用变分法近似计算椭球马克中的倾斜模不稳定性

本文利用变分法的基本概念,提出了一种在任意边界形状的情况下近似求解偏微分方程的方法。把求解偏微分方程的问题近似地化为求解常微分方程组的问题。尤其是当边界形状较为复杂时,其优越性更为显著。作者采用这种方法,对大椭圆度的球形马克(Spheromak)中的倾斜模(Tilting Mode)不稳定性进行了研究。得到的结论是:在扁椭球马克中,不会出现倾斜模不稳定性。 关键词：

APPROXIMATE CALCULATION OF THE TILTING MODE INSTABILITY IN AN ELLIPTICAL SPHEROMAK BY VARIATIONAL METHOD

Based on the variational principle, a new method for appoximately solving partial differential equation with an arbitrary boundary shape is proposed. Accordingly, the problem of solving a partial differential equation is reduced to one of solving a series of ordinary differential equations. This method proves to be more powerful when the boundary shape gets complicated. An application is made to the problem of the tilting mode instability for spheromak without restriction in ellipticity. The following physical conclusion is arrived at, namely, the oblate spheromak is better than elongated one as far as suppressing the tilting mode instability is concerned.