Neoclassical transport in strong gradient regions of large aspect ratio tokamaks

We present a new neoclassical transport model for large aspect ratio tokamaks where the gradient scale lengths are of the size of the poloidal gyroradius. Previous work on neoclassical transport across transport barriers assumed large density and potential gradients but a small temperature gradient, or neglected the gradient of the mean parallel flow. Using large aspect ratio and low collisionality expansions, we relax these restrictive assumptions. We define a new set of variables based on conserved quantities, which simplifies the drift kinetic equation whilst keeping strong gradients, and derive equations describing the transport of particles, parallel momentum and energy by ions in the banana regime. The poloidally varying parts of density and electric potential are included. Studying contributions from both passing and trapped particles, we show that the resulting transport is dominated by trapped particles. We find that a non-zero neoclassical particle flux requires parallel momentum input which could be provided through interaction with turbulence or impurities. We derive upper and lower bounds for the energy flux across a transport barrier in both temperature and density and present example profiles and fluxes.我们提出了一种适用于大纵横比托卡马克（tokamak）的新型新经典输运模型，该模型中梯度特征尺度与极向回旋半径（poloidal gyroradius）相当。此前针对输运垒（transport barrier）区域的新经典输运研究，通常假设存在较大的密度与电势梯度，但温度梯度较小，或是忽略了平均平行流的梯度。我们通过大纵横比与低碰撞性（low collisionality）展开近似，放宽了上述限制性假设。我们基于守恒量定义了一组新变量，在保留强梯度的前提下简化了漂移动理学方程（drift kinetic equation），并推导了香蕉区（banana regime）内离子对粒子、平行动量与能量的输运方程。模型同时纳入了密度与电势的极向变化分量。通过分析通行粒子与捕获粒子（trapped particle）的输运贡献，我们发现最终的输运过程由捕获粒子主导。我们发现，非零的新经典粒子通量需要平行动量输入，该输入可通过与湍流（turbulence）或杂质（impurity）的相互作用获得。我们推导了温度与密度维度下输运垒两侧能量通量的上下界，并给出了示例剖面与通量分布。