S. V. Konovalov

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.

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.

Axisymmetric Magnetorotational Instability in Ideal and Viscous Laboratory Plasmas

The original analysis of the axisymmetric magnetorotational instability (MRI) by Velikhov (Sov. Phys. JETP 9, 995 (1959)) and Chandrasekhar (Proc. Nat. Acad. Sci. 46, 253 (1960)), applied to the ideally conducting magnetized medium in the laboratory conditions and restricted to the incompressible approximation, is extended by allowing for the compressibility. Thereby, two additional driving mechanisms of MRI are revealed in addition to the standard drive due to the negative medium rotation frequency gradient (the Velikhov effect). One is due to the squared medium pressure gradient and another is a combined effect of the pressure and density gradients. For laboratory applications, the expression for the MRI boundary with all the above driving mechanisms and the stabilizing magnetoacoustic effect is derived. The effects of parallel and perpendicular viscosities on the MRI in the laboratory plasma are investigated. It is shown that, for strong viscosity, there is a family of MRI driven for the same condition as the ideal one. It is also revealed that the presence of strong viscosity leads to additional family of instabilities called the viscosity-driven MRI. Then the parallel-viscositydriven MRI looks as an overstability (oscillatory instability) possessing both the growth rate and the real part of oscillation frequency, while the perpendicular-viscosity MRI is the aperiodical instability.

Reduction of energetic particle loss by ferritic steel inserts in ITER

Alpha particle loss due to the toroidal field ripple is significantly enhanced in reversed shear plasmas, especially in a high-q regime. To ensure a tolerable heat load on the wall due to the loss of alpha particle in reversed shear discharges with various q profiles, ferritic steel (FS) inserts are considered as a countermeasure for reducing the ripple amplitude at a low cost. With this being the situation, an assessment of ripple loss for various conditions in ITER is an important study that should to be conducted in the International Tokamak Physics Activities. This paper describes an assessment result, indicating that FS inserts lead to a dramatic reduction of ripple loss. When the arrangement of the FS inserts is optimized, the resulting alpha particle loss is anticipated to be reduced by an order of magnitude or more, and the power loss fraction is as low as 1% even for a reversed shear plasma with a relatively high qmin of 3.

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)].

Unified electrodynamic theory of magnetorotational and related instabilities in a rotating plasma

A unified electrodynamic theory of magnetorotational and related instabilities in a rotating plasma is formulated. We consider a cylindrical plasma in a uniform longitudinal magnetic field with rotation sustained due to the radial gravitation force or/and radial plasma pressure gradient. Two marginal cases are analyzed: the simplest astrophysical one without the pressure gradient and the laboratory plasma without the gravitation force. The perturbations are described within the one-fluid magnetohydrodynamics (MHD) and the kinetics. For such equilibria and for both the approaches a universal local dispersion relation is derived in terms of the permittivity tensor. Four versions of this tensor are obtained: for the simplest MHD and kinetic astrophysical plasmas with constant pressure and for the general MHD and kinetic plasma models. In the simplest MHD astrophysical plasma model, the axisymmetric and nonaxisymmetric magnetorotational instabilities (MRIs) and convective instability are considered. It is shown that the nonaxisymmetric modes are less dangerous than the axisymmetric ones due to the strongly stabilizing magnetoacoustic effect and also because of the overstable effect. We found that the one-fluid model for nonaxisymmetric modes in long laboratory plasma predicts the enhanced effect of the pressure gradient, compared with the case of axisymmetric modes, as the squared length/width ratio of the system. The axisymmetric and nonaxisymmetric kinetic MRIs in a collisionless plasma with isotropic pressure are analyzed. It is shown that the latter instability looks like an overstability driven for the same condition as the axisymmetric one. The pressure anisotropy of the rotating plasma gives two hybrid instabilities: the rotational firehose and rotational mirror. For both the astrophysical and laboratory cases the pressure gradient effects in the kinetic model are considered and a family of axisymmetric and nonaxisymmetric kinetic pressure-gradient-driven instabilities is found.

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.

Microislands in tokamaks

Analytical treatment of magnetic islands with high poloidal mode numbers and widths smaller than ion Larmor radius (microislands) is presented. The profile functions and rotation frequencies of microislands in the scope of the standard two-fluid magnetohydrodynamics are investigated. The effects of anomalous perpendicular resistivity and anomalous perpendicular electron heat conductivity are included. It is shown that, in such a problem statement, the microislands are described in terms of two profile functions, one of which characterizes the electric field and perturbed plasma density (the microisland profile function) and second—perturbed electron temperature (the electron temperature profile function). Analytical expressions for these profile functions in the case of stationary microislands are derived. Contribution of the oscillatory parallel electric current (the polarization current) into the generalized Rutherford equation for the stationary island width is calculated. The problem of rotation frequ...

Fluid treatment of convective-transport threshold model of neoclassical tearing modes in tokamaks

A fluid treatment of convective-transport threshold model of neoclassical tearing modes (NTMs) in tokamaks is developed. A Grad-type system of moment equations of the drift kinetic equation with a model perpendicular transport is derived. The essence of this moment equation system is to allow for the parallel heat flux on an equal footing with pressure and temperature, what goes beyond the scope of the Braginskii approach. The suggested moment equation system is applied for analyzing the bootstrap current drive of NTMs. As a result, a threshold model of these modes is derived, which coincides qualitatively with the convective-transport threshold model initially formulated by means of intuitive considerations.