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.     

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.     

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.     

Experiments on the transportation of a magnetized plasma stream in the GOL-3 facility

The program of the deep upgrade of the GOL-3 multiple-mirror trap is presented. The upgrade is aimed at creating a new GOL-NB open trap located at the GOL-3 site and intended to directly demonstrate the efficiency of using multiple-mirror magnetic cells to improve longitudinal plasma confinement in a gasdynamic open trap. The GOL-NB device will consist of a new central trap, adjoint cells with a multiple-mirror magnetic field, and end tanks (magnetic flux expanders). Plasma in the central trap will be heated by neutral beam injection with a power of up to 1.5 MW and duration of 1 ms. At present, physical experiments directed at developing plasma technologies that are novel for this facility are being carried out using the 6-m-long autonomous part of the GOL-3 solenoid. The aim of this work was to develop a method for filling the central trap with a low-temperature start plasma. Transportation of a plasma stream from an arc source over a distance of 3 m in a uniform magnetic field with an induction of 0.5–4.5 T is demonstrated. In these experiments, the axial plasma density was (1–4) × 10²⁰ m^–3 and the mirror ratio varied from 5 to 60. In general, the experiments confirmed the correctness of the adopted decisions for the start plasma source of the GOL-NB device.     

Role of the mean curvature in the geometry of magnetic confinement configurations

Examples are presented of how the geometric notion of the mean curvature is applied to the vector of a general magnetic field and to magnetic surfaces. It is shown that the mean curvature is related to the variation of the absolute value of the magnetic field along its lines. Magnetic surfaces of constant mean curvature are optimum for plasma confinement in multimirror open confinement systems and rippled tori.     

Geometric properties of plasma equilibrium near a given magnetic surface

In order to describe plasma equilibrium near a given magnetic surface, it is sufficient to specify the shape of the surface, the distribution of the magnetic field strength on it, and two profile coefficients (the derivatives of the plasma pressure and current). Geometrically, this means that all the basis vectors of the flux coordinate system should be determined on the magnetic surface. Expressions for these vectors in an invariant basis are obtained. The maximum possible value of the pressure profile coefficient consistent with equilibrium is described by a universal geometric relationship that expresses the limiting value of the torsion of the magnetic field line on the magnetic surface as a function of the curvature of the surface. The relationships obtained are used to show that the stability of a system with closed magnetic field lines is governed by perturbations of the anti-Mercier type.     

Pressure profiles of a plasma confined by the magnetic field of a ring current

Pressure profiles p(ψ) marginal with respect to convective instability in a toroidal tubular plasma confined by the magnetic field of an internal levitated ring current and external ring currents are studied as functions of the shape of the magnetic separatrix. Configurations are found in which the maximum plasma pressure in a finite-width layer near the plasma boundary decreases by two orders of magnitude at the expense of artificially raising the effective length (characterized by the integral ∮dl/B) of the magnetic field lines near the separatrix surface. It is shown that, in the case of a straight cylindrical tubular plasma, which is the limiting case of a toroidal configuration with an arbitrarily large aspect ratio, the sufficient condition for the plasma to be MHD stable against both convective and kink perturbations is satisfied for local values β≤0.4. __________ Translated from Fizika Plazmy, Vol. 26, No. 6, 2000, pp. 519–528. Original Russian Text Copyright ￠ 2000 by Popovich, Shafranov.     

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.     

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.     

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.     

Electromagnetic oscillations near the critical surface in a magnetized plasma

It is shown that, in a plasma whose density varies across the magnetic field lines, electromagnetic oscillations that are localized near the critical surface can exist. Such oscillations can be excited spontaneously in a nonequilibrium plasma of closed magnetic confinement systems.     

Formation of an internal transport barrier and magnetohydrodynamic activity in experiments with the controlled density of rational magnetic surfaces in the T-10 Tokamak

Results are presented from experiments on the formation of an internal electron transport barrier near the q = 1.5 rational surface in the T-10 tokamak. The experiments were carried out in the regime with off-axis electron cyclotron resonance (ECR) heating followed by a fast plasma current ramp-up. After suppressing sawtooth oscillations by off-axis ECR heating, an internal transport barrier began to form near the q = 1.5 rational surface. In the phase of the current ramp-up, the quality of the transport barrier improved; as a result, the plasma energy confinement time increased 2–2.5 times. The intentionally produced flattening of the profile of the safety factor q(r) insignificantly affected magnetohydrodynamic activity in the plasma column in spite of the theoretical possibility of formation of substantial m/n = 3/2 and 2/1 magnetic islands. Conditions are discussed under which the flattening of the profile of the safety factor q near low-order rational surfaces leads to the formation of either an internal transport barrier or the development of an island magnetic structure induced by tearing modes.     

