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The dynamics of the rotating resistive wall modes (RWMs) is analyzed in the presence of a uniform ferromagnetic resistive wall with ≡μ/μ0≤4 (μ is the wall magnetic permeability, and μ0 is the vacuum one). This mimics a possible arrangement in ITER with ferromagnetic steel in test blanket modules or in future experiments in JT-60SA tokamak [Y. Kamada, P. Barabaschi, S. Ishida, the JT-60SA Team, and JT-60SA Research Plan Contributors, Nucl. Fusion 53, 104010 (2013)]. The earlier studies predict that such a wall must provide a destabilizing influence on the plasma by reducing the beta limit and increasing the growth rates, compared to the reference case with =1. This is true for the locked modes, but the presented results show that the mode rotation changes the tendency to the opposite. At >1, the rotational stabilization related to the energy sink in the wall becomes even stronger than at =1, and this "external" effect develops at lower rotation frequency, estimated as several kHz at realistic conditions. The study is based on the cylindrical dispersion relation valid for arbitrary growth rates and frequencies. This relation is solved numerically, and the solutions are compared with analytical dependences obtained for slow (s/dw≫1) and fast (s/dw≫1) "ferromagnetic" rotating RWMs, where s is the skin depth and dw is the wall thickness. It is found that the standard thin-wall modeling becomes progressively less reliable at larger, and the wall should be treated as magnetically thick. The analysis is performed assuming only a linear plasma response to external perturbations without constraints on the plasma current and pressure profiles. [ABSTRACT FROM AUTHOR]

Magnetic interaction of the plasma perturbations with the nearby resistive wall is considered as a resistive wall mode (RWM) problem, but with two essential differences from the traditional thin-wall approach. First, the wall is treated as magnetically thick, which means that the skin depth is not assumed larger than the wall thickness. Second, the plasma is allowed to enter the region where the RWM must be deeply unstable without rotation. The latter corresponds to the plasma operation above the no-wall stability limit demonstrated in the DIII-D tokamak [E. J. Strait et al., Phys. Plasmas 11, 2505 (2004)]. It is shown that the rotational stabilization observed in these experiments can be reproduced in this model if the mode is forced to rotate with a frequency above a critical level. The analytical estimates show that this effect (absent in the model based on the thin-wall approximation) is strong at realistic parameters. The model also predicts that the locking of the rotationally stabilized mode gives rise to instability with a growth rate much larger than its thin-wall estimate. [ABSTRACT FROM AUTHOR]

It is shown that, at rapid changes of the heating power, the magnetically confined equilibrium plasma almost completely absorbs the injected energy, so that its only small part goes to the magnetic field. The result is obtained within the standard MHD theory with use of exact consequences of the force-balance equations in toroidal geometry. It is assumed that, when heated, the plasma evolves from one equilibrium state to another with the magnetic field frozen-in. Another constraint is the conservation of the toroidal magnetic flux in the plasma-wall vacuum gap. It is shown that the plasma interaction with magnetic field (which is traditionally neglected in the analysis of heat transport in tokamaks and stellarators) is the natural mechanism of fast redistribution of energy in the plasma, observed in some experiments in these devices at switchon of powerful heat sources. [ABSTRACT FROM AUTHOR]

The article presents a study on the possibility of stable branches of the plasma oscillations which may be stimulated by energetic particles. The research mentions that magnetohydrodynamic (MHD) instabilities are a suppression of indispensable condition. In conclusion, Kruskal-Schwarzschild (KS) type solutions are formed due to magnetic well and strong plasma temperature gradient.

