Energy absorption in cold inhomogeneous plasmas: the Herlofson paradox

Abstract

The Herlofson paradox is exemplified by a capacitor containing cold, collisionless, inhomogeneous plasma as the dielectric: its response to a sinusoidal driving signal can exhibit continuous energy absorption, even though the system is lossless. The underlying mechanism has been explained generally by Barston in terms of the transient response of the system. In this paper, we confirm Barston 's conclusions by examining in detail several analytically tractable cases of delta-function and sinusoidal excitation, and consider the effects of collisions and non-zero electron temperature in determining the steady state fields and dissipation. Energy absorption without dissipation in plasmas is analogous to that occurring after application of a signal to a network of lossless resonant circuits. This analogy is pursued, and extended to cover Landau damping in a warm homogeneous plasma, in which the resonating elements are the electron streams making up the velocity distribution. Some of the practical consequences of resonant absorption are discussed, together with a number of paradoxical plasma phenomena which can also be elucidated by considering a superposition of normal modes rather than a single Fourier component.