Convective stability of a plasma in a system of coupled adiabatic open cells in the Kruskal-Oberman model

The Kruskal-Oberman kinetic model is used to determine the conditions for the convective stability of a plasma in a system of coupled axisymmetric adiabatic open cells in which the magnetic field curvature has opposite signs. For a combination of a nonparaxial simple mirror cell and a semicusp, the boundaries of the interval of values of the flux coordinate where the plasma can be stable are determined, as well as the range in which the ratio of the pressures in the component cells should lie. Numerical simulations were carried out for different particle distributions over the pitch angle.     

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 waveguides in space plasma

The waveguide properties of two characteristic formations in the Earth’s magnetotail—the plasma sheet and the current (neutral) sheet—are considered. The question of how the domains of existence of different types of MHD waveguide modes (fast and slow, body and surface) in the (k, ω) plane and their dispersion properties depend on the waveguide parameters is studied. Investigation of the dispersion relation in a number of particular (limiting) cases makes it possible to obtain a fairly complete qualitative pattern of all the branches of the dispersion curve. Accounting for the finite size of perturbations across the wave propagation direction reveals new additional effects such as a change in the critical waveguide frequencies, the excitation of longitudinal current at the boundaries of the sheets, and a change in the symmetry of the fundamental mode. Knowledge of the waveguide properties of the plasma and current sheets can explain the occurrence of preferred frequencies in the low-frequency fluctuation spectra in the magnetotail. In satellite observations, the type of waveguide mode can be determined from the spectral properties, as well as from the phase relationships between plasma oscillations and magnetic field oscillations that are presented in this paper.     

Correction of the axial asymmetry of the poloidal magnetic field in the Globus-M spherical tokamak

The toroidal inhomogeneity of the poloidal magnetic field—the so-called error fields that arise due to imperfections in manufacturing and assembling of the electromagnetic system-was measured in the Globus-M spherical tokamak. A substantial inhomogeneity corresponding to the n = 1 mode, which gave rise to a locked mode and led to discharge disruption, was revealed. After compensation of this inhomogeneity with the help of special correction coils, the discharge duration increased and the global plasma parameters improved substantially. A technique for determining and compensating the n = 1 mode inhomogeneity is described, the measured dependences of the penetration threshold of the m = 2/n = 1 mode on the plasma parameters are given, and results of experiments in which record parameters for the Globus-M tokamak were achieved after correction of the poloidal magnetic field are presented.     

Equations for nonlinear MHD convection in shearless magnetic systems

A closed set of reduced dynamic equations is derived that describe nonlinear low-frequency flute MHD convection and resulting nondiffusive transport processes in weakly dissipative plasmas with closed or open magnetic field lines. The equations obtained make it possible to self-consistently simulate transport processes and the establishment of the self-consistent plasma temperature and density profiles for a large class of axisymmetric nonparaxial shearless magnetic devices: levitated dipole configurations, mirror systems, compact tori, etc. Reduced equations that are suitable for modeling the long-term evolution of the plasma on time scales comparable to the plasma lifetime are derived by the method of the adiabatic separation of fast and slow motions.     

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.     

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.     

Choice of coordinates on a toroidal magnetic surface

Construction of global angular coordinates on an arbitrarily shaped toroidal surface is considered. It is shown that global orthogonal, isothermal, and semigeodesic geometric coordinates can always be introduced on a toroidal surface. Such coordinates can be rather efficient in solving problems of plasma equilibrium and stability in a magnetic field. At the same time, it is impossible to introduce global geodesic coordinates and coordinates based on curvature lines. It is proposed to use a magnetic analogy to search for transformations of global angular geometric coordinates that simplify the expression for the length element on an arbitrary toroidal surface. An algorithm for the computation of such coordinates is offered. With this approach, a “virtual” magnetic field such that its force lines, as well as the lines orthogonal to them, are closed is searched for on the toroidal surface. These lines comprise a geometric coordinate grid on an actual magnetic surface formed by the actual magnetic field.     

