Volume 8, Issue 5, May 2001
Index of content:
 LETTERS


A fluid–kinetic hybrid electron model for electromagnetic simulations
View Description Hide DescriptionA fluid–kinetic hybrid electron model for electromagnetic simulations of finiteβ plasmas is developed based on an expansion of the electron response using the electron–ion mass ratio as a small parameter. (Here β is the ratio of plasma pressure to magnetic pressure.) The model accurately recovers low frequency plasma dielectric responses and faithfully preserves nonlinear kinetic effects (e.g., phase space trapping). Maximum numerical efficiency is achieved by overcoming the electron Courant condition and suppressing high frequency modes. This method is most useful for nonlinear kinetic (particleincell or Vlasov) simulations of electromagnetic microturbulence and Alfvénic instabilities in magnetized plasmas.

Discrete symmetries in axisymmetric toroidal plasma confinement
View Description Hide DescriptionSeveral discrete symmetry parameters characterizing axisymmetric toroidalplasmas have been introduced. For a device without up–down symmetry such parameters are related to the handedness of the toroidal current, related to the direction of the toroidal velocity, and characterizing the handedness of the toroidalmagnetic field. All these parameters can acquire values ±1, thereby making eight different combinations. For a device with up–down symmetry only the mutual orientation of the toroidal current, toroidal velocity, and toroidalmagnetic field remain important. Based on the general expression for the Lagrangian for charged particles in an external magnetic field, we identify the invariance properties of this Lagrangian (and, accordingly, of plasma behavior) with respect to these transformations. Reduced plasma models, based on the Maxwell–Boltzmannequations, and on the magnetohydrodynamic equations, are also considered. An analysis of the plasma behavior in the context of the symmetry properties may be helpful in identifying the most probable theoretical models of plasmatransport.

Experimental evidence for spatial damping of lefthand circularly polarized waves in an electron cyclotron resonance region
View Description Hide DescriptionSelective launch, propagation, and absorption of righthand (R) and lefthand (L) circularly polarized waves are investigated using an inhomogeneously magnetized plasma. When the R wave gets closer to the electron cyclotron resonance (ECR) point, the wave vanishes in the strong magneticfield region before reaching the ECR point. On the other hand, the L wave, which has been considered not to be related to ECR, is clearly observed to be also absorbed near the ECR point. The former and latter phenomena are discussed in terms of the contribution of highenergy tail electrons and polarization reversal of the L wave to the R wave within the plasma, respectively.

Experimental observation of ionacoustic waves in an inhomogeneous dusty plasma
View Description Hide DescriptionThe propagation of a dustionacoustic wave(DIAW)wave down the steep density gradient in an inhomogeneous diffusive dusty plasma is experimentally studied. It is observed that the presence of the dust enhances the plasma inhomogeneity. The phase velocity of the DIAW increases rapidly with distance and becomes supersonic. The interplay between the effects of the density nonuniformity and collisional damping results in the continuous transition of the relative amplitude of the DIAW from damping to growth. The experimental data are in agreement with theoretical prediction and confirm the importance of densitydependent ion–dust collisions.

Control of magnetic fluctuations in the reversed field pinch with edge current drive
View Description Hide DescriptionThe generation of auxiliary current in the extreme edge of the reversed field pinch is shown to affect edge and core resonant magnetic fluctuations, the recurrence time of relaxation oscillations (sawteeth), and the energy and particle confinement. Current is driven in the edge by electrostatic current sources. Although the injected current is expected to primarily affect edge resonantfluctuations, the coupling of edge and core modes enables changes in the extreme edge to have global consequences.

 ARTICLES

 Basic Plasma Phenomena, Waves, Instabilities

The radial structure of a plasma column sustained by a surface wave
View Description Hide DescriptionThe selfconsistent radial profiles are obtained for a steadystate, surfacewavesustained, unmagnetized argon plasma in a cylindrical dielectric tube surrounded by a conductor. The density profiles obtained using the correct constant meanfreepath ion–neutral collision differ considerably from those obtained using the common (but here quite incorrect) approximation of constant mean free time, but are little affected by changes in the profile of wave energy deposition. Various profiles for some typical cases are also compared for three different electron heat transport assumptions. These electron heat transport coefficients are as follows: (i) The correct value, (ii) the correct value, to obtain the essentially isothermal case, and (iii) the correct value, to approximate negligible heat transport (the adiabatic case). From the comparison of the temperature profiles, it became clear that the best electron heat transport simplification is to take the electrons to be isothermal [i.e., assumption (ii)], in which case only the total absorption per unit length is important, and not the details of the surface wave behavior.

