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Plasma leakage velocity through a low-β line cusp
Volume 60A, number 3
PHYSICS LETrERS
21 February 1977
PLASMA LEAKAGE VELOCITY THROUGH A LOW-j3 LINE CUSP K.N. LEUNG, R.E. KRIBEL, D.G. FITZSIMONS and G.R. TAYLOR Department of Physics, Madizn College, Harrisonburg, Virginia 22801, USA Received 23 September 1976 Revised manuscript received 13 January 1977 The plasma leakage velocity through a low-j3 line cusp measured by a double Langmuir probe is shown to be slightly less than the ion acoustic speed.
Confinement of plasma by low-j3 multi-cusp fields have been reported in several articles. By using a “picket-fence” configuration, Leung et al. [1] have studied the loss rate of primary electrons and plasma through a current produced line cusp. Also measurements by Hershkowitz et al. [2] showed that the halfwidth of the leakage aperture of plasma through a low2 13with line7ecusp hybrid and gyroradius (7e7i)~’ andis~twice as thetheelectron ion gyroradii. However, no direct measurements of the leakage velocity of plasma through a magnetic cusp have been reported. Some authors [3] have assumed that this yelocity is the ion acoustic speed C~= (Te/Mi)”2 while others [4, 5] have used the ion thermal velocity V. = (T~/M 2where M 1)uI 1 is the ion mass and Te and T1 are the electron and ion temperature, respectively. In this letter, we present experimental results which show that the plasma is leaking out a low-13 line cusp with a velocity slightly less than the ion acoustic speed. Experiments were carried out in a 40 liter thinwalled stainless steel vessel with the top flange and side wall covered externally by ceramic permanent magnets (B 1.7 kG at the pole face). A magnetic grid constructed from four rows of ceramic magnets separates the vessel into a driver and a target region. With the poles of the magnets in the grid arranged as shown in fig. 1, line cusps (B 500 G at x = 0, y = 0) are formed between the magnet rows along the z-direction [6] Plasma which is generated in the driver region by means of electron emission from the tungsten filaments will leak through the cusps into the target region. The leakage velocity of the plasma through these low-13 line cusps is measured by means of a double Langmuir probe which is made of two tantalum discs (diam. 3.5 mm) with a very thin sheet of mica .
MAGNETS /
/
FILAMENT
/
~
/
,~‘>
—
DRIVER _____
~ ~jjj~J [s~j
REGION ~LX_____ IN
~I 1~j~
/ TARGET
REGION
-~
Fig. 1. Schematic diagram showing the magnetic grid and the
multidipole device. sandwiched in between. This double probe is movable and it can be positioned at the center of the cusp. Since there is a flow of plasma from the driver into the target side, the ion distribution function is shifted in the direction of the flow and the ion saturation current collected by the two planar probes facing in opposite directions will not be the same [7, 8] The difference in current U~is related to the plasma flow yelocity by V = Uj/neA where n is the local plasma density, e is the electron charge and A is the collection area of each probe [8] The plasma density at the cen.
.
203
Volume 60A, number 3
PHYSICS LETFERS
21 February 1977
Table 1 The leakage velocities at the cusp for three different types of IO~ -—
the driver chamber are given by ~c and n respectively 0c C~ V Ion
E U, U
-
plasmas. plasma the cusp at the center of Helium The (cm3) 9.9 (cm3) 1.4 _______________________________ 10~ (cm sec’) (cm 5.5 Argon Xenon 5.4 2.8 X 108 i09 density i0~ 4.2 8.1 xXati09 iü~ 127 Xand ~ i05 8.5 1.7 X xsec1) i05 i04 ________________
IO~ y (cm) Fig. 2. Argon plasma leakage velocity measured at various distance from the cusp.
