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.     

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.     

Experimental modeling of a novel magnetic confinement system: Galathea with a myxine in the shape of a convex polyhedron

A new type of magnetic confinement system—a Galathea with a myxine in the shape of a convex polyhedron—is proposed. The system was modeled experimentally by passing an RF current through the myxine. On the one hand, the myxine acts as an inductor whose electric field ionizes the gas and, on the other, it acts as an RF magnetic confinement system. A steady-state plasma produced and confined in this system is almost spherical in shape. The electron density and specific (per unit volume) glow intensity of the plasma produced are found to be higher than those in conventional helical inductors.     

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.     

Boundary of the adiabatic motion of a charged particle in a dipole magnetic field

The motion of a charged particle in a dipole magnetic field is considered using a quasi-adiabatic model in which the particle guiding center trajectory is approximated by the central trajectory, i.e., a trajectory that passes through the center of the dipole. A study is made of the breakdown of adiabaticity in the particle motion as the adiabaticity parameter χ (the ratio of the Larmor radius to the radius of the magnetic field line curvature in the equatorial plane) increases. Initially, for χ?0.01, the magnetic moment μ of a charged particle undergoes reversible fluctuations, which can be eliminated by subtracting the particle drift velocity. For χ?0.1, the magnetic moment μ undergoes irreversible fluctuations, which grow exponentially with χ. Numerical integration of the equations of motion shows that, during the motion of a particle from the equatorial plane to the mirror point and back to the equator in a coordinate system related to the central trajectory, the analogue of the magnetic moment μ is conserved. In the equatorial plane, this analogue undergoes a jump. The long-term particle dynamics is described in a discrete manner, by approximating the Poincaré mapping. The existence of the regions of steady and stochastic particle motion is established, and the boundary between these regions is determined. The position of this boundary depends not only on the adiabaticity parameter χ but also on the pitch angle. The calculated boundary is found to agree well with that obtained previously by using the model of a resonant interaction between particle oscillations associated with different degrees of freedom.     

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.     

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.     

Application of the Lambert <Emphasis Type="Italic">W</Emphasis> function in mathematical problems of plasma physics

Examples of solutions to transcendental equations that arise in mathematical problems of plasma physics are considered. Earlier, such equations were solved only by approximate methods. The use of a new function—the Lambert W function—has made it possible to obtain explicit exact solutions that can help to refine the existing relevant theories. As examples, the following problems from different branches of plasma physics are considered: the equilibrium charge of a dust grain in a plasma, the structure of the Bohm sheath, the diameter of the separatrix in a Galathea-Belt system, the transverse structure of an electron beam in a plasma, the energy loss rate of a test charged particle in a plasma, and the structure of the Sagdeev pseudopotential for ion acoustic waves.     

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.     

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.     

MAGNETIC FIELD STIMULATION OF HYBRIDOMA CELLS IN VITRO

Non-ionizing physical field interactions with cells, both in situ and in vitro, is of current interest globally. This is from various directions—starting from their abilities to induce permanent modifications in cell behavior in situ, through carcinogenesis and mutagenesis, to utilizing field effects for possibly enhancing the viable cell population in vitro. This results in parallel increase in some high-value, low-volume biochemical production. In the present study, screening experiments were carried out with a unique cell line—hybridoma (OKT3) (secreting monoclonal antibodies [MAbs] against T3 surface antigens of human peripheral CD₄⁺ cells)—for a possible enhancement in the yield of extremely high value product (MAb). Overall, in the absence of any such data globally, there is apparently an urgent need for screening of such “field effects” on various other cell types in vitro for various reasons; e.g., low cost of manipulation, nonpolluting nature of interactions, distinct possibility of enhancement of produced biochemical titers, etc. In the present study, we observed various responses of the cell population both to magnetic fields alone and in combination with other known chemical stimulants of viable biomass (mono- and poly-lysine). Fifty hertz, 0.8 mT magnetic field and below, in conjunction with bulkier poly-lysine molecules, needs to be investigated further for a possible resonance-induced anti-interaction between these known mitogens and their cell surface receptors, which possibly could be extrapolated to other growth factor-receptor interactions in magnetic field environments, in situ.     

An instrument for sorting of magnetic microparticles in a magnetic field gradient.

