The parallel permittivity of magnetized toroidal plasmas with elliptic magnetic surfaces

The asymptotic solution of the Vlasov equation under the drift approximation, for an axially symmetric toroidal plasma configuration with an elliptic cross section of magnetic surfaces, is presented. The analytical expressions for the parallel component of the dielectric permittivity tensor are obtained. These expressions are used for theoretical analyses of the trapped and untrapped electron influence on the collisionless wave dissipation. The evaluated dielectric tensor components can be used for computer calculations of the radio frequency field structure and the collisionless dissipated power related to trapped and untrapped electrons in tokamak plasmas.This work was supported by the State University of Rio de Janeiro (UERJ), Rio de Janeiro Research Foundation (FAPERJ) and Brazilian National Council of Research (CNPq).     

Dielectric Characteristics for Radio Frequency Waves in a Laboratory Dipole Plasma

Transverse and parallel dielectric permittivity elements have been derived for radio frequency waves in a laboratory dipole magnetic field plasma. Vlasov equation is resolved for both the trapped and untrapped particles as a boundary value problem to define their separate contributions to the dielectric tensor components. To estimate the wave power absorbed in the plasma volume the perturbed electric field and current density components are decomposed in a Fourier series over the poloidal angle. In this case, the dielectric characteristics can be analyzed independently of the solution of the Maxwell's equations. As usual, imaginary part of the parallel permittivity elements is necessary to estimate the electron Landau damping of radio frequency waves, whereas imaginary part of the transverse permittivity elements is important to estimate the wave dissipation by the cyclotron resonances. Computations of the imaginary part of the parallel permittivity elements are carried out in a wide range of the wave frequencies. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Study of dust ion-acoustic wave propagation in the Lorentzian magnetized dusty plasma

Dust ion-acoustic waves propagation in the magnetized dusty plasma including ions, electrons and dust particulates are studied by using kinetic equation. For unbounded and collisionless plasma and in the presence of uniform external magnetic field B₀, electrons and ions with Lorentzian distribution function and dust particles with Maxwellian one are considered. Calculating dielectric tensor through the Vlasov equation solution, in the parallel propagation, dispersion relation is derived and suprathermal particle effects on the Landau damping is studied. It is shown that the Landau damping effect vanishes for parallel propagation.     

Effect of subsonic toroidal flows on plasma poloidal rotation and ion heat conductivity. In collisional plasmas of elongated tokamaks

The ion poloidal rotation and heat conductivity in collisional plasmas of axially-symmetric tokamaks with elongated cross-sections and with subsonic toroidal plasma flows are considered. It is shown that subsonic toroidal plasma flows, induced by neutral beam injection or radio frequency waves, can strongly affect the poloidal plasma velocity and ion heat conductivity in collisional plasmas of tokamaks. The transport coefficients also depend on the tokamak ellipticity parameter which, in combination with the Mach number, allows to operate transport processes at smaller values of the toroidal Mach number. The importance of taking into account the ion-electron heat exchange and electron temperature toroidal perturbations to find ion temperature toroidal perturbations is demonstrated. This work was partially supported by the State University of Rio de Janeiro (UERJ) and the Rio de Janeiro Research Foundation (FAPERJ).     

等离子体湍流能量传输的尺度相关性

对于空间环境中近乎无碰撞的等离子体,可采用Vlasov方程进行理论描述,基于Vlasov方程,讨论了等离子体湍流能量传输和耗散的过程:由亚格子应力引起的尺度间的能量传输,电场做功,压强张量做功（压强张量与速度梯度张量的相互作用）.通过混合Vlasov-Maxwell（HVM）数值模拟,进一步研究了能量传输通道之间的联系与区别.不同能量传输通道尽管在不同尺度起主要作用,但其空间的分布非常相似,即各能量传输通道之间存在一定的空间相关.结合近年数值模拟和卫星观测的结果,可以大致概括等离子体湍流从磁流体动力学（magnetohydrodynamic,MHD）尺度到动理学尺度的能量传输过程.      

