Volume 11, Issue 3, March 2004
Index of content:
 LETTERS


Bose–Einstein condensation and intermediate state of the photon gas
View Description Hide DescriptionThe possibility of the establishment of equilibrium between a photon and a dense photon bunch is studied. The condition of production of the Bose–Einstein condensate is obtained in the case when the density of plasma does not change. It is shown that the inhomogeneity of density of photons leads to a new intermediate state of the photon gas.

 ARTICLES

 Basic Plasma Phenomena, Waves, Instabilities

Particle acceleration during the counterstreaming instability in magnetized pair plasmas
View Description Hide DescriptionThe electromagnetic counterstreaming instability in unmagnetized pair (electronpositron) plasmas, which is influenced by the external magnetic field parallel to the streaming direction, is investigated both analytically and numerically. It is shown from the linear theory of relativistic cold four fluidsmodel that the generation of a quasistatic magnetic field whose wave vector is perpendicular to the streaming direction is restrained by the increasing external magnetic field. The linear theory is also confirmed by particleincell simulation. The theory and simulation show that the counterstreaming instability changes its character from magnetic to electrostatic nature when the external magnetic field increases as The electrostatic waves growing due to the electrostatic counterstreaming instability play an important role for producing fast electrons and positrons with energy of MeV. The process of highenergy particle production in relativistic shocks in magnetized pair plasmas may be applied to gammaray burst events.

OX mode conversion in an axisymmetric plasma at electron cyclotron frequencies
View Description Hide DescriptionThe cold plasma dielectric function is employed to represent the plasma response of an axisymmetric steady state to incident waves at frequencies on the order of the electron cyclotron frequency. A boundary layer analysis of Maxwell’sequation valid near the mode conversion region is carried out to obtain an approximate system of wave equations. The independent variables of the wave equations are the flux surface label and poloidal angle. The case is analyzed in which the O mode cutoff surface and X mode cutoff surface intersect. An integral representation of solutions is given. It is shown that for a wide class of incident waves all such waves are transmitted with total mode conversion and no mode reflection. This work cannot assure that solutions with mode reflection do not occur, although a broad search for solutions, possibly with mode reflection, was unsuccessful.

Optical, wave measurements, and modeling of helicon plasmas for a wide range of magnetic fields
View Description Hide DescriptionHelicon waves are excited in a plasma wave facility by a halfturn doublehelix antenna operating at 13.56 MHz for static magnetic fields ranging from 200 to 1000 G. A nonperturbing optical probe located outside the Pyrex™ plasma chamber is used to observe 443 nm Ar II emission that is spatially and temporally correlated with the helicon wave. The Ar II emission is measured along with wave magnetic and Langmuir probe density measurements at various axial and radial positions. 105 GHz interferometry is used to verify the bulk temperature corrected Langmuir probemeasurements. The measured peak Ar II emission phase velocity is compared to the measuredwavemagnetic field phase velocity and code predicted wave phase velocity for the transition and blue mode regimes. Very different properties of the optical emission peak phase and wavecharacteristics for the transition and helicon modes of operation are observed. Comparison of the experimental results with the ANTENAII code [Y. Mouzouris and J. E. Scharer, IEEE Trans. Plasma Sci. 24, 152 (1996)] is carried out for the wave field measurements for the two regimes of operation.

Dust quasiatom in a plasma
View Description Hide DescriptionA quasiatomic structure of the highfrequency oscillations of the electron density inside the plasma Debye sphere is proposed. The paper studies the internal oscillations of the plasma shielding, which screens the electric charge of a dust particle immersed in a plasma. It is shown that highfrequency oscillations can be established inside the Debye sphere. An equation similar to a timeindependent Schrödinger equation is derived. The ground state and the first excited state of the oscillating Debye sphere are studied in detail. The relevance of the investigation to enhanced scattering cross sections in dusty plasmas is discussed.