Analytical theory of magnetorotational and convective instabilities in a rotating cylindrical plasma with finite heat conductivity is developed and discussed. The heat conductivity is incorporated into the standardized equations of the regular magnetohydrodynamic approach to studying these instabilities. A case of high-β plasma (β is the ratio of plasma pressure to the magnetic field pressure) and the modes with parallel phase velocity much smaller than the sound velocity is particularly emphasized and considered in the quasi-incompressible approximation. It is shown that this approximation is more adequate than the Boussinesq approximation. Both these approximations lead to the same results for aperiodical instabilities of the axisymmetric modes which are hybrids of the magnetorotational and convective instabilities. On the other hand, the Boussinesq approximation overlooks the heat-conductivity-induced instabilities predicted by the quasi-incompressible approximation describing the dissipative excitation of the slow magnetoacoustic and Alfvén waves. Non-axisymmetric aperiodical instabilities are considered. It is shown that, for such modes, the role of convective instabilities is greater than for the magnetorotational instability. [ABSTRACT FROM AUTHOR]

High-frequency extensions of magnetorotational instability driven by the Velikhov effect beyond the standard magnetohydrodynamic (MHD) regime are studied. The existence of the well-known Hall regime and a new electron inertia regime is demonstrated. The electron inertia regime is realized for a lesser plasma magnetization of rotating plasma than that in the Hall regime. It includes the subregime of nonmagnetized electrons. It is shown that, in contrast to the standard MHD regime and the Hall regime, magnetorotational instability in this subregime can be driven only at positive values of dlnΩ/ dln r, where Ω is the plasma rotation frequency and r is the radial coordinate. The permittivity of rotating plasma beyond the standard MHD regime, including both the Hall regime and the electron inertia regime, is calculated. [ABSTRACT FROM AUTHOR]

A theoretical framework to describe the magnetic coupling of the toroidal plasma with the resistive wall and other sources of the field asymmetry is formulated. This is done for general toroidal geometry without restrictions on the plasma, while the wall is considered as a thin shell. Mathematically, the approach here exploits the Chance concept [M. S. Chance, Phys. Plasmas 4, 2161 (1997)], but with an essential difference: each source of the magnetic perturbation b (plasma, wall, external currents) is treated separately with account of their differences in space and nature. This allows much simpler formulation of the problem than was known before. The final equation couples the normal component of ∂b/∂t at the wall to the perturbation at the plasma surface. Step by step reduction of this first-principle equation is performed with demonstration of its main features, starting from the known problem of singularities. This also includes the reduction to axially symmetric geometry, large-aspect-ratio, and the cylindrical limits. In the latter case, the known “cylindrical” equation is reproduced, but now from the full “toroidal” equations. [ABSTRACT FROM AUTHOR]

A technique is developed for analytical study of instabilities in collisionless astrophysical rotating plasma with anisotropic pressure that may lead to magnetic turbulence. Description is based on a pair of equations for perturbations of the radial magnetic field and the sum of magnetic field and perpendicular plasma pressures. From these equations, a canonical second-order differential equation for the perturbed radial magnetic field is derived and, subsequently, the dispersion relation for local perturbations. The paper predicts two varieties of hybrid instabilities due to the effects of differential plasma rotation and pressure anisotropy: The rotational-firehose and rotational-mirror ones. When the gravitation force is weak compared with the perpendicular pressure gradient, a new family of instabilities (the pressure-gradient-driven) is revealed. [ABSTRACT FROM AUTHOR]

The rotational stabilization of the resistive wall modes (RWMs) is analyzed within the single-mode cylindrical Fitzpatrick-Aydemir model [R. Fitzpatrick, Phys. Plasmas 9, 3459 (2002)]. Here, the consequences of the Fitzpatrick-Aydemir dispersion relation are derived in terms of the observable growth rate and toroidal rotation frequency of the mode, which allows easy interpretation of the results and comparison with experimental observations. It is shown that this model, developed for the plasma with weak dissipation, predicts the rotational destabilization of RWM in the typical range of the RWM rotation. The model predictions are compared with those obtained in a similar model, but with the Boozer boundary conditions at the plasma surface [A. H. Boozer, Phys. Plasmas 11, 110 (2004)]. Simple experimental tests of the model are proposed. [ABSTRACT FROM AUTHOR]