Linear wave dispersion laws in unmagnetized relativistic plasma: Analytical and numerical results
View Description Hide DescriptionIn this paper dispersion laws for electrostatic and electromagnetic waves in a homogeneous and unmagnetized relativistic Vlasov plasma are derived. From the dispersion laws the relativistic plasma frequency, which is temperature dependent is derived. Using the standard technique of successive approximations, simple but powerful approximate relativistic dispersion laws are derived, resembling the electromagnetic dispersion law and the electrostatic Bohm–Gross dispersion law in the nonrelativistic case. The relation between the relativistic plasma frequency Debye wave number and the thermal velocity is established. The approximate dispersion laws are compared with numerical solutions of the full dispersion laws. The full dispersion equations are transformed so that they are well suited for numerical evaluation in the temperature range where a fully relativistic treatment is needed.

Dusty plasma expansion with a variable charge in a spherical configuration
View Description Hide DescriptionThe expansion of a dusty plasma into a vacuum with a variable charge is considered selfconsistently. Due to the plasma spatial finitude, loss terms are introduced in fluid equations. Particles attachment also imposes that the Boltzmann distribution be relaxed. A nonlinear differential equationssystem is obtained and solved numerically. A breakdown of the quasineutrality on the front along with a buildup of scaleinvariant waves are reported as well.

Evolution of perturbation in chargevarying dusty plasmas
View Description Hide DescriptionThe nonstationary problem of the evolution of perturbation and its transformation into nonlinear wave structure in dusty plasmas is considered. For this purpose two onedimensional models based on a set of fluid equations, Poisson’s equation, and a charging equation for dust are developed. The first (simplified) model corresponds to the case [Popel et al., Phys. Plasmas3, 4313 (1996)] when exact steadystate shock wave solutions can exist. This simplified model includes variablecharged dust grains, Boltzmann electrons, and inertial ions. The second (ionizationsource)model takes into account the variation of the ion density and the ion momentum dissipation due to dust particle charging as well as the source of plasma particles due to ionization process. The computational method for solving the set of equations which describe the evolution in time of a nonlinear structure in a chargevarying dusty plasma is developed. The case of the evolution of an intensive initial nonmoving region with a constant enhanced ion density is investigated on the basis of these two models. The consideration within the ionizationsourcemodel is performed for the data of the laboratory experiment [Luo et al., Phys. Plasmas6, 3455 (1999)]. It is shown that the ionizationsourcemodel allows one to obtain shock structures as a result of evolution of an initial perturbation and to explain the experimental value of the width of the shock wave front. Comparison of the numerical data obtained on the basis of the ionizationsourcemodel and the simplified model shows that the main characteristic features of the shock structure are the same for both models. Nevertheless, the ionizationsourcemodel is much more sensitive to the form of the initial perturbation than the simplified model. The solution of the problem of the evolution of perturbation and its transformation into shock wave in chargevarying dusty plasmas opens up possibilities for description of the real phenomena like supernova explosions as well as of the laboratory and active space and geophysical experiments.

Fluid and kinetic stability of virtual cathodes for the periodically oscillating plasma sphere
View Description Hide DescriptionRecent theoretical work [R. A. Nebel and D. C. Barnes, Fusion Technol. 38, 28 (1998); D. C. Barnes and R. A. Nebel, Phys. Plasmas5, 2498 (1998)] has suggested that a tiny oscillating ion cloud (referred to as the periodically oscillatingplasma sphere or POPS) may undergo a selfsimilar collapse that can result in the periodic and simultaneous attainment of ultrahigh densities and temperatures. However, a major uncertainty in this plasma system is the behavior of the electron cloud that forms a virtual cathode. Here it is demonstrated that the required electron cloud (which forms a harmonic oscillator potential) is susceptible to an instability related to buoyancydriven modes present in compressible fluids. Although it is demonstrated that no absolutely stable profiles with uniform electron density exist, stable profiles that are close to the required harmonic oscillator potential are found. A simple twostream analysis indicates that kinetic effects lead to a critical limit in above which the virtual cathodes are stable. This result is consistent with previous experimental observations.

