Cosmic-ray current-driven instabilities-revisiting environmental conditions

Abstract

The growth of magnetohydrodynamic fluctuations relevant to cosmic-ray (CR) confinement in and near their sources, and the effects of local plasma conditions is revisited. We consider cases where CRs penetrate a medium which may contain a fraction of neutral particles, and explore the possible effects of high-order CR anisotropies. An algorithm for calculating the dispersion relation for arbitrary distributions, and anisotropies is presented, and a general solution for power-law cosmic-ray distributions is provided. Implications for the resulting instabilities near to strong Galactic CR sources are discussed. We argue that CR streaming in weakly ionized plasmas eliminates the need for the existence of an evanescent band in the dispersion relation, a conclusion which may be confirmed by gamma-ray observations. The necessity for additional multiscale numerical simulations is highlighted, as understanding the non-linear behaviour is crucial.