Current-drive theory in the presence of fluctuations

我们从理论上研究了由于电和磁波动存在的射频（rf）波的电流驱动，得到了以下结果：从存在波动的相对论性Fokker-Planck方程出发，利用直接相互作用近似（DIA），推导出了集成平均分布函数的方程，该方程可作为开发射频电流驱动计算程序的基本方程。我们发现，与直接求解集成平均分布函数的方程相比，使用伴随方程可以使我们得到更解析的方法。利用该伴随方法，明确地计算了碰撞频率、波动幅度和相关长度等不同值下rf驱动电流密度的均方宽度和径向分布。给出了射频驱动电流密度的径向扩散方程及其扩散系数的解析表达式。显式计算结果表明，用伴随方程和径向扩散方程得到的电流分布在感兴趣的参数范围内吻合良好。在1-3的公式中使用了空间局部（空间马尔可夫）近似。为了研究空间非局部效应，我们在不使用局部近似的情况下对理论进行了重新表述，并推导了射频驱动电流密度的积分-微分方程。在较宽的参数范围内，空间非局域性对射频驱动电流密度分布的影响不显著。利用子系综平均的思想代替传统系综平均，对DIA进行了扩展，并将其应用于射频电流驱动理论。在这个公式中，我们可以把粒子在波动的电场和磁场中的俘获效应考虑进去。

We have theoretically studied the current drive due to radio-frequency (rf) waves in the presence of electric and magnetic fluctuations and have obtained the following results:1. Starting from the relativistic Fokker-Planck equation in the presence of fluctuations and using the direct-interaction approximation (DIA), we have derived the equation for the ensemble-averaged distribution function, which can be used as a basic equation in developing the computational code for the rf current drive.2. We have found that the use of adjoint equation leads us to the more analytical method compared with directly solving the equation for the ensemble-averaged distribution function. By means of this adjoint method, the mean-squared width and the radial profile of rf-driven current density are explicitly calculated for various values of the collision frequency, and the amplitude and correlation lengths of fluctuations.3. The radial diffusion equation for the rf-driven current density and the analytic expression for the diffusion coefficient in this equation are presented. The explicitly calculated results show that the current profiles obtained by using the adjoint equation and the radial diffusion equation agree well in the range of interesting parameters.4. The spatially local (spatial Markovian) approximation is used in the formulations of 1-3. In order to study the spatial nonlocal effect, we have reformulated the theory without the use of local approximation, and have derived the integro-differential equation for the rf-driven current density. The effect of spatial nonlocality on the profiles of rf-driven current density is show to be not significant in the wide range of parameters.5. Using the idea of the subensemble averaged instead of conventional ensemble average, we have extended the DIA, and have applied to the rf-current-drive theory. I n th i s formulation, we can incorporate the effect of particle trapping in the fluctuating electric and magnetic filed.