The structure of simulated quasi-parallel collisionless shock waves can be characterized by multiple scale lengths upon which the ion heating depends. The upstream wavelength follows closely that of the phase-standing whistler mode wave. The scale length of the principal magnetic field jump is approximately equal to or somewhat greater than the upstream wavelength. Thus, the upstream wavelength is the dispersive scale length which governs the magnetic field structure of the shock. For Alfv¿n Mach numbers MA>2.5, large-amplitude waves are generated in the downstream region. Wavelengths of these downstream waves are many times longer than the upstream waves and tend to increase with increasing Alfv¿n Mach number. The scale length of the principal plasma density jump, which gives us the viscous scale length, is comparable to the downstream wavelength. The ion heating is seen to occur in two stages. The first-stage heating occurs upstream of the principal density ramp and can be characterized by a power law equation of state with an index much greater than the adiabatic value of 5/3 and increases with increasing Alfv¿n Mach number.

The second-stage heating occurs at and downstream of the principal density jump and can be characterized by a power law index on the order of the adiabatic value. The results show that the ion heating occurs mainly around the principle density jump near the center of the shock transition region, while the increase in entropy takes place mainly in the upstream side of the shock transition region. This result is consistent with the suggestion that the ion heating is a consequence of the nonadiabatic scattering of the ions through the magnetic field structures of the shock including the upstream waves. ¿ Copyright 1990 by the American Geophysical Union