Ion equation of state in quasi-parallel shocks - A simulation result

Ion equation of state in the quasi-parallel collisionless shock is deduced from simulation results. The simulations were performed for theta(bn) = 10 deg, beta = 0.5 and M sub A in the range from 1.2 to 8, where M sub A is the Alfven Mach number, beta is the upstream ratio of plasma pressure to magnetic pressure, and theta(bn) is the angle between the shock normal and the upstream magnetic field. The equation of state can be approximated by a power law with different exponents in the upstream and downstream sides of the shock transition region. The exponent in the upstream side of the transition region is much greater than the adiabatic value of 5/3 and increases with M sub A. The exponent in the downstream side of the transition region is slightly less than 5/3. The results show that ion heating in the quasi-parallel shock is highly nonadiabatic with a large increase in entropy and in temperature ratio in the upstream side of the transition region, while the heating is highly isentropic with a large increase in temperature difference across the principal density jump in the downstream side of the transition region.