2006/04/24 by Peter A. Becker, P. A. Becker, T. Le +3 · 1 citation
Physics and Astronomy · #Astrophysics and Cosmic Phenomena #Pulsars and Gravitational Waves Research #Solar and Space Plasma Dynamics #astro-ph
paper · pdf · doi:10.1086/505319
published as Astrophys.J.647:539-551,2006 · Accepted for publication in ApJ
arxiv created 2006/04/24 · openalex publication_date 2006/08/10 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/31
Stochastic acceleration of charged particles due to interactions with magnetohydrodynamic (MHD) plasma waves is the dominant process leading to the formation of the high-energy electron and ion distributions in a variety of astrophysical systems. Collisions with the waves influence both the energization and the spatial transport of the particles, and therefore it is important to treat these two aspects of the problem in a self-consistent manner. We solve the representative Fokker-Planck equation to obtain a new, closed-form solution for the time-dependent Green's function describing the acceleration and escape of relativistic particles interacting with Alfvén or fast-mode waves characterized by momentum diffusion coefficient D ( p ) ∝ p q and mean particle escape timescale t esc ( p ) ∝ p q -2 , where p is the particle momentum and q is the power-law index of the MHD wave spectrum. In particular, we obtain solutions for the momentum distribution of the ions in the plasma and also for the momentum distribution of the escaping particles, which may form an energetic outflow. The general features of the solutions are illustrated via examples based on either a Kolmogorov or Kraichnan wave spectrum. The new expressions complement the results obtained by Park and Petrosian, who presented exact solutions for the hard-sphere scattering case ( q = 2) in addition to other scenarios in which the escape timescale has a power-law dependence on the momentum. Our results have direct relevance for models of high-energy radiation and cosmic-ray production in astrophysical environments such as γ-ray bursts, active galaxies, and magnetized coronae around black holes. In particular, we outline an application of the new results to black hole sources that produce outflows of relativistic hadrons, with associated predictions that can be tested using GLAST .