Linear study of the beam‐plasma interaction as a source mechanism for the broadband electrostatic emissions observed in the electron foreshock

Electron beams streaming back from the Earth's bow shock into the solar wind have been proposed as a possible source for the electron plasma waves observed by spacecraft in the electron foreshock. These waves often correspond to broadband electrostatic emissions extending both above and below the local electron plasma frequency. The linear beam‐plasma interaction is studied numerically. We focus on the generation of emissions with upper cutoff frequency of the order of or above 1.5 times the electron plasma frequency (ω pe ), which were reported from ISEE observations. Beam drift velocity, thermal spread and density are varied over a range which is consistent with the observations, and the effects on the frequency bandwidth over which emissions can grow are studied. It is shown that linear instability can develop, on the so‐called beam mode, in a frequency range from ω∼0 to above twice the electron plasma frequency, when electron beam drift velocity is of the order of 1.5 to 3 times the bulk electron thermal velocity and when the ratio between the beam and the plasma temperature is very low ( T b /T p ≤ 0.01). This large unstable frequency bandwidth decreases dramatically with increasing T b /T p . When T b /T p = 0.5, and the beam to plasma density ratio is close to N b /N p = 0.01, positive growth rate exists on a small frequency bandwidth, Δω/ω<0.1, close to ω pe . The cold beam case does not account for some broadband emissions observed with a low‐frequency cutoff below and close to ω pe . Broadband emissions can be generated by warm electron beams, but a beam density ratio N b /N p equal to or greater than 0.1 is required, which is 10 times greater than the upper limit ratio inferred from spacecraft observations.