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Volume 13, Issue 9, September 2006
 LETTERS


Threedimensional stereoscopy of Yukawa (Coulomb) balls in dusty plasmas
View Description Hide DescriptionA stereoscopic approach with standard video cameras for positioning and tracking of micrometer sized polymer particles in a radiofrequency gas discharge is presented. The stereoscopy is applied to simultaneously determine the positions of all particles in a threedimensional strongly coupled spherical dusty plasma (Yukawa ball). The accuracy of the stereoscopic method is discussed. The shell structure and the occupation number of various Yukawa balls are determined and compared to recent simulations and models.

 ARTICLES

 Basic Plasma Phenomena, Waves, Instabilities

Finite element implementation of Braginskii’s gyroviscous stress with application to the gravitational instability
View Description Hide DescriptionA general coordinateindependent expression for Braginskii’s form of the ion gyroviscosity in the twodimensional potential field representation is presented, and is implemented in a full twodimensional, twofluid extended magnetohydrodynamic(MHD) numerical model. The expression for the gyroviscous force requires no field to be differentiated more than twice, and thus is appropriate for finite elements with first derivatives continuous across element boundaries (finite elements). From the extended MHDmodel, which includes the full gyroviscous stress, are derived linear dispersion relations of a homogeneous equilibrium and of an inverteddensity profile in the presence of gravity. The treatment of the gravitational instability presented here extends previous work on the subject [M. N. Rosenbluth, N. A. Krall, and N. Rostoker, Nucl. Fusion Suppl.1, 143 (1962);K. V. Roberts and J. B. Taylor, Phys. Rev. Lett.8, 197 (1962)]. Linear and nonlinear simulations of the gravitational instability are presented. Simulations are shown to agree closely with the derived dispersion relations in the linear regime. The “gyroviscous cancellation” effect is demonstrated, and some limitations of the approximation are discussed.

ideal internal kink modes in a linetied screw pinch
View Description Hide DescriptionIt is well known that the radial displacement of the internal kink mode in a periodic screw pinch has a steep jump at the resonant surface where [Rosenbluth, Dagazian, and Rutherford, Phys. Fluids16, 1894 (1973)]. In a linetied system, relevant to solar and astrophysical plasmas, the resonant surface is no longer a valid concept. It is then of interest to see how linetying alters the aforementioned result for a periodic system. If the linetied kink also produces a steep gradient, corresponding to a thin current layer, it may lead to strong resistive effects even with weak dissipation. Numerical solution of the eigenmodeequations shows that the fastest growing kink mode in a linetied system still possesses a jump in the radial displacement at the location coincident with the resonant surface of the fastest growing mode in the periodic counterpart. However, linetying thickens the inner layer and slows down the growth rate. As the system length approaches infinity, both the inner layer thickness and the growth rate approach the periodic values. In the limit of small , the critical length for instability . The relative increase in the inner layer thickness due to linetying scales as .

Low frequency instabilities during dust particle growth in a radiofrequency plasma
View Description Hide DescriptionIn this paper, instabilities appearing in a dusty plasma are experimentally investigated. These low frequency selfexcited instabilities appear during dust particle growth and are characterized by a frequency spectrum evolving during this process. The onset, the time evolution and the main characteristics of these instabilities are investigated thanks to electrical and optical measurements. Both signals show a clear evolution scheme with a welldefined succession of phases. From the beginning to the end of this scheme, regular oscillations and/or chaotic regimes are observed. Finally, instabilities stop when the dust particle size reaches a few hundreds of nanometers and a stable threedimensional dust cloud is obtained. A dustfree region called void is then usually observed in the plasma center.

Electron energy distribution functions in lowpressure inductively coupled bounded plasmas
View Description Hide DescriptionThe electron energy distribution function(EEDF) in a lowpressure inductively coupled plasma confined between two infinite plates separated by is investigated using a onedimensional particleincell simulation including Monte Carlo collisions. At low pressure, where the electron mean free path is of the order of or greater than the system length, the EEDF is close to Maxwellian, except for its tail, depleted at high energy. We give clear evidence that this depletion is mostly due to the highenergy electrons escaping to the walls. As a result of the EEDF nonlocality, the break energy, for which the depletion of the Maxwellian starts, is found to track the plasma potential. At a higher pressure, the electron mean free paths of the various elastic and inelastic collisions become shorter than the system length, resulting in a loss of nonlocality and the break energy of the distribution function moves to energies lower than the plasma potential.

A semianalytic model for localized variable charge dust acoustic waves
View Description Hide DescriptionA semianalytic model for nonlinear variable chargedust acoustic waves is outlined. It is shown that rarefactive variable chargedustacoustic solitons involving cusped density humps can exist. The effects of dustdynamics as well as equilibrium dustcharge on these nonlinear localized structures are briefly discussed.