ter of the driver chamber is measured from the Langmuir probe characteristics. The local plasma density at the cusp is then obtained by comparing the ion saturation currents at the center of the driver region and at the cusp. In this measurement the double probe is oriented parallelto the direction of plasma flow to eliminate any streaming effect. The ion gyro-radius in the cusp region is larger than the probe dimensions in most of the experiments and thus the effects of the magnetic field are negligible. The probe shadow effect is also small because the ion mean free path is much larger than the probe dimension and most of the ions collected by the electrode facing the target chamber should originate outside the probe shadow. Fig. 2 shows the flow velocity V measured at several distances from the cusp for an argon plasma with the ion acoustic speed calculated from the measured electron temperature Te. The flow velocity decreases as one moves away from the cusp. Similar results are obtained for xenon and helium plasmas. The escape velocities at the cusp for the three plasmas are summarized in table 1. In each case, it is found that the escape velocity is slightly less than the ion acoustic speed and that the plasma density at the cusp is smaller than the density at the center of the driver
204
region by approximately a factor of 1.5. In conclusion we have measured the leakage velocity of three different plasmas through a low-13 line cusp by means of a double Langmuir probe. The leakage velocity is found to be slightly less than the ion acoustic speed. We would like to thank J. Lehman and T. Gallaher for technical assistance and S.L. Paul for constructing the magnetic grid. This work is supported in part by the Research Corporation.
References [1] K.N. Leung, N. Hershkowitz and T. Romesser, Phys. Lett. 53A (1975) 264. [2] N. Hershkowitz, K.N. Leung and T. Tomesser, Phys. Rev. Lett. 35 (1975) 277. [3] T. Christensen, N. Hershkowitz and K.N. Leung, to be published. [4] P.J. Hirt and M.Q. Tran, report LRP 77/7 3, Centre de Recherches en Physique des Plasmas, Ecole Polytechnique F~déralede Lausanne, Switzerland. [5] I. Spalding, in Advances in plasma physics, eds. A. Simon and W.B. Thompson (Interscience, New York, 1971), Vol. ~ ~ 79. [6] K.N. Leung, G.R. Taylor, J.M. Barrick, S.L. Paul and R.E. Kribel, Phys. Lett. 57A (1976) 145.
[71 R.
Kribel, C. Ekdahl and R. Lovberg, AIAA J. 9 (1971) 893. [8] R.H. Lovberg, in Methods of experimental physics, eds. H.R. Griem and R.H. Lovberg (Academic Press, New York, 1971) Vol. 9, p. 282.
PHYSICS LETrERS
21 February 1977
PLASMA LEAKAGE VELOCITY THROUGH A LOW-j3 LINE CUSP K.N. LEUNG, R.E. KRIBEL, D.G. FITZSIMONS and G.R. TAYLOR Department of Physics, Madizn College, Harrisonburg, Virginia 22801, USA Received 23 September 1976 Revised manuscript received 13 January 1977 The plasma leakage velocity through a low-j3 line cusp measured by a double Langmuir probe is shown to be slightly less than the ion acoustic speed.
Confinement of plasma by low-j3 multi-cusp fields have been reported in several articles. By using a “picket-fence” configuration, Leung et al. [1] have studied the loss rate of primary electrons and plasma through a current produced line cusp. Also measurements by Hershkowitz et al. [2] showed that the halfwidth of the leakage aperture of plasma through a low2 13with line7ecusp hybrid and gyroradius (7e7i)~’ andis~twice as thetheelectron ion gyroradii. However, no direct measurements of the leakage velocity of plasma through a magnetic cusp have been reported. Some authors [3] have assumed that this yelocity is the ion acoustic speed C~= (Te/Mi)”2 while others [4, 5] have used the ion thermal velocity V. = (T~/M 2where M 1)uI 1 is the ion mass and Te and T1 are the electron and ion temperature, respectively. In this letter, we present experimental results which show that the plasma is leaking out a low-13 line cusp with a velocity slightly less than the ion acoustic speed. Experiments were carried out in a 40 liter thinwalled stainless steel vessel with the top flange and side wall covered externally by ceramic permanent magnets (B 1.7 kG at the pole face). A magnetic grid constructed from four rows of ceramic magnets separates the vessel into a driver and a target region. With the poles of the magnets in the grid arranged as shown in fig. 1, line cusps (B 500 G at x = 0, y = 0) are formed between the magnet rows along the z-direction [6] Plasma which is generated in the driver region by means of electron emission from the tungsten filaments will leak through the cusps into the target region. The leakage velocity of the plasma through these low-13 line cusps is measured by means of a double Langmuir probe which is made of two tantalum discs (diam. 3.5 mm) with a very thin sheet of mica .
