initial results from the wisconsin...
TRANSCRIPT
INITIAL RESULTS FROM THE WISCONSIN TOKAPOLE
by
J. C. Sprott
Plasma Studies
University of Wisconsin PLP 712
These PLP reports are informal and preliminary and as such may contain errors not yet eljminated. They are for private circulation only and are not to be further transmitted without consent of the authors and major professor.
I. Introduction
This paper describes a new plasma confinement configuration at Wisconsin
and preliminary measurements of the plasmas contained therein. The device is
essentially a Tokamak embedded in what used to be called the Small Wisconsin
Toroidal Octupole, and hence the name, Tokapole (Tokamak surrounded by a multi
pole) . The device is an outgrowth of the ohmic heating studies on the octupole
which were begun by Lencionil in 1967 and continued most recently by Etzweiler2
.
The present configuration was made possible by the installation of stronger
hoop supports which allow the octupole field to be pulsed routinely at its maxi
mum (5 kV) amplitude, by the development of a 1 msec, 10 kW, 9 GHz ECRH source
for preionization, and most importmltly, by the installation of a new 48 turn
toroidal field coil in November 1976, which allows toroidal fields as high as
5 kG on axis with a half sine wave period of 4 msec and an L/R time of � 5 msec.
All of this was done without sacrificing any of the capabilities of the device
as a toroidal octupole.
The present configuration is similar to one at Gulf General Atomic3
in
which a toroidal field of 430 gauss was added to the DC Octupole and a toroidal
current of 4 kA was produced. In that experiment densities of 3 x 1011
cm-3
and conductivity electron temperatures of 27 eV were obtained.
Figure 1 shows same of the flux surface configurations which can be pro
duced in a toroidal octupole with ohmic heating. Fig lea) is the case with
no plasma current. Unlike a quadrupole in which a critical plasma current is
required to alter the flux surface topology4, 5
, an octupole with a degenerate
field null is topologically altered with an infinitessimal toroidal plasma
current. Fig l (b) shows the flux surfaces for a case in which the plasma
current is opposite to the hoop current. Fig led) is the case obtained in the
2
GGA octupole, and is identical to l (c) except for a rotation of 45° about the
minor axis. Cases (b) , (c) , and (d) have closed flux surfaces which do not
encircle a hoop and so resemble a Tokamak with a four node poloidal divertor.
Such configurations are being considered for impurity control in fusion reac-
tors (as in the UWMAK design study) , but have been investigated experimentally
to only a limited extent. In addition to the GGA octupole, the Princeton FM-16
and the Japanese JFT-2A device7 have tested some aspects of poloidal divertor
action, and the Princeton PDX device presently under construction is dedicated
to a thorough test of poloidal divertors.
Also of interest in predicting Tokapole behavior is the proliferation of
small, low field, research oriented Tokamaks as indicated in the table below:
Device R (em) a (em) BI (kG) I (kA @ q=3)
MIT Rector 57 17.5 x 70 4 40
MIT Versator I 54 13 5.5 30
MIT Versator II 40 15 x 15 9 85
UCLA Microtor 30 10 x 12.5 10 60
UCLA Macrotor 100 44 x 76 5 200
RPI Rentor 45 15 5 42
Cal Tech Tokamak 45.7 16.2 4 40
UC-Irvine Tokamak 60 17 5 40
For comparison, the Wisconsin Tokapole has a maxTImuffi toroidal field of 5 kG,
major radius R = 43 em and a minor radius determined by the distance from the
minor axis to the surface of the hoops of a = 13 em . For a safety factor at the
edge of q = 3, a plasma current of 32 kA would be expected.
For equilibrium, a Tokamak requires a programmed vertical field (and some-
times a horizontal field as well) . Because of the thick aluminum walls, the
3
Tokapole cannot have a fast time varying vertical field, unless the coils were
put inside the vacutml system. On the other hand, the L/R time of the hoops
and walls is ITUlch longer than the duration of the experiment and so image cur
rents could be expected to help provlde the equilibritml. However, the hoop
current is generally opposite to the plasma current, and so there could be a
problem with the equilibritml unless the plasma current becomes large enough
to reverse the currents in the hoops.