Analysis of lowfrequency waves in inhomogeneous and bounded plasmas
View Description Hide DescriptionElectrostatic perturbations with low frequencies (less than or comparable to the ion cyclotron frequency) are analyzed in bounded and inhomogeneous plasmas. The effects of an arbitrary size density gradient are studied and the corresponding equation for the spatially dependent wave amplitude is solved analytically. The general solution of the eigenvalue problem reveals a global mode that is subject to given boundary conditions while the appropriate eigenvalues determine the eigenfrequencies. Exact values of frequencies and wave numbers are presented for waves propagating in a plasma with a Gaussian density distribution.

Hall current and Alfvén wave
View Description Hide DescriptionIn ideal inhomogeneous magnetohydrodynamics(MHD), the Alfvén wave (the dominant low frequency mode of a magnetized plasma) displays a continuous spectrum associated with singular eigenfunctions. It is shown that the coupling of the Hall term with the sound wave induces higher (fourth) order derivative in the Alfvén mode equation, and by resolving the singularity replaces the MHD continuum by a discrete spectrum. The mode structure resulting from the Hall resolution of the singularity is compared with the standard electroninertia approach.
 Nonlinear Phenomena, Turbulence, Transport

The bouncekinetic model for driven nonlinear Langmuir waves
View Description Hide DescriptionThe bouncekinetic model is developed and applied to driven nonlinear Langmuir waves. The waves are described in terms of an eikonal with slow envelope variation. It is assumed that the bounce frequency of trapped electrons is large. A kinetic equation involving only slowly varying quantities is derived and it is shown that the characteristic equations form a Hamiltonian system. Conservation of particles, momentum, and energy are shown to depend on firstorder corrections to this kinetic equation. The low order correction moments are derived exactly from these conservation laws, eliminating the need for a complicated boundary layer treatment of the separatrix. Previous results for nonlinear Langmuir waves are reproduced by a simplified version of this theory which neglects variations of the amplitude envelope and phase velocity. A particleincell method is proposed for solution of the nonlinear kinetic problem. Extensions of this method required to correctly describe small amplitude waves are suggested. Such an extended model may be useful for the modeling of laserplasma interaction in the trapping regime.

Evolution of relativistic ions incessantly accelerated by an oblique shock wave
View Description Hide DescriptionThe evolution of a large number of nonthermal, energetic particles that encounter with an oblique shock wave is studied with theory and simulations. First, an attempt is made to analytically discuss conditions under which particles can cross the shock front multiple times. Also, the change in the parallel momentum of a relativistic particle at the shock front is examined in detail. Then, the time variation of an energy distribution function of 5000 energetic particles is investigated with simulations; where field profiles are obtained from particle simulations of shock waves, and test particle orbits are calculated by use of these fields. The shock speed and propagation angle are taken to be for which incessant acceleration is expected. The development of these particles in the momentum space is also shown.

Dust acoustic solitary waves and double layers in a dusty plasma with twotemperature trapped ions
View Description Hide DescriptionThe combined effects of trapped ion distribution, twoiontemperature, dust charge fluctuation, and dust fluid temperature are incorporated in the study of nonlinear dust acoustic waves in an unmagnetized dusty plasma. It is found that, owing to the departure from the Boltzmann ion distribution to the trapped ion distribution, the dynamics of small but finite amplitude dust acoustic waves is governed by a modified Korteweg–de Vries equation. The latter admits a stationary dust acoustic solitary wave solution, which has stronger nonlinearity, smaller amplitude, wider width, and higher propagation velocity than that involving adiabatic ions. The effect of twoiontemperature is found to provide the possibility for the coexistence of rarefactive and compressive dust acoustic solitary structures and double layers. Although the dust fluid temperature increases the amplitude of the small but finite amplitude solitary waves, the dust charge fluctuation does the opposite effect. The present investigation should help us to understand the salient features of the nonlinear dust acoustic waves that have been observed in a recent numerical simulation study.

Renormalizationgroup analysis on the stability of largescale electrostatic fluctuations of twodimensional plasmas
View Description Hide DescriptionStability of largescale electrostaticfluctuations of forced twodimensional plasma is studied by the use of the renormalizationgroup method. Largescale flows have been rendered important in regulating turbulentplasma states and many recent works focus on their generation out of turbulence. This work is motivated by the recent result that the longwavelength fluctuations can either grow or decay as a result of the interactions between the shortscale fluctuations depending anisotropically on the spectra of the smallscale turbulence. The Hasegawa–Mima model that is forced by an anisotropic Gaussian powerlaw noise is used and the renormalized viscosity up to the lowestorder coupling is computed. The result shows that the anisotropic portion of the viscosity may have opposite sign compared to the isotropic part, depending on the strength of the anisotropy.

