Uniform boundedness of the magnetic field in a resistive plasma

While the magnetic energy in a plasma can be easily bounded by classical energy inequalities, the behaviour of the maximum of the magnetic field is less clear. In fact, the field in chaotic flows appears to concentrate in progressively smaller regions of the domain, so that conceivably it could grow there without limit. However, we prove that as long as the magnetic energy and the plasma remain bounded, so does the magnetic field. The dependence of these bounds on the main plasma parameters is analysed. Copyright © 2003 John Wiley & Sons, Ltd.     

Nontwist symplectic maps in tokamaks

We review symplectic nontwist maps that we have introduced to describe Lagrangian transport properties in magnetically confined plasmas in tokamaks. These nontwist maps are suitable to describe the formation and destruction of transport barriers in the shearless region (i.e., near the curve where the twist condition does not hold). The maps can be used to investigate two kinds of problems in plasmas with non-monotonic field profiles: the first is the chaotic magnetic field line transport in plasmas with external resonant perturbations. The second problem is the chaotic particle drift motion caused by electrostatic drift waves. The presented analytical maps, derived from plasma models with equilibrium field profiles and control parameters that are commonly measured in plasma discharges, can be used to investigate long-term transport properties.     

Virtual Tokamak library software

We describe the concept of the Virtual Tokamak library, its functionality, major components, and method of use. The library is designed to predict, support, and interpret experiments as well as handle measurements on tokamak instruments implementing the idea of energy production on the basis of controlled thermonuclear fusion. The library software consists of an interactive graphic shell and a number of interrelated computer codes simulating various processes in the tokamak plasma, its structural elements, diagnostics and control system. This is a specific implementation of advanced information technologies including Internet technologies and approaches of distributed computations in the field of the mathematical modeling of plasma. The Virtual Tokamak is unique in terms of combined application and system software.     

Numerical simulation of anomalous plasma transport in the presence of magnetic turbulence

The structure of plasma in the interplanetary space is briefly presented, and the problems related to the variability of solar activity are discussed. The features of magnetic turbulence in the solar wind are also described. Magnetic field fluctuations are one of the causes of enhanced transport both in laboratory and astrophysical plasmas. To a first approximation, the plasma particles follow the magnetic field lines, whose equations form a non-linear one and a half degrees of freedom system. Unless the fluctuation level is very low, numerical simulations are needed to study such a system. We review three-dimensional numerical simulations of field line transport in anisotropic magnetic turbulence. Several transport regimes are found: for low Kubo number, anomalous transport is obtained, featuring both subdiffusion, corresponding to trapping in cantori structures, and superdiffusion, corresponding to Levy flights in the stochastic layer. Increasing the Kubo number, and hence stochasticity, quasilinear, intermediate, and percolative regimes are found, in the order. An expression of the diffusion coefficient valid for generalized anisotropy is presented.     

A symplectic mapping for the ergodic magnetic limiter and its dynamical analysis

A model for a new bidimensional sympletic mapping describing magnetic field line trajectories in a tokamak perturbed by ergodic magnetic limiter coils is presented. Numerical examples of these trajectories, computed for plasma described by large aspect-ratio equilibria, simulate the main characteristics of trajectories in the toroidal geometry. Also the importance of the symplecticity of the new mapping regarding certain features of non-linear dynamical analysis, for which a large number of iterations is necessary, is shown. Thus, some standard algorithms, such as the Lyapunov exponents and the rotational transforms, are applied with precision in order to characterize regular and chaotic regions in the parameter space, improving the study of bifurcations, routes to chaos, and diffusion in this system.     

具有结构内阻尼磁性刚体航天器姿态动力学稳定性分析

在地球引力场和磁场中,在考虑了航天器结构内阻尼及气体阻力的影响条件下,研究磁性刚体航天器在绕地球圆轨道运行时可能出现的混沌问题.根据动量矩定理建立动力学模型,应用Melnikov方法证明了动力系统在一定条件下会发生混沌行为,并且给出了解析判据.最后利用数值仿真分析了系统的动力学行为,理论结果与数值仿真结果相一致.     

