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.     

Tearing instability in a tokamak with a noncircular cross section

Using a straight-column model to describe tokamak plasma with a noncircular cross section, it is shown how to (i) find the boundary of tearing instability from the condition of existence of a magnetohydrodynamic plasma equilibrium different from that of a straight cylinder by solving a two-dimensional linear boundary-value problem with a second-order equation with respect to the flux coordinate and (ii) find the spatial structure of the tearing mode and the corresponding effective Δ' when there is only one resonance magnetic surface in the plasma for a given axial wavenumber by solving some kind of a boundary-value problem for the perturbation. The proposed approach is illustrated by numerical calculations for the case of an elliptical cross section as an example.     

Tearing instability of a force-free magnetic configuration in a collisionless plasma

The equilibrium and stability of a sheared force-free magnetic field in a collisionless plasma are investigated, and the main features of charged particle motion in such a field are analyzed. A steady solution is derived to the Vlasov-Maxwell equations for the charged particle distribution function that describes different equilibrium configurations. The tearing instability of the magnetic field configurations is studied both analytically and by particle-in-cell simulations.     

Coupled rotational dynamics of two MHD modes in the T-10 tokamak

The coupled rotational dynamics of the m/n = 2/1 and 3/2 MHD modes in an ohmic discharge and the m/n = 2/1 and 4/1 modes in a regime with on-axis electron-cyclotron resonance heating were studied experimentally. The specific features of rotation of these modes in the presence of an error magnetic field, in particular the dependence of the instantaneous frequency Ω(t) of the MHD mode on its spatial orientation at the current instant, were revealed. In analyzing the results obtained, MHD modes were identified with tearing modes (magnetic islands) having a corresponding spatial structure. A possible mechanism for the mutual influence of magnetic islands resulting in their consistent rotation is discussed.     

Magneto-thermal reconnection of significance to space and astrophysics

Magnetic reconnection processes that can be excited in collisionless plasma regimes are of interest to space and astrophysics to the extent that the layers in which reconnection takes place are not rendered unrealistically small by their unfavorable dependence on relevant macroscopic distances. The equations describing new modes producing magnetic reconnection over relatively small but significant distances, unlike tearing types of mode, even when dealing with large macroscopic scale lengths, are given. The considered modes are associated with a finite electron temperature gradient and have a phase velocity in the direction of the electron diamagnetic velocity that can reverse to the opposite direction as relevant parameters are varied over a relatively wide range. The electron temperature perturbation has a primary role in the relevant theory. In particular, when referring to regimes in which the longitudinal (to the magnetic field) electron thermal conductivity is relatively large, the electron temperature perturbation becomes singular if the ratio of the transverse to the longitudinal electron thermal conductivity becomes negligible.     

Nonlinear dynamics and chaotization of oscillations of a virtual cathode in an annular electron beam in a uniform external magnetic field

Results are presented from a numerical study of the effect of an external magnetic field on the conditions and mechanisms for the formation of a virtual cathode in a relativistic electron beam. Characteristic features of the nonlinear dynamics of an electron beam with a virtual cathode are considered when the external magnetic field is varied. Various mechanisms are investigated by which the virtual cathode oscillations become chaotic and their spectrum becomes a multifrequency spectrum, thereby complicating the dynamics of the vircator system. A general mechanism for chaotization of the oscillations of a virtual cathode in a vircator system is revealed: the electron structures that form in an electron beam interact by means of a common space charge field to give rise to additional internal feedback. That the oscillations of a virtual cathode change from the chaotic to the periodic regime is due to the suppression of the mechanism for forming secondary electron structures.     

