Plasma equilibrium in a double-dipole magnetic confinement system with a separatrix

Results are presented from theoretical studies of plasma equilibrium consistent with the convective stability of ideal interchange modes in axisymmetric configurations with an outward-decreasing field that may have a separatrix limiting the plasma volume. A two-dimensional numerical code is developed to solve the Grad-Shafranov equation with a convectively stable pressure distribution at an arbitrary value of β. The problem is solved for an actual geometry of the magnetic field produced by thin current rings. Configurations of a double-dipole confinement system are calculated for the parameters measured in experiments carried out in the Magnetor device, as well as for higher β values. A configuration of a model mirror system with a divertor is also calculated. The code allows one to optimize confinement systems operating at high β values at which equilibrium still can exist.     

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.     

Generation of low-frequency radiation by a nonequilibrium plasma of an RF discharge in a linear mirror magnetic confinement system

The generation of ion-cyclotron radiation in a plasma resonator formed by an RF discharge in a linear mirror magnetic confinement system is revealed and investigated. It is shown that the experimental setup makes it possible to study the composition of a multicomponent discharge plasma and to detect multiply charged ions. Collisional losses in such a resonator are estimated, and the pressure range within which the growth rate of the ion-cyclotron instability substantially exceeds the collisional damping rate is determined.     

Investigation of the helicon discharge plasma parameters in a hybrid RF plasma system

Results of an experimental study of the helicon discharge plasma parameters in a prototype of a hybrid RF plasma system equipped with a solenoidal antenna are described. It is shown that an increase in the external magnetic field leads to the formation of a plasma column and a shift of the maximum ion current along the discharge axis toward the bottom flange of the system. The shape of the plasma column can be controlled via varying the configuration of the magnetic field.     

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.     

Production and study of a high-temperature plasma in the central solenoid of the AMBAL-M device

Results are presented from experiments on the production and study of a hot dense plasma in the central solenoid of the AMBAL-M fully axisymmetric ambipolar magnetic confinement system. The hot plasma in the solenoid and end cell is produced by filling the system with a thermally insulated current-carrying plasma stream with developed low-frequency turbulence. The plasma stream is generated by a gas-discharge plasma source placed upstream from the magnetic mirror of the solenoid. As a result, an MHD-stabilized plasma with a length of 6 m, a diameter of 40 cm, a density of 2×10¹³ cm^?3, an ion energy of 250 eV, and an electron temperature of 60 eV is produced in the central solenoid. It is found that, in the quiescent decay phase, transverse plasma losses from the solenoid due to low-frequency oscillations and nonambipolar transport are rather small and comparable with the classical diffusion losses.     

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.     

Toroidal mirror system

A study is made of a toroidally linked mirror system with a zero rotational transform and a three-dimensional magnetic field that ensures good confinement of charged particles. A toroidally linked magnetic mirror configuration at low plasma pressures is calculated by numerically solving the isometry equation for the magnetic field to second order in the small parameter of the paraxial approximation. The calculations carried out with the VMEC code for a particular linked magnetic mirror configuration demonstrate the possibility of achieving good confinement of drifting particles. The calculated results show that it is, in principle, possible to link mirror cells into a toroidal configuration capable of providing plasma confinement at a tokamak level.     

Azimuthally asymmetric eigenmodes of a magnetized plasma cylinder around a dielectric rod in a circular waveguide

The electrodynamics of a circular waveguide with a dielectric rod surrounded by a magnetized plasma layer is considered. A general dispersion relation for azimuthally asymmetric perturbations is derived, and its solutions describing slow waves—specifically, electromagnetic and plasma modes, as well as (and primarily) hybrid waves that combine the properties of both mode types—are investigated numerically. For the fundamental waveguide mode of the system—the HE₁₁ mode—the parameters of the plasma layer are determined at which the mode cannot be subject to Cherenkov interaction with a relativistic electron beam at a given frequency. For both waveguide and plasma modes, the radial profiles of the longitudinal components of the electric field and Poynting vector, the fractions of RF power carried within the dielectric and plasma regions and vacuum gap, and the coupling impedance are calculated as functions of the parameters of the plasma layer. The evolution of the field structure during the formation of asymmetric hybrid waves is traced. The results of calculating the dispersion and coupling impedance are analyzed as applied to an antenna-amplifier—a relativistic traveling-wave tube operating on the HE₁₁ mode of the dielectric rod: specifically, the implementability of the concept in the presence of a plasma at the rod surface is estimated, and the possible role of azimuthally asymmetric and symmetric plasma modes is examined.     

Particle confinement in axisymmetric poloidal magnetic field configurations with zeros of B: Methodological note

Collisionless particle confinement in axisymmetric configurations with magnetic field nulls is analyzed. The existence of an invariant of motion—the generalized azimuthal momentum—makes it possible to determine in which of the spatial regions separated by magnetic separatrices passing through the magnetic null lines the particle occurs after it leaves the vicinity of a magnetic null line. In particular, it is possible to formulate a sufficient condition for the particle not to escape through the separatrix from the confinement region to the external region. In the configuration under analysis, the particles can be lost from a separatrix layer with a thickness on the order of the Larmor radius because of the nonconservation of the magnetic moment μ. In this case, the variations in μ are easier to describe in a coordinate system associated with the magnetic surfaces. An analysis is made of the applicability of expressions for the single-pass change Δμ in the magnetic moment that were obtained in different magnetic field models for a confinement system with a divertor (such that there is a circular null line).