II. Diagnostics
The most significant quantity in diagnosing the tokapole plasma is the
total toroidal plasma current. This measurement is made difficult by the fact
that the hoops carry a toroidal current that varies in time and that is often
much larger than the plasma current. The quantities that can be easily measured
are the poloidal gap voltage (VpG) and the current in the 60 turn primary wind
ing of the iron core ohmic heating transformer (I) . These quantities can be
used to infer a plasma current by considering the electrical circuit of figure
2(a) in which the ohmic heating transformer has been asstmled to have a unity
turns ratio. In the absence of plasma current (Ip
= 0) , the circuit consists
of an inductance (the hoops) and a small series resistance driven by a capa
citor bank (C) through an ignition switch. If the plasma current is asstmled
to flow on the octupole separatrix (see fig lea) ) , the plasma links 1/3 of the
total flux (since there is twice as much common flux as private flux in the
unperturbed octupole) and hence can be considered as a current source in parallel
with 1/3 of the total system inductance. The plasma is mostly resistive with
some inductance, but that should not matter in the calculation. Then the
poloidal gap voltage can be written as
v = IR + � L dI + ! L � (I - I ). PG 3 CIt 3 dt p
Integrating and solving for Ip
gives
Ip
= 3 [I - t, JVPG dt + � J I dt] .
4
(1)
Figure 2(b) shows a circuit that electronically performs the required mathe-
matical operation and yields at its output a signal proportional to the plasma
current. The actual circuit used is somewhat more complicated because the
resistance R is not quite constant in time (it results largely from skin currents
flowing in the hoops, walls, and primary windings) and because the toroidal
field coil links the transformer core and produces a signal proportional to
the toroidal field which must be bucked out. In practice the circuit can be
nulled to about 1% in the absence of plasma which is not quite adequate for
reliable plasma current measurements. Furthermore, the null condition is
dependent on the poloidal field amplitude and magnetic history of the iron core.
Consequently, measurements are usually made by taking an experimental pulse
without plasma (by turning off the pulsed gas source), and then taking a pulse
with plasma and subtracting the two signals to get Ip (t) By this technique
currents accurate to about +0: kA are obtained. The calibration can be checked
by removing the signal which bucks the toroidal field coil current in which
case this known current looks to the circuit like a plasma current, except
larger by a factor of 3 because it links all of the core flux.
The plasma current produces a poloidal field that opposes the octupole
field in the vicinity of the hoops (see fig l(b)). If the toroidal plasma
current is assumed to be contained within a circular surface of radius a centered
on the toroid's minor axis, then a can be estimated by equating the field due
to the plasma (� I /ZTIa) to the field due to the hoops (which varies as a3
o p
giving the result:
5
where a is in em and IH
is the total current in the four hoops. The actual
shape of the current channel is probably not circular, but rather more like a
square or diamond as shown in fig 1. There is good reason to believe that the
plasma current is largely contained within radius a since at larger radii the
flux lines encircle the hoop and so the conductivity should be strongly limited
by mirrors2
and obstacles (hoop supports and probes).
The Tokamak safety factor q can also be estimated if it is assunled that
the toroidal plasma current density is constant over the circular cross section
of radius a. Again, this is a reasonable asslmption since the electric field
and mirror ratio are nearly constant for r , a and since the confinement is
probably not adequate to produce strong gradients of density or temperature
within the current channel. The resulting q is independent of r and is given by
2 5a BT
q = I R P
where a is in cm, BT
is the toroidal field on axis in kG, Ip
is the toroidal
plasma current in kA, and R is the major radius (43 em).
The electron temperature can be estimated by again assuming a constant
current density, but over a square cross section with diagonal 2a, a voltage
per turn equal to 1/3 of the poloidal gap voltage (as in fig 2 (a)), and a
resistivity given by the Spitzer formulaS
with Z = 1:
where Ip is in amps, a is in an, V PG is in volts, and T e is in eV. This tempera
ture is often referred to as the "conductivity temperature" and is always lower
than the real temperature by a factor Ze��3 which for most Tokamaks is in the
range of 1-5 (or higher if very dirty).
6
Finally, this temperature can be used in conjunction with a Langmuir probe
to estimate the plasma density. To avoid placing a probe directly in the current
channel (which reduces the toroidal current by �20%), the probe was placed
in the upper outer "bridge" (the narrow region behind a hoop in the upper right
hand corner of fig l(b)). The probe has a special shape9
which enables it to
take a volume averaged density for the case without a plasma current channel.