BACKGROUND: The goal of our bioassay technique is to demonstrate high throughput, highly parallel, and high sensitivity quantitative molecular analysis that will expand current biomedical research capabilities. To this end, we have built and characterized a magnetophoresis instrument using a flow chamber in a magnetic field gradient to sort magnetic microparticles by their magnetic moment for eventual use as biological labels. METHODS: The flow chamber consists of a sample inlet, differential sheath streams, and eight outlets for collecting the microparticles after they have traversed the chamber. Magnetic microparticles are injected into the flow chamber that is positioned in a linear magnetic field gradient. The trajectory for each microparticle is determined by its total magnetic moment and size. The resulting populations of monodispersed magnetic microparticles in the different outlet bins are sorted by their magnetic moment; with the highest magnetic moments being deflected the furthest. RESULTS: We have characterized the system for sorting both superparamagnetic and ferromagnetic microparticles with approximate diameters of 8 microm and 4.0-4.9 microm, respectively. To characterize the instrument, we used microparticles with a known size distribution and varied the transit time through the chamber. This is equivalent to varying the magnetic moment, while allowing us to hold the particle properties constant from run-to-run. We demonstrated the ability to reproducibly change the distribution of the particles in the collection bins by varying transit time in good agreement with theory. We identified hydrodynamic instabilities responsible for causing dispersion in the flow. Improvements to the flow chamber hydrodynamics such as reducing the aspect ratio between the sample inlet and the chamber depth and stabilizing the sheath flow resulted in narrow sorting distributions. We measured a sorting reproducibility (percentage of particles returning to their original bin upon resorting individual populations) of 84-89%. CONCLUSIONS: We have developed a simple magnetophoresis system for reproducibly sorting magnetic microparticles. This technique will permit the use of microparticles with a wide range of magnetic moments to create a wide range of magnetic labels. Careful consideration of system design and operational parameters enables reliable and reproducible sorting of microparticles with varying size and magnetic content.     

Relaxation of plasma rotation in toroidal magnetic confinement systems

A study is made of the relaxation of plasma rotation in nonaxisymmetric toroidal magnetic confinement systems, such as stellarators and rippled tokamaks. In this way, a solution to the drift kinetic equation is obtained that explicitly takes into account the time dependence of the distribution function, and expressions for the diffusive particle fluxes and longitudinal viscosity are derived that make it possible to write a closed set of equations describing the time evolution of the ambipolar electric field E and the longitudinal (with respect to the magnetic field) plasma velocity U₀. Solutions found to the set of evolutionary equations imply that the relaxation of these two parameters to their steady-state values occurs in the form of damped oscillations whose frequency is about 2v_T/R (where v_T is the ion thermal velocity and R is the major plasma radius) and whose damping rate depends on the ion-ion collision frequency and on the magnetic field parameters. In particular, it is shown that, for tokamaks with a slightly rippled longitudinal magnetic field, the frequency of oscillations in the range q>2 (where q is the safety factor) is, as a rule, much higher than the damping rate. For stellarators, this turns out to be true only of the central plasma region, where the helical ripple amplitude ? of the magnetic field is much smaller than the toroidal ripple amplitude δ=r/R.     

Magnetic particles associated with the lateral line of the European eel Anguilla anguilla

Magnetization measurements of the European eel Anguilla anguilla demonstrated the presence of magnetic material concentrated in the region of the mandibular canals of the lateral line system. The data suggest that the material is magnetite, has a size suitable for magnetoreception and is of biogenic origin. The presence of magnetic particles in the lateral line system is discussed in relation to their possible role in allowing the fish to orientate with respect to the geomagnetic field during their extensive oceanic spawning migrations.     

Formation of current sheets in structurally stable and structurally unstable magnetic configurations with two null lines

The nonlinear dynamics of magnetoacoustic and Alfvén MHD perturbations in structurally unstable magnetic configurations with two null lines (X-lines) is studied both analytically and numerically. It is shown that these perturbations cause the electric current to evolve nonlinearly in such a manner that a structurally unstable configuration of the magnetic field transforms into a structurally stable configuration. Such a transformation is forbidden in ideal magnetohydrodynamics but can occur in the process of magnetic field line reconnection. The final magnetic configuration to which the system evolves is shown to contain no separatrices connecting the null lines.     

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.     

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.     

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.     

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.