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arXiv 0812.3993astro-ph
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非线性扩散激波加速的稳态解

Steady-State Solutions in Nonlinear Diffusive Shock Acceleration

B. Reville, J. G. Kirk, P. Duffy

摘要:

非线性扩散激波加速方程的定态解在宇宙线加速理论中起着重要的作用。它们的存在通常要求允许一部分加速粒子从系统中逃逸。因为散射平均自由程被认为是能量的递增函数,所以这个条件通常被实现为能量空间中的上限-一旦粒子的能量超过这个极限,则允许粒子从系统的任何部分逃逸。然而,由于加速粒子是负责大幅放大的环境磁场在上游的冲击波阵面的区域,我们研究了另一种方法,其中粒子逃逸的空间边界。我们使用一个简单的迭代方案,构造固定的数值解耦合动力学和流体动力学方程。对于适合超新星遗迹的参数,我们找到了稳定的解决方案,有效的加速时,逃逸边界被放置在增长和平流的强烈驱动的非共振波的平衡点。我们还提出了能量依赖的分布函数接近的能量,它切断-诊断,原则上是可以观察到的。

英文摘要:

Stationary solutions to the equations of non-linear diffusive shock acceleration play a fundamental role in the theory of cosmic-ray acceleration. Their existence usually requires that a fraction of the accelerated particles be allowed to escape from the system. Because the scattering mean-free-path is thought to be an increasing function of energy, this condition is conventionally implemented as an upper cut-off in energy space -- particles are then permitted to escape from any part of the system, once their energy exceeds this limit. However, because accelerated particles are responsible for substantial amplification of the ambient magnetic field in a region upstream of the shock front, we examine an alternative approach in which particles escape over a spatial boundary. We use a simple iterative scheme that constructs stationary numerical solutions to the coupled kinetic and hydrodynamic equations. For parameters appropriate for supernova remnants, we find stationary solutions with efficient acceleration when the escape boundary is placed at the point where growth and advection of strongly driven non-resonant waves are in balance. We also present the energy dependence of the distribution function close to the energy where it cuts off - a diagnostic that is in principle accessible to observation.

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