Electron velocity space hole modes

In space plasmas the local electron distribution is formed by ballistic motion from different source regions. Since electrons with positive and negative parallel (v-parallel) velocities have different sources and experience different interactions with the large-scale electromagnetic fields, the electron distribution function near v-parallel = 0 should possess considerable structure, including the possibility of velocity space holes, i.e., regions where the phase space density is zero, and sharp discontinuities. A particular hole distribution, which may occur upstream of slow shocks in the distant geomagnetic tail, is shown to support a nonstandard plasma wave mode with frequencies between the ion and electron plasma frequencies and parallel phase speed above the ion, but well below the electron, thermal speed. The hole mode can be destabilized by a positive slope in the low parallel velocity electron distribution, and the growth rate is strongly enhanced if the electron parallel temperature exceeds the perpendicular temperature; the mode can also be excited by a hot, fast ion beam. The hole modes exist only for a narrow range of propagation angles about the magnetic field direction.