4 Conclusion

We have considered the Alfvén-wave transmission and test-particle acceleration problem (Vainio & Schlickeiser 1998, 1999) for shocks with anisotropic pressure. In our model, the firehose factors on both sides of the shock are predetermined parameters. For a detailed analysis, we chose a model with isotropic downstream pressure, and upstream pressure anisotropy that is bounded by the requirement of firehose stability. We showed that the pressure anisotropies have only a minor effect on wave transmission and particle acceleration for plasmas with low $\beta$. However, plasmas with upstream $\beta _{\parallel }\sim 2$ and $\beta _{\perp }\ll \beta _{\parallel }$ seem to develop qualitative effects on both the wave transmission and particle acceleration relative to the isotropic-pressure case. Our study revealed the capability of weak shocks propagating into such plasmas to accelerate particles effectively by creating a large change in the average scattering-center speed across the shock though the increase of the phase speed of low-frequency waves across the shock. Plasmas with large values of beta, $\beta _{\parallel }\gg 1$, can not develop very large anisotropies ( $\beta _{\perp }\ll \beta _{\parallel }$) without becoming firehose unstable, which again prevents large deviations in our model between the anisotropic and isotropic cases except for the weakest shocks with M<M_isotr(r=1). The low-Mach-number shocks are weakly entropy increasing in the ideal gas model and should, therefore, be studied more carefully using kinetic analysis. In conclusion, the results of our study point out the importance of kinetic analysis of up- and downstream plasma to fully understand the physics of shock acceleration.

Acknowledgements

R. V. acknowledges the financial support of the Academy of Finland (project # 46331) and the PLATON Network (EC contract # HPRN-CT-2000-00153).