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Title: Radio frequency sheaths in an oblique magnetic field

Abstract

The physics of radio-frequency (rf) sheaths near a conducting surface is studied for plasmas immersed in a magnetic field that makes an oblique angle θ with the surface. A set of one-dimensional equations is developed that describes the dynamics of the time-dependent magnetic presheath and non-neutral Debye sheath. The model employs Maxwell-Boltzmann electrons, and the magnetization and mobility of the ions is determined by the magnetic field strength, and wave frequency, respectively. The angle θ, assumed to be large enough to insure an electron-poor sheath, is otherwise arbitrary. Concentrating on the ion-cyclotron range of frequencies, the equations are solved numerically to obtain the rectified (dc) voltage, the rf voltage across the sheath, and the rf current flowing through the sheath. As an application of this model, the sheath voltage-current relation is used to obtain the rf sheath impedance, which in turn gives an rf sheath boundary condition for the electric field at the sheath-plasma interface that can be used in rf wave codes. In general, the impedance has both resistive and capacitive contributions, and generalizes previous sheath boundary condition models. The resistive part contributes to parasitic power dissipation at the wall.

Authors:
;  [1]
  1. Lodestar Research Corporation, 2400 Central Avenue, Boulder, Colorado 80301 (United States)
Publication Date:
OSTI Identifier:
22489994
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physics of Plasmas; Journal Volume: 22; Journal Issue: 6; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
70 PLASMA PHYSICS AND FUSION TECHNOLOGY; BOLTZMANN STATISTICS; BOUNDARY CONDITIONS; CURRENTS; ELECTRIC FIELDS; ELECTRIC POTENTIAL; ELECTRONS; ION MOBILITY; MAGNETIC FIELDS; MAGNETIZATION; ONE-DIMENSIONAL CALCULATIONS; PLASMA; PLASMA SHEATH; RADIOWAVE RADIATION; SURFACES; TIME DEPENDENCE; WALLS

Citation Formats

Myra, J. R., and D'Ippolito, D. A.. Radio frequency sheaths in an oblique magnetic field. United States: N. p., 2015. Web. doi:10.1063/1.4922848.
Myra, J. R., & D'Ippolito, D. A.. Radio frequency sheaths in an oblique magnetic field. United States. doi:10.1063/1.4922848.
Myra, J. R., and D'Ippolito, D. A.. Mon . "Radio frequency sheaths in an oblique magnetic field". United States. doi:10.1063/1.4922848.
@article{osti_22489994,
title = {Radio frequency sheaths in an oblique magnetic field},
author = {Myra, J. R. and D'Ippolito, D. A.},
abstractNote = {The physics of radio-frequency (rf) sheaths near a conducting surface is studied for plasmas immersed in a magnetic field that makes an oblique angle θ with the surface. A set of one-dimensional equations is developed that describes the dynamics of the time-dependent magnetic presheath and non-neutral Debye sheath. The model employs Maxwell-Boltzmann electrons, and the magnetization and mobility of the ions is determined by the magnetic field strength, and wave frequency, respectively. The angle θ, assumed to be large enough to insure an electron-poor sheath, is otherwise arbitrary. Concentrating on the ion-cyclotron range of frequencies, the equations are solved numerically to obtain the rectified (dc) voltage, the rf voltage across the sheath, and the rf current flowing through the sheath. As an application of this model, the sheath voltage-current relation is used to obtain the rf sheath impedance, which in turn gives an rf sheath boundary condition for the electric field at the sheath-plasma interface that can be used in rf wave codes. In general, the impedance has both resistive and capacitive contributions, and generalizes previous sheath boundary condition models. The resistive part contributes to parasitic power dissipation at the wall.},
doi = {10.1063/1.4922848},
journal = {Physics of Plasmas},
number = 6,
volume = 22,
place = {United States},
year = {Mon Jun 15 00:00:00 EDT 2015},
month = {Mon Jun 15 00:00:00 EDT 2015}
}
  • The physics of radio-frequency (rf) sheaths near a conducting surface is studied for plasmas immersed in a magnetic field that makes an oblique angle θ with the surface. A set of one-dimensional equations is developed that describe the dynamics of the time-dependent magnetic presheath and non-neutral Debye sheath. The model employs Maxwell-Boltzmann electrons, and the magnetization and mobility of the ions is determined by the magnetic field strength, and wave frequency, respectively. The angle, θ assumed to be large enough to insure an electron-poor sheath, is otherwise arbitrary. Concentrating on the ion-cyclotron range of frequencies, the equations are solved numericallymore » to obtain the rectified (dc) voltage, the rf voltage across the sheath and the rf current flowing through the sheath. As an application of this model, the sheath voltage-current relation is used to obtain the rf sheath impedance, which in turn gives an rf sheath boundary condition for the electric field at the sheath-plasma interface that can be used in rf wave codes. In general the impedance has both resistive and capacitive contributions, and generalizes previous sheath boundary condition models. The resistive part contributes to parasitic power dissipation at the wall.« less
  • Cited by 6
  • Two-dimensional particle simulations of the sheath in front of a flat Langmuir probe mounted into a particle absorbing plate are performed to study the influence of a strong magnetic field (relation between Larmor radii and Debye length: [rho][sub [ital e]][le][lambda][sub D], [rho][sub [ital i]][much gt][lambda][sub D]) which is oriented obliquely to the probe surface. Ion-attracting probes are considered and the sheath is assumed to be collisionless. The full particle orbits in the homogeneous magnetic field and the self-consistent electric potential are calculated with a particle-in-cell (PIC) code with two spatial coordinates and three velocity components (2[ital d],3[ital v]). The mainmore » results are: In the sheath the ion trajectories are bent towards the normal to the probe surface so that the ion flow is focused to the edges of the probe. This leads to an enhancement of the ion current as compared to the current flowing in the flux tube subtended by the probe. As a consequence the current does not saturate at large (negative) probe voltage, because the thickness of the Debye sheath, and thus the effective probe size, grows with increasing probe voltage. This effect is particularly strong if the sheath thickness is about as large, or larger than, the projection of the probe size along the magnetic field lines. These results can help to explain the ion-current nonsaturation found in recent measurements with Langmuir probes in the boundary layer of magnetically confined plasmas.« less
  • An analytic model is derived for electromagnetic radio-frequency (rf) wave propagation in a plasma-filled waveguide with rf sheath boundary conditions. The model gives a simplified description of the rf fields and sheath potentials near an ion cyclotron range of frequencies antenna under certain conditions. The present work lifts the restriction to a low density plasma ('tenuous plasma model') described in a previous paper [D. A. D'Ippolito and J. R. Myra, Phys. Plasmas 16, 022506 (2009)] to include the full plasma dielectric tensor with the ordering epsilon{sub perpendicular}approxepsilon{sub x}approx1, epsilon{sub ||}>>1 for the case where the magnetic field is well alignedmore » with the antenna. It is shown that retaining epsilon{sub x}approx1 provides an additional drive term for the rf sheath. This effect is shown to be negligible in most practical situations suggesting that the tenuous plasma model does not miss any essential finite-density effects. The condition to recover the tenuous plasma result is derived. Expressions for the sheath voltage and sheath power dissipation are given in the arbitrary density limit, and a comparison of several mechanisms for dissipating power in rf sheaths is discussed.« less