Dielectric tensor elements for the description of waves in rotating inhomogeneous magnetized plasma spheroids

The dielectric permittivity tensor elements of a rotating cold collisionless plasma spheroid in an external magnetic field with toroidal and axial components are obtained. The effects of inhomogeneity in the densities of charged particles and the initial toroidal velocity on the dielectric permittivity tensor and field equations are investigated. The field components in terms of their toroidal components are calculated and it is shown that the toroidal components of the electric and magnetic fields are coupled by two differential equations. The influence of thermal and collisional effects on the dielectric tensor and field equations in the rotating plasma spheroid are also investigated. In the limiting spherical case, the dielectric tensor of a stationary magnetized collisionless cold plasma sphere is presented.     

Effect of viscosity on dust–ion acoustic shock wave in dusty plasma with negative ions

The properties of dust–ion acoustic (DIA) shock wave in a dusty plasma containing positive and negative ions is investigated. The reductive perturbation method has been used to derive the Korteweg–de Vries–Burgers equation for dust acoustic shock waves in a homogeneous, unmagnetized and collisionless plasma whose constituents are Boltzmann distributed electrons, singly charged positive ions, singly charged negative ions and cold static dust particles. The KdV–Burgers equation is derived and its stationary analytical solution is numerically analyzed where the effect of viscosity on the DIA shock wave propagation is taken into account. It is found that the viscosity in the dusty plasma plays as a key role in dissipation for the propagation of DIA shock.     

Entropy generation across Earth's collisionless bow shock

Earth's bow shock is a collisionless shock wave but entropy has never been directly measured across it. The plasma experiments on Cluster and Double Star measure 3D plasma distributions upstream and downstream of the bow shock allowing calculation of Boltzmann's entropy function H and his famous H theorem, dH/dt≤0. The collisionless Boltzmann (Vlasov) equation predicts that the total entropy does not change if the distribution function across the shock becomes nonthermal, but it allows changes in the entropy density. Here, we present the first direct measurements of entropy density changes across Earth's bow shock and show that the results generally support the model of the Vlasov analysis. These observations are a starting point for a more sophisticated analysis that includes 3D computer modeling of collisionless shocks with input from observed particles, waves, and turbulences.     

The tensor of time-averaged stresses for plasma with an oscillating field

The tensor of time-averaged stresses arising in a plasma under the effect of a magnetostatic and an oscillating field is derived. The plasma is assumed to be collisionless, quasineutral, the particle velocities being far smaller than the wave phase velocities. The case of cyclotron resonance is excluded. The resultant tensor is proved to be symmetric.     

Quantum plasma description and Landau damping

The Schrödinger equation is shown to replace the Vlasov equation to simulate a classical collisionless plasma, provided we take a sophisticated initial condition. The Landau damping is then recovered within a high degree of accuracy.     

Non-equilibrium Dynamics of an Infinite Range XY Model in an External Field

We study the XY model with infinite range interactions in an external magnetic field. The simulations show that in the thermodynamic limit this model does not relax to the thermodynamic equilibrium—instead it becomes trapped in a non-ergodic out-of-equilibrium state. We show how the relaxation towards this non-equilibrium state can be studied using the properties of the collisionless Boltzmann (Vlasov) equation.     

Nonlinear Landau Damping in Spherically Symmetric Vlasov Poisson Systems

The Vlasov Poisson system is a partial differential equation widely used to describe collisionless plasma. It is formulated in a six-dimensional phase space, this prohibits a numerical solution on a complete phase space grid. In some applications, however, spherical symmetry is given, which introduces singularities into the Vlasov Poisson equation. We focus on such problems and propose a stable algorithm using accommodating boundaries. At first, the method is tested in the linear regime, where analytical solutions are available. Thereafter it is applied to large disturbances from equilibrium.     