Researches on operating region of Tokamak device with soft X-ray tomography

The structures of three operating regions in HT-6B Tokamak have been studied by soft X-ray tomographic system with high sensibility and high time-space resolution. One of the requisites for forming sawtooth discharge is the effective heating action in the central region. In the sawtooth region there are five evolutional phases and five types of magnetic surface structures correspondingly; that is, the concentric, the eccentric, the double-core, the “MHD-type” and the “ultra-MHD type” magnetic surface structures. In the MHD oscillation region, there is a stable “MHD-type” magnetic surface structure. It consists of a crescent “hot core” and a circular “cold bubble” and rotates in the diamagnetic direction of electrons. In the resonant region, the resonant helical field improves the heating status and suppresses the MHD disturbances; therefore the single “MHD-type” magnetic surface changes into a sawtooth type one.     

Mathematical model of the Galathea-belt toroidal magnetic trap

We consider a mathematical model of equilibrium configurations of plasma, magnetic field, and electric field in a toroidal trap with two ring conductors with current loaded into plasma. We present the mathematical apparatus of the model based on the numerical solution of boundary value problems for the Grad–Shafranov equation (a differential equation of elliptic type for the magnetic flux function), solution methods for these problems, and numerically obtained properties of equilibrium configurations. We indicate the differences in configurations in the toroidal trap and in its analog straightened into a cylinder.     

无力磁场和Beltrami流

场矢量处处平行其旋度的管式矢量场具有复杂的拓扑结构．而且通常表现出混饨行为．本文提供了具有常数比例因子的这类矢量场在三种基本坐标系内的解析解,并指出完全导电流体内的一个Beltrami流能维持一个定常无力磁场,如果磁场矢量处处平行速度．     

Quasi-separatrix layers and three-dimensional reconnection diagnostics for line-tied tearing modes

In three-dimensional magnetic configurations for a plasma in which no closed field line or magnetic null exists, no magnetic reconnection can occur, by the strictest definition of reconnection. A finitely long pinch with line-tied boundary conditions, in which all the magnetic field lines start at one end of the system and proceed to the opposite end, is an example of such a system. Nevertheless, for a long system of this type, the physical behavior in resistive magnetohydrodynamics (MHD) essentially involves reconnection. This has been explained in terms comparing the geometric and tearing widths [1] and [2]. The concept of a quasi-separatrix layer [3] and [4] was developed for such systems. In this paper we study a model for a line-tied system in which the corresponding periodic system has an unstable tearing mode. We analyze this system in terms of two magnetic field line diagnostics, the squashing factor [5], [6] and [7] and the electrostatic potential difference [8] and [9] which has been used in kinematic reconnection studies. We discuss the physical and geometric significance of these two diagnostics and compare them in the context of discerning tearing-like (reconnection-like) behavior in line-tied modes.     

On chaotic graphs and applications in physics and biology

El Naschie’s ε^∞ theory in Quantum space time is given and discussed geometrically and topologically as a category of fuzzy spaces, these fuzzy categories in which lines are fuzzy fractal lines. In this paper, we represent the chaotic graphs as many fuzzy fractal lines up to ∞. We will describe them by chaotic matrices. Many fuzzy systems (chaotic systems) are described and applied in [8], [9], [10], [11], [12]. This article introduces some operations on the chaotic graphs such as the union and the intersection; also both of the chaotic incidence matrices and the chaotic adjacency matrices representing the chaotic graphs induced from these operations will be studied. Theorems governing these studies are obtained. Some applications on chaotic graphs are given [18], [19], [20], [21].     

Chaotic motion of magnetotactic bacteria

The motion of a magnetotactic bacterium submitted to an oscillating magnetic field was studied. The nature of the U-turn process, which occurred when the magnetic field was reversed, was investigated. It is analytically shown that this process presents a chaotic behavior. When the magnetic field is reversed the bacterium may decide if the turning will be to the right side or to the left side. Such choice is highly sensitive to the initial conditions, making it impossible to predict which side will be taken in the U-turn.     

On the convexity of equilibrium plasma configurations

We investigate the problem of plasma confinement by a magnetic field in an infinite cylinder. We show that if the cylinder has convex cross-section, then there exists an equilibrium plasma configuration with convex cross-section.     

