Diffusive shock acceleration in supernova remnants: On the validity of the Bohm limit

A lot of theoretical effort has been achieved in cosmic ray scattering theory during the previous years. On the other hand several authors employed the so-called Bohm limit to replace cosmic ray diffusion coefficients in the diffusive transport equation for describing particle acceleration in supernove remnants and in other environments. In this article it is shown how the Bohm limit can be derived from cosmic ray diffusion theory by assuming a strong turbulent magnetic field component. Also a test-particle code is employed to explore the regimes for which the Bohm limit is valid and for which not. These results are important to distinguish between the parameter regimes for which the Bohm limit is valid and for which traditional diffusion theories have to be applied.