Theoretical study on production of super high beta plasmas by rotating magnetic field

本文研究了离子流体和电子流体的旋转稳定性，研究了电阻摩擦和旋转磁场（RMF）对电子施加的力的平衡，以保持场反转构型（FRC）处于稳态。采用了无限长等离子体、刚性旋转离子和电子、均匀等离子体密度等简单解析模型。考虑了离子旋转、径向等离子体流动以及由于通量守恒引起的分离矩阵半径变化的影响，在降维零维模型中对平衡旋转进行了线性稳定性分析。由线性化方程的特征值推导出给出稳定性判据的解析表达式。根据稳定性判据，对目前的实验结果作了解释，并对今后的实验结果作了评论。通过数值求解具有非平衡初始值的离子和电子旋转速率方程，研究了RMF在FRC中电流驱动的瞬态行为。通过在平衡离子和电子旋转中引入扰动来研究动态响应，以检验RMF在浅穿透平衡附近的稳定性。只要扰动较小，电子在浅穿透稳定平衡上的旋转始终保持在初始平衡附近。另一方面，不稳定平衡中的电子旋转增加与RMF同步，导致正扰动的完全穿透，而负扰动的电子旋转在RMF后进一步减少。结果与线性稳定性分析结果一致。RMF在FRC中穿透的标准是在物理基础上从理论上推导出来的，即RMF直接作用于电子流体的驱动力必须在整个过程中超过离子阻力，电子流体才能与RMF达到同步旋转，从而使RMF在FRC中完全穿透。该准则比以往的准则更能解释数值模拟结果和实验观测结果。该判据还可用于用旋转磁场使热FRC处于稳态的实验指导。少

The stability of the rotation of the ion and electron fluids is studied on the balance of the forces exerted on the electrons by the resistive friction and the Rotating Magnetic Field (RMF) applied for the sake of maintaining Field Reversed Configuration (FRC) in steady state. The simple analytical model such as infinite-long plasma, rigidly rotating ions and electrons and uniform plasma density are used. The linear stability analysis of the equilibrium rotation is carried out in the reduced zero-dimensional model which includes the effects of ion rotation, radial plasma flow and separatrix radius change due to the flux conservation within the flux conserver. The analytical expression which gives the stability criterion is derived from the eigenvalues of the linearized equations. Based upon the stability criterion, an interpretation of the present experimental results and comments of the future experiments are given as for the penetration of the RMF into the FRC.The transient behaviors … More of current drive with an RMF in an FRC are studied by numerically solving the rate equations for the ion and electron rotations with the non-equilibrium initial values. The dynamic responses are investigated by introducing the perturbation into the equilibrium ion and electron rotations in order to examine the stability around the equilibrium of the shallow penetration of an RMF. The electron rotation on the stable equilibrium of the shallow penetration remains to be near the initial equilibrium so long as the perturbation is small. On the other hand, the electron rotation in the unstable equilibrium increases to be synchronous with an RMF and to result in the full penetration for the positive perturbation and decreases further behind an RMF for the negative one. The results are consistent with the linear stability analysis.The criterion for the penetration of an RMF in an FRC is derived theoretically on a physical base that the driving force of an RMF acting directly on an electron fluid must exceed the ion drag force throughout the process for the electron fluid to reach the synchronous rotation with the RMF, resulting in the full penetration of RMF in an FRC. The criterion explains the numerical simulation results and the experimental observations better than those previously used. The criterion is also useful for the guide of the experiments of making a hot FRC in a steady state by applying a rotating magnetic field. Less