  It is thought that solar energetic ions associated with
coronal/interplanetary shock waves are accelerated to high energies by the
diffusive shock acceleration mechanism. For this mechanism to be efficient,
intense magnetic turbulence is needed in the vicinity of the shock. The
enhanced turbulence upstream of the shock can be produced self-consistently by
the accelerated particles themselves via streaming instability. Comparisons of
quasi-linear-theory-based particle acceleration models that include this
process with observations have not been fully successful so far, which has
motivated the development of acceleration models of a different nature. The aim
of this work is to test how well our self-consistent quasi-linear SOLar
Particle Acceleration in Coronal Shocks (SOLPACS) simulation code, developed
earlier to simulate proton acceleration in coronal shocks, models the particle
foreshock region. We applied SOLPACS to model the energetic storm particle
(ESP) event observed by the STEREO A spacecraft on November 10, 2012. In the
simulations, all but one main input parameter of SOLPACS are fixed by the
in-situ plasma measurements from the spacecraft. By comparing a simulated
proton energy spectrum at the shock with the observed one, we were able to fix
the last simulation input parameter related to the efficiency of particle
injection to the acceleration process. A subsequent comparison of simulated
proton time-intensity profiles in a number of energy channels with the observed
ones shows a very good correspondence throughout the upstream region.
