【作者】 李杨；

【导师】 高喆； 李继全；

【作者基本信息】 清华大学 ， 核科学与技术， 2018， 博士

【摘要】 托卡马克等离子体的环向旋转可以致稳电阻壁模等磁流体不稳定性,改善托卡马克的约束性能。实验研究发现,等离子体可以在没有外部驱动的情况下自发地旋转起来。这种现象称为自发旋转,目前主要通过平行动量湍流输运的理论来解释。本文主要解析地研究了离子平行动量的湍流输运理论。首先我们在平板位形近似下的研究此问题,主要包括了静电湍流冷流体模型、静电湍流动理学模型和电磁湍流动理学模型三部分。这三个部分组成了一套比较系统和完整的平行动量输运理论框架。然后我们初步地探讨了托卡马克环位形中的动量湍流输运问题。本文主要的工作和结论如下:1.发展了一套研究离子在静电湍流和电磁湍流的平行动量输运问题的动理学方法。证明在平板位形近似下,方程中不存在非共振项,只存在共振通量和共振力。给出了共振通量的物理解释:共振离子受到共振极向力,并在磁场作用下沿着径向漂移,与此同时输运平行动量。共振力则是共振离子和波之间的平行动量交换。并且证明平行动量在共振离子和波之间传递过程中就是守恒的。2.本文还发现了在电磁模型中的磁流体极限下,极向流的影响变得十分重要,直接决定了扰动磁场的加速效率;3.初步推导了环位形模型的动量输运方程。我们发现由于磁场曲率和梯度导致了离子的漂移,会使得压强扰动参与到离子的动量输运中来。此外,气球模的本征模结构可能会导致非共振的通量项和力项。4.在Hasegawa-Wakatani湍流模型下,采用EDQNM方法研究了非线性应力项的效应。在诸如blob等边界强湍流结构中,非线性应力与准线性应力可比。当边界的大尺度湍流结构的径向尺度远大于极向尺度时,非线性应力会导致由边界向内的动量流,并且边界的旋转方向也可能由此而反转。在此过程中,涡量非线性耦合是主导的机制。非线性应力的首阶项仍可以理解为离子动量的对流效应。更多还原

【Abstract】 Toroidal rotation in tokamak plasma can stabilize several MHD instabilities such as RWM,and hence can improve tokamak operation.It is found in experiments that plasmas in tokamak can rotate toroidally without any momentum input.This phenomenon is so-called intrinsic rotation and can be explained by turbulent parallel momentum transport.This dissertation is devoted to investigate turbulent transport of ion parallel momentum analytically.Firstly we studied this problem in slab geometry,including electrostatic cold fluid model,electrostatic kinetic model and electromagnetic kinetic model.Then toroidal geometry is considered preliminarily.Main work and results of this dissertation are summarized as below:1.A kinetic approach is developed for ion parallel momentum equation in both electrostatic and electromagnetic turbulence.It is proved that nonresonant terms are cancelled.A new physical explanation is given for resonant momentum flux: by interacting with waves,resonant ions feel a poloidal force,which make them drift radially with background magnetic field and parallel momentum is transported through magnetic flux surface by resonant ions.Resonant force can be interpreted as a parallel momentum source or exchanging rate of parallel mometum between resonant ions and waves,which is caused by resonance.It is proved that the parallel momentum is conserved;2.It is noted that poloidal flow plays an important role in electromagnetic model.In MHD limit,Lorentz force due to poloidal flow and vector potential acts on ions just like parallel electric field;3.A preliminary model with toroidal geometry is derived.Ions are drifting due to the inhomogeneity of magnetic field,which makes pressure perturbation take part in parallel momentum transport.And the flux and force terms can be nonresonant due to ballooning mode structure.4.Nonlinear stress term is derived using EDQNM method in three dimensional Hasegawa-Wakatani system.It is shown that the nonlinear stress is comparable to quasilinear one in strong turbulence regime such as blobs.And if the radial scale length of large edge coherent structure is bigger than its poloidal scale length,nonlinear residual stress will provide opposite torque to quasilinear one and negative nonlinear diffusivity,which introduces inward momentum flux,so that the rotation in edge region is possibly reversed and momentum is convected into core region.Moreover,it is found that nonlinear coupling for vorticity is the dominating mechanism in parallel momentum transport and the leading term of nonlinear stress can also be interpreted as convection effect.更多还原