  Observations of non-thermal emission from several supernova remnants suggest that magnetic fields close to the blastwave are much stronger than would be naively expected from simple shock compression of the field permeating the interstellar medium (ISM). We investigate in some detail a simple model based on turbulence generation by cosmic-ray pressure gradients. Previously this model was investigated using 2D MHD simulations.   Motivated by the well-known qualitative differences between 2D and 3D turbulence, we further our investigations of this model using both 2D and 3D simulations to study the influence of the dimensionality of the simulations on the field amplification achieved. Further, since the model implies the formation of shocks which can, in principle, be efficiently cooled by collisional cooling we include such cooling in our simulations to ascertain whether it could increase the field amplification achieved. Finally, we examine the influence of different orientations of the magnetic field with respect to the normal of the blastwave.   We find that dimensionality has a slight influence on the overall amplification achieved, but a significant impact on the morphology of the amplified field. Collisional cooling has surprisingly little impact, primarily due to the short time which any element of the ISM resides in the precursor region for supernova blastwaves. Even allowing for a wide range of orientations of the magnetic field, we find that the magnetic field can be expected to be amplified by, on average, at least an order of magnitude in the precursors of supernova blastwaves. 
Cosmic-ray pressure driven magnetic field amplification: dimensional,   radiative and field orientation effects