With the current channel, the density is characteristic of the divertor scrape
off region only, but it may be that the particle lifetime in the divertor region
(Nl msec) exceeds the time required for a particle to escape from the current
channel and so the densities would not be very different. In any case the
density is estimated using the conductivity temperature T and the ion saturation e
current density JSAT as follows:
10 10 JSAT n = ----
� where J
SAT is in mA/cm2, Te is in eV and n is in cm-3. Actually, the probe is
operated as a floating double probe by returning the current not to the
grounded tank wall, but rather to a second larger electrode in the bridge a
short distance away, thereby reducing the probe's sensitivity to the floating
potential changes which are typically 15-20 volts. Further corrections are
made for the fact that the 45 volt probe bias may not be large compared with
either kTe/e or the voltage drop across the 10�resistor used to measure JSAT.
The complete formula with these corrections is
10 10 JSAT n = ----------------------------
� {I - eXp[(0.00265 JSAT-45)/Te]}
(5)
1
III. Typical Results
The Tokapole can be operated in either of two modes: 1) If the toroidal
field is applied first and then the octupole is pulsed on near the peak of BT,
the plasma current flows in the same direction as the hoop current, and the
configuration of fig Ub) is obtained. 2) If the octupole field is turned
on before the toroidal field, and the toroidal field reaches its peak while
the octupole field is decaying, the plasma current flows opposite to the hoop
current. A third mode in which the toroidal field is pulsed on near the peak
of the octupole field results in large poloidal currents and a topology as in
fig lea). Although all three cases have been studied, only case 1) will be
discussed here because 1) it most closely resembles a Tokamak, 2) it produces
the highest plasma current, and 3) it is the most extensively studied.
Figure 3 shows the time dependence of the magnetic fields for this case.
Although the toroidal field has been operated at S kG peak on axis for a 4 msec
half period, most of the experiments have been done with a 3 kG field and a
2 msec half period. This is because for fields above 3 kG, the 9 GHz ECRH
preionization is ineffective and because the falling toroidal field apparently
helps to heat the plasma and keep the conductivity and hence the toroidal current
from decaying. Also shown is the ECRH preionization power and the poloidal
gap voltage which is determined almost entirely by the hoops. Recall that the
single turn voltage at the position of the plasma is VpG/3. The Tokapole,
unlike a Tokamak, is characterized by a fixed toroidal electric field, and the
plasma current is determined by the plasma properties. In a Tokamak, the
plasma current is fixed and the voltage varies with the plasma. Figure 3 also
shows a typical case of the plasma current as measured by the method previously
described. The current reaches a peak of - 2S kA at a time of - 800 �sec after
the beginning of the ohmic heating pulse. At the time of peak current the
8
plasma radius is a - 10 em, the safety factor is q - 1, the conductivity elec
tron temperature is - 25 eV and the average density is _ 5 x 1012 em-3 Since
this density is measured in the bridge region, the peak density on the axis of
the current channel is probably � 1013 crn-3 The poloidal field produced by
the plasma should be _ 500 gauss at a radius of 10 em.
The rapid determination of these quantities was made possible by a computer
program developed by Alan Biddle in which analog signals representing Ip' VpG'
JSAT, and BT are digitized and used to calculate the quantities of interest
during the minute or so between experimental pulses. A sample of the computer
printout is shown in fig 4. Three experimental pulses are shown, the first
case is under normal conditions, the second is with the toroidal field reduced
to 1.5 kG and the third is with the poloidal gap voltage reduced to half its
normal value. In addition to the values at the time of peak current, the program
also calculates the conductivity temperature and electron density at 200Msec
intervals throughout the discharge. These quantities along with a and q are
plotted in figure 5 as a function of time for the normal (BT = 3 kG) discharge.
With the assistance of Rich Groebner, some attempt was made to estimate
h 1 1 . h H . 1 . 1 1· . h dlO t e actua e ectron temperature uSlng t e e Slllg et-trlp et lne ratlo met 0 •
The Tokapole was run with He gas at less than optimum conditions giving plasma
currents of 5-10 kA and conductivity temperatures of - 15 eVe The measured
electron temperature was typically 20-35 eV giving a Zeff of rv2-3. It is not
known whether the Zeff is the same for the higher current hydrogen 'discharges,
but the value obtained is certainly within reason.
