M. S. Shirokov

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.

Kinetic reversed-shear Alfvén eigenmodes

Alfven eigenmodes in tokamak discharges with reversed shear are theoretically studied taking into account the effects of finite Larmor radius. It is predicted that, similarly to the kinetic toroidal Alfven eigenmodes in positive-shear discharges, a new branch of eigenmodes in reversed-shear discharges exists, called here the kinetic reversed-shear Alfven eigenmodes.

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.

The role of thermal plasma density gradient in the problem of Alfvén cascades in tokamaks

The localization effect of thermal plasma density gradient on the Alfven cascades in tokamaks is studied. It is shown that this effect can be stronger than the toroidal magnetohydrodynamic effect considered by Breizman et al. [Phys. Plasmas 10, 3649 (2003)] as squared aspect ratio. Thus, the Alfven cascade modes can be theoretically shown in cylindrical geometry approximation. Then the role of thermal plasma density gradient can be dominant if the localization effect of density gradient of large-orbit hot ions [Berk et al., Phys. Rev. Lett. 87, 185002 (2001)] is sufficiently weak.

Transport threshold model of subsonic neoclassical tearing modes in tokamaks

A transport threshold model of subsonic neoclassical tearing modes (NTMs) in tokamaks is developed. The basic procedure is to include the velocity-dependent term into the single-fluid heat-conductivity equation and to complement this equation with the single-fluid parallel plasma motion equation. These equations permit the determination of the perturbed plasma temperature and the bootstrap current drive of NTMs, for both strong and weak perpendicular heat transport, which is the precondition for developing the above model. It is shown that the subsonic NTMs transport threshold model can be more realistic than the standard transport model of NTMs suggested by Fitzpatrick [Phys. Plasmas 2, 825 (1995)].

Generation of zonal flows by ion-temperature-gradient and related modes in the presence of neoclassical viscosity

Generation of zonal flows by primary waves that are more complex than those considered in the standard drift-wave model is studied. The effects of parallel ion velocity and ion perturbed temperature and the part of the nonlinear mode interaction proportional to the ion pressure are taken into account. This generalization of the standard model allows the analysis of generation of zonal flows by a rather wide variety of primary modes, including ion temperature gradients, ion sound, electron drift, and drift-sound modes. All the listed effects, which are present in the slab geometry model, are complemented by effects of neoclassical viscosity inherent to toroidal geometry. We show that the electrostatic potential of secondary small-scale modes is expressed in terms of a nonlinear shift of the mode frequency and interpret this shift in terms of the perpendicular and parallel Doppler, nonlinear Kelvin-Helmholtz (KH), and nonlinear ion-pressure-gradient effects. A basic assumption of our model is that the prima...

Two-stream-like mechanism of zonal-flow generation by Rossby waves in a shallow rotating fluid

It is shown that the small-scale Rossby waves in a shallow rotating fluid placed in a gravitational field can generate large-scale zonal flows by means of a two-stream-like mechanism. This mechanism is revealed under the conditions when the Lighthill instability criterion is not satisfied.

Role of anomalous transport in onset and evolution of neoclassical tearing modes

A key role in the evolution of the neoclassical tearing modes (NTMs) belongs to the radial profiles of the perturbed plasma flow, temperature and density which are determined by the conjunction of the longitudinal and cross-field transport arising from thermal conduction, particle diffusion and viscosity. In a tokamak, the perpendicular transport of particles, heat and momentum is typically anomalous. In this paper the results of theoretical studies on the influence of anomalous perpendicular heat transport and anomalous ion perpendicular viscosity on early stages of NTM evolution are presented. Several parallel transport mechanisms competitive with anomalous cross-island heat transport in the formation of the perturbed electron and ion temperature profiles within the island are considered. The perturbed electron temperature profile is established in competition between anomalous perpendicular electron heat conductivity and parallel electron heat convection. The formation of the ion perturbed temperature profile was found to be dependent on the island rotation frequency. The perpendicular ion heat conductivity is balanced by the parallel transport associated with the ion inertia for an island rotating with subsonic frequency or with island rotation with respect to the plasma for supersonic islands. The partial contributions from the plasma electron and ion temperature perturbations in the bootstrap drive of the mode and magnetic curvature effect were taken into account in construction of a generalized transport threshold model of NTMs. This model gives more favourable predictions for NTM stability and qualitatively modifies the scaling law for βonset. The anomalous perpendicular ion viscosity is shown to modify the collisionality dependence of the polarization current effect, reducing it to the low collisionality limit. In its turn a viscous contribution to the bootstrap drive of NTMs is found to be of the same order as a conventional bootstrap drive for the islands of width close to the characteristic one of the transport threshold model. A viscous contribution to the perturbed bootstrap current is destabilizing for the island rotating in the ion diamagnetic drift direction. In this case, an alternative threshold mechanism should be considered.