<Emphasis Type="Bold">A Research of Magnetic Control Ferrite Photonic Crystal Filter</Emphasis>

In this article, an anisotropic magnetized ferrite photonic crystal model is analyzed by using the finite-difference time-domain method. The electromagnetic wave propagates in anisotropic ferrite material and forms two kinds of Eigen propagation mode: left-hand circular polarization (LCP) mode and right-hand circular polarization (RCP) mode. Therefore, the ferrite material is used to produce photonic crystal and wave polarized by these two kinds of polarization modes can be obtained. Because the electromagnetic properties of the ferrite material are greatly influenced by the bias magnetic field, the ferrite photonic crystal band gap can be controlled by adjusting the intensity of the bias magnetic field, and then a magnetron photonic crystal filter is formed. The results show that the magnetic photonic crystal with the bias magnetic field to the LCP/RCP wave forms different pass band and band gap, which can obtain different forms of polarized wave.     

Dynamics of magnetotactic bacteria in a rotating magnetic field

The dynamics of the motile magnetotactic bacterium Magnetospirillum gryphiswaldense in a rotating magnetic field is investigated experimentally and analyzed by a theoretical model. These elongated bacteria are propelled by single flagella at each bacterial end and contain a magnetic filament formed by a linear assembly of approximately 40 ferromagnetic nanoparticles. The movements of the bacteria in suspension are analyzed by consideration of the orientation of their magnetic dipoles in the field, the hydrodynamic resistance of the bacteria, and the propulsive force of the flagella. Several novel features found in experiments include a velocity reversal during motion in the rotating field and an interesting diffusive wandering of the trajectory curvature centers. A new method to measure the magnetic moment of an individual bacterium is proposed based on the theory developed.     

Effect of the external magnetic field on the critical current for the onset of a virtual cathode in an electron beam

The critical current at which an unsteady oscillating virtual cathode forms in an electron beam is studied as a function of the external magnetic field guiding the beam electrons. It is shown that the critical beam current decreases with external magnetic field and that there is an optimum magnetic induction at which the critical current for the onset of an oscillating virtual cathode in the beam is minimum. For a strong guiding magnetic field, the critical beam current is described by relationships derived under the assumption that the motion of the beam electrons is one-dimensional. Such behavior is explained by the characteristic features of the dynamics of the beam electrons in longitudinal and radial directions in the interaction space at different inductions of the external magnetic field.     

Electron dynamics in a parabolic magnetic field in the presence of an electrostatic wave

A study is made of the problem of electron dynamics in the presence of a plane electrostatic wave in a model in which the Earth’s magnetic field is parabolic. The problem is reduced to a Hamiltonian system with two degrees of freedom, which is investigated by the methods of perturbation theory. The structure of the phase space of the system is described, and the phenomena of capture into the resonance and scattering on the resonance are considered. It is shown that these phenomena lead to breaking of the second (longitudinal) adiabatic invariant and stochastization of the electron dynamics.     

Kinetic models of current sheets with a sheared magnetic field

Thin current sheets, whose existence in the Earth’s magnetotail is confirmed by numerous spacecraft measurements, are studied analytically and numerically. The thickness of such sheets is on the order of the ion Larmor radius, and the normal component of the magnetic field (B _z ) in the sheet is almost constant, while the tangential (B _x ) and shear (B _y ) components depend on the transverse coordinate z. The current density in the sheet also has two self-consistent components (j _x and j _y , respectively), and the magnetic field lines are deformed and do not lie in a single plane. To study such quasi-one-dimensional current configurations, two kinetic models are used, in particular, a numerical model based on the particle-in-cell method and an analytical model. The calculated results show that two different modes of the self-consistent shear magnetic field B _y and, accordingly, two thin current sheet configurations can exist for the same input parameters. For the mode with an antisymmetric z profile of the B _y component, the magnetic field lines within the sheet are twisted, whereas the profiles of the plasma density, current density component j _y , and magnetic field component B _x differ slightly from those in the case of a shearless magnetic field (B _y = 0). For the symmetric B _y mode, the magnetic field lines lie in a curved surface. In this case, the plasma density in the sheet varies slightly and the current sheet is two times thicker. Analysis of the dependence of the current sheet structure on the flow anisotropy shows that the sheet thickness decreases significantly with decreasing ratio between the thermal and drift plasma velocities, which is caused by the dynamics of quasi-adiabatic ions. It is shown that the results of the analytical and numerical models are in good agreement. The problems of application of these models to describe current sheets at the magnetopause and near magnetic reconnection regions are discussed.     

