Surrogate approximation of the Grad–Shafranov free boundary problem via stochastic collocation on sparse grids
Surrogate approximation of the Grad–Shafranov free boundary problem via stochastic collocation on sparse grids
复制标题
通过稀疏网格上的随机配置对 Grad-Shafranov 自由边界问题进行代理逼近
DOI：
10.1016/j.jcp.2021.110699
复制
发表时间：
2022
影响因子：
4.1
通讯作者：
Sánchez-Vizuet, Tonatiuh
中科院分区：
文献类型：
--
作者：
Elman, Howard C.;Liang, Jiaxing;Sánchez-Vizuet, Tonatiuh
在磁约束聚变装置中，等离子体的平衡构型由流体中的流体静压与由外部线圈阵列和等离子体本身产生的磁力之间的平衡决定。等离子体的位置是未知的，必须作为自由边界问题的解来获得。确定组合磁场行为的偏微分方程取决于一组物理参数（线圈的位置、通过线圈的电流强度、磁导率等）。这些都是不确定和可变的。限制区域又是这些随机参数的函数。在这项工作中，我们认为通过外部线圈的电流强度的变化作为不确定性的主要来源。这导致尺寸等于电抗器中线圈数量的参数空间。借助建立在参数空间稀疏网格上的代理函数，采用蒙特卡罗方法研究了参数随机性对等离子体边界重要特征的影响，如边界的位置、边界的撞击点和三角形和延伸率等。替代函数的使用减少了蒙特卡罗模拟所需的时间，减少的因子范围在7到30之间。
In magnetic confinement fusion devices, the equilibrium configuration of a plasma is determined by the balance between the hydrostatic pressure in the fluid and the magnetic forces generated by an array of external coils and the plasma itself. The location of the plasma is not knowna prioriand must be obtained as the solution to a free boundary problem. The partial differential equation that determines the behavior of the combined magnetic field depends on a set of physical parameters (location of the coils, intensity of the electric currents going through them, magnetic permeability, etc.) that are subject to uncertainty and variability. The confinement region is in turn a function of these stochastic parameters as well. In this work, we consider variations on the current intensities running through the external coils as the dominant source of uncertainty. This leads to a parameter space of dimension equal to the number of coils in the reactor. With the aid of a surrogate function built on a sparse grid in parameter space, a Monte Carlo strategy is used to explore the effect that stochasticity in the parameters has on important features of the plasma boundary such as the location of thex-point, the strike points, and shaping attributes such as triangularity and elongation. The use of the surrogate function reduces the time required for the Monte Carlo simulations by factors that range between 7 and over 30.