如果要產生核融合反應，首先就必須提高物質的溫度，使原子核和電子分開，處於這種狀態的物質稱為「電漿」，再克服原子核間相斥的電磁力來進行核融合。目前的困境是如何維持並控制達成核融合反應的溫度以及密度，以實現可以自給能量的能源。托克馬克是一種用強磁場束縛電漿引發核融合反應的大型反應器。在托克瑪克實驗，了解電漿的粒子以及熱量的傳輸是很重要的，因此發展了所謂的傳輸運算程式。NCLASS是可以用在任何傳輸運算程式的輔助程式，主要用來計算新古典傳輸係數。新古典傳輸指的是在類似托克瑪克的螺旋狀磁場結構下的傳輸，通常會略大於古典的傳輸係數。基本上我們只要提供NCLASS一組磁面平均平行磁場的黏滯力的解析表示式，他就能很快地計算出新古典傳輸係數。有另外一個輔助程式NEO也是在計算新古典傳輸係數，與NCLASS不同的是他採用數值解漂移動力學方程(drift kinetic equation)，雖然得出結果的時間相對長卻是相對準的。
由於在束縛粒子的蕉形軌道區中有限的縱橫比(finite aspect ratio)的情況，NCLASS所得出的新古典傳輸係數與NEO得出的結果差了15-20%，因此我們想要改善NCLASS的準確度，以實現又快又準的計算出新古典傳輸係數。原始的NCLASS採用的是代入近似到L=1(第2項)勒壤得多項式的碰撞運算子得出的漂移動力學方程的解析解，並使用一特別的減法技巧，直接由解出的分佈函數得出磁面平均平行磁場的黏滯力，此解不包含背景場粒子的貢獻。為了改善NCLASS的準確度，我們代入近似到L=3(第4項)勒壤得多項式的碰撞運算子得出的漂移動力學方程的解析解，發展延伸的減法技巧，直接由解出的分佈函數得出改善的磁面平均平行磁場的黏滯力，發現其黏滯係數包含背景場粒子的貢獻。
Taguchi也在2013年做了這個項目，但他得出改善的磁面平均平行磁場的黏滯力的方法與我們不同，但我們得到和Taguchi一樣的結果，這也就是說我們發展的延伸的減法技巧是可行的。另外我們也提供了可以用來改善NCLASS在束縛粒子的蕉形軌道區中有限縱橫比的情況下的準確度的黏滯係數之核心被積分式KaB。

NCLASS [Houlberg, W. A., et al. Physics of Plasmas 4.9 (1997): 3230-3242.] is a code-package for calculating neoclassical transport quantities from the given analytical expressions of the flux-surface averaged parallel viscosity for interpretative simulation of tokamak experiments. There exists 15-20\% discrepancies in the transport coefficients when they are compared with the numerical results in the banana regime in finite aspect ratio in tokamaks [Belli, E. A., and J. Candy. Plasma Physics and Controlled Fusion 50.9 (2008): 095010.]. To improve the accuracy of the viscosity used in NCLASS, we extend the direct calculation method using the subtraction technique in [Hirshman, S. P., and D. J. Sigmar. Nuclear Fusion 21.9 (1981): 1079.] which is different from that used in [Taguchi, M. Physics of Plasmas 21.5 (2014): 052504.]. We obtain the same solution as Taguchi which has contributions from the field particle response to the viscosity. To improve NCLASS code, we provide an expression of the kernel KaB in the viscosity integrand that contains the field particle response.

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