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).     

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.     

Are circadian oscillators structurally unstable?

The common belief is that all biological oscillations are of limit cycle type. It is shown in this article that the phase response curves simulated on a two-species Lotka-Volterra linear (i.e. non-limit cycle type) oscillator, do look similar to those obtained by experimental methods by different workers. The form of the phase response curves, the existence of singularities and the mirror-image symmetry of opposite perturbations are modelled on the Lotka-Volterra system. The study, which is strongly indicative of the possibility that the underlying oscillator (or oscillators) is (are) not structurally stable, also indicates the necessity of designing critical experiments, capable of distinguishing between limit cycle and non-limit cycle oscillators, since the single-pulse phase resetting does nothing to distinguish between them.     

Islands and ergodicity of the plasma current in toroidal magnetic confinement systems

Magnetic and current structures arising due to resonant perturbations of an equilibrium current-carrying magnetic configuration are analyzed using the Hamiltonian formalism. Special attention is paid to axisymmetric tokamak and pinch configurations. It is shown that, due to the very different dependences of the magnetic and current rotational transforms on the plasma pressure, the resonances (islands) of the magnetic field may not coincide with those of the current. The perturbed force-free equilibrium of a cylindrical pinch in which the field and current islands overlap is analyzed. The long-lived ribbon structures observed in the JET tokamak are explained as a manifestation of a force-free magneto-current island.     

Specificities of one-dimensional dissipative magnetohydrodynamics

One-dimensional dynamics of a plane slab of cold (β ? 1) isothermal plasma accelerated by a magnetic field is studied in terms of the MHD equations with a finite constant conductivity. The passage to the limit β → 0 is analyzed in detail. It is shown that, at β = 0, the character of the solution depends substantially on the boundary condition for the electric field at the inner plasma boundary. The relationship between the boundary condition for the pressure at β > 0 and the conditions for the electric field at β = 0 is found. The stability of the solution against one-dimensional longitudinal perturbations is analyzed. It is shown that, in the limit β → 0, the stationary solution is unstable if the time during which the acoustic wave propagates across the slab is longer than the time of magnetic field diffusion. The growth rate and threshold of instability are determined, and results of numerical simulation of its nonlinear stage are presented.     

Distinctive features of collisionless gradient drift instabilities in a high-β plasma in a highly nonuniform magnetic field

A set of Vlasov-Maxwell equations for collisionless electromagnetic drift instabilities of high-β plasma configurations with a nonuniform magnetic fields is solved. The effect of the transverse static magnetic field variation and magnetic field line curvature, as well as the plasma temperature and density gradients, is considered. It is shown that, in a nonuniform magnetic field, the behavior of the instabilities differs substantially from that in a uniform field. Electromagnetic modes propagating strictly transverse to the lines of the static magnetic field are analyzed in detail, and unstable solutions are obtained for both extraordinary and ordinary waves. Numerical results show that, in the latter case, instability occurs when the magnetic field decreases toward the periphery and the plasma temperature and density gradients are oppositely directed.     

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.     

Model magnetic field configurations with islands

Helical perturbations of the tokamak magnetic field can give rise to magnetic islands in the vicinity of the rational magnetic surfaces at which the pitch of the magnetic field lines coincides with that of the perturbation. The widely known relationship between the magnetic island width and the perturbation amplitude is valid under the assumptions that the island width is small in comparison to the radius of the rational surface and that the perturbation amplitude is constant in the radial direction. The latter assumption indicates that the island width is small in comparison to the radial size of the region where the perturbation current is localized. The calculations carried out for four model magnetic field configurations show that the geometry of the magnetic islands depends on the extent to which the perturbation current is localize and that the width of the magnetic islands is smaller than that calculated from the familiar relationship. The larger the perturbation amplitude, the greater this difference: it may be as large as 25% for the strong perturbations arising during disruptions. The calculations are based on the solution of the geometric problem of constructing the lines of the magnetic field determined by the given distributions of the initial current and perturbation current; the equilibrium equation is not considered. The question of the direction of the perturbation current within the island relative to the direction of the initial unperturbed current is discussed. The perturbation current flowing in an island is directed opposite to the initial current with a radially decreasing density; for this reason, such an island can naturally be called a “negative” island. Together with the formation of negative islands, the formation of “positive” ones is also considered. The latter are shown to form under the following conditions: the perturbation current density should be higher than the density of the current that produces the unperturbed field and the perturbation current itself should be localized in a sufficiently narrow radial layer. The positive islands are smaller in size than negative ones.     

Magnetorotational instability of a weakly ionized accretion disk with vertical and azimuthal magnetic fields

Magnetorotational instability of a weakly ionized accretion disk with an admixture of charged dust grains in a magnetic field with the axial and toroidal components is analyzed. The dispersion relation for perturbations perpendicular to the disk plane is derived with allowance for both the Hall current and the finite transverse plasma conductivity. It is shown that dust grains play an important role in the disk magnetic dynamics. Due to the effect of dust grains, the Hall current can reverse its direction as compared to the case of electron-ion plasma. As a result, the instability threshold shifts toward the short-wavelength range. Under certain conditions, electromagnetic fluctuations of any length can become unstable. It is established that the instability criterion for waves of any scale length is satisfied within a finite interval of the density ratio between the dust and electron plasma components. The width of this interval and the instability growth rate as functions of the plasma parameters and the configuration of the magnetic field in the disk are analyzed.     

