. The beams of electrons are not confined in the conventional tokamak sense
due to the low poloidal magnetic field. The vertical field plays an important role in the

propagation of the low current beams.