Shock acceleration with cosmic ray backreaction in high Mach number collisionless shocks.

Understanding collisionless shocks and their role in shaping nonthermal particle distributions remains a central focus of plasma physics. A key question is how nonthermal particles modify shock structures as they are energized via diffusive shock acceleration (DSA). Fully kinetic simulations provide many insights -- including particle injection physics and self-generated electromagnetic turbulence -- but are too computationally expensive to study long-term shock evolution and asymptotic spectra of accelerated cosmic rays. We study the long-term impact of proton acceleration in quasi-parallel shocks using the MHD-PIC method that treats cosmic rays as particles and thermal plasma as a fluid. While this approach is computationally efficient, it requires specifying injection of supra-thermal particles. We present an injection prescription that self-consistently responds to the varying levels of magnetic turbulence near the shock. Simulations with this prescription allow studies of cosmic ray feedback on the shock structure and the subsequent evolution of cosmic ray spectrum. We find that high Mach number shocks produce steeper spectra than expected in standard DSA theory due to the modification of particle transport in strongly amplified magnetic turbulence near the shock. These findings are important for the interpretation of emission spectra from young supernova remnants and transient sources.