This Rapid Communication sets forth the mechanism by which mesoscale staircase structures condense to form macroscopic states of enhanced confinement. Density, vorticity, and turbulent potential enstrophy are the variables for this model. Formation of the staircase structures is due to inhomogeneous mixing of (generalized) potential vorticity (PV). Such mixing results in the local sharpening of density and vorticity gradients. When PV gradients steepen, the density staircase structure develops into a lattice of mesoscale "jumps" and "steps," which are, respectively, regions of local gradient steepening and flattening. The jumps then merge and migrate in radius, leading to the emergence of a new macroscale profile structure, so indicating that profile self-organization is a global process, which may be described by a local, but nonlinear model. This work predicts and demonstrates how mesoscale condensation of staircases leads to global states of enhanced confinement.

A new, frequency modulation mechanism for zonal flow pattern formation is presented. The model predicts the probability distribution function of the flow strength as well as the evolution of the characteristic spatial scale. Magnetic toroidicity-induced global phase dynamics is shown to determine the spatial structure of the flow. A key result is the observation that global phase patterning can lead to zonal flow formation in the absence of turbulence inhomogeneity.

Abstract This paper presents a comparative study of zonal flow screening in positive and negative triangularity tokamaks. Neoclassical screening sets the strength of zonal flow shear for fixed drive and damping. Orbit calculations show that the radial excursions of trapped particles are reduced in negative triangularity tokamaks, as compared to positive triangularity. Yet surprisingly, the neoclassical dielectric susceptibility actually increases with decreasing triangularity, such that the susceptibility is higher for negative triangularity than for positive triangularity. This is because the reduction in neoclassical polarization by shrinking the banana width is offset by the increase in neoclassical polarization by the enhancement of trapped fraction for negative triangularity. As a result, the zonal flow screening length is actually enhanced for negative triangularity, as compared to positive triangularity. Hence, the zonal flow residual is smaller for negative triangularity than for positive triangularity. Results from gyrokinetic simulations support the analytic calculations.

Abstract 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.

Recent experimental observations have suggested key characteristics of internal transport barrier (ITB) formation near low- q surfaces in off-axis minimum- q (OAMq) discharges. These observations identify mean profile flattening localized to the low- q surface as a transition precursor in the absence of observable magnetic field perturbations. This observation suggests an electrostatic model of ITB formation which accounts for strong transport in the immediate vicinity of the low- q surface, as well as the formation of an ITB nearby the surface. Here, a low- m electrostatic convective cell driven by modulational instability of the background drift wave turbulence is discussed in the context of ITB formation near low- q resonances in OAM q discharges. Unlike pure m=n=0 zonal flows, convective cells are capable of intense mixing localized around low- q resonant surfaces, thus relaxing ∇T and ∇n profiles at the kB=0 resonance. However, nearby, but off the low- q resonant surface the magnitude of convective cell shear is maximal, providing an effective means of triggering a transport barrier there. Field line bending coupled with collisional viscosity are found to strongly damp the intensity of the vortical flows except in the case of weak magnetic shear. Furthermore, collisionless nonlinear saturation mechanisms such as nonlinear wave trapping are largely circumvented due to the strong mixing of the convective cell. This suggests that low- m convective cells may play a key role in the regulation of turbulent transport near low- q resonances for OAMq discharges. © 2007 American Institute of Physics.

The electron temperature gradient mode has been proposed as a primary mechanism for electron transport. The possibilities of magnetic secondary instabilities (“zonal” magnetic fields and magnetic “streamers”) are investigated as novel potential mechanisms for electron transport regulation and enhancement, respectively. In particular, zonal magnetic field growth and transport regulation is investigated as an alternative to electrostatic zonal flows. Growth rates and implications for electron thermal transport are discussed for both electrostatic and magnetic saturation mechanisms. The possibility of magnetic streamers (mesoscale radial magnetic fields), and their potential impact on electron thermal transport, is also considered.

