V. V. Arsenin

The EPSILON experimental pseudo-symmetric trap

Within the framework of the Adaptive Plasma Experiment (APEX) conceptual project, a trap with closed magnetic field lines, the Experimental Pseudo-Symmetric Closed Trap (EPSILON), is examined. The APEX project is aimed at theoretical and experimental development of the physical foundations for a steady state thermonuclear reactor designed on the basis of an alternative magnetic trap with tokamak-like large β plasma confinement. A discussion is given of the fundamental principle of pseudo-symmetry, which a magnetic configuration with tokamak-like plasma confinement should satisfy. Examples are given of calculations in the paraxial approximation of pseudo-symmetric curvilinear elements with a poloidal modulus B isoline. The EPSILON trap, consisting of two direct axisymmetric mirrors linked by two curvilinear pseudo-symmetric elements, is considered. To increase the equilibrium β, the plasma currents are short-circuited within curvilinear equilibrium elements. An untraditional scheme of MHD stabilization for a trap with closed field lines by use of axisymmetric mirrors with a divertor is analysed. The experimental installation EPSILON-One Mirror Element (OME), which is under construction for experimental investigation of stabilization by divertor, is discussed. The opportunity for applying the ECR method of plasma production in EPSILON-OME in conditions of high density and low magnetic field is examined.

MHD stability of a plasma in an axisymmetric open divertor configuration

For a plasma with confined in a system of two simple axisymmetric mirror cells separated by a divertor cell, a radial plasma pressure profile is obtained that is stable against convective modes and drops off to zero at the separatrix. The shape of the marginally stable pressure profile depends on the geometric parameters (such as mirror ratios and the localization of the divertor cell), the ratio of the pressure in the mirrors cells to the pressure in the divertor cell, and the degree of pressure anisotropy.

Plasma equilibrium in axisymmetric open divertor configurations

The equilibrium of a plasma with isotropic pressure in a periodic divertor configuration with a poloidal magnetic field is calculated. The issue of how the plasma equilibrium changes as the parameter β≡8πp/B2 increases is considered for a fairly representative class of pressure profiles p(ψ) (where ψ is the flux coordinate). It is shown that the plasma can be in equilibrium up to β values (in terms of the vacuum magnetic field at the divertor axis) on the order of unity.

On the resonance amplification of magnetic perturbations near the threshold of tearing instability in a tokamak

Using a cylindrical model, a relatively simple description is presented of how a magnetic field perturbation stimulated by a low external helical current or a small helical distortion of the boundary and generating magnetic islands penetrates into a plasma column with a magnetic surface q=m/n to which tearing instability is attached. Linear analysis of the classical instability with an aperiodic growth of the perturbation in time shows that the perturbation amplitude in plasma increases in a resonant manner as the discharge parameters approach the threshold of tearing instability. In a stationary case, under the assumption on the helical character of equilibrium, which can be found from the two-dimensional nonlinear equation for the helical flux, there is no requirement for the small size of the island. Examples of calculations in which magnetic islands are large near the threshold of tearing instability are presented. The bifurcation of equilibrium near the threshold of tearing instability in plasma with a cylindrical boundary, i.e., the existence of helical equilibrium (along with cylindrical equilibrium) with large islands, is described. Moreover, helical equilibrium can also exist in the absence of instability.

Stabilization of ballooning modes by nonparaxial cells

An analysis is made of the effect of high-curvature stabilizing nonparaxial elements (cells) on the MHD plasma stability in open confinement systems and in confinement systems with closed magnetic field lines. It is shown that the population of particles trapped in such cells has a stabilizing effect not only on convective (flute) modes but also on ballooning modes, which govern the maximum possible β value. In the kinetic approach, which distinguishes between the effects of trapped and passing particles, the maximum possible β values consistent with stability can be much higher than those predicted by the MHD model.

Plasma equilibrium in axisymmetric poloidal magnetic field configurations in flux coordinates

A simple derivation is given of equilibrium equations in flux coordinates in the general case of an anisotropic-pressure plasma. The issue of how to formulate the boundary conditions for these equations is discussed for two types of configurations—a straight system and a system with an internal conductor. Examples of numerical solutions to the equilibrium problem for these configurations are presented.

Large-Scale Perturbations due to a Small-Scale Instability in a Finite-Conductivity Plasma

By considering kink modes in a plasma cylinder in a strong axial magnetic field as an example, it is demonstrated that, because of the finite plasma conductivity (the finite longitudinal plasma permittivity ɛ∥), large-scale perturbations can grow with time due to a small-scale instability that develops near a certain magnetic surface.

Isodynamic axisymmetric equilibrium near the magnetic axis

Plasma equilibrium near the magnetic axis of an axisymmetric toroidal magnetic confinement system is described in orthogonal flux coordinates. For the case of a constant current density in the vicinity of the axis and magnetic surfaces with nearly circular cross sections, expressions for the poloidal and toroidal magnetic field components are obtained in these coordinates by using expansion in the reciprocal of the aspect ratio. These expressions allow one to easily derive relationships between quantities in an isodynamic equilibrium, in which the absolute value of the magnetic field is constant along the magnetic surface (Palumbo’s configuration).

MHD plasma stabilization in a chain of axisymmetric adiabatic open mirror cells

Conditions for convective plasma instability in a chain of axisymmetric adiabatic mirror cells with different signs of magnetic field curvature are analyzed. The boundaries of the region that can be occupied by a stable hollow plasma in a system of two connected cells—a nonparaxial simple mirror cell and a semicusp—are determined, as well as the interval of allowed values of the ratio between the pressures in the cells. Because of the large magnetic field curvature in the component cells, the safety factor that is achieved at both—external and internal—plasma boundaries in accordance with the average min-B principle can be high. It is assumed that the unperturbed pressure in each cell is almost isotropic, in which case the mirror ratio should necessarily be large. A key role in the stability of the plasma is played by its compressibility. A comparison is made between the conditions for complete plasma stabilization against arbitrary perturbations and the conditions for stability of individual cells against the global mode. The stability of the cells against the global mode is sufficient, but not necessary, for stabilizing the chain. The analysis is done by using orthogonal coordinates associated with the unperturbed magnetic field (flux variables). Numerical simulations were carried out for nonparaxial cells from a certain three-parameter family.

MHD stability of a finite-pressure plasma in axisymmetric configurations of the poloidal magnetic field

A set of linear integrodifferential equations is presented for the plasma displacement components that minimize the Kruskal-Oberman functional of the potential energy of an MHD perturbation. Marginal stability results when the smallest eigenvalue of this set of equations is zero.