Cosmic ray ( CR ) spectra , both measured upon their arrival at the Earth ’ s atmosphere and inferred from the emission in supernova remnants ( SNRs ) , appear to be significantly steeper than the “ standard ” diffusive shock acceleration ( DSA ) theory predicts .
Although the reconstruction of the primary spectra introduces an additional steepening due to propagation effects , there is a growing consensus in the CR community that these corrections fall short to explain the newest high-precision data .
Using 2D hybrid simulations , we investigate a new mechanism that may steepen the spectrum during the acceleration in SNR shocks .

Most of the DSA treatments are limited to homogeneous shock environments .
To investigate whether inhomogeneity effects can produce the necessary extra steepening , we assume that the magnetic field changes its angle along the shock front .
The rationale behind this approach is the strong dependence of the DSA efficiency upon the field angle , \theta _ { \mathrm { Bn } } .
Our results show that the variation of shock obliquity along its face results in a noticeable steepening of the DSA spectrum .
Compared to simulations of quasi-parallel shocks , 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 SNR conditions are briefly considered .