轴对称磁静平衡态Ⅰ.微变换方法

轴对称磁静平衡态被广泛用来描述不同尺度的恒星大气结构。对这类平衡态,可引入所谓磁通量函数来描述磁场,它满足一变系数、非线性椭圆型方程。迄今为止,人们只就线性情况的某些特例给出该方程的解析解;对较为复杂的情况,特别是非线性情况,还未找到有效的办法进行解析处理。本文将应用微变换方法求上述变系数、非线性方程的相似解,并给出普遍结果。有关特解的具体形式及对太阳大气的应用将在本系列的下几篇论文中另作讨论。 

Axisymmetric Magnetostatic Equilibria I. Method of Infinitesimal Transformations

Axisymmetric magnetostatic equilibria have been widely applied to discribing stellar atmospheric structures of various scales.The so-called magnetic flux function may be introduced for such equilibria to represent the magnetic field,and it satisfies a nonlinear,elliptic equation with variable coefficients.Analytic solutions have been given only for certain spe-cialications of this equation so far,whereas in more complicated cases,especially nonlinear cases,no effective approach is found for analytic treatment.This paper uses the so-called method of infinitesimal transformations to derive similarity solutions of the nonlinear elliptic equation with variable coefficients,mentioned above,and presents some general results.The concrete forms of the solutions and their application to the solar atmosphere is relegated to the subsequent papers of this series.