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.     

Microwave processes in the Octupole Galathea

Results are presented from experimental studies of electromagnetic emission and plasma oscillations in the plasma-frequency range in the Octupole Galathea confinement system. Experiments are performed in the electric-discharge mode at low magnetic fields (the barrier field is 0.002–0.01 T); the working gas is argon or hydrogen. It is found that the most intense microwave oscillations at frequencies of 1–5 GHz are excited near the plasma axis and in the magnetic-barrier region. The oscillations are excited by the discharge current and decay after the voltage is switched off. The experiments show that microwave oscillations excited in the magnetic-barrier region are responsible for the small value of the energy confinement time in the system.     

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).     

Formation of a cylindrical ion beam in the field of an axisymmetric system of ring currents at a low Hall current

A study is made of the structure of an accelerating layer with a closed Hall current and the geometry of an ion beam in an external magnetic field created by an arbitrary axisymmetric system of ring currents under conditions such that the Hall current can be ignored. It is shown that the ion trajectories are perpendicular to the magnetron cutoff surface for electrons and that the cathode plasma boundary coincides with a magnetic field line. A magnetic field configuration is found in which the cutoff surface is a plane surface perpendicular to the axis of the system. It is shown that, for a small ratio of the gyroradius of the electrons (in terms of the maximum energy acquired by them in the layer) to the characteristic size of the structure, such a configuration provides sufficient means to ensure the formation of slightly converging ion beams or those that are essentially parallel to the system axis.     

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.     

Launching of Microwaves into a Dense Plasma in Open Confinement Systems

A study is made of the propagation of microwave beams in a plasma and their passage through the critical surface. It is shown that, in order for microwaves to penetrate deeply into a dense plasma, it is necessary to launch them through a magnetic mirror at a slight angle to the device axis. The characteristic features of ray trajectories are analyzed both ahead of and behind the critical surface. In a dense plasma behind the critical surface, microwaves tend to run out of the axial region toward the plasma periphery. This tendency may be unfavorable for heating plasmas whose radial density profiles are strongly peaked about the system axis. The problems under analysis are particularly important for assessing the prospects for ECR heating of dense plasmas in open confinement systems.     

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).     

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.     

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.     

Linear Transformation of Electromagnetic Wave Beams of the Electron-Cyclotron Range in Toroidal Magnetic Configurations

The field structure of quasi-optical wave beams tunneled through the evanescence region in the vicinity of the plasma cutoff in a nonuniform magnetoactive plasma is analyzed. This problem is traditionally associated with the process of linear transformation of ordinary and extraordinary waves. An approximate analytical solution is constructed for a rather general magnetic configuration applicable to spherical tokamaks, optimized stellarators, and other magnetic confinement systems with a constant plasma density on magnetic surfaces. A general technique for calculating the transformation coefficient of a finite-aperture wave beam is proposed, and the physical conditions required for the most efficient transformation are analyzed.     

Magnetic probe measurements of the current sheath on the PF-3 facility

Results are presented from experimental studies of the dynamics of the current sheath (CS) on the PF-3 plasma focus facility. The parameters of the sheath, including the current distribution in it, were measured using absolutely calibrated magnetic probes installed at different positions with respect to the facility axis and the anode surface. The CS dynamics in discharges operating in argon and neon was investigated, and the skin depth in different stages of the discharge was determined. One of the probes was installed at a distance of ≈2 cm from the facility axis, which made it possible to estimate the efficiency of current transfer to the region of pinch formation. Operating modes were obtained in which the current dynamics detected by magnetic probes at different distances from the axis agreed well with the dynamics of the total discharge current until the instant of singularity in the current time derivative. It is shown that shunting breakdowns can lead to the formation of closed current loops. The shunting of the discharge current by the residual plasma is directly related to the efficiency of snowplowing of the working gas by the CS as it propagates from the insulator toward the facility axis.     

Influence of the radial profile of the electric potential on the confinement of a high-β two-component plasma in a gas-dynamic trap

One of the most important problems to be studied in the gas-dynamic trap (GDT) facility is the investigation of MHD stability and cross-field transport in a plasma with a relatively high value of β = πp/B ². Recent experiments demonstrated that the radial electric field produced in the plasma by using radial limiters and coaxial end plasma collectors improves plasma stability in axisymmetric magnetic mirror systems without applying special MHD stabilizers. The experimental data presented in this work show that stable plasma confinement can be achieved by producing a radial potential drop across a narrow region near the plasma boundary. Creating radial electric fields of strength 15–40 V/cm causes a shear plasma flow, thereby substantially increasing the plasma confinement time. When all the radial electrodes were grounded, the confinement was unstable and the plasma confinement time was much shorter than the characteristic time of plasma outflow through the magnetic mirrors. Measurements of cross-field plasma fluxes with the use of a specially designed combined probe show that, in confinement modes with differential plasma rotation, transverse particle losses are negligibly small as compared to longitudinal ones and thus can be ignored. It is also shown that, when the GDT plasma is in electric contact with the radial limiters and end collectors, the growth rate of interchange instability decreases considerably; such a contact, however, does not ensure complete MHD stability when the electrodes are at the same potential.     

