Volume 13, Issue 2, February 2006
 ARTICLES

 Basic Plasma Phenomena, Waves, Instabilities

Finding the radial parallel temperature profile in a nonneutral plasma using equilibrium calculations on experimental data
View Description Hide DescriptionIn 1992, Eggleston et al.[D. L. Eggleston et al., Phys. Fluids B4, 3432 (1992)] reported on a technique for measuring the radial temperature profile in a pureelectron plasma confined in a MalmbergPenning trap by partially dumping the plasma onto a charge collector at the end of the trap. For short plasmas and short confining rings, the assumptions in their paper are violated and a more general calculation is needed. This paper presents a variation of the standard equilibrium calculation to find the temperature profile of a pureelectron plasma. Eggleston’s shortcut “evaporation” temperature method is found to require a correction factor that can be calculated using methods described in this paper. For typical conditions, the evaporation method overstates the actual temperature by a factor ranging from 1.1 to 1.5 or more, depending on the plasma’s total charge and temperature and the geometry of the trap.

Resonance parametric instability in microwave gas discharges produced by circular polarization fields
View Description Hide DescriptionBy studying the interaction between an intense microwave field with circular polarization weaker than an atomic field with a dilute gas, and making use of the electron distribution function (EDF), which is nonequilibrium and anisotropic, the interaction between highfrequency electric field with produced plasma is studied. By solving the dispersion equation for two different limits, it is found that the produced plasma is unstable and parametric resonance hydrodynamic instability takes place on this kind of plasma.

A novel aspect of dust in plasma
View Description Hide DescriptionNonlinear screening of the dust grains immersed in a homogenous fully ionized electronion plasma is investigated. Assuming conservation of entropy, an important relation is obtained between the maximum potential (and therefore the charge) of the dust grain and the temperature of the electrons. The ThomasFermi equation is derived for the potential of a dust grain in a nondegenerate plasma suggesting the existence of dust atom with a well defined atomic radius. Furthermore, based on the BornOppenheimer approximation, the notion of a dustgrain molecule is introduced in which the protons act like a kind of “glue” which binds two negatively charged dust grains together, and the motion of the grains have little influence on that binding force. Finally, considering the weak interaction between the proton clouds of two dust grains, an expression of exchange energy is obtained.

Nonlinear waves in nonplanar and nonuniform dusty plasmas
View Description Hide DescriptionThe nonlinear properties of the dust acoustic solitary wave and shock wave in inhomogeneous nonplanar dusty plasmas are considered theoretically and numerically. The effects of nonthermally distributed ions, nonadiabatic dust charge fluctuation, and the inhomogeneity caused by nonuniform equilibrium particle density, nonuniform equilibrium charging, and nonplanar geometry on waves are presented. When is small but finite, where is the charging time scale and is the hydrodynamical time scale, a variable coefficients nonplanar Korteweg–de Vries (KdV) Burgers equation governing the nonlinear waves is derived by the perturbation method. The analytical expressions for the evolution of soliton and shock wave (both oscillatory and monotone shock) are obtained and the theoretical results are confirmed by the numerical solution of the nonlinear wave equation.

Laboratory observation of secondary shock formation ahead of a strongly radiative blast wave
View Description Hide DescriptionHigh Mach numberblast waves were created by focusing a laser pulse on a solid pin, surrounded by nitrogen or xenon gas. In xenon, the initial shock is strongly radiative, sending out a supersonic radiative heat wave far ahead of itself. The shock propagates into the heated gas, diminishing in strength as it goes. The radiative heat wave also slows, and when its Mach number drops to two with respect to the downstream plasma, the heat wave drives a second shock ahead of itself to satisfy mass and momentum conservation in the heat wave reference frame; the heat wave becomes subsonic behind the second shock. For some time both shocks are observed simultaneously. Eventually the initial shock diminishes in strength so much that it can longer be observed, but the second shock continues to propagate long after this time. This sequence of events is a new phenomenon that has not previously been discussed in the literature. Numerical simulation clarifies the origin of the second shock, and its position is consistent with an analytical estimate.