The formulation of the energy principle proposed by Boozer [Phys. Plasmas 6, 831 (1999)] for the analysis of the toroidal plasma stability with respect to the resistive wall modes is discussed. One of its main features is the introduction of a surface current on the “control surface,” through which the influence of an external environment on the plasma is simulated. Here the classical example “ideal plasma-vacuum-the ideal wall” is used to show that, with such modeling, the energy conservation in the ideal magnetohydrodynamics is broken. This can be one of the possible reasons of the systematic discrepancy of plasma stability limits calculated with the VALEN code [Bialek et al. Phys. Plasmas 8, 2170 (2001)], where the discussed model is used, from the results of other codes. [ABSTRACT FROM AUTHOR]

The problem of feedback stabilization of the resistive wall modes (RWMs) in a tokamak is discussed. An equilibrium configuration with the parameters accepted for the stationary ITER scenario 4A is considered as the main scenario. The effect of the vacuum chamber’s shape on the plasma stability is studied. Ideal MHD stability is analyzed numerically by using the KINX code. It is shown that, in a tokamak with the parameters of the designed T-15M tokamak, RWMs can be stabilized by a conventional stabilizing system made of framelike coils. However, the maximum possible gain in β in such a tokamak is found to be smaller than that in ITER. It is shown that, in this case, a reduction in the plasma–wall gap width by 10 cm allows one to substantially increase the β limit, provided that RWMs are stabilized by active feedback. © 2004 MAIK “Nauka / Interperiodica”. [ABSTRACT FROM AUTHOR]

The recently proposed concept of the transport barrier formation in a tokamak plasma as a bifurcation of the equilibrium state with a change in the toroidal magnetic field over the entire plasma column, including the plasma edge, is analyzed. The analysis is performed in the cylindrical approximation. It is shown that, in the framework of the discussed concept, all of the equilibrium solutions are continuous functions of the parameters involved, bifurcations are absent, and the result is determined by the model assumptions that are necessary in order to make the task self-contained. Removing even part of these restrictive assumptions can substantially change the result. Under typical conditions, the effect of the plasma rotation on the plasma equilibrium is negligibly small. Besides, from the viewpoint of the formal analysis of the force balance, the rotation does not facilitate but, in contrast, hampers the formation of a positive pressure jump. [ABSTRACT FROM AUTHOR]

The equilibrium of a tokamak plasma with a toroidal flow is discussed. It is shown that the centrifugal force of this rotation always reduces the equilibrium beta limit. An opposite view is analyzed, and the arguments supporting this view are considered. It is shown that, although the equilibrium conditions may be locally improved through a special choice of the profile of the plasma rotation velocity, toroidal rotation, on the whole, has a negative effect on the plasma equilibrium. However, under typical tokamak conditions, a decrease in the equilibrium β limit due to plasma rotation is insignificant and, consequently, the effect of the rotation of a hot plasma on its equilibrium can be neglected. © 2003 MAIK “Nauka / Interperiodica”. [ABSTRACT FROM AUTHOR]

A universal method for introducing flux coordinates in toroidal equilibrium plasma configurations is proposed. The characteristic features of this method are a prescription of two scalar functions, one of which determines the explicit form of the Jacobian, and a universal form of the equations for arbitrary flux coordinates. This makes the method simple, clear, and effective. © 1997 American Institute of Physics. [ABSTRACT FROM AUTHOR]

The article presents the zonal geodesic acoustic modes (ZGAMs) in a tokamak and the theoretical predictions were noted. The study aims to solve the problem on the possibility to predict ZGAM through kinetic theory of collisionless plasmas. The author concludes that the ZGAM existence is possible under the collisionless plasmas.

The article presents a response from the author of the article "Energy Principle in the Boozer Model." According to the author, there are no assertions ascribed to him in the comments of the article. The author also reacts to the comment, which states that there is something wrong with the mathematical formulation of the plasma response used in the VALEN code.