Charged particel transport in interstellar plasmas: Improved theory for scattering of cosmic rays in turbulent fields

宇宙射线、带电尘埃粒子和湍流磁场是星际介质的重要组成部分。从磁约束聚变研究到天体物理学，理解和预测带电粒子在湍流介质中的传输是许多相关学科的关键挑战。在天体物理学中，它是宇宙射线在星际磁场中的散射、加速和空间扩散。这个提议的目的有两个：首先，我们想要研究快速粒子在宇宙磁场中的输运，应用最近在基于渗流理论的托卡马克物理背景下发展起来的标度概念。这是因为尽管湍流尺度非常不同，但垂直于背景场的散射机制基本相同。其次，我们想要发展一个改进的部分湍流磁场中快速带电粒子的弱湍流输运理论，该理论避免了通常对粒子轨道的拟线性近似，并适当地考虑了最近的非线性改进。采用了磁湍流的三个统计性质：(1)准定常湍流，(2)有限湍流解相关时间的存在，(3)空间均匀湍流。与标度理论不同，弱湍流输运理论通常利用Corsin独立性假设，允许用两个二阶关联函数的乘积来表示四阶关联函数。这一建议的两个中心目标是(1)分别从弱湍流和标度输运理论计算宇宙线散射率，以及(2)通过比较它们来验证或反驳宇宙湍流磁场的科尔辛假设的有效性。这样改进的输运理论将被应用于特定的星际现象，如宇宙线粒子在引导磁场存在大尺度平行空间梯度时的扩散激波加速。

Cosmic rays, charged dust particles and turbulent magnetic fields are important constituents of the interstellar medium. Understanding and predicting the transport of charged particles in turbulent media is a key challenge in a number of related disciplines, ranging from magnetic confinement fusion research to astrophysics. In astrophysics, it is the scattering, acceleration and spatial diffusion of cosmic rays in interstellar magnetic fields. The purpose of this proposal is two-fold:First, we want to investigate the transport of fast particles in cosmic magnetic fields, applying scaling concepts which were developed recently in the context of tokamak physics based on the percolation theory. This can be done since although the turbulent scales are extremely different, the scattering mechanisms perpendicular to the background field are basically the same.Secondly, we want to develop an improved weak turbulence transport theory of fast charged particles in a partially turbulent magnetic field, that avoids the usually made quasilinear approximation to the particle orbits, and properly takes into account recent nonlinear improvements. Three statistical properties of the magnetic turbulence are adopted: (1) quasi-stationary turbulence, (2) the existence of a finite turbulence decorrelation time, and (3) spatially homogenous turbulence. In contrast to the scaling theory, weak turbulence transport theories often make use of the Corrsin independence hypothesis allowing one to express a fourth order correlation function in terms of the product of two second order correlation functions. Two central goals of this proposal are (1) the calculation of cosmic ray scattering rates from weak turbulence and scaling transport theories, respectively, and (2) their comparison to verify or disprove the validity of the Corrsin hypothesis for cosmic turbulent magnetic fields. The so improved transport theory will be applied to selected interstellar phenomena such as the diffusive shock acceleration of cosmic ray particles in the presence of large scale parallel spatial gradients of the guide magnetic field.