Continuum model for the breathing oscillation of a spherical complex plasma
View Description Hide DescriptionA nonlinear equation of motion for the breathing oscillation of a spherical complex plasma is derived. A spherical complex plasma, or “dust ball,” is a threedimensional arrangement of identical charged particles interacting through a shielded Coulomb force (i.e., a Yukawa potential) with a Debye length and confined by a threedimensional, isotropic, parabolic potential well for which the singleparticle oscillation frequency is . The dependence of the equilibrium radius and smallamplitude breathing frequency on is computed. Exact analytical results are given for the continuum limit (i.e., a spherical Yukawa fluid). The squared breathing frequency for the unshielded Coulomb interaction , irrespective of , and increases to as . The effects of a finite number of particles are modeled by assuming an inner cutoff for the Yukawa potential a distance from any point in the complex plasma sphere. Three physical regimes are identified: a Coulomb regime where and corrections to the infinite case are small, a nearestneighbor regime, where and nearestneighbor interactions dominate, and a plasma regime where and continuum plasma theory is applicable. For , in the nearestneighbor regime, while in the plasma regime.

Variational principle for linear stability of flowing plasmas in Hall magnetohydrodynamics
View Description Hide DescriptionLinear stability of equilibrium states with flow is studied by means of the variational principle in Hall magnetohydrodynamics(MHD). The Lagrangian representation of the linearized Hall MHDequation is performed by considering special perturbations that preserves some constants of motion (the Casimir invariants). The resultant equation has a Hamiltonian structure which enables the variational principle. There is however some difficulties in showing the positive definiteness of the quadratic form in the presence of flow. The dynamically accessible variation is a more restricted class of perturbations which, by definition, preserves all the Casimir invariants. For such variations, the quadratic form (the second variation of Hamiltonian) can be positive definite. Some conditions for stability are derived by applying this variational principle to the double Beltrami equilibrium.

Analysis of lowpressure dc breakdown in nitrogen between two spherical iron electrodes
View Description Hide DescriptionThe influence of afterglow period , voltage increase rate , and electrode gap on breakdown voltage for a nitrogenfilled tube with spherical electrodes of diameter and has been investigated. The data for the breakdown voltage were obtained for the case when there is a presence of atoms, which release secondary electrons via recombination on the cathode. By fitting the experimental data of breakdown voltage mean values as a function of the voltage increase rate, the static breakdown voltages for afterglow periods of 15 and 100 s were estimated. The electrical field as a function of the electrode gap using breakdown voltage mean values was also determined. It is shown that experimental results of the breakdown voltage mean value as a function of in the interval of from 0.82 to 1.62 mm can be very well described with Paschen’s law, valid for the case of parallelplate electrodes.

Thermally excited fluctuations as a pure electron plasma temperature diagnostic
View Description Hide DescriptionThermally excited charge fluctuations in pure electron plasma columns provide a diagnostic for the plasma temperature over a range of . Three different nonperturbative methods have been developed to determine the plasma temperature. The first method fits the nearLorentzian spectrum of thermal fluctuations near a single weakly damped mode. This method works well where the modes are weakly damped, i.e., when . The second method utilizes the emission spectrum over a broad frequency range encompassing several modes and the nonresonant fluctuations between modes. This method works for long columns with , so that Landau damping is dominant and well modeled by theory. The third method compares the total (frequencyintegrated) number of fluctuating image charges on the wall antenna to a simple thermodynamic calculation. This method works when .

Stabilization of the filamentation instability and the anisotropy of the background plasma
View Description Hide DescriptionThe interaction of a relativistic electron beam with an anisotropicMaxwellianplasma is investigated, with a focus on the stabilization condition for the filamentation instability. It is found that this condition is very sensitive to the anisotropy degree of the background plasma so that the investigation of the beam instability may not be easily decoupled from the state of the background plasma in typical fusion conditions. Furthermore, regardless of the plasma isotropy, filamentation can no longer be suppressed when the beam density exceeds a threshold value that is determined.
 Nonlinear Phenomena, Turbulence, Transport

Large amplitude shock wave in a strongly coupled dusty plasma due to delayed charging
View Description Hide DescriptionThe effect of delayed charging on nonlinear characteristics of a large amplitude longitudinal dust acoustic wave in the “kinetic regime” of a strongly coupled dusty plasma described by the generalized hydrodynamic equation has been investigated. Numerical investigations reveal that delayed charging induced anomalous dissipation causes the generation of a large amplitude shock wave in a strongly coupled dusty plasma only for Mach numbers lying between a minimum and a maximum value. It is found that the shock can cause the state transition from a strongly coupled to a weakly coupled state. In the case of high dust flow velocity the shock height is higher than the case of low flow velocity in comparison with the ion thermal velocity.

