Ultra-long simulations of collisionless relativistic shocks in front-comoving frame: evidence for a steady state and its properties
Abstract
We present a series of unprecedently long 2D3V PIC simulations of unmagnetized relativistic e−e+-pair shocks performed in a front-comoving frame. By implementing a moving-wall boundary condition in the downstream together with continuous injection at the upstream boundary, we maintain a fixed simulation domain size, opening the way to perform substantially longer simulations. Our longest runs extend beyond 100000 ωp−1, exceeding the duration of the previously published simulations by a factor of several. Across a diverse set of simulations --- varying upstream/downstream lengths, transverse sizes, and particle-per-cell counts --- we find strong evidence that the shock, {modelled for a long-time in the front-comoving frame,} approaches an asymptotic, time-independent state. In the downstream region, the steady state depends only on the upstream temperature at the injection boundary and {remains the same if we change the downstream and upstream lengths.} The upstream precursor evolves slower and retains a dependence on the simulation's upstream length, that may be of minor observational consequence, since radiation from astrophysical shocks predominantly originates from the downstream region. {Our simulations also indicate} that Fermi-type acceleration is limited in energy and a true power-law tail never forms. Another important finding is that the downstream magnetic field has a soliton-like structure, where individual magnetic domains evolve independently, each comprising a compact, highly magnetized core embedded within an extended, weakly magnetized region. The magnetic-field distribution around the centers of these spots has approximately Lorentzian profile.
Versions
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BibTeX
@misc{garasev2026ultralong,
title = {{Ultra-long simulations of collisionless relativistic shocks in front-comoving frame: evidence for a steady state and its properties}},
author = {Mikhail Garasev and Evgeny Derishev},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2607.14235},
eprint = {2607.14235},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.14235},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Ultra-long simulations of collisionless relativistic shocks in front-comoving frame: evidence for a steady state and its properties
AU - Mikhail Garasev
AU - Evgeny Derishev
PY - 2026
DA - 2026/10/30
PB - arXiv
DO - 10.48550/arxiv.2607.14235
UR - https://arxiv.org/abs/2607.14235
AB - We present a series of unprecedently long 2D3V PIC simulations of unmagnetized relativistic e^−e^+-pair shocks performed in a front-comoving frame. By implementing a moving-wall boundary condition in the downstream together with continuous injection at the upstream boundary, we maintain a fixed simulation domain size, opening the way to perform substantially longer simulations. Our longest runs extend beyond 100000 ω_p^−1, exceeding the duration of the previously published simulations by a factor of several. Across a diverse set of simulations --- varying upstream/downstream lengths, transverse sizes, and particle-per-cell counts --- we find strong evidence that the shock, {modelled for a long-time in the front-comoving frame,} approaches an asymptotic, time-independent state. In the downstream region, the steady state depends only on the upstream temperature at the injection boundary and {remains the same if we change the downstream and upstream lengths.} The upstream precursor evolves slower and retains a dependence on the simulation's upstream length, that may be of minor observational consequence, since radiation from astrophysical shocks predominantly originates from the downstream region. {Our simulations also indicate} that Fermi-type acceleration is limited in energy and a true power-law tail never forms. Another important finding is that the downstream magnetic field has a soliton-like structure, where individual magnetic domains evolve independently, each comprising a compact, highly magnetized core embedded within an extended, weakly magnetized region. The magnetic-field distribution around the centers of these spots has approximately Lorentzian profile.
ER -