Analytic distribution functions for an ion plasma crossing an MHD shock
Argelander Institut für Astronomie der Universität Bonn, Abteilung f. Astrophysik und Extraterrestrische Forschung, Auf dem Hügel 71, 53121 Bonn, Germany e-mail: msiewert@astro.uni-bonn.de
Received:
11
August
2006
Accepted:
24
October
2006
Context.Very recently, we derived the Boltzmann equation for a collisionless plasma crossing an MHD shock, such as that found in astrophysical situations.
Aims.We aim to solve the Boltzmann equation analytically, to obtain exact downstream velocity distribution functions for a given upstream distribution function and an MHD compression ratio.
Methods.We apply the general Boltzmann equation to the case of a purely perpendicular shock and solve it using a separation Ansatz.
Results.We obtain a simple, analytical relation between the upstream and downstream velocity distribution functions, which is valid for all physical plasmas. Having obtained the desired relation, we also derive an analytical relation for MHD velocity moments of arbitrary order.
Key words: plasma / shock waves / magnetohydrodynamics (MHD) / Sun: solar wind
© ESO, 2007