Nonlinear translational symmetric equilibria relevant to the L-H transition

摘要

Nonlinear z-independent solutions to a generalized Grad-Shafranov equation(GSE) with up to quartic flux terms in the free functions and incompressibleplasma flow non parallel to the magnetic field are constructedquasi-analytically. Through an ansatz the GSE is transformed to a set of threeordinary differential equations and a constraint for three functions of thecoordinate x, in cartesian coordinates (x,y), which then are solvednumerically. Equilibrium configurations for certain values of the integrationconstants are displayed. Examination of their characteristics in connectionwith the impact of nonlinearity and sheared flow indicates that theseequilibria are consistent with the L-H transition phenomenology. For flowsparallel to the magnetic field one equilibrium corresponding to the H-state ispotentially stable in the sense that a sufficient condition for linearstability is satisfied in an appreciable part of the plasma while anothersolution corresponding to the L-state does not satisfy the condition. Theresults indicate that the sheared flow in conjunction with the equilibriumnonlinearity play a stabilizing role.