Nonlocal theory of drift type waves in a collisional dusty plasma
View Description Hide DescriptionA nonlocal theory of lowfrequency drifttype waves has been developed in a magnetized collisional dusty plasma in a sheared slab geometry. It is shown that the wellknown stability of the drift waves in a sheared slab geometry does not hold in the presence of dust particles and a new unstable mode exists for typical laboratory plasma parameters.

Modeling of discharges generated by electron beams in dense gases: Fountain and thunderstorm regimes
View Description Hide DescriptionIn this paper we present an analysis of the predicted dynamics of plasmas generated in air and other gases by injecting beams of highenergy electrons. Two distinct regimes are found, differing in the way that the excess negative charge brought in by the ionizing electron beam is removed. In the first regime, called a fountain, the charge is removed by the back current of plasma electrons toward the injection foil. In the second, called a thunderstorm, a substantial cloud of negative charge accumulates, and the increased electric field near the cloud causes a streamer to strike between the cloud and a positive or grounded electrode, or between two clouds created by two different beams. A quantitative analysis, including electron beam propagation, electrodynamics, charge particle kinetics, and a simplified heat balance, is performed in a onedimensional approximation.

Nonlinear electrostatic waves in a magnetized dustion plasma
View Description Hide DescriptionIt is shown that the nonlinear equation governing the dynamics of coupled dustacoustic and dustcyclotron waves in a magnetized dustion plasma can be written in the form of an energy integral. The latter is analyzed analytically as well as numerically to investigate the properties of arbitrary amplitude solitary waves. It is found both analytically as well as numerically that there exist solitary waves only with a negative potential. The implications of these results to some space and astrophysical dusty plasma systems, especially to planetary ring systems and cometary tails, are briefly discussed.
 Nonlinear Phenomena, Turbulence, Transport

Nonlinear solutions of a Maxwellian type for the Vlasov–Poisson equations
View Description Hide DescriptionThe nonlinear dynamics of collisionless unmagnetized plasma is considered. Timedependent oneparticle distribution functions of a Maxwellian type that can be expressed as a series in positive powers of the electrostatic potential are obtained. The influence of conditions on the formation and existence of Maxwellian equilibria is discussed.

Rapid dissipation of magnetic field energy driven by plasma flows in forcefree collisionless pair plasmas
View Description Hide DescriptionIt is shown by using a twodimensional fully electromagnetic and relativistic particleincell code that magnetic field energy can be strongly dissipated when external plasma flowinteracts with the forcefree magnetic field configuration in pair plasmas. During the early stage of the interaction, the streaming instability occurs, which induces the electromagnetic perturbations associated with the generation of a quasistatic magnetic field. In the nonlinear stage, the forcefree magnetic field becomes unstable against the firehose instability, and then magnetic islands are formed through magnetic reconnection. The dissipated magnetic field energy is converted to plasma heating, as well as highenergy particle production. The energy spectrum in the highenergy region shows a law of the exponential type. When the plasma flow velocity becomes relativistic the effective energy conversion from the initial magnetic field energy is observed, with a conversion rate of about 90%. The interaction process between the forcefree collisionless plasmas and the relativistic plasmaflows may play an important role for effective magnetic field energy conversion, formation of filament structures, and highenergy particle production in astrophysical plasmas.

