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Plasma confinement by a magnetic shell configuration
Volume 51 A, number 2
PHYSICS LETTERS
10 February 1975
PLASMA CONFINEMENT BY A MAGNETIC SHELL CONFIGURATION ES. WEIBEL and M.W. TRAN Centre de Recherches en Physique des plasmas, Ecole Polytechnique F&d&ale de Lausanne, Switzerland Received 26 November 1974 The confinement properties of a new magnetic shell configuration have been investigated experimentally. The diffusion coeffkient D has been determined. _
We have experimentally examined the confinement properties of a configuration which we call a magnetic shell, and which is generated by two arrays of currents flowing parallel to the z-axis. The currents of one of the arrays flow in the positive z-direction and intersect the xy-plane at the points x = ma, y = b, m = integer, while the currents of the second array flow in the negative z-direction and intersect the xy-plane at the pointx =ma,y = -b. The magnitude of all currents is equal to I. This magnetic shell configuration - MSCis shown schematically in fig. la. The line integral -$dZ/B taken over a spatial period has the value -00 on the field line whichgoes to infinity and increases monotonically as one moves either towards the xz-plane or towards a current line. Thus the MSC can stably confine a low p plasma in the half space on one side of the xz-plane. The currents lying in the plane outside the plasma can of course be replaced by a uniformly distributed current layer in the plane y = b (fig. lb). This configuration can be bent into cylindrical symmetry, fig. lc. The earliest mention of an MSC in the literature seems have been made by Firsov [l]. It is clear the the MSC belongs to the family of the multipole confinement geometries [2], albeit with a very large number of poles. The poles shield the interior of the plasma keeping it free of magnetic fields. The USC has no cusps and is thus not a “picket fence”. Wong [3] is at present independently examinin an MSC. We tested the confinement properties of the MSC on a rectangular plasma box [4], five faces of which were covered with permanent magnets while the sixth was closed with an MSC (fig. Id). The currents are carried in water cooled copper tubes of 6 mm diameter, spaced u = 2b = 40 mm. The current I could be varied
from zero to 1 kA. At this current the voltage drop along the conductors is 2 V/m. At maximum current the field on the surface of the conductors is 330 gauss,
b
4
Plasma
box
Fig. 1. Different magnetic shell confiiurations. a) Flat magnetic shell confiiation. b) A magnetic shell confiiation with uniformly dlstrihuted return current. c) The same structure but bent into cylindrical symmetry. d) lk device on which measurements presented here have been made.
71
PHYSICS LETTERS
Volume 51 A, number 2
;CS
10 February 1975
a
_._._Tc --. ----
LOSS
. .._--.
r
x
x LOO-
L x
--L.-._* -..
/
‘L..
1..
JOOI
. I /
[200- f #,I I I
loo-
b
b
Fig. 2. Variations of plasma-density ne, electron temperature Te, confinement time T within the plasma box losses a through the MSC (fa. 2a), density fluctuation level at 3 cm outside the MSC mid-plane (fQ.2b), as a function of I.
cross section [4]. The losses o represent the ratio of the ion saturation current within the box to the ion saturation current measured outside the box at a distance of 7 cm from the mid-plane of the MSC. Finally we measured the fluctuations of the electron saturation current at various positions v#hin the MC. AUmeasurements were repeated for a set of parameters (see table 1). Fig. 2 shows the results of these measurements for: argon pressure = 5 X 10m5torr, ionizing current 200 mA, as a function of the current I. The curves obtained
and the mean field on the mid-plane is 3 14 gauss. A singly ionized argon plasma was produced within the box by injecting a current Zi of up to 200 mA of electrons at 40 V. We have measured, as a function of the current I: density n, and electron temperature T, of the plasma within the box, by means of a flat Langmuir probe (4 5 mm). The confinement time r was measured as the decay time of the electron density after super imposing a small step on the accelerating voltage of the injected electrons; this changes their ionizing
Table 1 Argon pmssme Ionizing current
72
torr mA
5 x 10-s 80
5 x 10-S 200
10’ 120
3x10’ 80
3x104 200
5x10-4 40
Volume 51A, number 2
PHYSICS LETTERS
for the other sets of parameters show qualitatively similar behaviour. We observe that the electron density within the box increases monotonically with I. The losses Q!first decrease, then increase to a peak and finally fall off inversely proportional to I. The fluctuations follow this behaviour indicating that the losses are correlated with the noise. The frequency spectrum of these fluctuations is peaked at 100 kHz. The confinement time is inversely proportional to the losses a. The peak of the losses occurs when the ion Larmor radius becomes comparable to the spacing 40 mm, of the currents (I= 400 A, B, =126G,Ti=2000deg,pi=31mm). In our experiments the ion Armor radius never becomes very small, so that the physics of the continement is rather intricate and not well understood at this time. We can summarize our observations by introducing an average diffusion coefficient defined as (nlu) = eta dkwi D=a -
10 February 1975
7.4 m see-2 in this case. This is not surprising considering that some field lines of our MSC intersect metallic surfaces so that large density gradients can exist across the lines giving turbulbnce and anomalous diffusion. In spite of this it clear that Plasma Boxes can be built in which the plasma is entirely confined by MSC which would allow better confinement at higher temperatures than is presently possible with permanent magnets. A larger MSC with cylindrical symmetry and higher B-field is presently under construction at the CRPP. We wish to acknowledge the technical support of Mr. H. Ripper. Fruitful discussions with Prof. A.Y. Wong [3], Dr. M. Bitter and Dr. A Heym are greatly appreciated. This work was performed under the auspices of the Fonds National Suisse de la Recherche Scientifique.
