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On modelling Coulomb collisions in toroidal plasmas with relevance for orbit averaged Monte Carlo operators

机译：关于与轨道平均蒙特卡洛算子相关的环形等离子体中的库仑碰撞建模

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摘要

2D Monte Carlo operators describing the Coulomb collisions in pitch angle and radius are studied, which are applicable to axisymmetric toroidal plasmas. The coupling between the spatial and velocity coordinates in toroidal plasmas requires the spatial Jacobian to be included in the collision operator, which is essential to solve the Fokker-Planck equation correctly. The sharp variation of diffusion at the trapped-passing boundary for a tokamak gives rise to differences in the de-trapping probability of the particles into co- and counter-passing orbits, which also produces asymmetry in the distribution function. This problem is solved by using standard and non-standard drift terms, and by symmetrizing the transport across the trapped-passing boundary. Collision operators that relax the distribution function to a prescribed density profile have been developed for simplified models. To obtain converged results, different models are developed and tested that are applicable to diffusion problems with discontinuous diffusion coefficients.
机译：研究了在俯仰角和半径上描述库仑碰撞的二维蒙特卡洛算子，该算子适用于轴对称环形等离子体。环形等离子体中空间坐标和速度坐标之间的耦合要求将空间雅可比行列包括在碰撞算子中，这对于正确求解Fokker-Planck方程至关重要。托卡马克在俘获通过边界处扩散的急剧变化引起了粒子进入共同通过和反向通过轨道的去俘获概率的差异，这也产生了分布函数的不对称性。通过使用标准和非标准漂移项，以及通过跨过陷阱边界的传输对称化，可以解决此问题。对于简化模型，已经开发了将分配函数放宽到指定密度分布的碰撞算子。为了获得收敛的结果，开发并测试了适用于具有不连续扩散系数的扩散问题的不同模型。

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