The effect of anisotropic gas pressure on Alfven-wave transmission and test-particle acceleration at parallel shock waves

Alfven-wave transmission through a parallel shock in case of an anisotropic gas pressure (P-parallel to not equal P-perpendicular to) is considered fr om the point of view of test particle acceleration in such shock waves. Tre ating the shock's gas compression ratio and the firehose factor, phi = 1-4 pi (P-parallel to-P-perpendicular to)/B-2, on both sides of the shock as gi ven parameters, we calculate the wave-transmission coefficients for circula rly-polarized Alfven waves of finite amplitude. We also give an equation fo r the shock's gas compression ratio including the effects of pressure aniso tropy and waves. We study wave transmission and test-particle acceleration in a model, where the downstream plasma is isotropic and the upstream plasm a remains stable against the firehose instability (phi >0). The results can be arranged in a following manner with respect to the upstream parallel pl asma beta, beta (parallel to) equivalent to 8 piP(parallel to)/B-0(2) (with B-0 being the ordered magnetic field): (i) for shocks with beta (parallel to) much less than 2 the results for particle acceleration are only quantit atively different for anisotropic upstream plasma; (ii) for beta (parallel to) similar to 2, large anisotropies alter the wave-transmission and partic le acceleration picture completely relative to the isotropic case yielding much harder energy spectra with spectral indices 1 < <Gamma> < 2 for all sh ocks with 1 < r < 4; (iii) for very hot and firehose-stable plasmas, the qu alitative changes in particle acceleration due to pressure anisotropies are limited to the weakest shocks and, thus, should be analyzed in a non-linea r manner to confirm the results.