,
n0
where no is the density within the box, (nl u) is the particle flux leaving the MSC. According to our measurements D can be reasonably well represented by the formula D = 2.9 X 10-2B-1 T1j6 , with D, B, T measured in m2/s, VslmZ, K. However the dependence on T may be spurious due to uncertainties in the measurements. In fact the numerical values of D are suspiciously close to the Bohm value: for instance for p. = 5 X 10B5 torr, Ii = 200 mA, I = 1kAwefmda!=0.045,B=0.0314Vs/m2,Te= 4.3 X 104K, uTj = 3 X lo3 m/s the value inferred from our measurements is D = 5.4 m secB2 while Deb =
References [ 11 O.B. Firsov! A Plasma in a magnetic Grid @ii. lb but not la nor lc), from Plasma physik and the problem of controlled thermonuclear reactors, ed. M.A. Leontovich, Vol. III, p. 386. [21 S. Yoshikawa, Nuclear Fusion 13 (1973) 433. [31 A.Y. Wang : A Large Surface Magnetic Confinement Device, report PPG-192, Plasma Physics Group, University of California, Los Angeles, Sept. 1974. Presented to the CRPP duriw a visit of Prof. Wong in Sept. 1974. At this time our MSC was built, but not yet tested. 141P.J. Hirt and M.Q. Tran: Rot. 1974 Spring Meeting of the Swiss Physical Society, to be published in HPA. See also P.J. Hid and M.W.Tran, report LRP 77/74,
available from the CRPP.
73
PHYSICS LETTERS
10 February 1975
PLASMA CONFINEMENT BY A MAGNETIC SHELL CONFIGURATION ES. WEIBEL and M.W. TRAN Centre de Recherches en Physique des plasmas, Ecole Polytechnique F&d&ale de Lausanne, Switzerland Received 26 November 1974 The confinement properties of a new magnetic shell configuration have been investigated experimentally. The diffusion coeffkient D has been determined. _
We have experimentally examined the confinement properties of a configuration which we call a magnetic shell, and which is generated by two arrays of currents flowing parallel to the z-axis. The currents of one of the arrays flow in the positive z-direction and intersect the xy-plane at the points x = ma, y = b, m = integer, while the currents of the second array flow in the negative z-direction and intersect the xy-plane at the pointx =ma,y = -b. The magnitude of all currents is equal to I. This magnetic shell configuration - MSCis shown schematically in fig. la. The line integral -$dZ/B taken over a spatial period has the value -00 on the field line whichgoes to infinity and increases monotonically as one moves either towards the xz-plane or towards a current line. Thus the MSC can stably confine a low p plasma in the half space on one side of the xz-plane. The currents lying in the plane outside the plasma can of course be replaced by a uniformly distributed current layer in the plane y = b (fig. lb). This configuration can be bent into cylindrical symmetry, fig. lc. The earliest mention of an MSC in the literature seems have been made by Firsov [l]. It is clear the the MSC belongs to the family of the multipole confinement geometries [2], albeit with a very large number of poles. The poles shield the interior of the plasma keeping it free of magnetic fields. The USC has no cusps and is thus not a “picket fence”. Wong [3] is at present independently examinin an MSC. We tested the confinement properties of the MSC on a rectangular plasma box [4], five faces of which were covered with permanent magnets while the sixth was closed with an MSC (fig. Id). The currents are carried in water cooled copper tubes of 6 mm diameter, spaced u = 2b = 40 mm. The current I could be varied
from zero to 1 kA. At this current the voltage drop along the conductors is 2 V/m. At maximum current the field on the surface of the conductors is 330 gauss,
b
4
Plasma
box
Fig. 1. Different magnetic shell confiiurations. a) Flat magnetic shell confiiation. b) A magnetic shell confiiation with uniformly dlstrihuted return current. c) The same structure but bent into cylindrical symmetry. d) lk device on which measurements presented here have been made.