Synthesis and simulation of a two-level magnetic control system for tokamak-reactor plasma

Synthesis and simulation of a hierarchical (two-level) magnetic system for controlling a tokamakreactor plasma throughout the entire divertor discharge stage, including the plasma current ramp-up phase, are carried out. The plasma vertical velocity is stabilized about zero by using a proportional controller in a scalar control loop. The gain of the controller—the coefficient that ensures the required stability margins—is found by using a second-order linear model constructed by solving the identification problem on the basis of numerical experiments carried out with the DINA plasmophysical computer code. The internal cascade (the lower level of the system) for tracking the scenario currents in the poloidal magnetic field coils is synthesized by using the complete dynamic channel decoupling method. The external cascade (the upper level of the system) for tracking the plasma current and shape is synthesized by using the method of pseudoseparation of the control channels and the multidimensional diagonal proportional-integral controller, with proportional, integrating, and double integrating units connected in parallel in each channel. In the hierarchical control system, the lower level (the internal cascade) is subordinated to the upper level (the external cascade). The external cascade acts on the internal one by the signals that set the required currents in the coils of the central solenoid and of the poloidal magnetic field in order to ensure the required plasma current and shape in accordance with the output signals from the plant, which are transmitted through the vector feedback channel. The lower level is aimed exclusively at tracking the reference inputs by tracking the currents in the control coils. An operating mode of the system under the conditions of current saturation in the control coils is proposed and implemented. Results are presented from numerical simulations of the two-level (cascade) control system for reference scenario no. 2 of the ITER database (www.iter.org) with the DINA nonlinear code.     

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.     

MHD stability of a collisionless anisotropic plasma in a system with an internal conductor

A study is made of the MHD stability of a collisionless anisotropic-pressure plasma in a nonparaxial magnetic configuration with an internal conductor in cylindrical geometry. A stability criterion for flutelike modes is obtained, and the families of marginally stable profiles of the longitudinal and transverse plasma pressures are calculated by using the Chew-Goldberger-Low anisotropic MHD equations. Possible marginally stable plasma states are considered with allowance for the expected turbulent relaxation and self-organization processes, on the one hand, and isotropization processes, on the other. A stability criterion for Alfvén modes is also derived in the Chew-Goldberger-Low model.     

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.     

Equilibrium,stability, and estimate of plasma confinement in the L-5 compact torsatron

Possible parameters of a plasma in a compact torsatron that is to be constructed at the Prokhorov Institute of General Physics, Russian Academy of Sciences (the L-5 project) are discussed. The properties of the original vacuum configuration created by the external coils are described. The equilibrium of a plasma with a free boundary and the stability of local MHD modes are investigated. The effective magnetic field ripples and the structural factor of the bootstrap current in the 1/ν regime are calculated, as well as collisionless losses of trapped α-particles. The dependence of these properties on the relative plasma pressure is examined. It is shown that the maximum possible <β> (the ratio of the gas-kinetic plasma pressure to the magnetic field pressure, averaged over the volume of the plasma column) consistent with equilibrium exceeds 2.0%. The power of the external sources for plasma heating in the anticipated operating modes is estimated using the present-day scalings. The efficiency of different methods for calculating the magnetic fields and, accordingly, the magnetic surfaces created by the external coils is analyzed in the Appendix.     

Configuration analysis and optimization on multipolar Galatea trap

Multipolar Galatea magnetic trap simulation model was established with the finite element simulation software COMSOL Multiphysics. Analyses about the magnetic section configuration show that better magnetic configuration should make more plasma stay in the weak magnetic field rather than the annular magnetic shell field. Then an optimization model was established with axial electromagnetic force, weak magnetic field area and average magnetic mirror ratio as the optimization goals and with the currents of myxines as design variables. Select appropriate weight coefficients and get optimization results by applying genetic algorithm. Results show that the superiority of the target value of typical application parameters, including the average magnetic mirror can reduce more than 5%, the weak magnetic field area can increase at least 65%, at the same time, axial electromagnetic force acting on the outer myxines can be reduced to less than 50 N. Finally, the results were proved by COMSOL Multiphysics and the results proved the optimized magnetic trap configuration with more plasma in the weak magnetic field can reduce the plasma diffusion velocity and is more conducive for the constraint of plasma.     

