Ultra-long simulations of collisionless relativistic shocks in front-comoving frame: evidence for a steady state and its properties
前向共动坐标系下超长时无碰撞相对论激波模拟:稳态存在的证据及其性质
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 approaches an asymptotic, time-independent state. In the downstream region, the steady state depends only on the upstream temperature at the injection boundary and does not depend on a particular numerical realization. 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. We also find 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.
展开 ▾创新性地使用前向共动坐标系与移动壁边界,将模拟时长延长至以往的四倍以上,首次证实下游稳态存在且不依赖于数值实现;同时揭示下游磁场呈独立演化的孤子状结构,费米型粒子加速在约十倍均分能量处停滞,未形成理论预期的幂律谱。
相对论无碰撞激波是解释伽马射线暴余辉等天体物理辐射的关键场所。早期PIC模拟(如 Chang+ 2008, Spitkovsky 2008)确立了Weibel不稳定性产生磁场和粒子加速的基本框架,但受限于计算时长,未能触及稳态。迄今最长的下游共动系模拟 Grošelj+ 2024 持续至约 26000 ω_p^{-1},仍观察到缓慢演化。本研究引入前向共动坐标系配合动壁边界,将模拟推进至超过 10^5 ω_p^{-1},首次发现下游区域(主要辐射区)的磁场分布与粒子谱趋于渐近稳态,证实传统纯等离子体激波模型可存在稳态解。然而,所得稳态参数(磁场强度、粒子加速能量)与GRB余辉多波段观测的推断值(Derishev & Piran 2021)存在显著差距,提示现有Weibel激波模型或需纳入辐射反馈等额外物理。前向共动系方法大幅降低了长期模拟的计算成本,为未来在辐射损失时标上自洽研究激波粒子谱和磁场衰变开辟了道路。
预印本 2026-07-15 · 收录 2026-07-18