Stochastic wave energization in collisionless shocks using PIC simulations

Context. A significant level of conceptual ambiguity persists in the astrophysical literature regarding the term “stochastic acceleration”. While traditionally attributed to diffusive shock acceleration (DSA) mediated by magnetic turbulence, a rapid alternative–stochastic wave energization (SWE)–has been established. The latter is driven by the chaotization of particle trajectories within steep, localized electric-field gradients. Aims. We investigate the physical origin of ion heating at collisionless shocks by testing whether the SWE signatures observed in situ at the bow shock are reproducible in a numerical environment. Our goal is to validate the transition from adiabatic motion to stochastic acceleration under the stochasticity conditions defined by χ = ( m / qB 2 )∇ ⋅ E ⊥ > 1. Methods. Using high-resolution 2D particle-in-cell (PIC) simulations, we were able to resolve the microphysical structure of the shock ramp and downstream turbulence. We performed a detailed correlation analysis between the local plasma temperature and the χ parameter to distinguish between adiabatic and stochastic heating. Results. The simulations reveal a robust positive correlation between the magnitude of χ and the perpendicular ion temperature, T ⊥ . Ion heating occurs preferentially in localized regions where the stochasticity criterion | χ |> 1 is satisfied. Overall, SWE is found to be the dominant energization channel, consistently exceeding electrostatic potential gains, while shock drift acceleration (SDA) is suppressed in this turbulent environment due to the pervasive violation of the first adiabatic invariant. Furthermore, the maximum particle velocity is physically constrained by the local E ⊥ / B speed, consistent with the upper bound on the stochastic energization process. Conclusions. Our findings establish SWE as a fundamental mechanism for ion heating in collisionless shocks. By identifying localized charge non-neutrality (| χ |> 1) as the primary scattering center for stochastic energization, this work effectively replaces traditional diffusive paradigms with a physically grounded framework that has the capacity to reconcile numerical simulations with magnetospheric observations.