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

The correlated studies discussed here used high-quality and frequent in sit u measurements provided by the Wind spacecraft to investigate the propertie s of the foreshock plasma (measured by Wind/3DPlasma) and the enhanced plas ma waves (detected by Wind/WAVES). A time-of-flight electron distribution m odel was developed in a generalized Lorentzian plasma using experimental da ta. The Wind/3DP results show that typical foreshock electron distributions are well approximated by this model, although discernible "bumps" in distr ibutions that may be unstable are not often observed or resolved by the 3DP instrument. We used unstable distributions described by the model to initi alize our study. In addition to verifying the interdependence of dispersion , cutoff velocity and beam density that was previously found in a Maxwellia n beam-plasma system, our dispersion solutions demonstrate how the dispersi on topology and wave spectral bandwidths evolve as a consequence of wave mo difications of time-of-flight distributions. By identifying sections of dis tributions that interact with each of the growing and damping branches, we analyzed the role played by nonthermal electrons in the evolution of the in stability. Our results complement those from previous investigations and, m ore importantly, provide information about the linear behavior of the syste m 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 foresh ock nonthermal plasma are a significant factor in producing the observed el ectromagnetic emissions.