I. Shock amplitude relations

We derive relations between the pressure, density, magnetic field strength, velocity, and other quantities across shocks for the case of longitudinal tube waves. Due to the extreme coupling of the Rankine-Hugoniot relations for this type of waves, these relationships cannot be given separately as function of a given shock strength Ms, contrary to the case of acoustic waves. In case of weak shocks, however, those relationships can successfully be decoupled and evaluated. In this paper, the analytic expansion for these amplitude relations are given. We also compare our analytical results with numerical results for shocks of small and moderately large strength. Comparisons are given for cases with different values of plasma-β.