Diffusion Model of Saturation Current Collection by a Planar Langmuir Probe in a Strong Magnetic Field

Abstract

Plasma presheath and saturation current collection by a planar Langmuir probe in a strong magnetic field perpendicular to the probe surface ares described with the diffusion model. The model takes into consideration the geometry of the probe, that is its size and shape, and dependence of the cross-field charged particles' transport into the effective collection region of the probe on the parallel-field transport to the probe. Experimental study of planar Langmiur probe I -V characteristics in D.C. discharge argon plasma in strong magnetic fields confirms the possibility of deriving the cross-field diffusion coefficient, DY, from the measured electron satuation current. Additional dependence of the electron saturation current on the parallel-field diffusion coeficient, Dt, and the ion temperature, T, derived in the approximate Stangeby's study using the diffusion model of current collection by a planar surface (STANCEBY, P. C., J. Phys. D: Appl. Phys. 15 (1982) 1007) can be eliminated with more rigorous calculation. Series of measurements on two neutral prcssurcs and various magnetic fields gave reproducible values of Df, approximately given by relation Df x ( S n / ( n ) ) k,T,/(eB).

Langmuir probe in low temperature, magnetized plasmas: Theory and experimental verification

“…Stanojevic and co-workers further developed Stangeby's model in strongly magnetized, low temperature, Ar discharge plasmas. 4,5 In their improved model, Stanojevic and co-workers divided the whole perturbed region near the probe into two subregions: a ''free-fall region'' with the characteristic scale length of the collision mean free path, and a long ''interaction region'' where macroscopic quasineutrality is conserved by ambipolar current collection. From the series of measurements, they calculated the cross-field diffusion coefficient as approaching the corresponding D Ќ Bohm when B was greater than 2-3 kG.…”

Interpretation of a Planar Langmuir Probe Current — Voltage Characteristic in a Strong Magnetic Field

“…On the other hand, these values of FY are mostly lower than those calculated with various fluid and kinetic models of ion flow to a planar surface [7] or the values calculated with the diffusion model of saturation current collection presented in our previous study [8], with the exception of the HUTCHINSON'S fluid theory of ion collection by probes in strong magnetic fields with plasma flow [20, 211. A notable limitation of these theories is that they ail use one-dimensional approximations of real three-dimensional situations. However, it was shown in our previous study that consideration of the three-dimensional effects can only increase the ion saturation current reduction factor, F;, thus it seems that if the assumptions of the model are correct, the only conclusion can be that the ion part of the planar probe current-voltage characteristic indeed has a discontinuity at the probe bias at which the electron current is saturated.…”

“…The STANGEBY'S model was a starting point of our previous study of saturation current collection by a planar Langmuir probe in a strong magnetic field [8]. This study also includes the ideas of the STANGEBY'S model of current collection by a planar' probe in the general, "non-saturation", case and considers the probe geometry effects presented in our previous study.…”

“…This dependence can be easily understood assuming that L x (42)(D,,/D,)1'2 (see eq. (9)) and using the expression for the cross-field diffusion coefficient obtained in our previous study, D, x (6n/(n)) k,T,l(eB) [8], thus eq. (86) gives the measured dependence of vpRl on the magnetic field.…”

“…The discharge current, I,, was 0.6 A in both cases, except for B 5 0.2 T, on the lower neutral pressure, where I , i 0.4 A. Some more details about the measurements can be found in our previous article [8].…”