IV. Flux Plots
With measurements of the toroidal plasma current, it is possible to calcu-
late more precisely the flux surfaces which result. For this purpose a computer
code (SIPLOT) was used. The code calculates flux surfaces for a linear octupole
9
with 4 equal filimentary currents to represent the hoops and 12 filamentary
image currents to represent the walls. The dimensions are scaled to closely
approximate the toroidal octupole. Figure 6 shows one quadrant of an octupole
without plasma current. The poloidal flux contours are at intervals of � 1/10
of the total flux (called Dories) . Figure 7 shows a case with a filimentary
current down the axis with a magnitude of 10% of the total current in the four
hoops (corresponding very nearly to the 25 kA case discussed earlier) . In
figure 8 the plasma current is also 10% of the hoop current but in the opposite
direction. Figure 9 is a more realistic case in which the current is 10% of
the hoop current but distributed with a constant current density over a circular
surface of radius a centered on the axis. Figure 10 is the same as figure 9
but with the current in the opposite direction. Figure 11 is the same as figure
9 but with a plasma current equal to 20% of the hoop current. Figure 12 is the
same as figure 9 but redrawn with all four quadrants, and it probably represents
the best estimate of the Tokapole flux plot.
Note that for the case of plasma current in the same direction as the hoop
current (fig 12) , there is very little magnetic flux between the center of the
current channel and the surface of the hoops «1 Dory) , and so the confinement
may not be very good, especially at high temperatures. The absolute containment zone
(banana orbit size) of protons with energy greater than about 25 eV would
extend from the minor axis to the surface of the hoops. A particle might still
be confined for the time required to VB drift across the toroidal field, however.
At 25 eV and BT
= 3 kG, this time is � 600 �sec.
V. Comparison with SLMULT
A zero dimensional computer code (SLMULT) has been used to successfully
predict the results of a wide variety of experimental cases in the Wisconsin
toroidal octupole. The program includes a subroutine (OHMIC) for ohmic heating
10
but does not take into account the modification of the flux surfaces by the
plasma current. Nevertheless, a blind application of the program (Jan. 5, 1977
version) resulted in a prediction not wildly out of agreement with experiment
(at the time of peak current):
Quantity
Toroidal Current (Ip)
Density (n)
Electron Temp (Te)
Ion Temp (Ti)
Ion Sat Current (JSAT)
Neutral Density (n ) o
Experiment
2S kA
S x 1012 cm-3
24 eV
?
1000 mA/dil2
?
SIMULT
?
2.5 x 1012 em-3
4 eV
3 eV
500 mA/an2
2 x 1012 an-3
The calling program �IN) along with the printout of the results for SIMULT
are included in the Appendix. A graph showing the time dependence of the simula
tion results is shown in figure 13. Figure 13 should be compared with the experi-
mental results in figure 5. The results suggest an underestimation of the
heating due to the toroidal current which is just what would be expected from
neglecting the existence of the current channel. Future work will include
refinements of SIMULT to more accurately represent the Tokapole cases.
VI. Experimental Scalings
With so many parameters available, there are numerous possible scalings
that could be studied. Neutral H2 gas is pulsed in a short burst to a pressure
of about 10-.4 torr about 16 msec before the fields are applied. The pumping
speed is -lOOQ£/sec, and the pressure does not decay appreciably during the
experiment. At higher pressures the electron temperature drops, and at lower
pressures the density drops, both of which decrease the plasma current.
All of the measurements described here were done with constant and near
optimal gas pressure. At moderately low pressures, occasional pulses
11
exhibit runaway behavior as evidenced by a large plasma current ( � 20 kA)
which peaks early in time ( � 200 �sec) with relatively small densities
(�lOlO - lOll cm-3). This regime is diffucult to reproduce, and conse
quently,. the existence of high energy electrons (as evidenced by x-rays or
synchrotron radiation) has not been verified. Figure 14 shows the peak plasma
current as a function of pressure (actually puff valve dial setting with 600
torr manifold pressure) with and without the 9 GHz ECRH preionization. The
effect of the preionization is to enable the plasma to be formed at lower pressures.
The timing of the onset of the ohmic heating and the ECRH preionization
can be varied and the plasma current is found to be optimal for the case shown
in fig 3, although the timing is not very critical. All of the cases discussed
are with this timing. The plasma current always peaks about 700-S00}lsec after
the beginning of the ohmic heating pulse for all cases considered.
