S. Toda

Theoretical study of the structure of the electric field in helical toroidal plasmas by the use of an anomalous transport model

A set of transport equations is analysed, including the bifurcation of the electric field. The structure of the electric field is studied by the use of a theoretical model for anomalous transport diffusivities. A steep gradient of the electric field is obtained at the electric domain. The suppression of anomalous transport diffusivity is studied in the presence of a strong shear of the electric field. The hard transition between the multiple ambipolar solutions is examined in the structure of the radial electric field. The soft transition (without the multiple ambipolar electric field) is also obtained.

Physics of internal transport barrier of toroidal helical plasmas

The role of zonal flows (ZFs) in the formation of an internal transport barrier in a toroidal helical plasma is analyzed. The turbulent transport coefficient is shown to be suppressed when the plasma state changes from the branch of a weak negative radial electric field to the strong positive one. This new transition of turbulent transport is caused by the change of the damping rate of the ZFs. It is clearly demonstrated, theoretically and experimentally, that the damping rate of the ZFs governs the global confinement of toroidal plasmas.

Transport analysis of the effect of zonal flows on electron internal transport barriers in toroidal helical plasmas

The role of zonal flows in the formation of transport barrier in helical plasmas is analysed using the transport code. A set of one-dimensional transport equations is analysed, including the effect of zonal flows. The turbulent transport coefficient is shown to be suppressed when the plasma state takes the strong positive radial electric field. This bifurcation of the turbulent transport is newly caused by the change of the damping rate of zonal flows. It is theoretically demonstrated that the damping rate of zonal flows plays an important role in global confinement in toroidal plasmas.

Nonlinear stability of magnetic islands in a rotating helical plasma

Coexistence of the forced magnetic reconnection by a resonant magnetic perturbation (RMP) and the curvature-driven tearing mode is investigated in a helical (stellarator) plasma rotated by helical trapped particle-induced neoclassical flows. A set of Rutherford-type equations of rotating magnetic islands and a poloidal flow evolution equation is revisited. Using the model, analytical expressions of criteria of spontaneous shrinkage (self-healing) of magnetic islands and sudden growth of locked magnetic islands (penetration of RMP) are obtained, where nonlinear saturation states of islands show bifurcation structures and hysteresis characteristics. Considering radial profile of poloidal flows across magnetic islands, it is found that the self-healing is driven by neoclassical viscosity even in the absence of micro-turbulence-induced anomalous viscosity. Effects of unfavorable curvature in stellarators are found to modify the critical values. The scalings of criteria are consistent with low-β experiments in...

Coherent Structure of Zonal Flow and Nonlinear Saturation

The nonlinear structure of the zonal flow in toroidal plasma is investigated in the case that the autocorrelation times of drift waves are much shorter than the autocorrelation time of zonal flow. It is found that the turbulent drive of the zonal flow starts to decrease at a high velocity shear of the zonal flow. By this mechanism, the zonal flow evolves into a stable stationary structure in turbulent plasmas. Flow velocity and radial wavelength are obtained.

Physics of collapses: probabilistic occurrence of ELMs and crashes

A statistical picture for the collapse is proposed. The physics picture of the crash phenomenon, which is based on the turbulence-turbulence transition, is extended to include the statistical variance of observables. The dynamics of the plasma gradient and the turbulence level are examined, with the hysteresis nature in the flux-gradient relation. Probabilistic excitation is predicted. The critical condition is described by the statistical probability.

A theoretical model of H-mode transition triggered by condensed neutrals near X-point

The effects of neutrals near the X-point of tokamaks on the L/H transition are examined. Four mechanisms for bipolar losses, i.e. the loss cone loss, the bulk viscosity loss, the charge-exchange (CX) loss between ions and neutrals and the anomalous loss, occur simultaneously in high-temperature plasmas. Neutral particles near the X-point are found to trigger the H-mode transition. They cause an additional ion loss cone loss via collisions. The lower limit of the neutral density near the X-point for the onset of the H-mode transition is estimated. Neutral particles at the main plasma are shown to prevent the H-mode transition because of CX loss.

Influence of resonant magnetic perturbation on a rotating helical plasma

Nonlinear stability of magnetic islands in a helical plasma with resonant magnetic perturbation (RMP) is investigated using reduced magnetohydrodynamic equations including neoclassical viscosity. Coexistence of RMP-driven islands and the resistive interchange mode is numerically simulated. The self-healing of locked magnetic islands by neoclassical flows is observed. It is found that the curvature effect modifies the threshold of the self-healing, where the unfavorable curvature drives not only the interchange mode but also the curvature-driven tearing mode. An analytical model based on a Rutherford equation with a momentum equation is also introduced to understand the simulation results. Criterion of the self-healing considering the curvature effect is newly obtained.

Selection of a Radial Wavelength of Zonal Flows

The nonlinear dynamics of coherent zonal flows is studied with periodic boundary conditions. We study nonlinear differential equations of zonal flows, which were previously derived in an analytic wave-kinetic model. Competition between the short wavelength zonal flow and the long wavelength zonal flow is studied. Although many stable stationary solutions are allowed, the radial periodicity length turns out to be a value around a particular length, when random small amplitude perturbations are chosen as the initial flow state.

Statistical theory of L?H transition in tokamaks

A statistical model for the bifurcation of the radial electric field Er is developed in view of describing L–H transitions of tokamak plasmas. Noise in micro-fluctuations is shown to lead to random changes of Er, if a deterministic approach allows for more than one solution. The probability density function for and the ensemble average of Er are obtained. The L-to-H and the H-to-L transition probabilities are calculated, and the effective phase limit is derived. Due to the suppression of turbulence by shear in Er, the limit deviates from Maxwells rule. The ensemble average of heat flux as well as that of Er do not show a hysteresis in contrast to the deterministic model. Experimental condition for observing the hysteresis is also addressed.