Volume 7, Issue 1, January 2000
Index of content:
 LETTERS


Interaction between an Alfvén wave and a particle undergoing acceleration along a magnetic field
View Description Hide DescriptionThe energy exchange between a plasma particle and an Alfvén wave propagating along a magnetic field is considered. It is shown that, in the presence of an accelerating force parallel to the background magnetic field, there exists a new channel for nonresonant energy transfer between the wave and the particle.

 SPECIAL TOPICS SECTION: STRONGLYCOUPLED PLASMAS


Crystalline order in lasercooled, nonneutral ion plasmas
View Description Hide DescriptionLasercooled trapped ions can be strongly coupled and form crystalline states. In this paper we review experimental studies that measure the spatial correlations of ion crystals formed in Penning traps. Both Bragg scattering of the coolinglaser light and spatial imaging of the laserinduced ion fluorescence are used to measure these correlations. In spherical plasmas with more than ions, bodycenteredcubic (bcc) crystals, the predicted bulk structure, are the only type of crystals observed. The orientation of the ion crystals can be phase locked to a rotating electricfield perturbation. With this “rotating wall” technique and stroboscopic detection, images of individual ions in a Penning trap are obtained. The rotating wall technique also provides a precise control of the timedilation shift due to the plasma rotation, which is important for Penning trap frequency standards.

Quasilocalized charge approximation in strongly coupled plasma physics
View Description Hide DescriptionThe quasilocalized charge approximation (QLCA) was proposed in 1990 [G. Kalman and K. I. Golden, Phys. Rev. A 41, 5516 (1990)] as a formalism for the analysis of the dielectric responsetensor and collective mode dispersion in strongly coupled Coulomb liquids. The approach is based on a microscopic model in which the charges are quasilocalized on a shorttime scale in local potential fluctuations. The authors review the application of the QLC approach to a variety of systems which can exhibit strongly coupled plasma behavior: (i) the onecomponent plasma (OCP) model in three dimensions (e.g., lasercooled trapped ions) and (ii) in two dimensions (e.g., classical 2D electron liquid trapped above the free surface of liquid helium), (iii) binary ionic mixture in a neutralizing uniform background (e.g., carbon–oxygen white dwarf interiors), (iv) charged particle bilayers (e.g., semiconductor electronic bilayers), and (v) charged particles in polarizable background (e.g., laboratory dusty plasmas).

Longitudinal collective modes of strongly coupled dusty plasmas at finite frequencies and wavevectors
View Description Hide DescriptionDusty plasmas offer a unique method for testing dynamical wave theories in the strong Coulomb coupling regime. Recently, there have been many theoreticalmodels, based on either a generalized hydrodynamic or on kinetic descriptions, developed to describe dust acoustic waves under conditions of strong coupling. These theories attempt to extend the usual acoustic wavedispersion relation to the strong coupling regime and, in some cases, to finite frequencies and wave vectors beyond the hydrodynamic limit. Here a multicomponent kinetic theory is used to obtain the dust acoustic wavedispersion relation in terms of an approximate dynamic local field correction, and comparison is made with the viscoelastic Navier–Stokes description.

Strong collisions and response function for twocomponent plasmas
View Description Hide DescriptionThe dielectric function for a twocomponent (hydrogen) plasma at arbitrary degeneracies is considered in the entire (k,ω)space. Applying a generalized linear response theory, it is expressed in terms of determinants of equilibrium correlation functions which allow for a systematic perturbative treatment. The relation to dynamical localfield factors is given. Collisions are treated in Born approximation leading to a (k,ω)dependent collision integral. The link to the conductivity is given in the longwavelength limit. Strong collisions are included in the frequency dependent conductivity. Sum rules are discussed.

Molecular dynamics calculation of the thermal conductivity and shear viscosity of the classical onecomponent plasma
View Description Hide DescriptionThe thermal conductivity and shear viscosity of the threedimensional classical onecomponent plasma (OCP) were determined by molecular dynamics experiments. In the simulations the velocity of the particles was spatially modulated, and the transport coefficients were calculated from the relaxation time of the modulation profile. The results are given for the range of the plasma coupling parameter The reduced shear viscosity was found to exhibit a minimum at in agreement with previous calculations. In the range our method yields values 20%–50% higher compared to some of the previously obtained data, while very good agreement was found at the position of the minimum of The reduced thermal conductivity exhibits a minimum (similarly to at between 15 and 20. The calculations presented here result in 30%–40% lower thermal conductivity compared to previously available data.