Of more interest is the scaling of the plasma current and other parameters
with toroidal field strength and ohmic heating voltage. Figure l5 (a) shows
the variation of the peak plasma current with ohmic heating voltage for BT =
3 kG, measured in units of the voltage to which the poloidal field bank is
charged. (5 kV on the bank gives about 20 volts/turn at the plasma at the
time of peak current.) Figure l5(b) shows the variation of the peak current
with toroidal field for B = 5 kV, again measured in units of the voltage to p which the toroidal field bank is charged. (5 kV on the bank gives about 3 kG
on axis at the time of peak field.) The two curves are remarkably similar
and each give a quadratic dependence of plasma current on the respective field.
Assuming Ip � Bp2 BT
2, the scaling of other parameters can be inferred from
equations (2) - (4) :
a � B 1/4
B 1/2 �
I 1/8
P T P
-3/2 q � B
P
T � B 1/3
B 2/3
� I 1/6 e p T P
12
Note that a and T depend only on plasma current and that the dependence e
is very weak in both cases. In figure 16 a and T are plotted as a function , e
of I for many different combinations of BT
and B , and the results are p p
consistent with the above sca1ings. Note also that q is independent of BT
and depends only on the ohmic heating voltage. Coincidentally, at the
maximum available ohmic heating voltage (Bp
= 5 kV) q is almost exactly
equal to unity. In figure 17, q is plotted as a function of Bp
for BT
=
5 kV (3 kG) and as a function of BT
for Bp
= 5 kV, and the results are
consistent with the above scalings.
The other interesting scaling is the density as a function of Bp
and BT
which is shown in figure 18. Although the scaling is more complicated than
a simple power law, the data can be reasonably well fit with
� B 8/3
B 4/3
ne p T .
Actually this scaling is a result of some hindsight because it happens to
be just what is required to give a constant energy confinement time defined by
n T V e e 'IE = I V /3 ' p PG
where V is taken as the total volume of the toroid (not the volume of the
current channel) which is 3 x 105
cm3
. Fram the fit to the data, the energy
confinement time is 'IE = 8 �sec. A statistical analysis of the 33 data
points in figure 18 gives 'IE = 11.4 ! 6 �sec. This time is about equal to
13
the transit time of a few eV neutral across the plasma. Note that LE is
much shorter than the 800 �sec required for the current to build up, and so
the plasma is apparently in a quasi-steady state. In fact, the decay of the
current after the peak in figure 3 can be accounted for entirely by the
decay in BT
and VPG CIp
� BT
Z V
ZpG) , and so if the toroidal field and poloidal
gap voltage were left on longer, Ip
would be nearly constant. However, the
ohmic heating transformer is being operated near its volt-second limit (but
without cocking) , and so lengthening the pulse by a large factor does not
appear feasible.
The ohmic heating power absorbed by the plasma is given by
and is about sao kW with 5 kV on both capacitor banks. Since LE = const,
the energy stored in the plasma has the same scaling and is � 5 joules for 5 kV
on both banks. Note that since the toroidal field dominates the poloidal
field over most of the volume, the plasma � defined by
� =
Z� n kT o e
B 2 T
is independent of BT
, varies as Bp
3, and has a maximum value of � o. 01%. The
t'poloidal beta" is larger, but still only � 1%.
For the typical Tokapole parameters, the mean free path of a thermal
HZ neutral is :s 1 em and so the interior of the plasma is probably burned
out of thermal neutrals, and is replenished by � 7 - 8 eV Franck Condon
neutrals. This conclusion is further supported by the fact that the H�
light peaks early in the discharge and is falling sharply at the time of
peak current.
14
A lower limit on the ion temperature can be obtained by assuming that
the ions are heated only by classical collisions with the electrons and that
the ion lifetime is equal to the energy confinement time. Such a calcula
tion gives T. > 0.5 eV. l
VI I. Sunnnary and Future Plans
The typical operating parameters and scaling of the Tokapole are summarized
in figure 19 for a toroidal field of 3 kG on axis and the maximum available
ohmic heating voltage of 20 volts/turn.
