Nonlinear z-independent solutions to a generalized Grad-Shafranov equation (GSE) with up to quartic flux terms in the free functions and incompressible plasma flow non parallel to the magnetic field are constructed quasi-analytically. Through an ansatz the GSE is transformed to a set of three ordinary differential equations and a constraint for three functions of the coordinate x, in cartesian coordinates (x,y), which then are solved numerically. Equilibrium configurations for certain values of the integration constants are displayed. Examination of their characteristics in connection with the impact of nonlinearity and sheared flow indicates that these equilibria are consistent with the L-H transition phenomenology. For flows parallel to the magnetic field one equilibrium corresponding to the H-state is potentially stable in the sense that a sufficient condition for linear stability is satisfied in an appreciable part of the plasma while another solution corresponding to the L-state does not satisfy the condition. The results indicate that the sheared flow in conjunction with the equilibrium nonlinearity play a stabilizing role.
Vlasov versus reduced kinetic theories for helically symmetric equilibria
在Vlasov理论框架下，得到了磁轴附近螺旋对称平衡的一个新的运动常数。鉴于这一运动常数的Vlasov理论进行了比较，漂移动力学和陀螺动力学理论近轴。结果表明，在轴对称平衡的情况下[H。Tasso和G. N. Throumoulopoulos，Phys.Plasmas 18，064507（2011）]，其上的弗拉索夫电流密度可以明显不同于漂移动力学和回旋动力学电流密度。这表明了一些限制的影响，减少动力学理论，特别是有关高能粒子的物理中心区域的磁约束等离子体。
Seifert type magnetohydrostatic equilibria in rotationally symmetric toroidal domains
Instituto de Ciencias Matemáticas, Consejo Superior de Investigaciones Científicas（西班牙高等科学研究委员会数学科学研究所）；Faculty of Physics, University of Bucharest（布加勒斯特大学物理学院）
Low-shear three-dimensional equilibria in a periodic cylinder
本文对具有磁通面套的非对称环形理想磁流体力学（MHD）平衡方程进行了展开，其中物理量在柱角$θ$和$z$上具有周期$2π$.在恒定的环向角通量表面的横截面被假定为近似圆形，并给出了圆柱形通量表面$r=1$的数据。此外，我们假设磁场线在最低阶磁通面上是闭合的，磁剪切相对较小。我们扩展了Weitzner [Physics of Plasmas 23，062512（2016）]在平坦环面中的早期工作，并证明了可以使用磁通量作为展开参数对所有阶进行幂级数展开。与平环面相比，柱面度规为展开式引入了某些新的特征。然而，处理共振奇点的基本方法仍然是相同的。结果，即使缺乏收敛性证明，再次支持光滑，低剪切非对称环形MHD平衡的可能性。
