Islands and ergodicity of the plasma current in toroidal magnetic confinement systems

Magnetic and current structures arising due to resonant perturbations of an equilibrium current-carrying magnetic configuration are analyzed using the Hamiltonian formalism. Special attention is paid to axisymmetric tokamak and pinch configurations. It is shown that, due to the very different dependences of the magnetic and current rotational transforms on the plasma pressure, the resonances (islands) of the magnetic field may not coincide with those of the current. The perturbed force-free equilibrium of a cylindrical pinch in which the field and current islands overlap is analyzed. The long-lived ribbon structures observed in the JET tokamak are explained as a manifestation of a force-free magneto-current island.     

Physical nature of the electric current produced by the asymmetry of particle motion in toroidal magnetic confinement systems

A new type of longitudinal electric current is revealed by analyzing the drift trajectories of charged particles in a tokamak—the current that may be referred to as the asymmetry current because it is associated with the asymmetry of the boundary between trapped and transit particles in phase space. The generation of this current is explained by the fact that the motions of the particles that cross the magnetic surface at a given point in opposite directions are qualitatively different. The asymmetry current results from the toroidal variations of the magnetic field and is maintained by the radial momentum flux of transit particles. The contribution of the particles of different species to the asymmetry current density is proportional to their pressure, is independent of the gradients of the plasma parameters, is maximum at the magnetic axis, and decreases toward the plasma periphery. In contrast to standard neoclassical theory, the asymmetry current can be found only from exact particle trajectories. The asymmetry current is calculated for tokamaks with differently shaped magnetic surfaces and for a model stellarator. By exploiting the newly revealed asymmetry current, together with the bootstrap current, it may be possible to substantially simplify the problem of creating a tokamak reactor.     

Calculation of the charged particle source in a toroidal magnetic confinement system (hydrodynamic approach)

In order to model transport processes in magnetic confinement systems, it is necessary to have information on the charged particle source. This in turn requires calculation of the inward flux of neutral particles. In this paper, a method for solving this problem in the hydrodynamic approach for the neutral gas is proposed. The average velocity of neutral particles and the spatial distribution of their density are determined. The obtained expression for the neutral density almost completely coincides with that calculated previously by solving the kinetic equation. However, the computational time required to solve the problem in the proposed hydrodynamic approach is much shorter than that in the kinetic approach.     

Geometric properties of magnetic field lines on toroidal magnetic surfaces in the context of plasma equilibrium

An analysis of plasma equilibrium in a magnetic confinement system includes studies of how the shape of the magnetic surfaces is distorted with varying magnitude and profile of the plasma pressure. Such studies allow one, in particular, to determine the maximum β value consistent with equilibrium, β_eq, i.e., the maximum plasma pressure above which the equilibrium in a confinement system under analysis is impossible. Since the magnetic field lines form magnetic surfaces, their global relationship with equilibrium is obvious. Here, special attention is paid to a local relationship between equilibrium and geometric properties of the magnetic field lines.     

Use of internal current rings in long closed magnetic confinement systems

A closed magnetic confinement system is considered in the shape a corrugated torus into one or several mirror cells of which current rings are introduced that reverse the magnetic field on the axis. An internal current ring surrounded by plasma creates a magnetic configuration with an average magnetic well on the axis. The axial plasma region of such a configuration is stabilized by cusps, whereas the outer region can be stabilized by a divertor, provided that the plasma pressure gradually decreases toward the periphery. The use of internal current rings may be profitable in stellarators in which the confinement region can be divided into several regions by magnetic mirrors.     

Convectively stable pressure profile in magnetic confinement systems with internal rings

A convectively stable pressure profile in a long multiple-mirror (corrugated) magnetic confinement system with internal current-carrying rings is calculated. The plasma energy content in the axial region can be increased by using an internal ring that reverses the on-axis magnetic field direction and gives rise to an average magnetic well near the axis. The pressure profile in the outer region—outside the magnetic well—is considered in detail. It is shown that, in the radial pressure profile, a pedestal can be formed that leads to a higher pressure drop between the center and the plasma edge. The pressure profile is calculated from the Kruskal-Oberman criterion—a necessary and sufficient condition for the convective stability of a collisionless plasma. The revealed pedestal arises near the boundary of the average magnetic well in the region of the smallest but alternating-sign curvature of the magnetic field lines due to a break in the convectively stable pressure profile. Such a shape of the stable pressure profile can be attributed to the stabilizing effect of the alternating-sign curvature of the field lines in the multiple-mirror magnetic confinement systems under consideration.     

MHD plasma stability in alternative toroidal systems and the local dispersion relation

The local dispersion relation obtained for an inhomogeneous anisotropic high-pressure plasma in the Chew-Goldberger-Low approximation is used to qualitatively study small-scale MHD plasma instabilities in alternative magnetic configurations in which the plasma compressibility plays a significant stabilizing role. It is established that it is important to satisfy the Bernstein-Kadomtsev condition in order to reduce the growth rate of the quasi-flute oscillations. Moderate plasma anisotropy is shown not to have a substantial destabilizing effect on the MHD plasma stability under the Bernstein-Kadomtsev condition in alternative systems. The situation in which the electron compressibility vanishes while the ion compressibility is nonzero is discussed; it is shown that, in this situation, the Bernstein-Kadomtsev condition becomes more stringent as the longitudinal wavenumber increases.     

Stability of localized MHD perturbations in confinement systems with closed magnetic field lines

Conditions are determined for the stability of a finite-pressure plasma against perturbations localized near a magnetic field line in a magnetic confinement system without average minimum-B. The marginal stability (ω²=0) is achieved at the pressure profile p∝U ^?5/3 (where $U = \oint {\frac{{dl}}{B}}$ ), provided that the pressure is lower than a certain critical value above which an unstable incompressible mode in which the displacement as a function of the coordinate along the field line has zeros appears at some magnetic field line.     

