Anomalous effects on classical and neoclassical transport

我们用统计动力学中的重整化方法研究了涨落引起的等离子体输运，得到了以下结果：1.利用泛函积分方法，研究了随机磁场中的粒子扩散。在直接相互作用近似(DIA)的框架下，利用波动磁场上动力学方程的泛函表示的系综平均和模拟库仑碰撞的随机变量，导出了系综平均分布函数和对无限小外部扰动的响应函数的闭合方程组。从这些方程中可以发现，跨场扩散系数可以通过求解非线性常微分方程组来获得。2.从理论上研究了涨落对Bootstr…的影响托卡马克中有更多AP电流。基于系综平均分布函数和响应函数的一组封闭方程，我们导出了自举电流密度的径向扩散方程。由涨落引起的反常径向扩散以及有限香蕉宽度效应显著地修正了磁轴附近的常规自举电流。它还表明，这种修改导致了完全自举托卡马克的可能性。用类似的方法得到了射频驱动电流密度的径向扩散方程。3.将DIA应用于次系综平均函数，而不是传统的系综平均函数，我们得到了次系综平均分布函数及其响应函数的闭合方程组。这种闭合理论通过引入粒子轨迹效应，近似地提供了拉格朗日描述。通过求解一个非线性常微分方程组和一个确定的粒子轨迹方程，计算了湍流等离子体中的流动扩散系数。较少

We have investigated the plasma transport due to fluctuations using a renormalization technique of statistical dynamics and obtained the following results :1.Employing a functional integral method, we have studied the particle diffusion in a stochastic magnetic field. With the ensemble average of a functional representation to a kinetic equation over the fluctuating magnetic field and the random variables modeling the Coulomb collisions, a closed set of equations for an ensemble-averaged distribution function and a response function to an infinitesimal external perturbation is derived within the framework of the direct-interaction approximation (DIA). It is found from these equations that the cross-field diffusion coefficients can be obtained by solving nonlinear ordinary differential equations. We have explicitly calculated diffusion coefficients for various parameters in the shearless and sheared configurations.2.We have theoretically studied the effect of fluctuations on the bootstr … More ap current in tokamaks. Based upon a closed set of equations for the ensemble-averaged distribution function and the response function, we have derived a radial diffusion equation for the bootstrap current density. The anomalous radial diffusion due to fluctuations as well as the finite-banana width effect is shown to significantly modify the conventional bootstrap current near the magnetic axis. It is also shown that this modification leads to the possibility of a completely bootstrapped tokamak. The radial diffusion equation for the rf-driven current density is also obtained using the similar method.3.Applying the DIA to subensemble-averaged functions instead of conventional ensemble-averaged ones, we have derived a closed set of equations for a subensemble-averaged distribution function and its response function. This closure theory approximately provides the Lagrangian description by incorporating particle trajectory effect. The running diffusion coefficient in turbulent plasma is shown to be calculated by solving a nonlinear ordinary differential equation together with an equation for deterministic particle trajectories. Less