Spatial Ion-Wave Echoes

Abstract

Theory and experiments of spatial ion-wave echoes are reported. In the collisionless approximation, the calculated line shape of the second-order echo is found to be a universal function of Δx/δ, the distance from the expected position of the echo divided by the Landau damping length of the ion-wave constituting the echo. Higher-order echoes predicted by Gould are observed up to the fourth order with respect to the external fields at the predicted positions with the predicted dependence of their amplitude on the amplitude of the primary waves. In addition, new types of higher-order echoes which result from the electric fields of other echoes are predicted and observed. Measurements of the peak amplitude of the second-order echo as a function of the separation l between the two exciters indicates that the memory of the past excitation retained in the distribution function damps exponentially with the attenuation length proportional to the wavelength of the excited wave. The effect of ion-neutral collisions on the peak amplitude is studied and explained fairly well by a simple relaxation time model, but the predicted effect of ion-ion collisions based on a Fokker-Planck-type equation is not observed within the separation length l of 20 cm and the plasma density of 1010/cm3.