  Supernova remnants (SNR) are now widely believed to be a source of cosmic
rays (CRs) up to an energy of 1 PeV. The magnetic fields required to accelerate
CRs to sufficiently high energies need to be much higher than can result from
compression of the circumstellar medium (CSM) by a factor 4, as is the case in
strong shocks. Non-thermal synchrotron maps of these regions indicate that
indeed the magnetic field is much stronger, and for young SNRs has a dominant
radial component while for old SNRs it is mainly toroidal. How these magnetic
fields get enhanced, or why the field orientation is mainly radial for young
remnants, is not yet fully understood. We use an adaptive mesh refinement MHD
code, AMRVAC, to simulate the evolution of supernova remnants and to see if we
can reproduce a mainly radial magnetic field in early stages of evolution. We
follow the evolution of the SNR with three different configurations of the
initial magnetic field in the CSM: an initially mainly toroidal field, a
turbulent magnetic field, and a field parallel to the symmetry axis. Although
for the latter two topologies a significant radial field component arises at
the contact discontinuity due to the Rayleigh-Taylor instability, no radial
component can be seen out to the forward shock. Ideal MHD appears not
sufficient to explain observations. Possibly a higher compression ratio and
additional turbulence due to dominant presence of CRs can help us to better
reproduce the observations in future studies.
