Calculation of the vacuum Green's function valid even for high toroidal mode numbers in tokamaks
Calculation of the vacuum Green's function valid even for high toroidal mode numbers in tokamaks
复制标题
DOI：
10.1016/j.jcp.2006.06.025
复制
发表时间：
2007
期刊：
影响因子：
--
通讯作者：
M. Chance;A. Turnbull;P. Snyder
中科院分区：
文献类型：
--
作者：
M. Chance;A. Turnbull;P. Snyder
目前的评估绿色函数用于轴对称几何形状的真空计算中的磁标量位已被发现是不足的，即使是适度高，n，环模数。这与gato、pest和其他磁流体稳定性程序计算的边缘局部剥离-膨胀模式有关。不足之处是由于损失的数值精度所产生的向上递归关系用于产生的功能从值在n=0从完整的椭圆积分的第一和第二种。为了改善这一点，一个直接集成的积分表示的功能制作，以实现必要的高精度适度高的模式数，适当考虑到奇异行为的被积函数。在更高的模式数的损失的数值精度，由于取消从振荡行为的被积函数是进一步避免明智地变形到复平面的积分轮廓，以获得一个新的积分表示的绿色的功能。通过结合使用这些技术，可以实现接近机器的精度（大约12-16位数）。相关的勒让德函数的关系，以及一种新的积分表示这些也被描述。
The present evaluation of the Green’s function used for the magnetic scalar potential in vacuum calculations for axisymmetric geometry has been found to be deficient even for moderately high, n, the toroidal mode number. This is relevant to the edge localized peeling-ballooning modes calculated by gato, pest and other mhd stability codes. The deficiency was due to the loss of numerical precision arising from the upward recursion relation used for generating the functions from the values at n=0 from the complete elliptic integrals of the first and second kinds. To ameliorate this, a direct integration of the integral representation of the function is crafted to achieve the necessary high accuracy for moderately high mode numbers, with due consideration to the singular behavior of the integrand involved. At higher mode numbers the loss of numerical precision due to cancellations from the oscillatory behavior of the integrand is further avoided by judiciously deforming the integration contour into the complex plane to obtain a new integral representation for the Green’s function. Near machine precision, roughly 12–16 digits, can be achieved by using a combination of these techniques. The relation to the associated Legendre functions, as well as a novel integral representation of these are also described.