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

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 S 11 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.