Magnetic pulse affects a putative magnetoreceptor mechanism

Clusters of superparamagnetic (SP) magnetite crystals have recently been identified in free nerve endings in the upper-beak skin of homing pigeons and are interpreted as being part of a putative magnetoreceptor system. Motivated by these findings, we developed a physical model that accurately predicts the dynamics of interacting SP clusters in a magnetic field. The main predictions are: 1), under a magnetic field, a group of SP clusters self-assembles into a chain-like structure that behaves like a compass needle under slowly rotating fields; 2), in a frequently changing field as encountered by a moving bird, a stacked chain is a structurally more stable configuration than a single chain; 3), chain-like structures of SP clusters disrupt under strong fields applied at oblique angles; and 4), reassemble on a timescale of hours to days (assuming a viscosity of the cell plasma eta approximately 1 P). Our results offer a novel mechanism for magnetic field perception and are in agreement with the response of birds observed after magnetic-pulse treatments, which have been conducted in the past to specifically test if ferrimagnetic material is involved in magnetoreception, but which have defied explanation so far. Our theoretical results are supported by experiments on a technical SP model system using a high-speed camera. We also offer new predictions that can be tested experimentally.     

Pulsatile flow of blood through a stenosed tube: effect of periodic body acceleration and a magnetic field

A proper understanding of the interactions of body acceleration and a magnetic field with blood flow could be useful in the diagnosis and treatment of some health problems. In the work reported in this paper we studied the pulsatile flow of blood through stenosed arteries, including the effects of body acceleration and a magnetic field. Blood is regarded as an electrically conducting, incompressible, couple-stress fluid in the presence of a magnetic field along the radius of the tube. The effects of the body acceleration and the magnetic field on the axial velocity, flow rate, and fluid acceleration were obtained analytically by use of the Hankel transform and the Laplace transform. Velocity variations under different conditions are shown graphically. The results have been compared with those from other theoretical models, and are in good agreement. Finally, our mathematical model gives a simple velocity expression for blood flow so it will help not only in the field of physiological fluid dynamics but will also help medical practitioners with elementary knowledge of mathematics.     

Dynamics of plasma−dust structures formed in a trap created in the narrowing of a current channel in a magnetic field

The geometry and dynamics of plasma?dust structures in a longitudinal magnetic field is studied experimentally. The structures are formed in a glow-discharge trap created in the double electric layer produced as a result of discharge narrowing by means of a dielectric insert introduced in the discharge tube. Studies of structures formed in the new type of glow-discharge trap are of interest from the standpoint of future experiments with complex plasmas in superstrong magnetic fields in which the dust component is magnetized. Different types of dielectric inserts were used: conical and plane ones with symmetric and asymmetric apertures. Conditions for the existence of stable dust structures are determined for dust grains of different density and different dispersity. According to the experimental results, the angular velocity of dust rotation is ≥10 s^–1, which is the fastest type of dust motion for all types of discharges in a magnetic field. The rotation is interpreted by analyzing the dynamics of individual dust grains.     

Skin Effects in a Dusty Plasma

A multifluid MHD model is applied to study the magnetic field dynamics in a dusty plasma. The motion of plasma electrons and ions is treated against the background of arbitrarily charged, immobile dust grains. When the dust density gradient is nonzero and when the inertia of the ions and electrons and the dissipation from their collisions with dust grains are neglected, we are dealing with a nonlinear convective penetration of the magnetic field into the plasma. When the dust density is uniform, the magnetic field dynamics is described by the nonlinear diffusion equations. The limiting cases of diffusion equations are analyzed for different parameter values of the problem (i.e., different rates of the collisions of ions and electrons with the dust grains and different ratios between the concentrations of the plasma components), and some of their solutions (including self-similar ones) are found. The results obtained can also be useful for research in solid-state physics, in which case the electrons and holes in a semiconductor may be analogues of plasma electrons and ions and the role of dust grains may be played by the crystal lattice and impurity atoms.     

