MACH - a computer code for solution of the poloidal asymmetry eigenvalue problem in tokamaks

Abstract
Evaluation of the poloidal dependence of the plasma density involves solving the equation for momentum balance along the magnetic field. This is transformed into an eigenvalue equation of the Mathieu type with an extra damping term. The method presented here for determination of the appropriate eigenvalue is much faster than traditional matrix determinant methods.

Title of program: MACH
Catalogue Id: ACPY_v1_0

Nature of problem
The ions in a tokamak plasma gyrate around and stream along magnetic field lines that encircle the torus in both the poloidal (short- circumference) and toroidal (long circumference) directions. In the infinite aspect ratio limit, the geometry is cylindrical and the plasma ion density is poloidally symmetric, but at finite aspect ratios the symmetry is broken. Given a poloidal "Mach number" that is related to the plasma rotation velocity, the poloidal variation of the plasma density is determine ...

Versions of this program held in the CPC repository in Mendeley Data
ACPY_v1_0; MACH; 10.1016/0010-4655(94)90077-9

This program has been imported from the CPC Program Library held at Queen's University Belfast (1969-2019)

摘要
针对等离子体密度极向相关性的评估，需求解沿磁场的动量平衡方程。该方程可转化为带有额外阻尼项的马蒂厄（Mathieu）型本征值方程。本文提出的适用于求解该本征值的方法，相较于传统矩阵行列式法具有更高的运算效率。

程序名称：MACH
目录编号：ACPY_v1_0

问题概述
托卡马克（tokamak）等离子体中的离子会沿环绕环面（torus）的磁力线做回旋运动与平行流动，该磁力线同时沿极向（poloidal，短周长方向）与环向（toroidal，长周长方向）环绕环面。当纵比（aspect ratio）趋近于无穷大时，等离子体区域几何近似为圆柱型，等离子体离子密度呈极向对称；而当纵比为有限值时，该对称性将被破坏。在给定与等离子体旋转速度相关的极向马赫数（Mach number）后，即可求解等离子体密度的极向变化规律……

该程序在Mendeley数据平台的CPC程序库中留存的版本为：ACPY_v1_0; MACH; 10.1016/0010-4655(94)90077-9

本程序源自贝尔法斯特女王大学托管的CPC程序库（1969-2019年）