An analysis of instability dynamics in a stochastic magnetic field is presented for the tractable case of the resistive interchange. Externally prescribed static magnetic perturbations convert the eigenmode problem to a stochastic differential equation, which is solved by the method of averaging. The dynamics are rendered multi-scale, due to the size disparity between the test mode and magnetic perturbations. Maintaining quasi-neutrality at all orders requires that small-scale convective cell turbulence be driven by disparate scale interaction. The cells in turn produce turbulent mixing of vorticity and pressure, which is calculated by fluctuation-dissipation type analyses, and are relevant to pump-out phenomena. The development of correlation between the ambient magnetic perturbations and the cells is demonstrated, showing that turbulence will ‘lock on’ to ambient stochasticity. Magnetic perturbations are shown to produce a magnetic braking effect on vorticity generation at large scale. Detailed testable predictions are presented. The relations of these findings to the results of available simulations and recent experiments are discussed.

Electric field profile structure—especially its shear—is a natural order parameter for the edge plasma, and characterizes confinement regimes ranging from the H-mode (Wagner et al. 1982 Phys. Rev. Lett. 49 , 1408–1412 ( doi:10.1103/PhysRevLett.49.1408 )) to the density limit (DL) (Greenwald et al. 1988 Nucl. Fusion 28 , 2199–2207 ( doi:10.1088/0029-5515/28/12/009 )). The theoretical developments and lessons learned during 40 years of H-mode studies (Connor & Wilson 1999 Plasma Phys. Control. Fusion 42 , R1–R74 ( doi:10.1088/0741-3335/42/1/201 ); Wagner 2007 Plasma Phys. Control. Fusion 49 , B1–B33 ( doi:10.1088/0741-3335/49/12b/s01 )) are applied to the shear layer collapse paradigm (Hong et al. 2017 Nucl. Fusion 58 , 016041 ( doi:10.1088/1741-4326/aa9626 )) for the onset of DL phenomena. Results from recent experiments on edge shear layers and DL phenomenology are summarized and discussed in the light of L → H transition physics. The theory of shear layer collapse is then developed. We demonstrate that shear layer physics captures both the well known current (Greenwald) scaling of the DL (Greenwald 2002 Plasma Phys. Control. Fusion 44 , R27–R53 ( doi:10.1088/0741-3335/44/8/201 ); Greenwald et al. 2014 Phys. Plasmas 21 , 110501 ( doi:10.1063/1.4901920 )), as well as the emerging power scaling (Zanca, Sattin, JET Contributors 2019 Nucl. Fusion 59 , 126011 ( doi:10.1088/1741-4326/ab3b31 )). The derivation of the power scaling theory exploits an existing model, originally developed for the L → H transition (Diamond, Liang, Carreras, Terry 1994 Phys. Rev. Lett. 72 , 2565–2568 ( doi:10.1103/PhysRevLett.72.2565 ); Kim & Diamond 2003 Phys. Rev. Lett. 90 , 185006 ( doi:10.1103/PhysRevLett.90.185006 )). We describe the enhanced particle transport events that occur following shear layer collapse. Open problems and future directions are discussed. This article is part of a discussion meeting issue ‘H-mode transition and pedestal studies in fusion plasmas’.

The mean E×B shear in a stochastic magnetic field is calculated, using the radial force balance relation and transport equations. This analysis is relevant to the L→H transition with resonant magnetic perturbations (RMP), and special focus is placed upon the physics of non-ambipolar transport and radial current. The key physical process is the flow of fluctuating current along wandering magnetic fields. The increments in poloidal and toroidal rotation, density and ion pressure are calculated. The radial envelope of the magnetic perturbations inside the plasma defines a new scale l_env, which is the characteristic scale of the magnetic fluctuation intensity profile. The net particle outflow due to stochastic magnetic fields is calculated and is determined by the net radial current through the separatrix. Implications for the L→H transition are discussed.

An analysis of instability dynamics in a stochastic magnetic field is presented for the tractable case of the resistive interchange. Externally prescribed static magnetic perturbations convert the eigenmode problem to a stochastic differential equation, which is solved by the method of averaging. The dynamics are rendered multi-scale, due to the size disparity between the test mode and magnetic perturbations. Maintaining quasi-neutrality at all orders requires that small-scale convective cell turbulence be driven by disparate scale interaction. The cells in turn produce turbulent mixing of vorticity and pressure, which is calculated by fluctuation-dissipation type analyses, and are relevant to pump-out phenomena. The development of correlation between the ambient magnetic perturbations and the cells is demonstrated, showing that turbulence will 'lock on' to ambient stochasticity. Magnetic perturbations are shown to produce a magnetic braking effect on vorticity generation at large scale.Detailed testable predictions are presented. The relations of these findings to the results of available simulations and recent experiments are discussed. I. INTRODUCTIONThe dynamics of instability, relaxation, and turbulence are (taken collectively) fundamental to magnetic confinement physics. Here, 'relaxation' includes the evolution of plasma free energy (in the presence of sources and sinks), and the resulting transport [1]. Relaxation determines plasma confinement and possible bifurcations between different states thereof [2].Recently, a new element has been added to this already challenging problem. Good confinement is no longer deemed sufficient. Rather, good confinement must be achieved along with