Scaling of forced magnetic reconnection in the Hallmagnetohydrodynamic Taylor problem
View Description Hide DescriptionTwodimensional, incompressible, zero guidefield, nonlinear HallMHD (magnetohydrodynamical) simulations are used to investigate the scaling of the rate of forced magnetic reconnection in the socalled Taylor problem. In this problem, a smallamplitude boundary perturbation is suddenly applied to a tearing stable, slab plasma equilibrium; the perturbation being such as to drive magnetic reconnection within the plasma. This type of reconnection, which is not due to an intrinsic plasma instability, is generally known as “forced reconnection.” The inclusion of the Hall term in the plasma Ohm’s law is found to greatly accelerate the rate of magnetic reconnection. In the linear HallMHD regime, the peak instantaneous reconnection rate is found to scale like where Ψ is the reconnectedmagnetic flux, the collisionless ion skin depth, η the resistivity, and the amplitude of the boundary perturbation. In the nonlinear HallMHD regime, the peak reconnection rate is found to scale like

Regular and stochastic orbits of ions in a highly prolate fieldreversed configuration
View Description Hide DescriptionIon dynamics in a fieldreversed configuration are explored for a highly elongated device, with emphasis placed on ions having positive canonical angular momentum. Due to angular invariance, the equations of motion are that of a two degreeoffreedom system with spatial variables ρ and ζ. As a result of separation of time scales of motion caused by large elongation, there is a conserved adiabatic invariant, which breaks down during the crossing of the phasespace separatrix. For integrable motion, which conserves an approximate onedimensional effective potential was obtained by averaging over the fast radial motion. This averaged potential has the shape of either a double or single symmetric well centered about ζ=0. The condition for the approach to the separatrix and therefore the breakdown of the adiabatic invariance of is derived and studied under variation of and conservedangular momentum, Since repeated violation of results in chaotic motion, this condition can be used to predict whether an ion (or distribution of ions) with given initial conditions will undergo chaotic motion.

Linear and nonlinear properties of RaodustAlfvén waves in magnetized plasmas
View Description Hide DescriptionThe linear and nonlinear properties of the Raodustmagnetohydrodynamic (RDMHD) waves in a dusty magnetoplasma are studied. By employing the inertialess electron equation of motion, inertial ion equation of motion, Ampère’s law, Faraday’s law, and the continuity equation in a plasma with immobile charged dust grains, the linear and nonlinear propagation of twodimensional RDMHD waves are investigated. In the linear regime, the existence of immobile dust grains produces the Rao cutoff frequency, which is proportional to the dust charge density and the ion gyrofrequency. On the other hand, the dynamics of amplitude modulated RDMHD waves is governed by the cubic nonlinear Schrödinger equation. The latter has been derived by using the reductive perturbation technique and the twotimescale analysis which accounts for the harmonic generation nonlinearity in plasmas. The stability of the modulated wave envelope against nonresonant perturbations is studied. Finally, the possibility of localized envelope excitations is discussed.

Onset of the nonlinear regime and finiteresistivity effects for the resistive kink instability
View Description Hide DescriptionThe development of the resistive kink instability into the nonlinear regime is analyzed dynamically. Two small parameters are involved: the fixed dimensionless resistivity η and the timedependent amplitude of the mode, that measures the amount of nonlinearities in the system. While, for small, the outer domain is predicted to be ruled by linear ideal magnetohydrodynamic equations, one tracks selfconsistently the location of the critical layer and derives the dominant dynamical equations inside it. As becomes of order a nonlinear exponential growth due to a balance between convective and mode coupling terms is predicted for moderately low values of η and the early nonlinear regime below this threshold is quantitatively computed. The nonlinear saturation of the instability should take place for at most of the order This analysis provides a general pattern to model the onset of the nonlinear regime of internal modes.
 Magnetically Confined Plasmas, Heating, Confinement

