V. S. Tsypin

Regularized magnetic islands. II. The role of polarization current

The role of polarization current in the problem of rotating magnetic islands in the absence of drift effects is discussed for the case of nonregularized and regularized velocity profiles governed by the perpendicular viscosity. The polarization current is calculated taking into account the finite ion Larmor radius effects. It is shown that, in correspondence with the general rule by Waelbroeck and Fitzpatrick [Phys. Rev. Lett. 78, 1703 (1997)], this current is destabilizing. The destabilizing contribution of the polarization current into the generalized Rutherford equation for the magnetic island width does not depend on whether the profile function is regularized or not. It is shown that the Larmor corrections to the current consist of the sum of two oppositely directed currents and do not contribute into the generalized Rutherford equation.

An approach to calculation of magnetic island rotation frequency

The problem of magnetic island rotation is analyzed. It is noted that for the correct solution of this problem the nonstationarity of profile functions should be taken into account. An approach to solving equations for nonstationary profile functions is developed for cases when drift and neoclassical effects can be neglected. The principal role of perpendicular viscosity in determining island rotation frequency is emphasized. The possibility of the existence of stationary magnetic islands in tokamaks with a rotating plasma and a resistive wall is shown.

Regularized magnetic islands. I. Hyperviscosity and profile functions

The problem of the magnetic island profile functions is analyzed. An idea is suggested that discontinuities of the profile function derivatives at the island separatrix, which appear in simplified plasma models, can be eliminated by means of more complete description, i.e., the profile functions can be regularized. As an example, the regularization of the electrostatic potential profile function is considered for the case of a slab geometry when its formation is governed by the perpendicular viscosity. It is shown that for regularization of such a profile function one should keep in the viscosity expression the terms with higher derivatives of the velocity, usually referred to as hyperviscosity terms. A model expression for the hyperviscosity is derived by the Grad-type method. Physically, the regularization is related to the appearance of a part of the profile function localized in the Larmor transition layer near the island separatrix.

Rotation-transport threshold model of neoclassical tearing modes

A rotation-transport threshold model of neoclassical tearing modes (NTMs) is suggested. It is assumed that weakening of the bootstrap current effect is determined by competition of perpendicular transport and island rotation, which is in contrast to the known transport threshold models dealing with the parallel transport or parallel convection instead of island rotation. It is shown that for sufficiently strong island rotation the perpendicular transport does not lead to decreasing the bootstrap current contribution into the island width evolution equation. It is explained that the island rotation can prevail over the parallel transport/convection mainly for the case of ion contribution into the bootstrap current effect. Interrelation between the rotation-transport threshold model and the known ones is discussed. A generalized transport threshold model of NTMs describing the competition of the perpendicular transport with the island rotation, parallel transport and parallel convection is formulated. It is shown that the perpendicular transport can lead to weakening the bootstrap drive contribution only if it overpowers all the competitive effects.

Zonal flows generated by small-scale drift-Alfvén modes

The generation of zonal flows by small-scale drift-Alfven (SSDA) modes is investigated. It is shown that these zonal flows can be generated by a monochromatic wave packet of SSDA modes propagating in the ion diamagnetic drift direction. The corresponding zonal-flow instability resembles a hydrodynamic one. Its growth rate depends on the spectrum purity of the wave packet; it decreases for relatively weak spectrum broadening and the instability turns into a resonant one, and eventually is suppressed, as the broadening increases. A general conclusion of this work is that the SSDA modes are less effective for driving zonal flows than standard drift modes.

Plasma residual rotation in the TCABR tokamak

This paper reports the first results on the measurement of the radial profiles of plasma poloidal and toroidal rotation performed on the TCABR tokamak, in the collisional regime (Pfirsch–Schluter), using Doppler shift of carbon spectral lines, measured with a high precision optical spectrometer. The results for poloidal rotation show a maximum velocity of (4.5 ± 1.0) × 103 m s−1 at , (a—limiter radius), in the direction of the diamagnetic electron drift. Within the error limits, reasonable agreement is obtained with calculations using the neoclassical theory for a collisional plasma, except near the plasma edge, as expected. For toroidal rotation, the radial profile shows that the velocity decreases from a counter-current value of (20 ± 1) × 103 m s−1, at the plasma core, to a co-current value of (2.0 ± 0.9) × 103 m s−1 near the limiter. An agreement within a factor 2, for the plasma core rotation, is obtained with calculations using the model proposed by Kim, Diamond and Groebner (1991 Phys. Fluids B 3 2050).

Runaway discharges in TCABR

It is found in experiments carried out in Tokamak Chauffage Alfven Bresilien (TCABR) that two regimes of runaway discharges (RADs) with very different characteristics are possible. The RAD-I regime, which is similar to that observed in other tokamaks, can be obtained by a gradual transfer from a normal resistive to a RAD by decreasing the plasma density. This regime can be well understood using the Dreicer theory of runaway generation. The total toroidal current contains a substantial resistive component and the discharge retains some features of standard tokamak discharges. The second runaway regime, RAD-II, was recently discovered in the TCABR tokamak (Galvao R.M.O. et al 2001 Plasma Phys. Control. Fusion 43 1181). The RAD-II regime starts just from the beginning of the discharge, provided that certain initial conditions are fulfilled and, in this case, the runaway tail carries almost the full toroidal current. The background plasma is cold and detached from the limiter due to the recombination process. The primary Dreicer process is suppressed in the RAD-II and the secondary avalanche process dominates, even at the start-up phase, in the generation of the toroidal current. It is possible to trigger a transition from the RAD-I to the RAD-II regime using plasma cooling by gas puffing. The experimental results are shown to be in reasonable agreement with theoretical predictions based on the runaway avalanche process.

Effect of anomalous perpendicular viscosity on bootstrap drive of neoclassical tearing modes

Anomalous perpendicular viscosity is incorporated into transport threshold models of neoclassical tearing modes (NTMs). It is shown that this viscosity, influencing the bootstrap drive, is stabilizing if NTMs rotate in the ion diamagnetic drift direction and destabilizing in the contrary case.

Transport threshold model of neoclassical tearing modes in the presence of anomalous perpendicular viscosity

Bootstrap drive of neoclassical tearing modes (NTMs) in the presence of anomalous perpendicular viscosity is calculated. Viscosity is shown to lead to dependence of the perturbed bootstrap current on the perturbed electric field. As a result, the bootstrap drive is qualitatively modified by the island rotation frequency and direction of the island rotation. The modified bootstrap drive is incorporated into the transport threshold model of NTMs.

Neoclassical generation of toroidal zonal flow by drift wave turbulence

Zonal-flow instabilities due to drift-wave turbulence in the presence of toroidicity-induced parallel (neoclassical) viscosity and allowing for the toroidal flow are studied. It is shown that, as a result of the neoclassical viscosity a new type of zonal-flow instability is possible, leading to the generation of the considerable toroidal zonal flow. The toroidal instability is complementary to the previously studied instability resulting in the poloidal flow generation and occurs as a second branch of the general dispersion relation describing the evolution of the poloidal and toroidal flow. Nonlinear saturation of the new instability is studied. It is shown that saturated zonal toroidal velocity, generated in this instability, is large compared to the mean cross-field drift velocity as the ratio q∕ϵ, where q is the safety factor and ϵ is the inverse aspect ratio. In addition to the broad turbulent spectrum of drift waves, a monochromatic wave packet is considered. It is revealed that for the case of suff...