Cosmic ray confinement in the diffusion approximation

Confinement of cosmic rays by turbulent magnetic fields and the relation between magnetic and cosmic ray energy densities are investigated. Cosmic rays are assumed to diffuse preferentially along magnetic field lines. The implementation into a nonconservative high-order finite difference code is discussed. By solving an explicitly time-dependent equation for the cosmic ray energy flux, causality is restored and the maximum propagation speed is in this way limited to physically meaningful values. This is particularly useful in order to avoid numerical problems near magnetic Xpoints. It is shown that significant amounts of kinetic energy can be converted into cosmic ray energy via compression. Two processes for magnetic cosmic ray confinement are discussed: (i) enhancement of the residence time of cosmic rays in magnetic structures due to decreased perpendicular diffusion and (ii) the ability of the magnetic tension force to oppose perpendicular expansion of the cosmic ray density. Both processes are verified in the diffusion approximation, but their effect is shown to be weak. In turbulent flows the finite life time of magnetic structures decreases the prominence of cosmic ray confinement even further.