非线性无力场的Low-Lou解法探讨

Abstract

非线性无力场是天体物理中的重要数学模型，它是一套非线性偏微分方程组，经常用于太阳及恒星磁场的理论研究。在轴对称情形下，该方程组归化为满足特定边界条件的带有未知参数的二阶非线性常微分方程，此即所谓的Low-Lou解法。本文提出一种参数打靶法，作为对Low-Lou解法的探讨和补遗，并给出更多可选的数值无力场。 Nonlinear force-free magnetic field is an important mathematical model in astrophysics, which is a set of nonlinear partial differential equations, often used in the theoretical studies of solar and stellar magnetic fields. In the axisymmetric case, this set of partial differential equations is reduced into a nonlinear ordinary differential equation of second order with an unknown parameter, satisfying certain boundary condition. This is the so-called Low-Lou approach of the problem. In this paper, we propose a parametric shooting method as a technical supplement for the Low- Lou approach, offering more optional numerical force-free magnetic fields.