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.     

Magnetic field perturbations as a tool for controlling enzyme-regulated and oscillatory biochemical reactions

The feasibility of magnetic field perturbations as a tool for controlling enzyme-regulated and oscillatory biochemical reactions is studied. Our approach is based on recent experimental results that revealed magnetic field effects on the in vitro activity of enzyme systems in accordance with the radical pair mechanism. A minimum model consisting of two coupled enzyme-regulated reactions is discussed that combines, in a self-consistent manner, magnetic field-sensitive enzyme kinetics with non-linear dynamical principles. Furthermore, a simple detector mechanism is described that is capable of responding to an oscillatory input. Results reveal that moderate-strength magnetic fields (B=1-100 mT) may effectively alter the dynamics of the system. In particular, a response behavior is observed that depends on: (1) the combination of static and time-varying magnetic fields; (2) the field amplitude; and (3) the field frequency in a non-linear fashion. The specific response behavior is critically determined by the biochemical boundary conditions as defined by the kinetic properties of the system. We propose an experimental implementation of the results based on the oscillatory peroxidase-oxidase reaction controlled by the enzyme horseradish peroxidase.     

Dynamics of the plasma injected into the gap of a plasma opening switch across a strong magnetic field

A method is proposed to increase the linear charge density transferred through a plasma opening switch (POS) and, accordingly, reduce the POS diameter by enhancing the external magnetic field in the POS gap. Results are presented from experimental studies of the dynamics of the plasma injected into the POS gap across a strong magnetic field. The possibility of closing the POS gap by the plasma injected across an external magnetic field of up to 60 kG is demonstrated.     

Magneto-inertial fusion with laser compression of a magnetized spherical target

The paper is devoted to the principles of magneto-inertial fusion and laser-plasma methods of generation of a Megagauss field during spherical implosion of a magnetized target. A model based on a magnetic confinement system, namely, a cusp configuration with inertial compression of the target by a laser driver, is developed. The dynamics of plasma in a cusp compressed under the effect of laser beams is precalculated. Analytical and numerical estimates of the particle number and magnetic field intensity during magneto-inertial plasma compression are obtained. The problems of irradiation of a spherically closed volume by a high-energy laser pulse are discussed.     

Spatial distribution of the RF power absorbed in a helicon plasma source

The spatial distributions of the RF power absorbed by plasma electrons in an ion source operating in the helicon mode (ω _ci < ω < ω _ce < ω _pe ) are studied numerically by using a simplified model of an RF plasma source in an external uniform magnetic field. The parameters of the source used in numerical simulations are determined by the necessity of the simultaneous excitation of two types of waves, helicons and Trivelpiece-Gould modes, for which the corresponding transparency diagrams are used. The numerical simulations are carried out for two values of the working gas (helium) pressure and two values of the discharge chamber length under the assumption that symmetric modes are excited. The parameters of the source correspond to those of the injector of the nuclear scanning microprobe operating at the Institute of Applied Physics, National Academy of Sciences of Ukraine. It is assumed that the mechanism of RF power absorption is based on the acceleration of plasma electrons in the field of a Trivelpiece-Gould mode, which is interrupted by pair collisions of plasma electrons with neutral atoms and ions of the working gas. The simulation results show that the total absorbed RF power at a fixed plasma density depends in a resonant manner on the magnetic field. The resonance is found to become smoother with increasing working gas pressure. The distributions of the absorbed RF power in the discharge chamber are presented. The achievable density of the extracted current is estimated using the Bohm criterion.