On the possibility of reflection of Alfvén waves in a curvilinear magnetic field

The propagation of Alfvén waves in a plasma immersed in a curvilinear magnetic field is investigated by using a 2D model. The waves are described by a 1D equation that formally coincides with the equation for the case of a quasi-uniform straight magnetic field with a modified Alfvén velocity that takes into account the longitudinal dependence of the Lame coefficients. It is shown that toroidal and poloidal Alfvén modes depend differently on the magnetic-field geometry. In the case of a 2D plane-parallel configuration of the magnetic field, poloidal modes are efficiently reflected from regions where the magnetic field lines sharply converge or diverge. This effect can result in the formation of open-field-line Alfvén quasi-resonators.     

Stability of a quasi-flute mode under the Bernstein-Kadomtsev condition in a toroidal confinement system

It is shown that the growth rate of the MHD instability in toroidal configurations is slower in a situation in which the Bernstein-Kadomtsev condition is satisfied while the Mercier stability criterion is not. Under the Bernstein-Kadomtsev condition, Alfvénic Mercier modes are not excited, but quasi-flute acoustic Mercier modes develop instead. In confinement systems with closed magnetic field lines, the Bernstein-Kadomtsev condition ensures MHD stability; however, a small rotational transform produced by magnetic perturbations can give rise to a quasi-flute acoustic instability whose growth rate is proportional to the perturbation amplitude, in which case the fastest growing oscillations are those with the shortest wavelengths.     

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.     

A nonlinear single-mode structure in a plasma with anisotropic temperature

An exact solution is derived to the equations of vortex electron anisotropic hydrodynamics for a plasma that is unstable against the Weibel instability driven by the electron temperature anisotropy. This solution describes saturation of the Weibel instability in the single-mode regime with an arbitrary wavelength and corresponds to a standing helical wave of magnetic perturbations in which the amplitude of the generated magnetic field varies periodically over time. The longitudinal and transverse (with respect to the rotating anisotropy axis) plasma temperatures are subject to the same periodic variations. In this case, the maximum magnetic field energy can be on the order of the plasma thermal energy.

     

Mapping structurally perturbed sites in DNA by replication arrest and run-off replication

We describe a technique for rapid fine mapping of sites of torsion-induced perturbations of DNA structure. The technique involves strand scission or chemical base modification at structurally perturbed sites, replication arrest in a double-strand DNA sequencing reaction, and size analysis of replication products by electrophoresis on sequencing gels. Besides being less complicated and faster than site identification by conventional end-labeling methods, the technique assures high sequence specificity through the use of oligomeric sequencing primers. This property should be useful for in vivo mapping of DNA structural perturbations with known sequence within complex genomes.     

MHD stabilization by the magnetic hill at a small rotational transform

The effect of very small rotational transform on the plasma stability in three-dimensional closed magnetic configurations with closed magnetic field lines, stabilized by the magnetic hill (i.e., by the plasma compressibility), is considered using ideal MHD theory. It is shown that, for infinitely small values of the rotational transform, the Suydam-Mercier criterion predicts the onset of acoustic instability with a finite growth rate, provided that the Bernstein-Kadomtsev criterion is satisfied. Consequently, for a vanishingly small rotational transform, the limiting transition from the Suydam-Mercier criterion to the Bernstein-Kadomtsev criterion is impossible. Taking into account the finite Larmor radius allows this limiting transition to be made. The Bernstein-Kadomtsev criterion ensures MHD stability at rotational transform values below a certain critical value determined by the ratio of the ion Larmor radius to the plasma minor radius. Under experimental conditions, this critical value is larger than that expected to be produced by the actual magnetic perturbations.     

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.     

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.     

A condition for small bootstrap current in three-dimensional toroidal configurations

It is shown that, if the maximum of the magnetic field strength on a magnetic surface in a threedimensional magnetic confinement configuration with stellarator symmetry constitutes a line that is orthogonal to the field lines and crosses the symmetry line, then the bootstrap current density is smaller compared to that in quasi-axisymmetric (qa) [J. Nührenberg et al., in Proc. of Joint Varenna?Lausanne Int. Workshop on Theory of Fusion Plasmas, Varenna, 1994, p. 3] and quasi-helically (qh) symmetric [J. Nührenberg and R. Zille, Phys. Lett. A 129, 113 (1988)] configurations.     

A structurally diversified linker enhances the immune response to a small carbohydrate hapten

The tether employed to covalently attach β-mannan disaccharide glycoconjugates influences the specificity of rabbit antibodies that protect against Candida albicans. Two glycoconjugates containing (1?→?2)-β-mannan disaccharides linked to chicken serum albumin (CSA) either via a structurally uniform or via a stereodiversified spacer were prepared and evaluated in immunization trials in mice and rabbits. Immunization with conjugate vaccine possessing a structurally diversified linker induced higher IgG titers against Candida albicans cell wall phosphomannan than a conjugate with a structurally uniform linker. These results suggest that affinity maturation and the specific antibody response can be shifted towards recognition of the desired hapten by employing a linker with diversified configuration.