Statistical theory of electromagnetic weak turbulence
View Description Hide DescriptionThe weak turbulencetheory as commonly found in the literature employs electrostatic approximation and is applicable to unmagnetized plasmas only. To this date, fully electromagnetic generalization of the existing weak turbulencetheory based upon statistical mechanical approach remains largely incomplete. Instead, electromagnetic effects are incorporated into the weak turbulence formalism by means of the semiclassical approach. The present paper reformulates the fully electromagnetic weak turbulencetheory from classical statistical mechanical (i.e., the Klimontovich) approach.

Nonplanar dustacoustic shock waves for twotemperature ions in dusty plasma with dissipative effects and transverse perturbations
View Description Hide DescriptionThe dissipation caused by fluid viscosity is investigated for unmagnified dusty plasma with twotemperature ions in a spherical geometry. Analytical investigation shows that the propagation of a smallamplitude wave is governed by the spherical KadomtsevPetviashviliBurgers equation. The shock wave solutions for dustacoustic shock waves with two types of charged dust grains, that is, constant charged dust grains and adiabatic variable charged dust grains, are studied. The effects caused by dissipation and transverse perturbations are also discussed.

Threedimensional nonlinear Schrödinger equation for dustacoustic waves and its stability in magnetized dusty plasma with twotemperature nonthermal ions and dust charge variation
View Description Hide DescriptionThe effect of twotemperature nonthermal ions and variable dust charge on smallamplitude nonlinear dustacoustic waves (DAW) is investigated. By using the reductive perturbation technique, the threedimensional nonlinear Schrödinger equation (3DNLSE) is first derived. The modulational instability of DAW in the magnetized dusty plasma is investigated as well. Meanwhile, some new and important stability regions are given. The effect of the nonthermal parameter is shown to play a significant role in the determination of the normalized dust charge. Further, setting this parameter to zero degenerates the system into one in the magnetized dusty plasma consisting of the isothermal ions.

The effect of safety factor and magnetic shear on turbulent transport in nonlinear gyrokinetic simulations
View Description Hide DescriptionThis paper reports on over 100 nonlinear simulations used to systematically study the effects of safety factor and magnetic shear on turbulent energy and particle transport due to ion temperature gradient(ITG)modes and trapped electron modes(TEM) for several reference cases using the GYROgyrokinetic code. All the simulations are collisionless, electrostatic, and utilize shifted circle geometry. The motivation is to create a database for benchmarking and testing of turbulent transport models. In simulations varying , it is found that the ion and electron energy transport exhibit an offset linear dependence on for . This result is valid for cases in which the spectrum is dominated by either TEM or ITGmodes. The particle transport also follows a linear dependence if the diffusivity is positive (outward). If a particle pinch is predicted, however, then is found to be insensitive to . In kinetic electron simulations varying the magnetic shear , the particle transport can exhibit a null flow at a particular value of . In the vicinity of the null flow point, the transport spectrum shows that some modes drive an inward flow while others drive an outward flow. For negative magnetic shear, the magnetohydrodynamic parameter is shown to be stabilizing for both the energy and particle transport but can be destabilizing for large positive shear. Compared to the ITG dominated case, the TEM cases show the same linear dependence, but a weaker dependence is exhibited for positive magnetic shear values when TEMmodes dominate the spectrum. In general, the , , and dependence of the transport including kinetic electrons is consistent with ITG adiabatic electron simulation results.

