磁流体涡旋动力学的若干研究

项目名称： 磁流体涡旋动力学的若干研究

项目编号： No.10805022

项目类型： 青年科学基金项目

立项/批准年度： 2009

项目学科： 电工技术

项目作者： 徐涛

作者单位： 华中科技大学

项目金额： 23万元

中文摘要： 按照计划，我们的工作有四部分：（1）利用Lagrangian 粒子轨道的方法, 研究了非中心对称超导体中的磁流体涡旋的不稳定性机理, 给出了大涡旋分裂成小涡旋时的定标率，计算了磁流体速度场导致涡旋产生、重组、分裂的的临界条件。（2）研究了磁场陷阱中二元Bose-Einstein凝聚中涡旋的不稳定性机理。（3）对于托卡马克等离子体中的撕裂模，必须满足Navier-Stokes方程，取旋度后，即为涡旋方程。申请者研究了J-TEXT托卡马克等离子体转动与撕裂模刺穿阈值的关系，对J-TEXT托卡马克的撕裂模的演化、锁模、锁模引发的破裂进 行了数值模拟，并与装置上的诊断信号进行了比照。这对于J-TEXT托卡马克的安全运行有重要的意义。（4）申请者深入研究了N序参量的Ginzburg-Landau模型的涡旋结构。对序参量的幅值是个任意变量，势能函数任意的条件下，给出了超导涡旋的环流定理，推导出了分数化磁通量，并且得到了修正的伦敦定律。申请者给出了Ginzburg-Landau模型的分数化数学结构，此结果具有普遍性。这结果在世界上首次得到。

中文关键词： 磁流体；涡旋

英文摘要： The report has four parts: (1)Helicity of vortices is studied in a single order parameter Ginzburg-Landau model with n×term. This unusual term changes the superconductor current, but does not change the quantum of magnetic flux, and the cross helicity of the probability density current in noncentrosymmetric superconductors. We compute the kinetic helicity and magnetic helicity of a superconductor and introduce a new helicity, i.e. a new topological invariant, to describe vortex phase.(2)The structure of the vortex in the two-component Bose-Einstein condensates is studied by method of Dirac δunction. The vortex can be characterized by Brouwer degree and Hopf index. The circulation of vortex can be a fraction, which is different from the usual result of one component condensate. (3)We have carried out numerical simulations to elucidate the relation between perturbation error fields and neoclassical tearing mode in J-TEXT Tokamak. The tearing modes excited by error field are suppressed in rotating plasmas. However, when the error-field amplitude rises above a certain critical value ψthreshold}, the plasma rotation is suddenly arrested.The interaction between the error-field and tearing mode is studied by nonlinear model. The evolution of neoclassical tearing mode in J-TEXT tokamak is calculated numerically. The threshold formula for mode locking in J-TEXT tokamak is given. (4)A two-gap superconductor allows several types of vortices, such as vortices carrying an arbitrary fraction of the magnetic flux quantum, which have no counterpart in ordinary one-gap superconductors. The topological structures of vortices are characterized by Brouwer degree and Hopf index. The London law in the two-gap superconductor is actually violated for the fractional vorticity of vortices. The vorticity is not a universal function of fundamental constants irrespective of microscopic details. Indeed, it depends on densities and the gradient of density. It is clearly that vortices are carrying an arbitrary fraction of magnetic flux quantum locally, which is different from the usually result of one-gap superconductor. The London law in N-gap superconductor is calculated for the case that each individual condensates is conserved or not conserved. Because the existence of background vorticity field, the vortices in nonconserved condensates is different from vortices in conserved condensates. The q term is originated from nonconserved wave function.

英文关键词： magnohydrodynamics;vortices