Electron kinetics in collisionless shock waves

We study the kinetic model of the formation of the energy spectrum of nonthermal electrons near the front of a quasilongitudinal, supercritical, collisionless shock wave. Nonresonant interactions of the electrons and the fluctuations generated by kinetic instabilities of the ions in the transition region inside the shock front play the main role in the heating and preacceleration of electrons. We calculate the electron energy spectrum in the vicinity of the shock wave and show that the heating and preacceleration of electrons occur on a scale of the order of several hundred ion inertial lengths in the vicinity of the viscous discontinuity. Although the electron distribution function is significantly nonequilibrium near the shock front, its low-energy part can be approximated by a Maxwellian distribution. The effective electron temperature T _eff ² behind the front, obtained in this manner, increases with the Mach number of the shock wave slower than it would if it followed the Hugoniot adiabat. We determine the condition under which the electron heating is ineffective but the electrons are effectively accelerated to high energies. The high-energy asymptotic behavior of the distribution function is that of a power law, with the exponent determined by the total compression ratio of the plasma, as in the case of acceleration by the first-order Fermi mechanism. The model is used to describe the case (important for applications) of acceleration of electrons by shock waves with large total Mach numbers, with the structure of these waves modified by the nonlinear interaction of nonthermal ions and consisting of an extended prefront with a smooth variation of the macroscopic parameters and a viscous discontinuity in speed with a moderate value of the Mach number. Zh. éksp. Teor. Fiz. 115, 846–864 (March 1999)