Studies of the impurity pellet ablation in the high-temperature plasma of magnetic confinement devices

The ablation of impurity pellets in tokamak and stellarator plasmas is investigated. Different mechanisms for shielding the heat fluxes from the surrounding plasma to the pellet surface are discussed. A model for impurity pellet ablation is developed that can account for both neutral and electrostatic shielding. It is shown that the experimental values of the impurity pellet ablation rate are well described by the neutral gas shielding model over a wide range of plasma temperatures and densities. Taking into account the electrostatic shielding leads to worse agreement between the predictions of the model and the experimental data; this result still remains unclear. Scaling laws are obtained that allow one to estimate the local ablation rate of impurity pellets made of various materials over a wide range of plasma parameters in the neutral gas shielding model.     

Beta-limiting MHD phenomena in toroidal systems

Equilibrium effects, neoclassical tearing modes, and resistive wall modes are discussed as phenomena limiting attainable plasma pressure, with emphasis on the current progress in theoretical studies at the Kurchatov Institute. The review is based on the results presented at the 11th International Congress on Plasma Physics (Sydney, 2002).     

Plasma convection near the threshold for MHD instability in nonparaxial magnetic confinement systems

Using a highly nonparaxial magnetic confinement system with an internal levitated ring as an example, it is shown that, in a plasma near the threshold for ideal MHD instability, the external heating and the original local dissipative processes may give rise to and maintain self-consistent nonlinear MHD convection, which leads to an essentially nonlocal, enhanced heat transport. A closed set of equations is derived that makes it possible to describe such convective processes in a weakly dissipative plasma with β～1. Numerical simulations carried out with a specially devised computer code demonstrate that the quasisteady regime of nonlinear convection actually exists and that the marginally stable profile of the plasma pressure is maintained. A large amount of data on the structure of the nascent convective flows is obtained and analyzed.     

Destruction of hyperbolic magnetic axes in steady three-dimensional toroidal magnetic structures

A study is made of the boundary regions of magnetic structures formed either near the last closed flux surface of the main magnetic configuration in a stellarator or near magnetic islands in more general toroidal confinement systems with topologically equivalent sheared magnetic configurations. With a relatively simple approximate analytic model based on the perturbation method, it was possible not only to reproduce earlier results on the destruction of hyperbolic magnetic axes in the three-dimensional toroidal magnetic configurations under consideration but also to obtain some new results, in particular, to analytically estimate the sizes of the separatrix regions of stochastic magnetic fields that arise in the main stellarator configuration and also near the inner chains of magnetic islands in any magnetic configuration under consideration. It is notable that the boundary region of the main stellarator magnetic configuration is a multiply connected structure, the outer part of which is largely governed by the current distribution in the magnetic system creating this configuration.     

Monitoring of the plasma isotope composition by charge-exchange neutral fluxes in a rippled toroidal magnetic field

To determine the hydrogen isotope ratio in plasma from charge-exchange neutral fluxes, certain assumptions are traditionally adopted, the most restrictive of which concerns the form of the ion distribution function, which is usually assumed to be Maxwellian. For large tokamaks, however, additional analysis is required in order to determine the energy range in which distortions of the distribution function will not lead to errors in isotope ratio measurements. The possible influence of drift motion on the ion distribution function is considered. Experimental results obtained in the ASDEX-Upgrade tokamak are presented. The role this mechanism plays during the transition to the H-mode in the auxiliary heating regime is compared to that in the ohmic heating regime.     

Interplay between intrinsic plasma rotation and magnetic island evolution in disruptive discharges

The behavior of the intrinsic toroidal rotation of the plasma column during the growth and eventual saturation of m/n = 2/1 magnetic islands, triggered by programmed density rise, has been carefully investigated in disruptive discharges in TCABR. The results show that, as the island starts to grow and rotate at a speed larger than that of the plasma column, the angular frequency of the intrinsic toroidal rotation increases and that of the island decreases, following the expectation of synchronization. As the island saturates at a large size, just before a major disruption, the angular speed of the intrinsic rotation decreases quite rapidly, even though the island keeps still rotating at a reduced speed. This decrease of the toroidal rotation is quite reproducible and can be considered as an indicative of disruption.     

Modeling of the parametric dependence of the edge toroidal rotation

Modeling of the edge toroidal rotation and its dependence on the edge plasma parameters is performed by means of the B2SOPS5.0 transport code for ohmic shots both for MAST and ASDEX Upgrade configurations. The impact of plasma current, toroidal magnetic field, plasma density, and temperature is investigated. The connection between the toroidal rotation and edge radial electric field is also studied. The results of the simulation are consistent with the parametric dependence predicted analytically. Published in Russian in Fizika Plazmy, 2008, Vol. 34, No. 9, pp. 791–797. The text was submitted by the authors in English.     

Stability of a quasi-flute mode under the Bernstein-Kadomtsev condition in a toroidal confinement system

It is shown that the growth rate of the MHD instability in toroidal configurations is slower in a situation in which the Bernstein-Kadomtsev condition is satisfied while the Mercier stability criterion is not. Under the Bernstein-Kadomtsev condition, Alfvénic Mercier modes are not excited, but quasi-flute acoustic Mercier modes develop instead. In confinement systems with closed magnetic field lines, the Bernstein-Kadomtsev condition ensures MHD stability; however, a small rotational transform produced by magnetic perturbations can give rise to a quasi-flute acoustic instability whose growth rate is proportional to the perturbation amplitude, in which case the fastest growing oscillations are those with the shortest wavelengths.