Finite Banana-Width Effect on Neoclassical Transport Theory

本研究项目的目的是通过放宽ρ_p/L≪1和ρ_p/γ≪1的限制来扩展传统的新古典输运理论，其中ρ_p为极向拉莫尔半径，L为梯度尺度长度，γ为局部小半径。有限香蕉宽度效应修正了传统的新古典无碰撞磁轴输运理论。提出了轴对称磁场中磁轴的新古典输运理论。利用这一理论，给出了磁轴上新经典输运系数与传统输运系数之间的简单插值公式，并推导了输运系数的解析表达式。由聚变产生的α粒子引起的自举电流也得到了。此外，还证明了有限香蕉宽度效应导致托卡马克仅由自举电流维持的概念。研究了这种完全自举托卡马克的性质。研究了在陡坡磁场中离子的能量通量。在均匀磁场中，垂直能量通量与密度和压力分布非局部相关。用一个简单的密度和压力剖面模型显式地计算了这个通量，并得到了它与ρ/L的关系，其中ρ为拉莫尔半径。在类似的方法中，导出了高原区径向能量通量的非局部输运方程。这些经典和新经典输运方程对任意ρ/L和ρ_p/L均有效。为了估计径向异常输运对沿磁场的电流的影响，研究了分布函数系综-波动平均的动力学方程。

The purpose of this research project is to extend the conventional neoclassical transport theory by relaxing the constraints ρ_p/L ≪ 1 and ρ_p/γ ≪ 1, where ρ_p is the poloidal Larmor radius, L is the gradient scale length and γ is the local minor radius.1. The finite banana-width effect modifies the conventional neoclassical transport theory around the magnetic axis in the collisionless regime. The neoclassical transport theory on the magnetic axis is proposed in an axisymmetric magnetic field. Using this theory, a simple interpolation formula between the neoclassical transport coefficients on the magnetic axis and the conventional ones is presented, and the analytic expressions for the transport coefficients are derived. The bootstrap current due to the fusion-produced alpha particles is also obtained. In addition, it is shown that the finite banana-width effect leads to the concept of a tokamak sustained only by the bootstrap current. The properties of this completely bootstrapped tokamak are also studied.2. An ion energy flux across a magnetic field in a presence of steep gradient has been studied. In a uniform magnetic field, the perpendicular energy flux is found to be nonlocally related to the density and pressure profiles. This flux is explicitly calculated for a simple density and pressure profile model and its dependency on ρ/L is obtained, where ρ is the Larmor radius. In the similar method, the nonlocal transport equation for the radial energy flux is derived in the plateau regime. These classical and neoclassical transport equations are valid for the arbitrary values of ρ/L and ρ_p/L.3. A kinetic equation for a distribution function ensemble-averaged over fluctuations has been studied in order to estimate the effect of radial anomalous transport on the current along the magnetic field.