【作者】 刘燕；

【导师】 龚学余；

【作者基本信息】 南华大学 ， 核技术及应用， 2007， 硕士

【摘要】 对托卡马克的理论和实验研究是当前受控核聚变研究的中心问题。对托卡马克中的电流驱动的数值计算研究也已成为当今数值模拟研究的一个焦点。特别是近几十年来,人们对离子回旋频率范围内的快波电流驱动的研究投入了大量的精力.本文主要对托卡马克中的快波电流驱动进行了较系统的理论研究,并确定了全波计算的数值计算方法。用全波方法研究环形对称托卡马克中的离子回旋频率范围内(ICRF)的快波电流驱动(FWCD)问题,研究中考虑了有限拉莫尔半径(FLR)效应和平行色散,建立起了全波计算的物理模型,得到了有限拉莫尔半径假设下的热等离子体介电张量和便于计算机编程计算的全波方程的具体形式,最终确定了研究托卡马克中离子回旋频率范围内的快波电流驱动的数值计算方法:在托卡马克位形下,采用Boozer坐标系即( e? r ,e?η,e?ζ), e?r沿径向, e?ζ沿磁场方向,( e? r ,e?η,e?ζ)三者正交呈右手螺旋。选择此坐标系可以使得平行波数k //在磁面上有尽可能少的变量。对麦克斯韦全波方程应用迦辽金弱变分变换,使对变量两次求旋的二阶微分方程变为对变量一次求旋的一阶积分-微分弱变分全波方程。对积分-微分弱变分全波方程方程的求解,在径向r上采用三次哈密顿有限元方法,在极向θ上应用快速傅立叶变换和卷积定理,主要通过这两种数值计算方法把积分-微分弱变分全波方程化为一个关于电场强度的大型带状线性方程组。大型带状线性方程组的求解应用了多种先进的非对称求解理论,采用了动态内存加载以及符号预排序和分析等先进技术,运用这些方法编写的求解大型带状线性方程组的程序包可以较高效、准确地求解关于电场强度的线性方程组。综合运用上述各种数值计算方法,我们编写了研究托卡马克中快波电流驱动的相关程序,并得到等离子体与波的基本参数(安全因子、电子温度、密度等)的径向分布,及平行波数、色散函数的径向分布和平行方向电场强度的初步结果。以上所得计算结果,都与TORIC code所得到的结果进行了对比,发现输出结果的分布与参考资料基本一致,这说明我们目前研究快波电流驱动的思路和运用的数学处理方法是正确的。程序还在进一步升级和完善中,目前所做的工作为进一步研究快波电流驱动问题奠定了坚实的基础。更多还原

【Abstract】 The investigation on radio frequency current drive has become one of the focus about numerical alanalysis on tokamaks . In the past decades ,considerable effort has been devoted to the numerical modeling of fast wave in the range of ion cyclotron wave curren drive.In this paper , The full wave numerical method is developed for analyzing fast wave current drive in the range of ion cyclotron waves in tokamak plasmas,taking into account finite larmor radius effects and parallel dispersion . The physical model ,the dielectric tensors on the assumption of Finite larmor radius effect and the form of full wave be used for computer simulation are developed . Finally,the numerical methods are confirmed as following :In tokamak coordinate ,we choose Boozer coordinate for analysis which can confirm parallel wave number k // has less variation on a magnetic surface.The first step towards the numerical solution of the wave equations is to put them into the Galerkin weak-variational form,which puts the full wave equation into a integral-differential full wave equation .The numerical solution for the integral-differential full wave equation based on Fast Fourier Thansform(FFT)in the poloidal angleθand cubic finite element method (FEM)in the radial variable r.for solving unsymmetric sparse linear systems, Ax=b, using the Unsymmetric MultiFrontal method. It uses dynamic memory allocation, and has a symbolic preordering and analysis phase that also reports the upper bounds on the nonzeros in L and U, flop count, and memory usage in the numeric phase. It can be used for real and complex matrices, rectangular and square, and both non-singular and singular.Using all of the numerical methods ,the code for analyzing fast wave current and solution the integro-differential full wave eqations is developed too .The actual code can give results as following: Distribution of local safety factor q, temperature of electron te, density of electron ne in direction r, parallel wave number k // , dispersion function and its derivative in direction r,and Distribution of the zero FLR part of dielectric tensor R ,L? ,S? ,and second FLR part of dielectric tensorρ(2),λ(2)and parallel E as Eζ.All of the parameters and results are similar to those obtained with TORIC code ,so ,it seems to that all of the numerical method for analyzing fast wave current drive are right .At present ,the code is being upgraded all the same .All of the work will contribute to further study of fast wave current drive。更多还原