Computer studies on the spontaneous fast reconnection evolution in various physical situations
View Description Hide DescriptionThe spontaneous fast reconnection evolution is studied in a long current sheet system in various physical situations, where the threshold of currentdriven anomalous resistivity is assumed to increase with the thermal velocity. If the initial threshold is sufficiently large in a lowβ plasma, the fast reconnection mechanism can fully be set up; on the other hand, if is so small that the anomalous resistivity can easily occur in the usual circumstances, the resulting diffusion region notably lengthens so that the reconnection process becomes much less effective. Also, the fast reconnection evolution is strongly influenced by plasma β in the ambient magnetic field region, and an essential condition for the fast reconnection mechanism to evolve explosively is that the plasma β is sufficiently small. In fact, only in a lowβ plasma does the magnetic tension force involved play the dominant role in the overall system dynamics and in the drastic magnetic energy release. It is also demonstrated that the fast reconnection evolution does not depend on the detailed functional form of the (currentdriven) anomalous resistivity model. This is because the positive feedback between the anomalous resistivity and the reconnection flow effectively works so long as an anomalous resistivity is assumed to increase with the relative electronion drift velocity.

On the stability of drift wave spectra with respect to zonal flow excitation
View Description Hide DescriptionA simple criterion that allows one to determine whether or not a given wave spectrum will generate zonal flows, is derived and analyzed. In the context of a coupled drift wave–zonal turbulence, the results are pertinent to the limit of small zonal flow damping, in which previous analyses found that the turbulence vanishes. However, the practically important issue of the drift wave amplitude threshold for zonal flow excitation was not resolved. In its formal mathematical appearance, the criterion obtained is similar to the wellknown Penrose criterion that is used for stability analysis of stellar distributions and particle distributions in plasmas. By contrast, the derived criterion, being applied to wave quanta rather than to particle distribution, shows that even “normal” (wave density decaying with wave number) distributions with an intensity above the threshold should generate zonal flows. This clearly points at the ubiquity of the latter.

High relaxed states with internal conductor plasma configuration
View Description Hide DescriptionIn a twofluid dissipationless plasma, strong coupling of magnetic field and flow velocity introduced by the Hall term leads to the equilibrium solution characterized by the “double curl Beltrami equation.” Internal conductor plasma configuration is investigated employing the double curl Beltrami formulation. Numerical results reveal that relaxed states of plasma exhibiting ultrahigh associated with minimum values of fieldaligned current and flow can be created which are suitable for the advanced fusion concept.
 Magnetically Confined Plasmas, Heating, Confinement

Particle transport in DIIID discharges with internal regions of enhanced confinement and counter injected neutral beams
View Description Hide DescriptionAn analysis of experimentally measured particle transport in tokamakplasmas with negative central magnetic shear is presented. The analysis is presented in terms of a simple model for turbulenttransport which allows the separation of diagonal and off diagonal terms and allows the direct comparison of particle and energy transport. Comparing the measured fluxes to the fluxes predicted by a simple quasi analytical model which specifies a relation between the diagonal and off diagonal terms allows an understanding of the reason for the difference between energy and particle fluxes. In the center of discharges with a region of enhanced confinement (or internal transport barrier), the ion thermal diffusivity becomes small and comparable to neoclassical values and the particle diffusivity also becomes small and approaches the neoclassical values.

Allorders spectral calculation of radiofrequency heating in twodimensional toroidal plasmas
View Description Hide DescriptionSpectral calculations of radiofrequency(rf)heating in tokamak plasmas are extended to two dimensions (2D) by taking advantage of new computational tools for distributed memory, parallel computers. The integral form of the wave equation is solved in 2D without any assumption regarding the smallness of the ion Larmor radius (ρ) relative to the perpendicular wavelength Results are therefore applicable to all orders in where Previous calculations of rfwave propagation and heating in 2D magnetized plasmas have relied on finite Larmor radius expansions and are thus limited to relatively long wavelengths. In this paper, no such assumption is made, and we consider short wavelength processes such as the excitation and absorption of ion Bernstein waves in 2D with Results show that this phenomenon is far more complex than simple onedimensional plasma models would suggest. Other applications include fully selfconsistent 2D solutions for highharmonic fastwave heating in spherical tokamaks. These calculations require the storage and inversion of a very large, dense matrix, but numerical convergence can be improved by writing the plasma current in the laboratory frame of reference. To accurately represent the wave spectrum in this frame, the local plasma conductivity is corrected to first order in where L is the equilibrium scale length. This correction is necessary to ensure accuracy in calculating the wave spectrum and hence the fraction of power absorbed by ions and electrons.