Transition in the dispersive properties of beam‐plasma and two‐stream instabilities

Abstract

The linear dispersion relation and the quasi‐linear evolution of the electron beam‐plasma instability are studied in intermediate regimes between the limits of the gentle bump‐on‐tail instability of Langmuir waves and purely reactive instability. The ranges of beam and plasma parameters which correspond to narrow‐banded plasma waves, broadband waves and waves with frequencies substantially below the electron plasma frequency are determined in a systematic and practical manner. The transition between these regimes and the changes in the topology of the dispersion relation are described by analytic theory and by detailed numerical solutions. All branches of the dispersion relation, including weakly damped modes which may be important in nonlinear wave coupling, are considered. Dissipative and reactive instability mechanisms are differentiated analytically and by comparing solutions of the exact dispersion relation with hybrid models using fluid components. Consequences for observations, especially in the electron foreshock, and for the design and analysis of simulation experiments are pointed out. The theory is also applicable to instabilities with ion beams or current driven instabilities. The study of the effects of increasing bulk temperature (or decreasing drift) applies in particular to the evolution from reactive Buneman instability to kinetic ion sound instability.