Abstract Prescriptions for electron injection into the diffusive shock acceleration process are required in many practical considerations of cosmic-ray astrophysics, particularly in modeling of the synchrotron emission of astrophysical sources. In particle-in-cell simulations of quasi-parallel magnetized collisionless shocks, we analyse the evolution of particle spectra. We find that in the later stages of shock evolution, the initially strong suprathermal part in the ion spectra fades, thus leaving the spectra composed of a Maxwellian and a power law. Once the electron and ion spectra flatten and become parallel, we find that the amounts of cosmic ray ions and electrons become similar. We make the step towards relating the micro and macro-scale physics by applying this injection rule to Blasi’s semi-analytical model of non-linear diffusive shock acceleration, in order to obtain the particle spectra and electron-to-proton ratio K ep at high energies. By using shock jump conditions that include the electron heating, we find K ep as a function of Mach number. For Mach number ∼ 100, our model finely reproduce the typically observed ratio for Galactic cosmic-rays K ep ∼ 1:100 in the test particle regime.

中文翻译：

---

非线性扩散冲击加速度：电子注入的秘诀

摘要 在宇宙射线天体物理学的许多实际考虑中，特别是在天体物理源的同步加速器发射的建模中，需要将电子注入到扩散激波加速过程中。在准平行磁化无碰撞冲击的细胞内粒子模拟中，我们分析了粒子光谱的演变。我们发现在激波演化的后期，离子谱中最初强的超热部分逐渐消失，从而留下由麦克斯韦和幂律组成的谱。一旦电子和离子光谱变平并变得平行，我们发现宇宙射线离子和电子的数量变得相似。我们通过将此注入规则应用于 Blasi 非线性扩散激波加速度的半解析模型，向关联微观和宏观尺度物理迈出了一步，以获得高粒子谱和电子质子比 K ep能量。通过使用包括电子加热在内的激波跳跃条件，我们发现 K ep 作为马赫数的函数。对于马赫数 ∼ 100，我们的模型精细地再现了在测试粒子状态下银河宇宙射线 K ep ∼ 1:100 的典型观察比率。