### Abstract:

The structure of the quasi-parallel collisionless shock wave is studied via a numerical simulation model. The model is compared to observations and theoretical predictions and within its limitations appears to reproduce the true shock structure reasonably well. Three electron equations of state and their effects on the simulation are examined. It is found that only the isotropic-adiabatic electron equation of state yields acceptable results in the simulation at high Mach numbers. The scale lengths of the shock are measured, normalized by the natural scale lengths of the plasma, and plotted as a function of the Alfven Mach number. It is found that the wavelength of the upstream waves follows that predicted for a phase standing whistler quite well and the scalelength of the jump in the magnitude of the magnetic field is generally greater than, but approximately equal to this wavelength. For Alfven Mach numbers $M\sb{A} >$ 2.5, waves are generated in the downstream region. Their wavelength and the scale length of the plasma transition are larger than the natural scale lengths of the plasma. The ion heating is seen to occur in two stages. In the first stage which occurs upstream of the principal shock ramp, the heating can be characterized by a polytropic power law equation of state with an exponent much greater than the isentropic-adiabatic rate of $\gamma$ = 5/3. The second stage of heating which occurs from the principal shock ramp to the downstream region is characterized by an exponent on the order of the isentropic-adiabatic rate. 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. It is suggested that the ion heating is a consequence of the non-adiabatic scattering of the ions through the magnetic field of the shock and its upstream precursor wave.