The most significant question raised by the results is why the energy confine-
ment time is as short as 10 �sec (and constant), and the closely related ques
tion of why the conductivity electron temperature is only 25 eV. The most
likely explanation is the excitation of impurity atoms released from the walls
by plasma bombardment. The energy confinement time and electron temperature
do not appear to be strongly influenced by the base pressure, however. Most
of the experiments were done with base pressures of - 2 x 10-7
torr, but the
results at 2 x 10-5 torr (a few hours after being up to air) are not signifi
cantly different. It will be important to measure the energy loss by impurity
radiation and to attempt more aggressive discharge cleaning techniques. If
the losses cannot be accounted for by radiation, then there might be a problem
with the equilibrium or stability of the Tokapole configuration, and this will
be studied both theoretically and experimentally. Because of the relatively
low temperatures, the brief duration of the discharge, the short electron
mean free path, and the experimental fact that a 1/4" diameter probe extended
all the way across the midplane depresses the current by only 20%, there is
hope that probes can be used to measure the spatial and temporal evolution
of all quantities of interest. The first priority item is to get an independent
measurement of the toroidal plasma current using local magnetic probes.
15
Of course we have every intention of operating the Tokapole with a 5 kG
toroidal field, and a KU-band microwave system (- 10 kW for 1 msec at 15.5-
17.5 GHz) has recently been installed on the machine for ECRH preionization.
If the scaling laws continue to extrapolate, we would expect to achieve
I � 70 kA T � 30 eV and n � 8 x 1012 cm-3 with POH � 1.4 MW. Later it
p ,
ec .
might be possible to go to even higher toroidal fields with the acquisition
of rnroe capacitors (72 kG at present) provided there is interest in doing so.
The Tokapole configuration also offers the possibility of various types
of rf heating. The first priority in such studies will be fast wave ion
cyclotron resonance heating. The density and radius are such that toroidal
eigenrnodes ought to exist and apparatus is presently under construction which
should be capable of supplying _ 1 �n� of rf power at either the fundamental
or second harmonic of the ion cyclotron resonance frequency.
16
ACKNOWLEDGEMENTS
The work described here would not have been possible without the diligent
efforts of Jaimie Barter, Joan Etzweiler, Rich Groebner, Don Holly, Alan Biddle,
Bruce Lipschultz, David Shepard and Tom Lovell and his crew of hourly students
in converting the octupole into a tokapole. Mike Zarnstorff and his assistants
were responsible for the computer data acquistion system which was of immeas
urable help in collecting and analyzing the data. This work was supported
by the u.S. Energy Research and Development Administration.
REFERENCES
1. D. E. Lencioni, Univ. of Wisc. Ph. D. Thesis (1969).
2. J. F. Etzweiler and J. C. Sprott, Bull. Am. Phys. Soc. �, 1049 (1976).
3. R. Prater, Y. Hamada, R. Freeman, C. Moeller, T. Tamano, and T. Ohkawa, Phys. Rev. Letters 34, 1432 (1975).
4. G. L. Schmidt, Univ. of Wisc. Ph. D. Thesis (1975).
5. W. C. Guss, Univ. of Wisc. Ph. D. Thesis (1976).
6. K. Ando, S. Ejima, S. Davis, R. Hawryluk, H. Hsuan, D. Meade, M. Okabayashi, N. Sauthoff, J. Schmidt, and J. Sinnis, Plasma Physics and Controlled Nuclear Fusion Research, Vol II, page 103, Vienna (1975r:-
7. S. Shimomura, H. Maeda, H. Ohtsuka, A. Kitsunezaki, T. Nagashima, S. Yamamoto, H. Kimura, M. Nagami, N. Ueda, A. Funahashi, T. Matoba, S. Kasai, H. Takeuchi, K. Takahashi, K. Kumagai, T. Tokutako, K. Anno, and T. Arai, Phys. Fluids 19, 1635 (1976).
8. F. Chen, Introduction to Plasma Physics, Plenum Press, New York (1974), page 162.
--
9. J. C. Sprott and E. J. Strait, IEEE Transactions on Plasma Science, PS-4, (1976).
10. R. W. P. McWhirter in Plasma Diagnostic Techniques, R. H. Huddlestone and S. L. Leonard, eds. , Academic Press, New York (1965), page 255.
APPENDIX
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TYPICAL TOKAPOLE PARAMETERS .AND SCALING
BT = 3 kG ( 5 kG maximum)
I = 2 5 kA (� B2 B2T)
P P
a = 10 em (� I 1/8) P
q = 1 (� B - 3/2 ) p
1/6 T = 2 5 eV (� I ) ec p
n = 5 x 1012 em- 3 (� B 8/3 B 4/3) e p T
LE = 10� sec (constant)
Fig 19