S.-I. Itoh

Physics of collapse events in toroidal plasmas

A review is made of the crash phenomena in toroidal plasmas. The emphasis is placed on the physics that causes the crash of global plasma parameters. Recent progress in the measurement has provided a unified view of various crash phenomena, i.e. the sudden occurrence of the crash, the sensitivity (or probabilistic dependence) of the occurrence of the crash on the global parameters, and the abrupt excitation of a symmetry-breaking perturbation (magnetic trigger). Essential observations that describe the physics of collapse are surveyed. The theoretical study of the nonlinear plasma dynamics is overviewed. Theories of the onset and explosive growth, which are based on magnetic braiding, are discussed. As an example, a picture based on a turbulence-turbulence transition is explained. A picture based on hysteresis and bifurcation, not on the linear instability criterion, emerging from advanced measurements and recent progress, describes the basic physics of the collapse.

Subcritical Excitation of Plasma Turbulence

Theory of current-diffusive interchange mode turbulence in plasmas in the presence of collisional transport is developed. Amplitude of stationary fluctuations is expressed in terms of the double-valued function of the pressure gradient. The backward bifurcation is shown to appear near the linear stability boundary. The subcritical nature of the turbulence is explicitly illustrated. The critical pressure gradient at which the transition from collisional transport to the turbulent one is to occur is predicted. This work provides a prototype of the transport theory for nonlinear-nonequilibrium systems.

Self-sustained turbulence and H-mode confinement in toroidal plasmas

A theory of the anomalous transport coefficient in toroidal helical systems (such as stellarators, torsatron and Heliotron devices) is developed. The theoretical formalism of self-sustained turbulence is applied to the interchange mode turbulence and ballooning mode turbulence. The nonlinear destabilization of microscopic modes by the current diffusivity is the key for the anomalous transport. A general form of the anomalous transport coefficient in toroidal plasmas is derived. The intrinsic importance of the pressure gradient, collisionless skin depth and Alfven transit time is confirmed. The geometrical factors which characterize the magnetic configurations are also obtained. The theory is extended to study the influence of parallel compressibility. The ion viscosities of the perpendicular and parallel momenta, electron viscosity and energy diffusion coefficient are obtained. The comparison with experimental results is also given.

Ion heat pulse after a sawtooth crash in the JAERI Fusion Torus‐2M tokamak

The ion heat pulse after a sawtooth crash is studied by a time‐of‐flight (TOF) neutral measurement. A rapid change of the bulk ion energy distribution near the edge is observed after a sawtooth crash. The delay time is measured, and the effective measuring position is estimated by a neutral transport code. Then a transient ion thermal conductivity, χiHP, of about (7–18) m2/s is evaluated for the low confinement mode (L‐mode) plasma. The simple diffusive model with constant χiHP, however, does not explain the amplitude of the pulse in the ion energy distribution.

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.

A model of giant ELMs

A theoretical model of giant ELMs (type-I ELMs) is developed. The theory of the self-sustained turbulence of the current-diffusive ballooning mode (CDBM) is developed in the presence of a steep pressure gradient and a radial electric field shear. Multifold states for the L-mode, H-mode and the third state with magnetic braiding are obtained. Transition to the state with magnetic braiding is found to occur if the pressure gradient becomes high enough. At this critical point, nonlinear excitation of the magnetic perturbation takes place, the growth time of which is of the order of the poloidal Alfven time. This event can cause catastrophic enhancement of the transport coefficient by a factor of almost 10. The avalanche of the transport catastrophe is also analysed, showing a very rapid radial propagation velocity. The magnetic braiding terminates if the pressure gradient becomes small, leading to a back transition to the H- (L-) mode. Under a constant power supply these processes can repeat themselves, causing periodic bursts. The period becomes shorter as the average power flux increases.

Transport Dynamics of Collapse in a Giant ELM

Dynamics of collapse in a giant ELM (Edge Localized Mode) is presented. A model of transport bifurcation between the H-mode and the magnetic braiding mode (M-mode) is applied to the simulational study of edge plasma dynamics. The bifurcation contains the hysteresis characteristics. The pressure profile development, the propagation of the bifurcation (transition) fronts and the resultant bursting fluxes are obtained. The appearance of a pivot point in the pressure profile, an avalanche followed to the transition front propagation, and the structure of the burst are shown.

Dynamic structure in self-sustained turbulence

A dynamical equation for self-sustained and pressure-driven turbulence in toroidal plasmas is derived. The growth rate of the dressed-test mode, which belongs to the subcritical turbulence, is obtained as a function of the turbulent transport coefficient. In the limit of a low fluctuation level, the mode has nonlinear instability and shows explosive growth. The growth rate vanishes when the driven transport reaches a stationary-turbulent level. The stationary solution is thermodynamically stable. The characteristic time, by which the stationary and self-sustained turbulence are established, scales with the ion-sound transit time and is accelerated by bad magnetic curvature. The influence of the pressure gradient as well as the radial electric field inhomogeneity are quantified.

Numerical study of chaos based on a shell model

A shell model is introduced to study a turbulence driven by the thermal instability (Rayleigh-Benard convection). This model equation describes cascade and chaos in the strong turbulence with high Rayleigh number. The chaos is numerically studied based on this model. The characteristics of the turbulence are analyzed and compared with those of the Gledzer-Ohkitani-Yamada (GOY) model. Quantities such as a mean value of total fluctuation energy, its standard deviation, time averaged wave spectrum, probability distribution function, frequency spectrum, the maximum instantaneous Lyapunov exponent, distribution of instantaneous Lyapunov exponents, are evaluated. The dependences of these quantities on the error of numerical integration are also examined. There is not a clear correlation between the numerical accuracy and the accuracy of these quantities, since the interaction between a truncation error and an intrinsic nonlinearity of the system exists. A finding is that the maximum Lyapunov exponent is insensitive to a truncation error. (c) 1999 American Institute of Physics.