托卡马克等离子的弛豫态分析.ppt

O U T L I N E 引言 应用变分原理得到体系的Euler_Lagrange 方程 Euler_Lagrange方程 等离子体电流与环向磁场的解析解 及其分析 Euler-Lagrange 方程的自恰解 主要理论结果与对NSTX弛豫态的分析 结论与讨论 引言 __等离子体弛豫行为 托卡马克等离子体是个复杂的非线性体系。实验表明在很多情况下，它将趋向于发展到一个 ‘self- consistent’ natural profile。而且在某些条件下会突变到另外的状态 [1-3]. 这意味着托卡马克等离子体可能存在着某种弛豫机制。 弛豫理论研究的成功之例：泰勒应用最小能量原理研究理想情况下等离子体的完全的弛豫，J/B比值空间均匀，并成功地预言了Z－Pinch等离子体的关键性质。 某些物理研究必须考虑弛豫性质，比如 DC-HICD (helicity injection current drive)，其理论基础即是建立在等离子体弛豫理论上。 应用最小耗散原理，包括磁螺旋平衡和能量平衡作为限制条件，研究任意纵横比托卡马克等离子体的弛豫态特性 The total energy dissipation : The magnetic helicity balance condition : The energy balance condition : We have the variational functional: Variational Functional and the Euler_Lagrange Equation (2) and are Lagrangian multiplies. Taking the first variation, we have: Variational Functional and the Euler_Lagrange Equation (3) Natural boundary condition Redefining and as and ，we obtain the equation and boundary condition as following: Equation Boundary condition Variational Functional and the Euler_Lagrange Equation (4) The cylindrical coordinates for Tokamak-axi-symmetric system The minor cross section is assumed a rectangle The plasma resistivity is assumed a homogeneous scalar Variational Functional and the Euler_Lagrange Equation (5) 得到柱坐标下的欧拉_拉格朗日方程 Equation is homogenized when we write is as Y satisfies the homogenous equation related to (1) as: and boundary condition Now we solve equation (3) under boundary condition (4). (Ref. C. Zhang et al. Nuclear Fusion, 2001) We take Y as the sum of two parts (5) Analytical Solution of the Euler_LagrangeEquation for Plasma Current Density (2)? For ， with um2 = ?2-(k1m)2 for 1?m ? n, um2 = (k1m)2 - ?2 for mn. In which k1m = x1m/ r00 , is the mth zero point of Bes