Context. It is thought that solar energetic ions associated with coronal and 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.

Aims. Our aim 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.

Methods. We applied SOLPACS to model the energetic storm particle (ESP) event observed by the STEREO A spacecraft on November 10, 2012.

Results. 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.

Conclusions. Our results strongly support the quasi-linear description of the foreshock region.