﻿ 非线性无力场的Low-Lou解法探讨 On the Low-Lou Approach for the Nonlinear Force-Free Magnetic Field

Vol.05 No.02(2016), Article ID:17494,6 pages
10.12677/AAM.2016.52022

On the Low-Lou Approach for the Nonlinear Force-Free Magnetic Field

Jian Qin, Yiwei Li

School of Applied Sciences, Taiyuan University of Science and Technology, Taiyuan Shanxi

Received: Apr. 15th, 2016; accepted: May 2nd, 2016; published: May 5th, 2016

ABSTRACT

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.

Keywords:Nonlinear Differential Equations, Shooting Method, Force-Free Field

1. 引言

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2. 参数打靶法

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3. 算例及分析

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Figure 1. Variation of the error function in the shooting range of 10−1~104 for a2

Table 1. Eigenvalues defined by Low-Lou equation in the range of 0.1~10,000

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Table 2. Force-free and divergence-free merits for the Low-Lou solutions

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4. 探讨与展望

On the Low-Lou Approach for the Nonlinear Force-Free Magnetic Field[J]. 应用数学进展, 2016, 05(02): 166-171. http://dx.doi.org/10.12677/AAM.2016.52022

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