Ionization equilibrium and equation of state in strongly coupled plasmas
View Description Hide DescriptionCalculation of the physical properties of reacting plasmas depends on knowing the state of ionization and/or the state occupation numbers. Simple methods have often been used to estimate ionization balance in plasmas, but they are not adequate for understanding a variety of new experimental and observational measurements. Theoretical methods to determine the ionization state of partially ionized plasmas must confront the effects of density on bound states and strong ion coupling. These methods can be separated into two categories. Chemical picture methods consider the system to be composed of distinct chemical species. Consequently, it is necessary to assert the effect of the plasma environment on internal states of these species. On the other hand, physical picture methods view the plasma in terms of its fundamental constituents; i.e., electrons and nuclei, so that plasma effects on bound states are a basic component of the theory. A discussion of some work representative of both of these philosophies will be given. Some comparisons between theories and with recent helioseismic observations and shock experiments will also be given.

Quantum kinetic equations for nonideal plasmas: Bound states and ionization kinetics
View Description Hide DescriptionIn this paper, nonequilibrium properties of strongly coupled plasmas are considered. Usually, such problems are dealt with using Boltzmann– or Lenard–Balescutype equations. However, for the application to strongly coupled plasmas, these equations exhibit several shortcomings. So, it is not possible (i), to describe the short time kinetics, (ii), to recover the correct (energy) conservation laws and thermodynamics, and, (iii), to account for the formation or destruction of bound states. Therefore, the kinetics of strongly coupled plasmas is considered starting from the Kadanoff–Baym equations, which are known to overcome the above limitations. This is demonstrated by a numerical solution of the twotime Kadanoff–Baym equations in second Born approximation. To be able to discuss approximations which are physically more interesting, it is advantageous to proceed to the time diagonal Kadanoff–Baym equations. In first order gradient expansion, generalizations of the Boltzmann and of the Lenard–Balescu kinetic equations are derived accounting for the bound state problem, too. Thus, the shortcomings (i)–(iii) mentioned above are overcome. Finally, the kinetic equations are applied to the problem of ionization kinetics.

Quantum, manybody, finitetemperature perturbation theory for an electron–ion system
View Description Hide DescriptionThe expansion in powers of the electron charge, e, for a neutral system of electrons (fermions) and ions (Maxwell–Boltzmann particles) is extended to order for arbitrary values of temperature and density. The methods of calculation of the series terms will be illustrated, and some of the consequences of these results will be discussed. The ionization profile so derived, at least at high temperatures, will be contrasted with Saha theory. Some special features of hydrogen related to the possible plasma phase transition will be noted.

 ARTICLES


Basic Plasma Phenomena, Waves, Instabilities

Particle canonical variables and guiding center Hamiltonian up to second order in the Larmor radius
View Description Hide DescriptionA generating function, expressed as a power series in the particle Larmor radius, is used to relate an arbitrary set of magnetic field line coordinates to particle canonical variables. A systematic procedure is described for successively choosing the generating function at each order in the Larmor radius so that the transformed particle Hamiltonian is independent of the Larmor phase angle. The particle guiding center Hamiltonian up to second order in the Larmor radius is thereby derived. The analysis includes finite electric fields in which the particle “electric drifts” can be of the order of the particle velocity. The transformations which relate an arbitrary set of toroidal magnetic flux coordinates to particle canonical variables are also discussed.

Some additional observations of the vortex instability in electron beams
View Description Hide DescriptionA number of observations have been made of the electron vortices that form in highdensity sheet beams traveling along magnetic field lines. The observations were done in sealed off high vacuum tubes. The tubes were equipped with pinhole cameras that permitted measurement of the current densities and the transverse velocities of the electrons in various parts of the beam. The vortex centers were, single sign of charge,plasmas and with increasing current in the beam, the charge density in the center increased until the Brillouin value was reached. Beyond this, the beam discontinuously went through a sequence of shapes, generally with fewer but larger vortices. The pinhole camera was used to measure the transverse velocities of electrons in various parts of the vortex and a surprising broad distribution was found in the center of the vortex of the high current forms.

