On collisionless energy absorption in plasmas: Theory and experiment in spherical geometry

Abstract

An investigation of the rf impedance characteristics of a small spherical probe immersed in a laboratory plasma is ongoing in the large Space Physics Simulation Chamber [D. N. Walker et al., Rev. Sci. Instrum. 65, 661 (1994)] at the Naval Research Laboratory. The data taken are from network analyzer measurements of the reflection coefficient obtained when applying a low level rf signal to the probe which is either near floating potential or negatively dc biased in a low pressure plasma. As is well known, sheaths form around objects placed inside plasmas. The electron density is smaller inside the sheath, and the reduction in density alters the plasma impedance. Surprisingly, the impedance becomes “resistive,” even though the plasma is effectively collisionless, at frequencies below the bulk plasma frequency, thus leading to collisionless energy absorption. This behavior comes directly from Maxwell's equations along with the cold fluid equations. The solutions obtained indicate that this form of plasma resistance is inversely proportional to the plasma density gradient evaluated at the location where the plasma frequency is equal to the applied frequency. The sphere for this work is typically near plasma potential or biased more negatively into the ion collection regime. Applying a supplemental, negative dc bias to the sphere thickens the sheath and tends to raise its resistance as the density gradient is softened. Much of the earlier work in the area of collisionless resistance concentrated primarily on planar probes as opposed to the present work which is concerned with spheres. Interpreting the results is simpler for a sphere and the results obtained agree well with theory as described. For comparison to the theory we use only the S11 parameter outputs (or reflection coefficients) of the network analyzer in the experimental series. Significant energy absorption is observed at frequencies generally near one-half the plasma frequency. One result of this work is that the most efficient transfer of power to the plasma occurs not unexpectedly when there is impedance matching between input impedance and output (collisionless) impedance. This paper is an exposition of these ideas along with data results and a comparison to theory for the spherical probe which has not been published in this form.

On the Non-Intrusive Determination of Electron Density in the Sheath of a Spherical Probe

“…The basic theory we have developed 13,14 is consistent with earlier works but is unique in that we are able to obtain an electron density profile from the surface of the probe to the bulk plasma in the low pressure case. In the high pressure case the method provides a new and useful measure of bulk electron density.…”

“…We treat for illustration purposes the spherical probe. The primary equations for impedance which arise as a result of the application of the ac signal to the spherical probe are given by: 14 from which resistance and reactance follow as, and, where the complex impedance, Z, is given by Ohm's Law, with V 0 the applied rf voltage and I 0 the rf current driven by V 0 into the sphere and out through the plasma. Also in the above equations, r s is the sphere radius, < is electron-neutral collision frequency, T is the applied frequency and T pe (r)) is the local plasma frequency.…”

“…Examples of this is shown are in Figures (4) through (6) where we plot results from two theoretical models versus the experimental results found by using Eqn (5). Figures (4) and (5) show density profiles for two different densities from the probe surface to the sheath edge using theory developed in our earlier work 14 . Figure (6) compares the experimental results to another commonly accepted theoretical profile which is derived without specifically requiring the existence of a presheath.…”

The planar Multipole Resonance Probe: a functional analytic approach

“…One class of APRS probes excites electrostatic resonances [2][3][4][5][6][7][8][9], which occur below ω pe and can be described by a model of the probeplasma system in an electrostatic approximation. Many approaches to understand these resonance phenomena have been reported [10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25]. They have in common, that their models are based on a fluid dynamical description and they focus only on a specific design of a certain probe.…”

Antenna Impedance Measures in a Magnetized Plasma. Part 1. Spherical Antenna

“…There is also a desire to understand antenna-plasma coupling better with the application of developing improved methods for plasma wave launching and detection in ionospheric and space environments [15]. Finally, there are basic plasma physics issues that can be uncovered with antenna impedance measurements [17].…”