Boundary value problems in plasma oscillations: The plasma capacitor

Abstract

A normal mode treatment is proposed for the solution of boundary value problems in plasma oscillations. The plasma distribution function and electric field are expanded in terms of the solutions of the coupled Vlasov and Maxwell equations. These normal mode solutions are somewhat unusual in that they are singular functions of the velocity variable, and, in fact, the expansion theorem is proved by means of a direct solution of an associated singular integral equation. As an application of the method we obtain the impedance of a plasma-filled parallel plate condenser. 1. INTRODUCTION 1 1 * In problems involving propagation of transverse waves, the full set of Maxwell's equations is required. However, the treatment is identical in its essentials.

Die Beobachtung von Plasmaresonanzen mit Hilfe der Mikrowellenemission

“…Weitergehende theoretische uberlegungen beziiglich der Amplitudenverhaltnisse im Spektrum, welches neben der Stofidimpfung sicher auch durch die LANDAU-DampfWg mitbestimmt wird, stammen z. B. von MOLLWO [4], SHURE [ 5 ] , GOULD (61 und WOLSCHKE [7]. Trotz zahlreicher Untersuchungen stehen gesicherte Ergebnisse noch aus.…”

The transient response of the cesium diode to potential pulses

“…when the applied frequency is less than 0/4 of the plasma •frequency. For w approaching 1, it may be shown (14) that the effective permittivity is approximated by G eff = 1 " ~ to In effect, the plasma capacitance is highly sensitive to the frequency when w -» 1, and becomes a blockade capacitor as 0: = 1 (Z£ -» 03 ). This interpretation suggests that the resonant frequency should be slightly lower than the plasma frequency oe^, which agrees to the model of dissipative parallel circuits.…”

“…C0 vhere q = e (n. -ng), and is the ion density. (Vr/at)g = -J (fyfg) -K (fyfj (14) where J (f^f^) is the close encounter function (5) defined as b r s (15) in which f^, is the velocity distribution function after collision, g = vr -v the relative velocity of the two types of particle before en counter, b is the impact parameter, s is the angle between the orbital plane and the plane containing the velocities of the two particles before encounter; and b represents the critical impact parameter.…”