Nonlinear damping of zonal modes in anisotropic weakly collisional trapped electron mode turbulence
View Description Hide DescriptionComprehensive spectral analysis of a fluid model for trapped electron mode (TEM)turbulence reveals that marginally stable zonal modes at infinitesimal amplitude become robustly damped at finite amplitude. Zonalmode structure, anisotropy, excitation, and wave number spectra are shown to result from interaction of the zerofrequency drift wave with the density advection nonlinearity. Heuristic dimensional balances, closure theory, and simulations manifest the primacy of the interaction, and yield energy transfer rates, fluctuation levels, spectra and finiteamplitudeinduced dissipation. Strong sensitivity to the zerofrequency wave induces a marked spectral energytransfer anisotropy that preferentially drives zonal modes relative to nonzonal modes. Zonalmode excitation is accompanied by the nonlinear excitation of a spectrum of damped eigenmodes. The mixing of unstable TEMeigenmodes with the damped spectrum subjects zonal modes to finiteamplitudeinduced damping. The combination of anisotropic transfer to zonal wave numbers and their nonlinear damping is shown to make this the dominant saturation mechanism for TEMturbulence.

Role of stable eigenmodes in saturated local plasma turbulence
View Description Hide DescriptionThe excitation of stable eigenmodes in unstable plasma turbulence, previously documented in collisionless trapped electron mode turbulence, is shown to be a generic behavior of local (quasihomogeneous) systems. A condition is derived to indicate when such excited eigenmodes achieve a sufficient level in saturation to affect the turbulence, and produce changes in saturation levels, instability drive, and transport. The condition is shown to be consistent with the results of collisionless and dissipative trapped electron turbulence, and is further illustrated by an entirely different model describing simple ion turbulence driven by the ion temperature gradient. The condition suggests that all eigenmodes of the ion model affect saturation, but none dominates. This is consistent with the results of simulations, which show nonlinear modifications to eigenmode structure, growth rate, and transport that occur intermittently in time, despite fixed driving gradients.

Theory of turbulence regulation by oscillatory zonal flows
View Description Hide DescriptionThe theory of turbulence regulation by oscillatory zonal flows is presented for passive scalar fieldmodels.Zonal flows are assumed to have linear spatial variation of the form , where has amplitude and frequency . The flux and fluctuation levels are found to scale as and , respectively, for . Here, is the effective decorrelation time, , , and is the typical poloidal wave number of the turbulence. The effect of stochasticity of oscillatory zonal flows on shear decorrelation is discussed. The results complement the theory of turbulence regulation by lowfrequency random zonal flows[E. Kim and P. H. Diamond, Phys. Rev. Lett91, 075001 (2003)].

Riemannian geometry of twisted magnetic flux tubes in almost helical plasma flows
View Description Hide DescriptionRiemannian geometry of curves applied recently by Ricca [Fluid Dyn. Res36, 319 (2005)] in the case of inflectional disequilibrium of twisted magnetic flux tubes is used here to compute the magnetic helicity forcefree field case. Here the application of Lorentz forcefree to the magnetic flux tube in tokamaks allows one to obtain an equation that generalizes the cylindrical tokamakequation by a term that contains the curvature of the magnetic flux tube. Another example of the use of the magnetic flux tube is done by taking the electron magnetohydrodynamics(MHD) fluid model (EMHD) of plasma physics that allows one to compute the velocity of the fluid in helical and almost helical flows in terms of the Frenet torsion of thin magnetic flux tubes. The cases of straight and curved twisted tubes are examined. Secondorder effects on the Frenet torsion arise on the poloidal component of the magnetic field, while curvature effects appear in the toroidal component. The magnetic fields are computed in terms of the penetration depth used in superconductors. The ratio between poloidal and toroidal components of the magnetic field depends on the torsion and curvature of the magnetic flux tube. It is shown that the rotation of the almost helical plasma flow contributes to the twist of the magnetic flux tube through the total Frenet torsion along the tube.

Mesoscale transport properties induced by near critical resistive pressuregradientdriven turbulence in toroidal geometry
View Description Hide DescriptionNumerical calculations of resistive pressuregradientdriven turbulence in toroidal geometry in a range of beta values where the pressure profile is close to critical show selfsimilarity of space and time scales. These selfsimilarity properties lead to a fractional diffusive equation for mesoscale tracerparticle transport. The indices of the fractional derivates are consistent with the ones found for resistive pressuregradientdriven turbulence in cylindrical geometry.