Theoretical studies of mean field electrodynamics for diffusive processes in the electron magnetohydrodynamic (EMHD) model is presented. In contrast to magnetohydrodynamics (MHD), the evolution of the magnetic field here is governed by a nonlinear equation in magnetic field variables. A detailed description of diffusive processes in two dimensions are presented in this paper. In particular, it has been shown analytically that the turbulent magnetic field diffusivity is suppressed from naive quasilinear estimates. It is shown that for complete whistlerization of the spectrum, turbulent diffusivity vanishes. The question of whistlerization of the turbulent spectrum is investigated numerically, and a reasonable tendency towards whistlerization is observed. Numerical studies also show suppression of magnetic field diffusivity in accordance with analytical estimates. © 2000 American Institute of Physics.

One of the main features of astrophysical shocks is their ability to accelerate particles to extremely high energies. The leading acceleration mechanism, the diffusive shock acceleration, is reviewed. It is demonstrated that its efficiency critically depends on the injection of thermal plasma into acceleration which takes place at the subshock of the collisionless shock structure that, in turn, can be significantly smoothed by energetic particles. Furthermore, their inhomogeneous distribution provides free energy for magnetohydrodynamic (MHD) turbulence regulating the subshock strength and injection rate. Moreover, the MHD turbulence confines particles to the shock front controlling their maximum energy and bootstrapping acceleration. Therefore, the study of the MHD turbulence in a compressive plasma flow near a shock is a key to the understanding of the entire process. The calculation of the injection rate became part of the collisionless shock theory. It is argued that the further progress in diffusive shock acceleration theory is impossible without a significant advance in these two areas of plasma physics.

A two-field model of potential vorticity (PV) staircase structure and dynamics relevant to both beta-plane and drift-wave plasma turbulence is studied numerically and analytically. The model evolves averaged PV whose flux is both driven by and regulates, a potential enstrophy field, $\varepsilon$. The model employs a closure using a mixing length model. Its link to bistability, vital to staircase generation, is analyzed and verified by integrating the equations numerically. Long-time staircase evolution consistently manifests a pattern of meta-stable quasi-periodic configurations, lasting for hundreds of time units, yet interspersed with abrupt ($\Delta t\ll1$) mergers of adjacent steps in the staircase. The mergers occur at the staircase lattice defects where the pattern has not completely relaxed to a strictly periodic solution that can be obtained analytically. Other types of stationary solutions are solitons and kinks in the PV gradient and $\varepsilon$ - profiles. The waiting time between mergers increases strongly as the number of steps in the staircase decreases. This is because of an exponential decrease in inter-step coupling strength with growing spacing. The long-time staircase dynamics is shown numerically be determined by local interaction with adjacent steps. Mergers reveal themselves through the explosive growth of the turbulent PV-flux which, however, abruptly drops to its global constant value once the merger is completed.

A minimal self-consistent model of the multiscale interaction of a tearing mode with drift wave turbulence is presented. A tearing instability in a cylindrical plasma interacting with electrostatic drift waves is considered, for reasons of simplicity. Wave kinetics and adiabatic theory are used to treat the feedback of tearing mode flows on the drift waves via shearing and radial advection. The stresses exerted by the self-consistently evolved drift wave population density on the tearing mode are calculated by mean field methods. The principal effect of the drift waves is to pump the resonant low- m mode via a negative viscosity, consistent with the classical notion of an inverse cascade in quasi-two-dimensional turbulence. This process can occur alone or in synergy with current gradient drive of the low- m mode. Speculations of the relation of this multiscale process to the more general issue of the fate of energy transferred to large scales by an inverse cascade are presented. The existence of nonlinearly driven vortices pinned to low- q surfaces as a class of highly anisotropic dissipative structures which terminate the inverse cascade is proposed. The evolution of a finite size magnetic island is discussed. © 2006 American Institute of Physics.