The Heating of Thermal Electrons in Fast Collisionless Shocks: The   Integral Role of Cosmic Rays
  Understanding the heating of electrons to quasi-thermal energies at collisionless shocks has broad implications for plasma astrophysics. It directly impacts the interpretation of X-ray spectra from shocks, is important for understanding how energy is partitioned between the thermal and cosmic ray populations, and provides insight into the structure of the shock itself. In Ghavamian, Laming & Rakowski (2007) we presented observational evidence for an inverse square relation between the electron-to-proton temperature ratio and the shock speed at the outer blast waves of supernova remnants in partially neutral interstellar gas. There we outlined how lower hybrid waves generated in the cosmic ray precursor could produce such a relationship by heating the electrons to a common temperature independent of both shock speed and the strength of the ambient magnetic field. Here we explore the mechanism of lower hybrid wave heating of electrons in more detail. Specifically we examine the growth rate of the lower hybrid waves for both the kinetic (resonant) and reactive cases. We find that only the kinetic case exhibits a growing mode. At low Alfv\'en Mach numbers (~15) the growth of lower hybrid waves can be faster than the magnetic field amplification by modified Alfv\'en waves. 
Cara E. Rakowski (1,2), J. Martin Laming (1) and Parviz Ghavamian (3)   ((1) Naval Research Laboratory (2) National Research...