Trapping saturation of the bump‐on‐tail instability and electrostatic harmonic excitation in Earth's foreshock

Abstract

Trapping saturation of the bump‐on‐tail instability is discussed using electron plasma Vlasov simulation results. The role of electrostatic harmonic excitation is considered in detail and shown to play a decisive role in the saturation of the instability. An extensive discussion of the simulation results is given to show that the results are not significantly limited by the finite number of Fourier modes used nor by the discrete distribution of those modes in wave number. It is argued that in the leading edge of Earth's electron foreshock a narrow wave number band of unstable field modes leads to trapping saturation of the bump‐on‐tail instability while simultaneously exciting electrostatic plasma waves at harmonics of the plasma frequency in similar narrow bands of shorter wavelengths. The argument is based (1) on the observations of Lacombe et al. (1985), who found intense plasma waves at the leading edge of the foreshock with a spectral distribution sufficiently narrow to trap particles in resonance with the waves, and (2) on numerical simulations of the foreshock electron plasma which indicate that trapping saturation of the bump‐on‐tail instability leads to phase space vortex formation with consequent excitation of electrostatic harmonics. Thus it is suggested that observations of electrostatic harmonics in the leading edge of the foreshock would strongly implicate trapping as the saturation mechanism for the bump‐on‐tail instability in that region.