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

Abstract

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 (ωpe), 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 (Tb/Tp ≤ 0.01). This large unstable frequency bandwidth decreases dramatically with increasing Tb/Tp. When Tb/Tp = 0.5, and the beam to plasma density ratio is close to Nb/Np = 0.01, positive growth rate exists on a small frequency bandwidth, Δω/ω<0.1, close to ωpe. The cold beam case does not account for some broadband emissions observed with a low‐frequency cutoff below and close to ωpe. Broadband emissions can be generated by warm electron beams, but a beam density ratio Nb/Np equal to or greater than 0.1 is required, which is 10 times greater than the upper limit ratio inferred from spacecraft observations.

Simulation studies of plasma waves in the electron foreshock: The generation of downshifted oscillations

“…thee beam temperatures, Tb/Te•<hb, the maximum unstable frequency is significantly above we. Downshifted oscillations have been characterized by the fact that the frequency corresponding to maximum growth is below the plasma frequency and decreases rapidly with decreasing drift [FuselieF et al, 1985;Cairns and Fung, 1988;Canu, 1989]. It is also found that growth at large wave numbers is cut off by Landau damping from the beam, but that there is no longer a cutoff at small wave numbers and frequencies.…”

“…It is interesting to note that the time scales found in the simulation are in line with the duration of individual wave bursts (some tens of milliseconds) found in foreshock observations, especially if the simulations are driven somewhat more weakly than was done here for numerical reasons. It may not be necessary to invoke a preexisting fine structure of varying drift within the foreshock [Fuselief et al, 1985;Canu, 1989] to account for changing frequency and bandwidth within bursts. Wave activity is found to consist of many individual burst.…”

Influence of electron nongyrotropy and anisotropy on parallel wave propagation: Numerical solution of dispersion relation

“…It is not expected a noticeable influence of the static magnetic field. This fact has been used to justify an electrostatic approach for the electron beam interaction at the foreshock region (Canu, 1989). For the same observational parameters presented by Anderson et al (1985), but considering now different intensities for the magnetic field, i.e.…”

Electron density in the Martian foreshock as a by‐product of the electron plasma oscillation observations

“…The energy of these electrons is much greater than the electron thermal velocity of the solar wind. A beam-plasma interaction with beam velocities on the order of the electron thermal velocity may explain plasma oscillations above and below the plasma frequency [Fuselier et al, 1985;Canu, 1989Canu, , 1990]. Etcheto and Faucheux [1984] and oeacombe et al [1985], using electric field data from the sounder on ISEE 1, were able to show that the spectral characteristics of the electron plasma oscillations are correlated with the local distribution function of the backstreaming electrons, and of course with the connection depth (distance between the spacecraft and the upstream boundary of the electron foreshock).…”