Digitally implemented spectral analysis techniques were used to investigate the frequency-dependent fluctuation-induced particle transport across a toroidal magnetic field. When the electric field pointed radially inward, the transport was inward and a significant enhancement of the plasma density and confinement time resulted

Hong, J.

Kim, Y. H.

Krawczonek, W. M.

Powers, E. J.

Roth, J. R.

English

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NASA TECHNICAL
MEMORANDUM
(NASA-TM-73800) INWARD TRANSPORT OF A
TOROIDALLY CONFINED PLASMA SUBJECT TO STRONG
i7	 RADIAL ELECTRIC FIELDS (NASA) 14 P CSCL 20I
FR
	
A02/MF A01tii
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NASA TM-73800
N78-10883
Unclas
G3/75 52350
INWARD TRANSPORT OFA TOROIDALLY CONFINED PLASMA
SUBJECT TO STRONG RADIAL ELECTRIC FIELDS
J. Reece Roth and Walter M. K.rawczonek
Lewis Research Center
i Cleveland, Ohio 44:135
and
Edward J. Powers, Jae Hong, and Young Kim
University of Texas
l	
Austin, Texas 78712
TECHNI., !L PA1? Fii2 to be presented at the
Annual Meeting of the Plasma
Physics Division of the
American Physical Society
Atlanta, Georgia, November 7-11, 1977
1
< '	 7 5y, s.
of
i1
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INWARD TRANSPORT OF A TOROIDALLY CONFINED PLASMA
SUBJECT TO STRONG RADIAL ELECTRIC FIELDS
J. Reece Roth and Waiter D1. Krawczonek
NASA Lewis Research Center
Cleveland, Ohio 44135
and
Edward J. Powers, Jae Hong, and Young Kim
Department of Electrical Engineering
University of Texas
Austin, Texas	 78712
ABSTRACT
Thu approach of the NASA Lewis Bumpy Torus Experiment is to
confine and heat a toroidal plasma by the simultaneous application
of strong do magnetic fields and electric fields. Digitally implemented
spectral analysis techniques were used to experimentally investigate
the frequency-dependent fluctuation-induced particle transport across
the toroidal mannetic field. It was observed that when the electric
field pointed radially inward, the transport was inward and a significant
enhancement of the plasma density and confinement time resulted.
i
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12
Georgel suggested that a suitable combination of magnetic and
electric fields might be used to confine ab well as heat a plasma of
fusion interest. Theoretical papers by Kovrizhnykh2D3 and Stix4 have
examined the effects of ambipolar electric fields on radial transport	 j
in toroidal plasmas. The purpose of the present paper is to show that
the density and confinement time of a toroidal plasma can be enhanced by
radial electric fields far stronger than the ambipolar values, and that,
if such electric fields point into the plasma, radially inward transport
can result.
The steady-state plasma in the NASA Lewis Bumpy Torus facility is
1
generated by a modified Penning discharge operated in conjunction with
a 12-coil bumpy torus magnetic field 1.5 meters in major diameters.
3	
The toroidal plasma is biased to high potentials by water-cooled electrode
rings which encircle the minor circumference of the plasma and are located
in the midplanes of two sectors of the toroidal array. Previous invest-
igations s have shown that, in common with Penning discharges and magnetron-
like devices, the plasma forms rotating spokes which gyrate around the
minor circumference of the plasma with velocities comparable to the E/B
r
3
	