Rayleigh–Taylor instability of magnetized density transition layer
View Description Hide DescriptionIn presence of a uniform magnetic field for a smoothly varying density profile in a limit of small Atwood numbers, an analytic solution is obtained. The spectrum of unstable modes is defined. It is shown that this spectrum is twosidebounded. The external magnetic field stabilizes some or all modes of the spectrum. It was shown that a finite width transition layer undergoes stratification. The magnetic field makes the stratification smoother. A velocity shear between the newly formed sublayers takes place.

Temporal evolution of linear drift waves in a collisional plasma with homogeneous shear flow
View Description Hide DescriptionTemporal evolution of linear drift waves in a collisional plasma with a homogeneous shear flow is treated analytically. The explicit solutions for the linearized Hasegawa–Wakatani system of equations, as well as for linearized Hasegawa–Mima equation, are obtained for this case on the basis of the nonmodal approach. In the weakcollision regime, the homogeneous shear flow is found to be a factor impeding the development of the ordinary modal resistive drift instability. This instability is excited only in the case of a weak velocity shear. For a stronger shear, the nonmodal effects, such as the blocking of drift wave packets and the linear transformation of drift waves into convective cells, determine the temporal evolution of driftlike perturbations. A nonmodal solution is found in the limit of strong collisions or sufficiently strong flow shear. The solution at the asymptotically large time possesses a convectivecell pattern.

Charged particle motion inside the retarding potential analyzer
View Description Hide DescriptionOne of the Ionospheric Plasma and Electrodynamics Instrument (IPEI) payload onboard the Republic of China satellite 1 (ROCSAT1) spacecraft is a Retarding Potential Analyzer (RPA) to measure the ionospheric plasma composition, temperature, and the ram velocity of the flow. A threedimensional computermodel has been developed to simulate the ion and electron motions inside the RPA of the IPEI payload. The dynamical changes in the charged particles’ motions corresponding to different electric potential profiles inside the RPA detector resulted in some distinctive measuring characteristics of the RPA detector, which show discrepancies in the measured of currents at the collector plate between the analytical model and the computer simulation. The important discoveries in the computermodel are: (a) Ion transparency cannot be represented by the physical grid sizes in the detector. The alignments of the grid wires will also affect the ion transparency. The grid planes should be aligned for the maximum optical transparency to detect light ion fluxes. (b) Cutoff energy for protons is not as sharp as indicated in the analytical model. The contamination in the collector current from lighter ion species is possible. (c) Electron contamination at the collector plate is noticed if the mesh sizes are larger than the electron Debye length.

Nonlinear Phenomena, Turbulence, Transport

Threedimensional spontaneous magnetic reconnection in neutral current sheets
View Description Hide DescriptionMagnetic reconnection in an antiparallel uniform Harris current sheet equilibrium, which is initially perturbed by a region of enhanced resistivity limited in all three dimensions, is investigated through compressible magnetohydrodynamic simulations. Variable resistivity, coupled to the dynamics of the plasma by an electron–ion drift velocity criterion, is used during the evolution. A phase of magnetic reconnection amplifying with time and leading to eruptive energy release is triggered only if the initial perturbation is strongly elongated in the direction of current flow or if the threshold for the onset of anomalous resistivity is significantly lower than in the corresponding twodimensional case. A Petscheklike configuration is then built up for Alfvén times, but remains localized in the third dimension. Subsequently, a change of topology to an Oline at the center of the system (“secondary tearing”) occurs. This leads to enhanced and timevariable reconnection, to a second pair of outflow jets directed along the Oline, and to expansion of the reconnection process into the third dimension. High parallel current density components are created mainly near the region of enhanced resistivity.