Effects of particles with large gyroradii on resistive magnetohydrodynamic stability
View Description Hide DescriptionFast ions in tokamaks are known to have a significant influence on global plasma instabilities. In normal mode analyses for tokamaks, the perturbed electric and magnetic fields have been evaluated at the position of the particle’s guiding center. The effect of spatial variation of the perturbed fields within the gyroradius for resistive internal magnetohydrodynamic(MHD) modes is considered in the present paper. The resulting tearing mode stability for the reversed field pinch(RFP) is investigated. Such effects are important for neutral beam injected particles in currentRFP experiments and for fusiongenerated alpha particles. The fast particle dielectric response is evaluated from the linearized Vlasov equation, and inserted into a cylindrical MHD model for the bulk plasma. The response is found for the simplified particles distribution function assuming that equilibrium magnetic field is uniform within the gyroorbit. The effect of large gyroradii is strong, and can be either stabilizing or destabilizing (depending on the radial distribution of the fast particle density). The effect is maximal when the fast particles reside near the tearingresonant surface.

A perturbative solution of the drift kinetic equation yields pinch type convective terms in the particle and energy fluxes for strong electrostatic turbulence
View Description Hide DescriptionApproximate linearized solutions to the drift kinetic equation (DKE) can provide physical insights into turbulent transport processes in a tokamakplasma. These types of solutions can provide a useful supplement to the results of numerical solutions to either the gyrokineticequation or to nonlinear fluid equations. Here the DKE is solved in an iterative fashion with an attempt to include the tokamak geometry in a realistic way. The gradients in the DKE are expressed in tokamak geometry, not just by the plane wave approximation. The ballooning type spatial dependence of the electrostaticturbulence is assumed to have a given poloidal dependence. There is no attempt to solve for the radial, poloidal or toroidal dependence of the turbulence. This approximate solution shows that the nonadiabatic part of the perturbed electron distribution function yields particle fluxes which have pinchlike terms proportional to the electron temperature gradient and the safety factor gradient. The terms proportional to the safety factor gradient are inward, but the terms proportional to the temperature gradient can be either inward or outward.

Study of kinetic shear Alfvén instability in tokamak plasmas
View Description Hide DescriptionKinetic shear Alfvén modes in tokamakplasmas (with or without temperature gradient) are numerically investigated in the full gyrokinetic limit. It is shown that, in the presence of ion temperature gradient(ITG), the threshold value of plasma pressure gradient is well below that for ideal magnetohydrodynamic ballooning instability. It is also demonstrated in a more general sense that, without ITG, the former is identical with the latter. The electromagnetic instability is also found to exist in the second stable region of the ideal modes when a finite ITG is present. The results are compared with previous similar analyses for kinetic collisionless ballooning modes. Possible correlation of the instability with tokamak experiments is discussed.

Modeling a resistive wall mode control system of the bang–bang type
View Description Hide DescriptionFeedback stabilization of the resistive wall mode is usually accomplished by using linear amplifiers. In this paper a study is made of a possibility of controlling resistive wall modes using switches instead of linear amplifiers, i.e., using bang–bang control. The motivation is that bang–bang control systems may be cheaper than conventional feedback systems. A distinct disadvantage of the bang–bang system is complexity due to its inherent nonlinearity. Further studies, particularly of engineering issues, are needed to determine the attractiveness of a bang–bang system.

Safety factor scaling of energy transport in mode plasmas on the DIIID tokamak
View Description Hide DescriptionThe scaling of energy transport with safety factor at fixed magnetic shear has been measured on the DIIID tokamak [Luxon, Nucl. Fusion42, 614 (2002)] for low confinement mode discharges. At constant density, temperature, and toroidalmagnetic field strength, such that the toroidal dimensionless parameters other than are held fixed, the onefluid thermal diffusivity is found to scale like with the ion channel having a stronger dependence than the electron channel in the outer half of the plasma. The measured scaling is in good agreement with the predicted scaling by the GLF23 transport model for the ion temperature gradient and trapped electron modes, but it is significantly weaker than the inferred scaling from empirically derived confinement scaling relations.