MAGNETS /
/
FILAMENT
/
~
/
,~‘>
—
DRIVER _____
~ ~jjj~J [s~j
REGION ~LX_____ IN
~I 1~j~
/ TARGET
REGION
-~
Fig. 1. Schematic diagram showing the magnetic grid and the
multidipole device. sandwiched in between. This double probe is movable and it can be positioned at the center of the cusp. Since there is a flow of plasma from the driver into the target side, the ion distribution function is shifted in the direction of the flow and the ion saturation current collected by the two planar probes facing in opposite directions will not be the same [7, 8] The difference in current U~is related to the plasma flow yelocity by V = Uj/neA where n is the local plasma density, e is the electron charge and A is the collection area of each probe [8] The plasma density at the cen.
.
203
Volume 60A, number 3
PHYSICS LETFERS
21 February 1977
Table 1 The leakage velocities at the cusp for three different types of IO~ -—
the driver chamber are given by ~c and n respectively 0c C~ V Ion
E U, U
-
plasmas. plasma the cusp at the center of Helium The (cm3) 9.9 (cm3) 1.4 _______________________________ 10~ (cm sec’) (cm 5.5 Argon Xenon 5.4 2.8 X 108 i09 density i0~ 4.2 8.1 xXati09 iü~ 127 Xand ~ i05 8.5 1.7 X xsec1) i05 i04 ________________
IO~ y (cm) Fig. 2. Argon plasma leakage velocity measured at various distance from the cusp.
ter of the driver chamber is measured from the Langmuir probe characteristics. The local plasma density at the cusp is then obtained by comparing the ion saturation currents at the center of the driver region and at the cusp. In this measurement the double probe is oriented parallelto the direction of plasma flow to eliminate any streaming effect. The ion gyro-radius in the cusp region is larger than the probe dimensions in most of the experiments and thus the effects of the magnetic field are negligible. The probe shadow effect is also small because the ion mean free path is much larger than the probe dimension and most of the ions collected by the electrode facing the target chamber should originate outside the probe shadow. Fig. 2 shows the flow velocity V measured at several distances from the cusp for an argon plasma with the ion acoustic speed calculated from the measured electron temperature Te. The flow velocity decreases as one moves away from the cusp. Similar results are obtained for xenon and helium plasmas. The escape velocities at the cusp for the three plasmas are summarized in table 1. In each case, it is found that the escape velocity is slightly less than the ion acoustic speed and that the plasma density at the cusp is smaller than the density at the center of the driver
204
region by approximately a factor of 1.5. In conclusion we have measured the leakage velocity of three different plasmas through a low-13 line cusp by means of a double Langmuir probe. The leakage velocity is found to be slightly less than the ion acoustic speed. We would like to thank J. Lehman and T. Gallaher for technical assistance and S.L. Paul for constructing the magnetic grid. This work is supported in part by the Research Corporation.
References [1] K.N. Leung, N. Hershkowitz and T. Romesser, Phys. Lett. 53A (1975) 264. [2] N. Hershkowitz, K.N. Leung and T. Tomesser, Phys. Rev. Lett. 35 (1975) 277. [3] T. Christensen, N. Hershkowitz and K.N. Leung, to be published. [4] P.J. Hirt and M.Q. Tran, report LRP 77/7 3, Centre de Recherches en Physique des Plasmas, Ecole Polytechnique F~déralede Lausanne, Switzerland. [5] I. Spalding, in Advances in plasma physics, eds. A. Simon and W.B. Thompson (Interscience, New York, 1971), Vol. ~ ~ 79. [6] K.N. Leung, G.R. Taylor, J.M. Barrick, S.L. Paul and R.E. Kribel, Phys. Lett. 57A (1976) 145.
[71 R.
Kribel, C. Ekdahl and R. Lovberg, AIAA J. 9 (1971) 893. [8] R.H. Lovberg, in Methods of experimental physics, eds. H.R. Griem and R.H. Lovberg (Academic Press, New York, 1971) Vol. 9, p. 282.