The generalized hydrodynamic equations for arbitrary collision frequency in a weakly ionized plasma
View Description Hide DescriptionElectron transport processes in a weakly ionized plasma with elastic electronneutral collisions are studied by using the hybrid fluid/kinetic approach. The standard hierarchy of fluid moment equations is closed with expressions for higher hydrodynamic moments (heat flux and viscosity) in terms of the lower moments (temperature, density, and fluid velocity). The heat fluxes and viscosity moments are determined in the linear approximation from the kinetic equation in the Chapman–Enskog form. The obtained system of moment equations describe the transport processes in weakly ionized plasmas in the most general ordering, when the electron mean free path is arbitrary with respect to the characteristic length scale of the system’s inhomogeneity, and collision frequency is arbitrary with respect to the characteristic frequency General expressions for the nonlocal (time and spatial dependent) transport coefficients are obtained. In the nonlocal limit, the derived transport coefficients describe the wave–particle (Landau) interaction effects. Implications of nonlocal effects on plasma heating mechanisms are discussed.

Theory of plasma–wall transition with account of variable ion temperature
View Description Hide DescriptionThe fluid model describing a transition from a weakly ionized collisiondominated plasma to a negative wall is supplemented with the ion energy equation, accounting for thermal energy exchange with atoms, expansion/compression work, and heating due to conversion of kinetic energy of the ion flow into thermal energy in collisions of ions with atoms. An asymptotic solution is obtained for the limit case when the Debye length is much smaller than the mean free path for collisions ionneutral. If the electron temperature exceeds the temperature of the atoms, the distribution of the ion temperature in the (quasineutral) Knudsen layer is nonmonotonic. In the case when the electron temperature exceeds the temperature of the atoms by two orders of magnitude or more, the ion temperature in the bulk of the Knudsen layer exceeds substantially the atom temperature, although it does not exceed about of the electron temperature.

DriftAlfvén fluctuations associated with a narrow pressure striation
View Description Hide DescriptionThis analytical and numerical study illustrates the linear stability properties of low frequency electromagnetic eigenmodes driven by fieldaligned pressure striations whose scale transverse to the confining magnetic field is on the order of the electron skindepth. A full electromagnetic formulation is given in terms of the coupling of the fluctuating axial fields and incorporates shear and compressional Alfvén waves,drift waves, and ion acoustic waves. The kinetic response of the electrons includes pitchangle scattering (Lorentz model) and the ions are treated as a magnetized, cold fluid. Detailed quantitative comparisons of the theoretical predictions are made with laboratory observations of fluctuations generated in controlled pressure depletions [J. E. Maggs and G. J. Morales, Phys. Plasmas4, 290 (1997)] and in narrow temperature plumes [A. T. Burke, J. E. Maggs, and G. J. Morales, Phys. Rev. Lett. 81, 3659 (1998)].

Oscillatory disintegration of a transAlfvénic shock: A magnetohydrodynamic simulation
View Description Hide DescriptionNonlinear evolution of a transAlfvénic shock wave (TASW), i.e., such at which the flow velocity passes through the Alfvén velocity, is computed in a magnetohydrodynamic approximation. The analytical theory suggests that an infinitesimal perturbation of a TASW results in its disintegration, and, thus, in finite variation of the flow, or in transformation into some other unsteady configuration. In the present paper, this result is confirmed by numerical simulations. It is shown that the disintegration time is close to its minimum value equal to the shock thickness divided by a velocity of separation of the emerging secondary structures. The secondary TASW that appears after the disintegration is again unstable with respect to disintegration. When the perturbation has a cyclic nature, the TASW undergoes oscillatory disintegration, during which it repeatedly transforms into another TASW. This process manifests itself as a train of shock and rarefaction waves, which consecutively emerge at one edge of the train and merge at the other edge.

Formation of vortex streets due to nonlinearly interacting ion–temperature–gradient modes
View Description Hide DescriptionStationary solutions of the nonlinear equations, which govern the dynamics of ion–temperature–gradient (ITG)electrostatic modes, are reexamined without and with magnetic field inhomogeneities. It is shown that for both cases the nonlinear equations admit vortex street solutions in those parameter regimes where spatially bounded double vortex solutions are forbidden. The ITGdriven vortex streets can be associated with coherent nonlinear structures that are observed in laboratory and computer simulationexperiments. Furthermore, vortex streets might play a detrimental role in the study of anomalous ion thermal transport in magnetically confined plasmas.