Chaotic convection in a ferrofluid

We report theoretical and numerical results on thermally driven convection of a magnetic suspension. The magnetic properties can be modeled as those of electrically non-conducting superparamagnets. We perform a truncated Galerkin expansion finding that the system can be described by a generalized Lorenz model. We characterize the dynamical system using different criteria such as Fourier power spectrum, bifurcation diagrams, and Lyapunov exponents. We find that the system exhibits multiple transitions between regular and chaotic behaviors in the parameter space. Transient chaotic behavior in time can be found slightly below their linear instability threshold of the stationary state.     

Structure of magnetic field lines

In this paper the Hamiltonian structure of magnetic lines is studied in many ways. First it is used vector analysis for defining the Poisson bracket and Casimir variable for this system. Second it is derived Pfaffian equations for magnetic field lines. Third, Lie derivative and derivative of Poisson bracket is used to show structure of this system. Finally, it is shown Nambu structure of the magnetic field lines.     

Inhibition or enhancement of chaotic convection via inclined magnetic field

In this paper, we investigate the onset of convection in a horizontal layer of fluid which is heated from the underside. An inclined magnetic field is applied to the layer. The Galerkin truncated approximations were used to obtain a Lorenz-like model. The nonlinear system was solved by the fourth-order Runge–Kutta method. The results show that the Hartmann number and the angle of inclination of the magnetic field could inhibit or enhance the onset of chaotic convection.     

Dynamics of electron in intense laser field

The induced magnetic field produced by a circular polarization laser pulse propagating in a cold plasma, and the dynamics of injected electron in the combination field of the laser field and the induced magnetic field are investigated. As a circular polarization laser propagates in a plasma, a quasistatic magnetic field in the direction of the wave propagation is rising. An evolution equation for the induced magnetic field is derived. Based on the derived equation, the properties of the induced magnetic field are discussed. The injected electron which satisfies the cyclotron resonance condition can be accelerated by the combination field. The energy equation for the injected electron is obtained. Finally, the classical dynamics of the injected electron in the combination field is analyzed.     

Remark on the dissipation of the magnetic helicity integral

We prove that the current helicity integral for a thin magnetic tube is directly proportional to the twist Tw of field lines, which appears in the Călugărianu formula as a summand. Using this approach, we analyze the law of the variation of magnetic helicity in a conducting medium with a nonzero magnetic diffusion coefficient and also the equation of the phase transition of the magnetic field under early universe conditions. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 158, No. 1, pp. 150–160, January, 2009.     

Classical solutions of the Vlasov–Poisson equations with external magnetic field in a half-space

We consider the first mixed problem for the Vlasov–Poisson equations with an external magnetic field in a half-space. This problem describes the evolution of the density distributions of ions and electrons in a high temperature plasma with a fixed potential of electric field on a boundary. For arbitrary potential of electric field and sufficiently large induction of external magnetic field, it is shown that the characteristics of the Vlasov equations do not reach the boundary of the halfspace. It is proved the existence and uniqueness of classical solution with the supports of charged-particle density distributions at some distance from the boundary, if initial density distributions are sufficiently small.     

Hybrid Simulation of Space Plasmas: Models with Massless Fluid Representation of Electrons. IV. Kelvin–Helmholtz Instability

This is a survey of the literature on hybrid simulation of the Kelvin–Helmholtz instability. We start with a brief review of the theory: the simplest model of the instability—a transition layer in the form of a tangential discontinuity; compressibility of the medium; finite size of the velocity shear region; pressure anisotropy. We then describe the electromagnetic hybrid model (ions as particles and electrons as a massless fluid) and the main numerical schemes. We review the studies on two-dimensional and three-dimensional hybrid simulation of the process of particle mixing across the magnetopause shear layer driven by the onset of a Kelvin–Helmholtz instability. The article concludes with a survey of literature on hybrid simulation of the Kelvin–Helmholtz instability in finite-size objects: jets moving across the magnetic field in the middle of the field reversal layer; interaction between a magnetized plasma flow and a cylindrical plasma source with zero own magnetic field.