3D Magnetic Holes in Collisionless Plasmas

Recent multispacecraft observations in the Earth’s magnetosphere have revealed an abundance of magnetic holes—localized magnetic field depressions. These magnetic holes are characterized by the plasma pressure enhancement and strongly localized currents flowing around the hole boundaries. There are several numerical and analytical models describing 2D configurations of magnetic holes, but the 3D distribution of magnetic fields and electric currents is studied poorly. Such a 3D magnetic field configuration is important for accurate investigation of charged particle dynamics within magnetic holes. Moreover, the 3D distribution of currents can be used for distant probing of magnetic holes in the magnetosphere. In this study, a 3D magnetic hole model using the single-fluid approximation and a spatial scale hierarchy with the distinct separation of gradients is developed. It is shown that such 3D holes can be obtained as a generalization of 1D models with the plasma pressure distribution adopted from the kinetic approach. The proposed model contains two magnetic field components and field-aligned currents. The magnetic field line configuration resembles the magnetic trap where hot charged particles bounce between mirror points. However, the approximation of isotropic pressure results in a constant plasma pressure along magnetic field lines, and the proposed magnetic hole model does not confine plasma along the field direction.     

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.     

Long-range spatial correlations in the turbulent edge plasma of the L-2M stellarator

Long-range spatial correlations in the turbulent plasma of the L-2M stellarator were revealed experimentally, and their relation to the geometry of magnetic surfaces was analyzed (Plasma Phys. Control. Fusion 50, 045001 (2008)). The operation modes of the facility in which fast transport transitions in plasma are possible were studied. Upon these transitions, the turbulence level is found to decrease substantially. It is shown that long-range spatial correlations are typical of relatively narrow frequency ranges. In particular, before a transport transition, such frequency ranges are f ～ 30–40 kHz and f ～ 1–3 kHz. After the transition, long-range spatial correlations in the frequency range of f ～ 30–40 kHz disappear due to a significant decrease in the turbulence level in this frequency range. At the same time, correlations in the low frequency range are retained and new correlations at frequencies of f ～ 6-12 kHz occur. It is found that global electromagnetic oscillations in the frequency range of f ～ 1–3 kHz are related to the m/n = 0/0 perturbation and its toroidal satellites (here, m and n are the poloidal and toroidal mode numbers, respectively). It is also shown that, after the transport transition, a three-dimensional localized electromagnetic mode at the frequency of the geodesic acoustic mode governed by the average magnetic field curvature is excited. At higher frequencies typical of a geodesic acoustic mode related to the three-dimensional curvature of the magnetic field, no long-range spatial correlations were observed both before and after the transport transition.     

Energy efficiency of electron plasma emitters

Electron emission influence from gas-discharge plasma on plasma emitter energy parameters is considered. It is shown, that electron emission from plasma is accompanied by energy contribution redistribution in the gas-discharge from plasma emitter supplies sources—the gas-discharge power supply and the accelerating voltage power supply. Some modes of electron emission as a result can be realized: “a probe measurements mode,” “a transitive mode,” and “a full switching mode.”     

The role of low molecular weight proteins in exposure of blood to laser radiation and varying magnetic field

In this work we studied variations of oxygen-binding capacity of hemoglobin under the separate and joint action of a nanointegrator—a special device that provides a low-intensity laser radiation (LILR, 655 nm)—and an alternating magnetic field (AMF) on blood (erythrocytes and plasma) in the presence of low molecular weight proteins (LWP). The action of LILR and AMF is demonstrated to increase oxygen absorption by 50% and, in the presence of LWP, by 80–100%. LILR reduces the activity of a blood enzyme superoxide dismutase (SOD) by 60% and, in the presence of LWP, by 40%. The joint action of LILR and AMF first stimulates and, after 30 min, inhibits SOD activity. It is shown that LILR and AMF action not only changes the anti-oxidant status of blood, but also promotes oxygen uptake by erythrocytes. The effect of radiation is enhanced due to nanomolecular changes in LWP structure that boost the absorption of oxygen by cells.