Self-consistent Alfven-wave transmission and test-particle acceleration atparallel shocks

The transmission of Alfven waves at parallel shocks is treated self-consist ently, i.e., taking the pressure and energy flux exerted by the waves into account when determining the shock's gas compression ratio. The resulting t est-particle acceleration and transport parameters at the shock are shown t o be functions of five parameters: the Alfvenic Mach number of the shock, t he upstream plasma beta, and the cross helicity, magnetic amplitude, and po wer-spectral index of the upstream waves. In a large region of parameter sp ace, the scattering-center compression ratio is significantly larger than t he gas compression ratio. For some conditions, it may get very large values that result in an extremely hard test-particle-energy spectrum of the cosm ic-rays accelerated at the shock. This result is qualitatively the same as that obtained by the same authors under the "test-wave" approach, i.e., ass uming that the waves have no impact on the shock's dynamics. However, the p resent analysis gives limits to the application of the previous results, an d widens the scope of the previous analysis by removing a mathematical sing ularity in shocks with squared Mach number approaching the test-wave-theory gas compression ratio.