在Cap-cyclide坐标下,基于B.Bernstein能量原理,利用Wangerin函数表示非圆截面等离子体的稳定解析解,而Wangerin函数的稳定性直接影响等离子体的稳定性.为此,通过Wangerin函数Nnm(v)的数值计算和数值可视化,探索其收敛性和稳定性.首先结合第一类完全椭圆积分的迭代算法和Jacobi椭圆函数的恒等式,通过计算机编程实现Wangerin函数Nnm(v)的数值计算,然后基于数值可视化方法对数值计算结果进行分析,得到它的一个重要性质:当模数k趋近于1或-1(|k |＜1)时,Wangerin函数Nnm(v)趋于稳定.%The Wangerin function was used to indicate the stable analytic results of non-circular toroidal plasma based on B. Bernstein energy principle with Cap-cyclide coordinates,and the stability of Wangerin function directly influenced that of plasma. Therefore, the convergence and stability properties were discussed by the numerical calculation and visualization of Wangerin function,firstly,the numerical calculation results were analyzed, first by use of incrative method with the first kind of complete elliptic integral and I-dentical equations of Jacobi elliptie functions to achieve the numerical solution of Wangerin function, then with numerical visualization method. Thus there come to be an important property of Wangerin function: the closer the modulo gets to 1 (or - 1), the more stable the Wangerin function is.
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