Gyrotropic Resonances in Afterglow Plasmas

Abstract

Resonances are observed in the reflection of radio waves from a decaying plasma column in an axial magnetic field. They are seen by monitoring the reflected signal as a function of time in the afterglow with the frequency and magnetic field held constant. When viewed collectively as a function of field strength, these observations trace the transition between Tonks-Dattner electroacoustic modes in the plasma sheath and gyrotropic longitudinal modes in the plasma core. At weak fields, the resonances are slightly displaced towards lower densities (later in the afterglow) and damped near each harmonic of the electron cyclotron frequency. As the field is increased beyond a threshold value, each mode is sharply shifted towards lower densities and rapidly attenuated until it reappears at a higher electron density, i.e., earlier in the afterglow. The observed phenomena are explained on the basis of the linearized Vlasov equation for an inhomogeneous plasma. As in the theory of Tonks-Dattner resonances, density gradients play a fundamental role in determining the resonance spectrum. Their effect is reflected in an approximate dispersion relation derived from the Vlasov equation by a perturbation approach. The resonance conditions are determined from this relation in the case of weak fields, or from the Bernstein relation in the case of stronger fields, by introducing a locally varying phase constant and applying a selection rule derived from the WKB approximation. Although the agreement between measured values and predicted results is only semiquantitative, the major trends are in accord with the theory. In particular, the analysis points out that the role of density gradients in establishing the transition between the weak- and strong-field limits is largely governed by the relative size of the Larmor radius compared with the effective scale length of the gradient.