Non-relativistic shocks accelerate ions to highly relativistic energies provided that the orientation of the magnetic field is closely aligned with the shock normal (quasi-parallel shock configuration). In contrast, quasi-perpendicular shocks do not efficiently accelerate ions. We model this obliquity-dependent acceleration process in a spherically expanding blast wave setup with the moving-mesh code {sc arepo} for different magnetic field morphologies, ranging from homogeneous to turbulent configurations. A Sedov-Taylor explosion in a homogeneous magnetic field generates an oblate ellipsoidal shock surface due to the slower propagating blast wave in the direction of the magnetic field. This is because of the efficient cosmic ray (CR) production in the quasi-parallel polar cap regions, which softens the equation of state and increases the compressibility of the post-shock gas. We find that the solution remains self-similar because the ellipticity of the propagating blast wave stays constant in time. This enables us to derive an effective ratio of specific heats for a composite of thermal gas and CRs as a function of the maximum acceleration efficiency. We finally discuss the behavior of supernova remnants expanding into a turbulent magnetic field with varying coherence lengths. For a maximum CR acceleration efficiency of about 15 per cent at quasi-parallel shocks (as suggested by kinetic plasma simulations), we find an average efficiency of about 5 per cent, independent of the assumed magnetic coherence length.
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