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arXiv 1503.06312physics.plasm-phphysics.comp-ph
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等离子体动力学理论的高斯径向基函数方法

The Gaussian Radial Basis Function Method for Plasma Kinetic Theory

Eero Hirvijoki, Jeff Candy, Emily Belli, Ola Embréus

摘要:

磁化等离子体的基本宏观描述是由非线性平方反比力Fokker-Planck碰撞算子补充的Vlasov方程[Rosenbluth等人,物理修订版,107,1957]。Vlasov部分描述了六维相空间中的平流,而碰撞算子涉及摩擦和扩散系数,这些系数是粒子分布函数的加权速度空间积分。Fokker-Planck碰撞算子是一个积分-微分双线性算子,并且该算子的数值离散化远非平凡。在这封信中,我们描述了一种新的方法来离散整个动力学系统的基础上扩展高斯径向基函数(RBFs)。这种方法特别适合于处理碰撞算子,因为摩擦和扩散系数可以解析计算。虽然RBF方法被认为是一个强大的计划,分散的多维数据的插值,高斯径向基函数也有一个深刻的物理解释为局部热力学平衡。在这封信中,我们概述了一般的理论,强调连接等离子体流体理论,也给二维和三维数值解的非线性福克-普朗克方程。预计新方法将在天体物理和实验室等离子体中得到广泛的应用。

英文摘要:

A fundamental macroscopic description of a magnetized plasma is the Vlasov equation supplemented by the nonlinear inverse-square force Fokker-Planck collision operator [Rosenbluth et al., Phys. Rev., 107, 1957]. The Vlasov part describes advection in a six-dimensional phase space whereas the collision operator involves friction and diffusion coefficients that are weighted velocity-space integrals of the particle distribution function. The Fokker-Planck collision operator is an integro-differential, bilinear operator, and numerical discretization of the operator is far from trivial. In this letter, we describe a new approach to discretize the entire kinetic system based on an expansion in Gaussian Radial Basis functions (RBFs). This approach is particularly well-suited to treat the collision operator because the friction and diffusion coefficients can be analytically calculated. Although the RBF method is known to be a powerful scheme for the interpolation of scattered multidimensional data, Gaussian RBFs also have a deep physical interpretation as local thermodynamic equilibria. In this letter we outline the general theory, highlight the connection to plasma fluid theories, and also give 2D and 3D numerical solutions of the nonlinear Fokker-Planck equation. A broad spectrum of applications for the new method is anticipated in both astrophysical and laboratory plasmas.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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