Avoidance of the harmful effects of runaway electrons (REs) in plasma-terminating disruptions is pivotal in the design of safety systems for magnetic fusion devices. Here, we describe a computationally efficient numerical tool, that allows for self-consistent simulations of plasma cooling and associated RE dynamics during disruptions. It solves flux-surface averaged transport equations for the plasma density, temperature and poloidal flux, using a bounce-averaged kinetic equation to self-consistently provide the electron current, heat, density and RE evolution, as well as the electron distribution function. As an example, we consider disruption scenarios with material injection and compare the electron dynamics resolved with different levels of complexity, from fully kinetic to fluid modes.

Program summary

Program Title: Dream

Developer's repository link: https://github.com/chalmersplasmatheory/DREAM

Licensing provisions: MIT

Programming language: C++, Python

Nature of problem: Self-consistently simulates the plasma evolution in a tokamak disruption, with specific emphasis on runaway electron dynamics. The runaway electrons can be simulated either as a fluid, fully kinetically, or as a mix of the two. Plasma temperature, current density, electric field, ion density and charge states are all evolved self-consistently, where kinetic non-thermal contributions are captured using an orbit-averaged relativistic electron Fokker-Planck equation, which couples to the plasma evolution. In the typical use case, the electrons are represented by two distinct populations: a cold fluid population and a kinetic superthermal population.

Solution method: The system of equations is solved using a standard multidimensional Newton's method. Partial differential equations—most prominently the bounce-averaged Fokker–Planck and current diffusion equations—are discretized using a high-resolution finite volume scheme that preserves density and positivity.

中文翻译：

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梦想：托卡马克破坏失控电子模拟的流体动力学框架

避免失控电子 (RE) 在等离子体终止破坏中的有害影响是磁聚变装置安全系统设计的关键。在这里，我们描述了一种计算效率高的数值工具，它允许在中断期间对等离子体冷却和相关的 RE 动力学进行自洽模拟。它求解等离子体密度、温度和极向通量的通量表面平均传输方程，使用反弹平均动力学方程自洽地提供电子电流、热量、密度和 RE 演化，以及电子分布函数。例如，我们考虑了材料注入的破坏场景，并比较了从完全动力学模式到流体模式的不同复杂程度下解决的电子动力学。

程序概要

节目名称： 梦想

开发者仓库链接： https : //github.com/chalmersplasmatheory/DREAM

许可规定：麻省理工学院

编程语言： C++、Python

问题性质：自洽模拟托卡马克破坏中的等离子体演化，特别强调失控电子动力学。失控的电子可以模拟为流体、完全动力学或两者的混合。等离子体温度、电流密度、电场、离子密度和电荷态都是自洽演化的，其中使用轨道平均相对论电子福克-普朗克方程捕获动力学非热贡献，该方程与等离子体演化耦合。在典型的用例中，电子由两个不同的群体表示：冷流体群体和动力学超热群体。

求解方法：方程组使用标准的多维牛顿法求解。偏微分方程——最突出的是反弹平均福克-普朗克方程和电流扩散方程——使用高分辨率有限体积方案进行离散化，保留密度和正性。