A GENERALIZED DIFFUSION TENSOR FOR FULLY ANISOTROPIC DIFFUSION OF ENERGETIC PARTICLES IN THE HELIOSPHERIC MAGNETIC FIELD
A GENERALIZED DIFFUSION TENSOR FOR FULLY ANISOTROPIC DIFFUSION OF ENERGETIC PARTICLES IN THE HELIOSPHERIC MAGNETIC FIELD
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DOI：
10.1088/0004-637x/750/2/108
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发表时间：
2012-02
期刊：
影响因子：
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通讯作者：
F. Effenberger;H. Fichtner;K. Scherer;Stephan Barra;J. Kleimann;R. D. Strauss
中科院分区：
文献类型：
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作者：
F. Effenberger;H. Fichtner;K. Scherer;Stephan Barra;J. Kleimann;R. D. Strauss
在最一般的情况下，宇宙射线在湍流磁场中的空间扩散可以是完全各向异性的，即，必须在局部场对齐框架中区分三个扩散轴。我们重新检查扩散张量从局部框架到全局框架的变换，其中通常制定并求解高能粒子的帕克输运方程。特别是，我们推广了变换公式，以允许明确选择两个主要局部垂直扩散轴。这种概括包括各向同性垂直扩散特殊情况下的“传统”扩散张量。对于局部框架，我们描述了选择 Frenet-Serret 三面体的动机，这与固有磁场几何形状有关。我们直接比较两种日光层磁场配置（即混合 Fisk 场和 Parker 场）的新旧张量单元。随后，我们研究了银河质子调制的标准三维模型中扩散张量的不同公式的重要性。为此，我们利用数字代码来评估相当于帕克输运方程的随机微分方程组，并呈现所得的调制光谱。对于低于几百 MeV 的能量，基于新张量公式计算出的微分通量与使用“传统”张量公式（仅对各向同性垂直扩散有效）获得的微分通量的偏差高达 60%，具体取决于日心距离。
The spatial diffusion of cosmic rays in turbulent magnetic fields can, in the most general case, be fully anisotropic, i.e., one has to distinguish three diffusion axes in a local, field-aligned frame. We reexamine the transformation for the diffusion tensor from this local to a global frame, in which the Parker transport equation for energetic particles is usually formulated and solved. Particularly, we generalize the transformation formulae to allow for an explicit choice of two principal local perpendicular diffusion axes. This generalization includes the “traditional” diffusion tensor in the special case of isotropic perpendicular diffusion. For the local frame, we describe the motivation for the choice of the Frenet–Serret trihedron, which is related to the intrinsic magnetic field geometry. We directly compare the old and the new tensor elements for two heliospheric magnetic field configurations, namely the hybrid Fisk and Parker fields. Subsequently, we examine the significance of the different formulations for the diffusion tensor in a standard three-dimensional model for the modulation of galactic protons. For this, we utilize a numerical code to evaluate a system of stochastic differential equations equivalent to the Parker transport equation and present the resulting modulated spectra. The computed differential fluxes based on the new tensor formulation deviate from those obtained with the “traditional” one (only valid for isotropic perpendicular diffusion) by up to 60% for energies below a few hundred MeV depending on heliocentric distance.