71
PHYSICS LETTERS
Volume 51 A, number 2
;CS
10 February 1975
a
_._._Tc --. ----
LOSS
. .._--.
r
x
x LOO-
L x
--L.-._* -..
/
‘L..
1..
JOOI
. I /
[200- f #,I I I
loo-
b
b
Fig. 2. Variations of plasma-density ne, electron temperature Te, confinement time T within the plasma box losses a through the MSC (fa. 2a), density fluctuation level at 3 cm outside the MSC mid-plane (fQ.2b), as a function of I.
cross section [4]. The losses o represent the ratio of the ion saturation current within the box to the ion saturation current measured outside the box at a distance of 7 cm from the mid-plane of the MSC. Finally we measured the fluctuations of the electron saturation current at various positions v#hin the MC. AUmeasurements were repeated for a set of parameters (see table 1). Fig. 2 shows the results of these measurements for: argon pressure = 5 X 10m5torr, ionizing current 200 mA, as a function of the current I. The curves obtained
and the mean field on the mid-plane is 3 14 gauss. A singly ionized argon plasma was produced within the box by injecting a current Zi of up to 200 mA of electrons at 40 V. We have measured, as a function of the current I: density n, and electron temperature T, of the plasma within the box, by means of a flat Langmuir probe (4 5 mm). The confinement time r was measured as the decay time of the electron density after super imposing a small step on the accelerating voltage of the injected electrons; this changes their ionizing
Table 1 Argon pmssme Ionizing current
72
torr mA
5 x 10-s 80
5 x 10-S 200
10’ 120
3x10’ 80
3x104 200
5x10-4 40
Volume 51A, number 2
PHYSICS LETTERS
for the other sets of parameters show qualitatively similar behaviour. We observe that the electron density within the box increases monotonically with I. The losses Q!first decrease, then increase to a peak and finally fall off inversely proportional to I. The fluctuations follow this behaviour indicating that the losses are correlated with the noise. The frequency spectrum of these fluctuations is peaked at 100 kHz. The confinement time is inversely proportional to the losses a. The peak of the losses occurs when the ion Larmor radius becomes comparable to the spacing 40 mm, of the currents (I= 400 A, B, =126G,Ti=2000deg,pi=31mm). In our experiments the ion Armor radius never becomes very small, so that the physics of the continement is rather intricate and not well understood at this time. We can summarize our observations by introducing an average diffusion coefficient defined as (nlu) = eta dkwi D=a -
10 February 1975
7.4 m see-2 in this case. This is not surprising considering that some field lines of our MSC intersect metallic surfaces so that large density gradients can exist across the lines giving turbulbnce and anomalous diffusion. In spite of this it clear that Plasma Boxes can be built in which the plasma is entirely confined by MSC which would allow better confinement at higher temperatures than is presently possible with permanent magnets. A larger MSC with cylindrical symmetry and higher B-field is presently under construction at the CRPP. We wish to acknowledge the technical support of Mr. H. Ripper. Fruitful discussions with Prof. A.Y. Wong [3], Dr. M. Bitter and Dr. A Heym are greatly appreciated. This work was performed under the auspices of the Fonds National Suisse de la Recherche Scientifique.
,
n0
where no is the density within the box, (nl u) is the particle flux leaving the MSC. According to our measurements D can be reasonably well represented by the formula D = 2.9 X 10-2B-1 T1j6 , with D, B, T measured in m2/s, VslmZ, K. However the dependence on T may be spurious due to uncertainties in the measurements. In fact the numerical values of D are suspiciously close to the Bohm value: for instance for p. = 5 X 10B5 torr, Ii = 200 mA, I = 1kAwefmda!=0.045,B=0.0314Vs/m2,Te= 4.3 X 104K, uTj = 3 X lo3 m/s the value inferred from our measurements is D = 5.4 m secB2 while Deb =
References [ 11 O.B. Firsov! A Plasma in a magnetic Grid @ii. lb but not la nor lc), from Plasma physik and the problem of controlled thermonuclear reactors, ed. M.A. Leontovich, Vol. III, p. 386. [21 S. Yoshikawa, Nuclear Fusion 13 (1973) 433. [31 A.Y. Wang : A Large Surface Magnetic Confinement Device, report PPG-192, Plasma Physics Group, University of California, Los Angeles, Sept. 1974. Presented to the CRPP duriw a visit of Prof. Wong in Sept. 1974. At this time our MSC was built, but not yet tested. 141P.J. Hirt and M.Q. Tran: Rot. 1974 Spring Meeting of the Swiss Physical Society, to be published in HPA. See also P.J. Hid and M.W.Tran, report LRP 77/74,
available from the CRPP.
73