A&A 378, 309-315 (2001)

DOI: 10.1051/0004-6361:20011191

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

**R. Vainio**

^{1, 2}and R. Schlickeiser^{2}^{1}Space Research Laboratory, Department of Physics, 20014 Turku University, Finland

^{2}Insitut für Theoretische Physik, Lehrstuhl IV: Weltraum- und Astrophysik, Ruhr-Universität Bochum, 44780 Bochum, Germany

(Received 16 February 2001 / Accepted 27 August 2001 )

** Abstract **

Alfvén-wave transmission through a parallel shock in case of an
anisotropic gas pressure (
) is considered from
the point of view of test particle acceleration in such shock waves. Treating
the shock's gas compression ratio and the firehose factor,
, on both sides of the shock as given
parameters, we calculate the wave-transmission coefficients for
circularly-polarized Alfvén waves of finite amplitude. We also give an equation
for the shock's gas compression ratio including the effects of pressure
anisotropy and waves. We study wave transmission and test-particle acceleration
in a model, where the downstream plasma is isotropic and the upstream plasma
remains stable against the firehose instability (). The results can
be arranged in a following manner with respect to the upstream parallel plasma
beta,
(with *B*_{0}
being the ordered magnetic field): (i) for shocks with
the results for particle acceleration are only quantitatively different for
anisotropic upstream plasma; (ii) for
, large
anisotropies alter the wave-transmission and particle acceleration picture
completely relative to the isotropic case yielding much harder energy spectra
with spectral indices
for all shocks with 1< *r*< 4; (iii) for
very hot and firehose-stable plasmas, the qualitative changes in particle
acceleration due to pressure anisotropies are limited to the weakest shocks and,
thus, should be analyzed in a non-linear manner to confirm the results.

**Key words:**acceleration of particles

**--**shock waves

**--**turbulence

Offprint request: R. Vainio, ravainio@utu.fi

**©**

*ESO 2001*