drift velocity. Ion kinetic temperatures up to 2.5 keV in deuterium have
been measured. The thermal velocity of these hot ions is comparable
I
to the spoke rotational velocitys.
}	 Radial profiles of the floating potential of the plasma were
ft
measured with a hydraulically actuated Langmuir probe 5 a 6 . Some results
9
from these measurements are; 1) the entire toroidal plasma floats to
{	 potentials comparable with the electrode ring voltage; 2) the entire
t
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plasma can be biased to high potential with positive or negative electrode
rings; 3) the radial electric fields point radially outward in the
vicinity of the plasma boundary for positive midplane electrode polarities,
and point radially inward toward the plasma when negative potentials
are applied to the electrode rings, as shown in Pig. 1; h) the electric
field strength within the plasma often exceeds 1 kV/cm.
The particle containment time T  in this steady-state plasma can
be obtained from the average electron number density, no , measured with
the microwave interferometer, the plasma rolume Vp
)
 and the do current,
Ia , flowing to the power supplyG,
TIe a V 
Tp =	 sec.
Ia
The effect of the direction of the electric field on particle
containment is shown in figure 2A, where the particle containment time
and the average electron number density are shown for a paired comparison
in which the only factors which differed were the polarity of the 2 mid-
plane electrode rings used and the geometric position of the midplane
electrodes, which was optimized for each polarity. The solid symbols
represent positive polarity, for which the radial electric fields
point (and push ions) radially outward. The open symbols in Pig. 2
represent negative polarity, which result in electric fields which point
(and push ions) radially inward. (loth the particle containment time and
the average electron number density are at least a factor of five higher
with the radial electric field pointing inward than is the case with it
pointing outward.
i
(1)
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4In order to understand this large difference in confinement,
measurements of the fluctuation-induced particle transport rates were made
with a new technique, the key ideas of which are described elsewhere8,9,10.
Low frequency (W« Gi) electrostatic potential fluctuations are assumed so
that a particle's fluctuating velocity may be modeled in terms of n/B
drift, where t is a fluctuating electric field and R is the static con-
fining toroidal magnetic field. The time averaged particle flux is then
given by;
ti
n v^ =^n B.L /B	 (Z)
In ref. 8, it is shown that the transport due to a small band of fre-
quencies centered at wis given by
T(b)) = k
e(W) n(w)Q(W)SINe,,p(W)J^^ Y (W)I.
	
