Plasma waves in the Earth's electron foreshock: 1. Time‐of‐flight electron distributions in a generalized Lorentzian plasma and dispersion solutions

The correlated studies discussed here used high‐quality and frequent in situ measurements provided by the Wind spacecraft to investigate the properties of the foreshock plasma (measured by Wind/3DPlasma) and the enhanced plasma waves (detected by Wind/WAVES). A time‐of‐flight electron distribution model was developed in a generalized Lorentzian plasma using experimental data. The Wind/3DP results show that typical foreshock electron distributions are well approximated by this model, although discernible “bumps” in distributions that may be unstable are not often observed or resolved by the 3DP instrument. We used unstable distributions described by the model to initialize our study. In addition to verifying the interdependence of dispersion, cutoff velocity and beam density that was previously found in a Maxwellian beam‐plasma system, our dispersion solutions demonstrate how the dispersion topology and wave spectral bandwidths evolve as a consequence of wave modifications of time‐of‐flight distributions. By identifying sections of distributions that interact with each of the growing and damping branches, we analyzed the role played by nonthermal electrons in the evolution of the instability. Our results complement those from previous investigations and, more importantly, provide information about the linear behavior of the system that will enable the simulation studies discussed in our companion paper [ Yin et al. , this issue] to examine possible nonlinear interactions and to address the issue of whether nonlinear wave‐wave interactions in the foreshock nonthermal plasma are a significant factor in producing the observed electromagnetic emissions.