Modeling of reference operating scenario of GOL-NB multiple-mirror trap

Currently, the GOL-NB multiple-mirror trap is being developed at the Budker Institute of Nuclear Physics, Siberian Branch, Russian Academy of Sciences. The main scientific goal pursued by building GOL-NB is direct demonstration of suppression of longitudinal losses of particles and energy from the trap by using sections with a multiple-mirror magnetic field, which can be attached to the central gas-dynamic trap. Plasma heating in GOL-NB will be accomplished by neutral beam injection with a power of up to 1.5MW. The paper presents the first results of modeling the dynamics of the plasma parameters and fast ions under the reference operating scenario of the trap in which traditional short magnetic mirrors, rather than multiple-mirror sections, are attached to the central trap. In such a configuration, the plasma lifetime in the trap is expected to be minimal. The modeling was performed by using the DOL kinetic code. As a result, the initial conditions of the experiments are refined and the requirements to the system of maintaining the particle balance in the trap are determined.     

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.     

Thin current sheets in collisionless plasma: Equilibrium structure,plasma instabilities,and particle acceleration

The review is devoted to plasma structures with an extremely small transverse size, namely, thin current sheets that have been discovered and investigated by spacecraft observations in the Earth’s magnetotail in the last few decades. The formation of current sheets is attributed to complicated dynamic processes occurring in a collisionless space plasma during geomagnetic perturbations and near the magnetic reconnection regions. The models that describe thin current structures in the Earth’s magnetotail are reviewed. They are based on the assumption of the quasi-adiabatic ion dynamics in a relatively weak magnetic field of the magnetotail neutral sheet, where the ions can become unmagnetized. It is shown that the ion distribution can be represented as a function of the integrals of particle motion—the total energy and quasi-adiabatic invariant. Various modifications of the initial equilibrium are considered that are obtained with allowance for the currents of magnetized electrons, the contribution of oxygen ions, the asymmetry of plasma sources, and the effects related to the non-Maxwellian particle distributions. The theoretical results are compared with the observational data from the Cluster spacecraft mission. Various plasma instabilities developing in thin current sheets are investigated. The evolution of the tearing mode is analyzed, and the parameter range in which the mode can grow are determined. The paradox of complete stabilization of the tearing mode in current sheets with a nonzero normal magnetic field component is thereby resolved based on the quasi-adiabatic model. It is shown that, over a wide range of current sheet parameters and the propagation directions of large-scale unstable waves, various modified drift instabilities—kink and sausage modes—can develop in the system. Based on the concept of a turbulent electromagnetic field excited as a result of the development and saturation of unstable waves, a mechanism for charged particle acceleration in turbulent current sheets is proposed and the energy spectra of the accelerated particles are obtained.     

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.     

Numerical simulation of drift-resistive ballooning turbulence in the presence of the GA mode in the plasma edge tokamak

Drift-resistive ballooning turbulence is simulated numerically based on a quasi-three-dimensional computer code for solving nonlinear two-fluid MHD equations in the scrape-off layer plasma in a tokamak. It is shown that, when the toroidal geometry of the magnetic field is taken into account, additional (geodesic) flux terms associated with the first poloidal harmonic (∼sinθ) arise in the averaged equations for the momentum, density, and energy. Calculations show that the most important of these terms is the geodesic momentum flux (the Stringer-Windsor effect), which lowers the poloidal rotation velocity. It is also shown that accounting for the toroidal field geometry introduces experimentally observed, special low-frequency MHD harmonics—GA modes—in the Fourier spectra. GA modes are generated by the Reynolds turbulent force and also by the gradient of the poloidally nonuniform turbulent heat flux. Turbulent particle and heat fluxes are obtained as functions of the poloidal coordinate and are found to show that, in a tokamak, there is a “ballooning effect” associated with their maximum in the weak magnetic field region. The dependence of the density, temperature, and pressure on the poloidal coordinate is presented, as well as the dependence of turbulent fluxes on the toroidal magnetic field.     

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.     

Influence of plasma pedestal profiles on access to ELM-free regimes in ITER

The influence of current density and pressure gradient profiles in the pedestal on the access to the regimes free from edge localized modes (ELMs) like quiescent H-mode in ITER is investigated. Using the simulator of MHD modes localized near plasma boundary based on the KINX code, calculations of the ELM stability were performed for the ITER plasma in scenarios 2 and 4 under variations of density and temperature profiles with the self-consistent bootstrap current in the pedestal. Low pressure gradient values at the separatrix, the same position of the density and temperature pedestals and high poloidal beta values facilitate reaching high current density in the pedestal and a potential transition into the regime with saturated large scale kink modes. New version of the localized MHD mode simulator allows one to compute the growth rates of ideal peeling-ballooning modes with different toroidal mode numbers and to determine the stability region taking into account diamagnetic stabilization. The edge stability diagrams computations and sensitivity studies of the stability limits to the value of diamagnetic frequency show that diamagnetic stabilization of the modes with high toroidal mode numbers can help to access the quiescent H-mode even with high plasma density but only with low pressure gradient values at the separatrix. The limiting pressure at the top of the pedestal increases for higher plasma density. With flat density profile the access to the quiescent H-mode is closed even with diamagnetic stabilization taken into account, while toroidal mode numbers of the most unstable peeling-ballooning mode decrease from n = 10?40 to n = 3?20.