SCELT (Symbolic Computation aided Eigenvalue and Linear code for Tokamaks): A full MHD eigenvalue code in toroidal geometry developed with the use of a symbolic computation technique

In this work, we report the construction of an eigenvalue computer code largely in C++ language, SCELT, by using the symbolic computation technique for the first time to solve the linearized single fluid magnetohydrodynamic (MHD) eigenvalue problem in toroidal geometry. A symbolic vector analysis module is developed to function the automatic derivation of the tedious linearized full MHD equations in the magnetic flux coordinate system. Furthermore, another module is developed to implement the automatic numerical discretization. These two modules dramatically reduce the human workload and obviate the possibility of a mistake during code development. The tools provide a means of constructing matrices from differential operations and can be used for (generalized) linear problems, such as source driven and eigenvalue problems. Demo uses of both the symbolic vector analysis module and automatic numerical discretization module, such as the Poisson equation and tokamak equilibrium equation, are presented to demonstrate their advantages and potential broad applications. The full MHD eigenvalue code developed with these two modules is verified by the internal kink mode and tearing mode tests.

本研究报道了一款主要基于C++语言开发的特征值计算程序SCELT，首次采用符号计算技术求解环形几何下的线性化单流体磁流体动力学（Magnetohydrodynamic, MHD）特征值问题。我们开发了符号矢量分析模块，用于自动推导磁通量坐标系下冗长的线性化完整MHD方程；此外还搭建了另一模块以实现自动数值离散化。这两个模块大幅降低了人工开发工作量，并消除了代码编写过程中人为出错的可能。该工具可通过微分运算构建矩阵，适用于（广义）线性问题，例如源驱动问题与特征值问题。文中展示了符号矢量分析模块与自动数值离散化模块的演示应用案例，包括泊松方程与托卡马克平衡方程，以体现其优势与潜在的广泛应用场景。基于这两个模块开发的完整MHD特征值程序，通过内扭模与撕裂模测试完成了验证。