Saturated magnetic field amplification at supernova shocks

Abstract

Cosmic-ray streaming instabilities at supernova shocks are discussed in the\nquasilinear diffusion formalism which takes into account the feedback effect of\nwave growth on the cosmic ray streaming motion. In particular, the nonresonant\ninstability that leads to magnetic field amplification in the short wavelength\nregime is considered. The linear growth rate is calculated using kinetic theory\nfor a streaming distribution. We show that the nonresonant instability is\nactually driven by a compensating current in the background plasma. The\nnonresonant instability can develop into a nonlinear regime generating\nturbulence. The saturation of the amplified magnetic fields due to particle\ndiffusion in the turbulence is derived analytically. It is shown that the\nevolution of parallel and perpendicular cosmic-ray pressures is predominantly\ndetermined by nonresonant diffusion. However, the saturation is determined by\nresonant diffusion which tends to reduce the streaming motion through pitch\nangle scattering. The saturated level can exceed the mean background magnetic\nfield.\n