电子回旋波驱动的托卡马克芯部等离子体极向旋转

提出了一个驱动托卡马克芯部等离子体极向旋转的新途径：用电子回旋波产生芯部等离子体极向旋转.物理机制如下：在高功率的电子回旋波加热的托卡马克等离子体中，共振局域化现象将产生极向电场从而形成极向外高内低的离子密度分布；这个极向离子的积累可以克服来自磁泵的阻尼而使等离子体极向旋转退稳定.从流体力学方程和漂移动力学方程中，得到了等离子体旋转退稳的判别式.结果表明现有的电子回旋波加热功率水平可以驱动芯部等离子体的极向旋转. 关键词：     

热电子等离子体无碰撞漂移波的稳定性

本文采用Vlasov方程,分析了热电子等离子体中低频交换模和漂移波的性质,讨论了热电子成分的稳定作用。稳定交换模要求热电子成分约为10％,稳定漂移波要求热电子成分约为30%。文中还讨论了离子有限Larmor半径、等离子体密度梯度和温度、磁场曲率、扰动波长等参数对稳定性的影响。同MHD近似下强碰撞漂移波的结果相比较,热电子对无碰撞漂移波有更好的稳定作用。 关键词：     

The dielectric tensor and field equations in the inhomogeneous cold collisionless magnetized drift plasmas with elliptical cross sections

In this Letter the dielectric permittivity tensor and field equations in multi layer cold collisionless magnetized inhomogeneous drift plasma columns with confocal elliptical cross sections are investigated. It will be shown that the dielectric tensor of each region can be written as non-operational Hermitian and pure spatial operational parts.     

Zur Theorie elektrostatischer Schwingungen in einem Vlasov-Plasma bei äußerem elektrischen Feld

Longitudinal plasma oscillations under the action of an external homogeneous time dependent electric field are examined with regard to the stability of the plasma. The basic model is an infinitely extended collisionless quasineutral two-component plasma. Starting from the linearized Vlasov equation dispersion relations are derived and discussed. It is shown that for an isothermal two-component plasma instabilities are possible, and limites for the area of instability are given. Further a second method of solution starting from an integral equation for the internal electric field is developed. The equivalence of both methods is shown by means of special cases.     

Analysis of the evolution of perturbations in a magnetized collisionless plasma with an integral-equation technique

Summary A technique recently proposed to study the classical problem of the evolution of small perturbations in a collisionless unmagnetized plasma is extended to a magnetized plasma. A time-convolutive integral equation for the plasma density is obtained from the Vlasov equation for a homogeneous plasma in a uniform, stationary magnetic field. The equation can be solved by means of simple numerical algorithms and, in some cases, analytical solutions can be obtained. The procedure proves to be analytically simpler than the classical one and is more convenient from a numerical point of view. Techniques of solution are presented and analytical and numerical results for electrostatic perturbations are discussed.     

Ion surface cyclotron waves at plasma-metal interfaces

The dispersion properties of slow electromagnetic surface waves propagating across a constant external magnetic field and along a plane plasma-metal interface at harmonics of the ion cyclotron frequency are studied. The motion of the plasma particles is described by a Vlasov-Boltzmann kinetic equation. The effects of the plasma size, the dielectric permittivity of the transition region between the plasma and metal, and the magnitude of the constant external magnetic field on the dispersion characteristics of ion surface cyclotron waves are studied. Zh. Tekh. Fiz. 69, 83–89 (October 1999)     

Electrostatic Waves in the Warm Magnetoplasma at the Cyclotron Harmonic Frequencies

Mode conversion and collisionless absorption of electromagnetic wave at the cyclotron harmonic frequencies in an inhomogeneous non-Maxwellian magnetoplasma have been studied. Under suitable energy transfer condition the converted electrostatic wave (plasma wave) either grows or damps. The expressions for the growth/damping rates of this wave have been derived and studied at the cyclotron harmonic frequencies. The effect of the temperature anisotropy on the growth/damping rate of the electrostatic wave at the second cyclotron harmonic frequency has been shown. Growth of such electrostatic waves at ionospheric heights may explain the observed upper hybrid resonance (UHR) echoes and noise bands at the second cyclotron harmonic frequency.