Study of the mechanism for fast ion heating in the GOL-3 multimirror magnetic confinement system

Results are presented from experimental studies of ion heating in the GOL-3 device. The experiments were carried out in a multimirror configuration with a local magnetic well. It was found that, during the injection of a relativistic electron beam, a decrease in the local density of the beam in a magnetic well, which is proportional to the decrease in the strength of the longitudinal magnetic field, results in the formation of a short plasma region with a low electron temperature. The measured longitudinal gradient of the plasma pressure corresponds to an electron temperature gradient of ～2–3 keV/m. Axially nonuniform heating of the plasma electrons gives rise to the macroscopic motion of the plasma along the magnetic field in each cell of the multimirror confinement system. The mixing of the counterpropagating plasma flows inside each cell leads to fast ion heating. Under the given experimental conditions, the efficiency of this heating mechanism is higher than that due to binary electron-ion collisions. The collision and mixing of the counterpropagating plasma flows is accompanied by a neutron and γ-ray burst. The measured ratio of the plasma pressure to the vacuum magnetic field pressure in these experiments reaches 0.2.     

Investigations of high-energy electrons of the microwave discharge plasma at configuration of the “Magnetor” Bi-dipole magnetic confinement system by X-ray radiation analyses

The results of the investigations of a group of fast electrons in a microwave discharge plasma in the “Magnetor” magnetic trap are presented. The data on the presence and location of this group of electrons is important for estimating the total plasma pressure taking the previous probe measurements into account. Fast electrons are found to be localized within the magnetic separatrix in the region of confinement of the main plasma. The maximal energy of fast electrons is higher than 25 keV.     

Heliospheric current sheet and effects of its interaction with solar cosmic rays

The effects of interaction of solar cosmic rays (SCRs) with the heliospheric current sheet (HCS) in the solar wind are analyzed. A self-consistent kinetic model of the HCS is developed in which ions with quasiadiabatic dynamics can present. The HCS is considered an equilibrium embedded current structure in which two main plasma species with different temperatures (the low-energy background plasma of the solar wind and the higher energy SCR component) contribute to the current. The obtained results are verified by comparing with the results of numerical simulations based on solving equations of motion by the particle tracing method in the given HCS magnetic field with allowance for SCR particles. It is shown that the HCS is a relatively thin multiscale current configuration embedded in a thicker plasma layer. In this case, as a rule, the shear (tangential to the sheet current) component of the magnetic field is present in the HCS. Taking into account high-energy SCR particles in the HCS can lead to a change of its configuration and the formation of a multiscale embedded structure. Parametric family of solutions is considered in which the current balance in the HCS is provided at different SCR temperatures and different densities of the high-energy plasma. The SCR densities are determined at which an appreciable (detectable by satellites) HCS thickening can occur. Possible applications of this modeling to explain experimental observations are discussed.     

Three-dimensional MHD simulations of forced magnetic reconnection

Results are presented from MHD simulations of three-dimensional flows of a high-conductivity plasma in the vicinity of a null point of a magnetic field. The excitation of an electric current at the boundary of the computation region results in self-consistent plasma flows and change in the structure of the magnetic field. Generally, in the vicinity of a null point, an MHD singularity arises that manifests itself in the formation of locally plane current sheets. It is shown that the current sheet can be oriented either along the separatrix surface of a magnetic configuration or perpendicular to it, except for axisymmetric configurations (or close to them), when the excitation of an electric current in the direction orthogonal to the separatrix surface does not lead to the formation of a current sheet.     

Investigation of plasma characteristics in an unbalanced magnetron sputtering system

Results are presented from experimental studies of a magnetron sputtering system for different configurations of the magnetic field above the cathode surface. The current-voltage characteristics of a magnetron discharge at different working gas pressures (0.08–0.3 Pa) and currents in the unbalancing coil were studied. The production and transport of charge carriers in a magnetron discharge with an unbalanced magnetic field was investigated by means of probe measurements of plasma characteristics and ion energies in the region between the substrate and the magnetic trap at the cathode surface. The radial distributions of the ion current density, plasma potential, and floating potential in the unbalanced operating mode are found to have pronounced extrema at the magnetron axis. It is shown that the plasma density near the substrate can be increased considerably when the axial magnetic field is high enough to efficiently confine plasma electrons and prevent their escape to the chamber wall.     

Hamiltonian formalism in the problem on the modification of the current density profile during the development of tearing instability in a tokamak

The formation of a magnetic island as a result of tearing instability can be interpreted as the bifurcation of an axisymmetric equilibrium configuration at which nested magnetic surfaces are preserved. The modification of the current density profile due to such bifurcation is studied using the Hamiltonian formalism. In the case of a long narrow island, the gradient profile changes to a profile with an extremum on the axis of the magnetic island.