(3)
B
The transport associated with T(w) depends upon the product of the RMS
n
values of density n(w) and potential fluctuations lf(W), the sine of the
phase angleo< mp (w) between the density and potential fluctuation, and the
degree of mutual coherence ^Kp (w) between the potential and density
fluctuations in the spectral band under consideration. The wavenumber
/V	 N
ke (w) ppears since the electrostatic approximation ( E =-V'r- • -iko(W)'T )
is assumed. The transport spectrum T(W) is a real quantity and may take
on either a positive or negative value, indicating that the transport is
in either an inward or outward direction, respectively. The transport spec-
trum T(m) was measured in a sector which did not contain an electrode ring,
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r
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r.
t
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5	 5J,
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at the outer boundary of the plasma.
On figure 3 are shown transport spectra corresponding to the
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data for an electrode current of I a	.75 amps plotted in figure 2.
The upper graph is the transport spectral density function. The lower
graph is the cumulative transport rate up to the frequency shown on the 	 1 v
abscissa. All ordinates are plotted in absolute units. In figure 3a, the
negative electrode case with radially inward electric fields has a transport
that is positive in sign, indicating radially inward transport.	 The
transport is associated with three discrete peaks, all below 150 kHz.	 For
this condition, the ion flux is radially outward in the sectors containing
the negative electrode rings 7 , and the net confinement is a balance between
infusion in the empty sectors and losses in the sectors with electrode rings.
In Fig. 3B, the positive electrode case has a transport which is negative in
..	
sign, or radially outward toward the surrounding walls. 	 The outward trans-
I
port for this case occurs over a broad frequency band out to 350k11z, a
and could be considered "turbulent transport."	 The cumulative transport
for the two electrode polarities is plotted as a function of electrodi:
ta
current in figure 2b. 	 For both electrode polarities, the radial transport
increases with increasing electrode current in an almost linear manner.
Y
The particle contianment time and average electron number density
in this plasma are extraordinarily sensitive to the value of a weak
t
vertical magnetic field applied to the containment volume, which is about
10" 3 of the toroidal magnetic field ll .	 These vertical fields are generated
by 2 coils wrapped around the exterior of the vacuum tank and range from j
minus to plus 100 gauss (positive is upward).	 The effect of this vertical
t
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}
G	 ^?
r
magnetic field on the average electron number density is shown in figure
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4a. When these date, were taken the electrode voltage, background pressure
of deuterium, maximum magnetic field, and other independent variables were
held constant. There exists a region between 20 and 32 gauss in which no
plasma could be generated.
The cumulative transport at the probe location in shown in f9, me 4b
as a function of the vertical magnetic field. The vertical magnetic fields
which result in the highest inward radial transport correspond to the
highest electron number densities observed, and the outward transport
rates correspond to those vertical fields where the density is low, and
the plasma is approaching extinction.
The transport spectral density function for six values of the }
vertical magnetic field plotted in figure 4 is shown in figure 5 in
absolute units for frequencies up to 500 kliz. When the vertical mag-
netic field is -10 gauss, the radially inward transport is dominated by
a large peak at 20 kHz. As the vertical magnetic field is increased to
+10 gauss, the inward transport is found over a broad, almost turbulent,
spectrum from 0-150 kiz, and a peak of inward transport also appears at
about 250 kliz. As the vertical magnetic field is increased to +15 and
+18 gauss, which are near the region of plasma extinction in figure 4,
the transport in the vicinity of 200 kliz reverses direction and flows radially 	 i
outward. The area under the curve in this portion of the spectrum dominates
the total transport and results in net radially outward transport of plasma.
Beyond the region of plasma quenching from 20-32 gauss, two major peaks at
LI
7a vertical field of 40 gauss dominate the transport and aro radially
inward. As the vertical magnetic field is further increased to 60 gauss,
the importance of the high frequency peak diminishes, and the total trans-
port rate becomes much smaller in magnitude.
The phase difference am ,p (w)	 between density and potential flue-
tuations was computed and plotted using standard digital spectral
analysis techniques 10 , Examination of these plots indicate that reversal
of the direction of transport associated with the peak near 250 kliz in
Fig, 5 occurs because a,,I (w)	 changes sign as the vertical magnetic ield
is changed from run to run. As indicated by Eq. (3), a change in sign of
o(, r (w) will result in a change in the direction of fluctuation-induced
transport T(P).
In summary, we have investigated: 1) low frequency (w«k),A)
fluctuation-induced transport using digitally implemented spectral
analysis techniques, and 2) the role of strong applied radial electric
fields and weak vertical magnetic fields on plasma density and particle
confinement times in a dumpy Torus geometry. The data demonstrate that
application of sufficiently strong radially inward electric fields result
in radially inward fluctuation-induced transport into the toroidal
electrostatic potential well. This inward transport is associated with
ii
higher average electron densities and longer particle confinement times
in the toroidal plasma,
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REFERENCES
George, Nature, Vol. 190, April 22, 1961, p.
Kovrizhnykh, Sov. Physics, JETP, Vol.29, No,
Kovrizhnykh,	 Vol. 35, No. 4,
Stix, Physics of fluids, Vol. 14, No. 3, pp.
Roth, G. A. Gerdin, Plasma Physics, Vol. 190
i 1.	 K.
2. L.
i
i
4. T.
i
S. J.
334.
3, pp. 475-9211969
pp. 709-16, 1972.
692-712, 1971.
No. S, (1977) pp. 429-446.
6. J. R. Roth, IEEE Tans. on Plasma Science, ( in press ).s
7. J. R. Roth, "Factors Affecting the Ion Kinetic Temperature, Number
Density, and Containment Times in the NASA Lewis Bumpy Torus Plasma,A'
NASA TN D-8466, 1977.
A.
M.
M.
N.
R.
B. E. J. Powers, Nuclear Fusion, Vol. 14, (1974), pp. 749-52.
9. C. M. Singh, N. 14. Krawezonok, J. R. Roth, E. J. Powers and J. Y.
Bong, "Fluctuation Induced Particle Transport in the NASA Lewis
Bumpy Torus?A Prop., of IEEE 1977 international Conference on Plasma
Scinece, 770111205-4 NPS, May 1977, p., 75,
10. D. E. Smith, E. J. Powers, and G. S. Caldwell, IEEE Trans, on Plasma
Science, Vol. PS-2, (1974) pp. 261-272.
11. J. R. Roth, "Optimization of Confinement in a Toroidal Plasma
Subject to Strong Radial Electric Fields," NASA TM-73690, May, 1977.
tl3^
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Figure Cations
i-:
Figure 1 - Schematic of electric field distribution around a negatively E
biased bumpy toroidal plasma.
Figure 2 - A paired comparison of the confinement obtained with positive
l
and negative bias of the toroidal plasma for 
8max	
2.4 tesla. ^€
Figure 2a - Average plasma number density and particle containment time
as functions of electrode current.
Figure 2b - Cumulative transport rate as a function of electrode current.
Figure 3 - Transport spectral density function and cumulative transport
rates for an	 electrode current of I a = .75 amps. a) negative
electrode polarity, b) positive electrode polarity.
ii
Figure 4 - Effect of a weak vertical magnetic field on plasma containment
Figure 4a - Average electron number density as a function of vertical
magnetic field.
Figure 4b - Cumulative transport at the location of the probe as a function
i
of vertical magnetic field.
Figure 5 - The transport spectral density function as a function of
f
frequency from 0-500 kHz.	 The vertical magnetic field By is
equal to:	 a) -10 gauss, b) +19 gauss, c) +15 gauss, d) +18
gauss, e) +40 gauss, and f) +60 gauss.
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Inward transport of a toroidally confined plasma subject to strong radial electric fields

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