Kinetische Theorie der Plasmaschwingungen im Plasmakondensator

Abstract

Stationary excitation of plasma oscillations by an external a!ternating electric field in a collisionless onedimensional plasma layer (plasma condenser) is examined. For this the linearized onedimensional VLASOV equation is integrated along the one-electron characteristics, assuming the electrons are reflected specularly a t the boundaries. In the case of a homogeneous plasma the resulting FREDHOLM integral equation for the electric field is solved exactly. Tho resulb agree with SHORE'S, received on the basis of distributional analysis it la VAN KAMPEN and CASE. In view of T O N K S -D A~E Rresonances the resonance properties of the homogeneous plasma condenser are discussed. Contrary to the hydrodynamics1 theory here we receive only a finite number of resomnces, increasing with the ratio r of layer diameter to DEBYE length.The ratio of series limit to main resonance position is nearly constant for r not too small. This agrees with DATTNER'S qualitative statements about TONICS-DATTNER resonances found experimentally. However, the kinetical effect of series limit and another one of a second serio of resonances a t lower frequencies are masked by strong LANDAU damping in this region of dispersion.The method of characteristics used here has the advantage of easily being generalized for the case of an inhomogeneous plasma condenser. For this case an integral equation €or the electric field is derived in full analogy to the procedure employed for the homogeneous plasma. Finally the kernel of this equation is specialized for a parabolic static potential.