Growth of electron plasma waves above and below ƒp in the electron foreshock

Abstract

With increasing penetration into the electron foreshock the characteristics of the electrostatic waves driven by streaming electrons change continuously from the familiar intense waves near the electron plasma frequency ƒp to weak bursts of broadband waves initially significantly above ƒp and then well below fp. Growth well below ƒp has been demonstrated theoretically for slow, cold electron beams, and the broadband waves below ƒp in the foreshock have been interpreted in terms of the very cold or sharp “cutoff” feature of a cutoff distribution for small cutoff speeds. However, an approximate theoretical criterion indicates that the electron beams studied hitherto are unstable to reactive rather than kinetic growth, thereby favoring very narrow‐band growth contrary to the observed broadband growth. In this paper we determine conditions for kinetic growth well above and below ƒp for both cold and warm beams over a wide range of beam densities and speeds. We verify that kinetic growth below ƒp is possible for cold, slow beams and for warm, dense beams (over a wide range of beam velocities). We then argue that the observed broadband waves below fp are naturally explained in terms of slow, dilute electron beams with cold features but that an explanation involving warm, dense beams is inconsistent with the available data. Broadband growth above ƒp is explained in terms of faster, warmer beams. A unified qualitative theory for the narrow‐band and broadband waves is proposed involving (1) cutoff distributions, (2) the spatial variation in the cutoff velocity throughout the foreshock, (3) initial reactive growth with modification of the particle distribution and subsequent kinetic growth for cutoff velocities appropriate for the waves near and above ƒp, (4) initial kinetic growth and preservation of the cutoff feature for cutoff velocities appropriate to growth below ƒp, and (5) limitation of kinetic growth by inhomogeneous quasi‐linear relaxation. This theory can account qualitatively for the spatial variations in the intensity, center frequency, and bandwidth of the electron plasma waves in the foreshock. However, further work is required to understand the preservation of the cold features required for growth below ƒp and the bursty nature of the broadband waves.