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Cosmic ray (CR) spectra, both measured upon their arrival at the Earth'satmosphere and inferred from the emission in supernova remnants (SNRs), appearto be significantly steeper than the "standard" diffusive shock acceleration(DSA) theory predicts. Although the reconstruction of the primary spectraintroduces an additional steepening due to propagation effects, there is agrowing consensus in the CR community that these corrections fall short toexplain the newest high-precision data. Using 2D hybrid simulations, weinvestigate a new mechanism that may steepen the spectrum during theacceleration in SNR shocks.  Most of the DSA treatments are limited to homogeneous shock environments. Toinvestigate whether inhomogeneity effects can produce the necessary extrasteepening, we assume that the magnetic field changes its angle along the shockfront. The rationale behind this approach is the strong dependence of the DSAefficiency upon the field angle, $\theta_\mathrm{Bn}$. Our results show thatthe variation of shock obliquity along its face results in a noticeablesteepening of the DSA spectrum. Compared to simulations of quasi-parallelshocks, we observe an increase of the spectral index by $\Delta q=0.1-0.15$.Possible extrapolation of the limited simulation results to more realistic SNRconditions are briefly considered.

Steepening of Cosmic Ray Spectra in Shocks with Varying Magnetic Field Direction