  Diffusive shock acceleration (DSA) of particles at collisionless shocks is
the major accepted paradigm about the origin of cosmic rays (CRs). As a theory
it was developed during the late 1970s in the so-called test-particle case. If
one considers the influence of CR particles at shock structure, then we are
talking about non-linear DSA. We use semi-analytical Blasi's model of
non-linear DSA to obtain non-thermal spectra of both protons and electrons,
starting from their quasi-thermal spectra for which we assumed the
$\kappa$-distribution, a commonly observed distribution in out-of-equilibrium
space plasmas. We treated more carefully than in previous work the jump
conditions at the subshock and included electron heating, resonant and,
additionally, non-resonant magnetic field instabilities produced by CRs in the
precursor. Also, corrections for escaping flux of protons and synchrotron
losses of electrons have been made.