Inhomogeneity scale lengths in a magnetized, lowtemperature, collisionless, Qmachine plasma column containing perpendicularvelocity shear
View Description Hide DescriptionRadial inhomogeneity scale lengths for radial electric field, ion density, and magneticfieldaligned (parallel) electrondrift velocity have been measured and interpreted in magnetized, lowtemperature, collisionless plasma. The effect of a narrow layer of inhomogeneity in these parameters on the excitation of electrostatic ioncyclotron waves is investigated. When the ion Larmor radius is on the order of, or larger than, the halfwidth at halfmaximum of the Gaussianlike, radially localized, radial electricfield profile , the radial profile of the azimuthal ion rotation velocity, measured using laserinduced fluorescence(LIF), has a peak that, because of finiteLarmorradius effects, is significantly lower than the peak of the combined radial profile of the and diamagnetic drift velocities. Results of an experimentally validated testparticle simulation are presented and applied using experimentally relevant electricfield profiles. Two experimental configurations are explored for which the ions enter into the electric field at different rates. In one configuration, the ions experience an effectively adiabatic increase in electricfield strength. In the other configuration, the increase in electricfield strength is effectively instantaneous. The simulation reproduces both the main features of the radial profile of LIFmeasured ion flow and the observed density depletion in regions of relatively high plasma potential for experimental conditions in which no waves were observed. The density depletion is interpreted as resulting from the finiteLarmorradius ion orbits in the presence of an inhomogeneous electric field with radial scale length .

Magnetoflow instability in symmetric field profiles
View Description Hide DescriptionSince Rayleigh’s early work on shearflow driven instabilities in fluids, it has been known that sheared flows are usually unstable only in the presence of an inflection point in the velocity profile. However, in magnetohydrodynamics, there are important instabilities for which no inflection point is required. In tokamak experiments, strongly sheared flows are associated with transport barriers. Instabilities that may limit the height and extent of transport barriers are of central importance. Here, we present linear and nonlinear simulations of an ideal magnetohydrodynamicinstability that is driven by sheared flows without inflection points—instead, the instability mechanism requires reversed magnetic shear. Several symmetric field profiles are studied. In general, the instability leads to current profile modifications that push the local minimum value of the safety factor upward. The possibility of causing disruption in a relatively slow time scale is pointed out when crosses a rational (especially integral) value. The time scale of the instability is governed by the transit time of the shear flow, which is typically smaller than that of the Alfvén velocity. Characteristics of this instability are compared with recent experimental observations.

Nonneutral plasma equilibria with weak axisymmetric magnetic perturbations
View Description Hide DescriptionThe effect of weak axisymmetric magnetic and/or electrostatic perturbations on the equilibrium of a nonneutral plasma in a MalmbergPenning trap is analyzed. Analytical and semianalytical solutions for the potential variations inside the trap are found in a paraxial limit of the perturbations for various radial density profiles of the plasma, including the case of global thermal equilibrium. It is shown that a magnetic perturbation produces a potential variation with a sign which is changing along the plasma radius. The fraction of magnetically and electrostatically trapped particles thus created is calculated explicitly for the case of a Maxwellian distribution function, and it is shown to be independent from the sign of the magnetic field perturbation. The analysis of the potential perturbation is extended to the case of an anisotropic distribution function, with an arbitrary ratio between the parallel and the perpendicular plasma temperature. Twodimensional thermal equilibrium simulations for parameters relevant to the CamV device [A. A. Kabantsev, J. H. Yu, R. B. Lynch, and C. F. Driscoll, Phys. Plasmas10, 1628 (2003)] confirm the predictions of the analytical theory for smooth and weak perturbations of the magnetic field.

A comparison of ultrarelativistic electron and positronbunch propagation in plasmas
View Description Hide DescriptionBeamdriven acceleration of electrons and positrons by the electric field of the plasma wakefield is considered in detail using a selfconsistent relativistic cylindrical particleincell code with implicit electromagnetic solver. The plasmacharacteristics, such as the particle motion, the density, the temperatures, the wake fields, and the energies and their transfer, are investigated. Strong local energization and heating of the plasmaelectrons are observed. Small groups of ions in the wake can also attain temperatures higher than the secondary ionization potential of lithium vapor. It is verified that an electron bunch indeed excites a wakefield of higher energy than a positron bunch, which, in fact, behaves like a negative charge plasma bunch because of the suckin of background plasmaelectrons.

New approach for the study of linear Vlasov stability of inhomogeneous systems
View Description Hide DescriptionThis paper presents an alternative technique for solving the linearized VlasovMaxwell set of equations, in which the velocity dependence of the perturbed distribution function is described by means of an infinite series of orthogonal functions, chosen as Hermite polynomials. The orthogonality properties of such functions allow us to decompose the Vlasov equation into a set of infinite coupled linear equations. With a suitable truncation relation, the problem is transformed in an eigenvalue problem. This technique is based on solid but easy concepts, not attempting to evaluate the integration over the unperturbed trajectories and can be applied to any equilibrium. Although the solutions are approximate, because they neglect contributions of higher order coefficients of the series, the physical meaning of the loworder coefficients is clear. Furthermore the accuracy of the solution, which depends on the number of terms taken into account in the Hermite series, appears to be merely a problem of computational power. The method has been tested for a 1D Harris equilibrium, known to give rise to several instabilities like tearing, drift kink, and lower hybrid. The results are shown in agreement with those obtained by Daughton with a traditional technique based on the integration over unperturbed orbits.

Electron plasmas: Confinement and mode structure in a small aspect ratio toroidal experiment
View Description Hide DescriptionToroidal electron plasmas have remained less explored due to their poor confinement properties. Their equilibrium, stability, and confinement properties are therefore not entirely understood and continue to remain a topic of intense ongoing research. Large aspectratio theory suggests poor confinement in toroidal devices can be overcome by the application of a radial electric field; this has been verified successfully in some of the recent experiments. In the present paper, we report the longest confinement time without these external forces. Increasing the toroidicity has helped us to generate these forces intrinsically. To this end, a trap to confine electron plasmas has been created in a small aspectratio torus. Electrons after being injected from a thermionic source are seen to remain confined with a purely toroidalmagnetic field. The confinement time is far more than known single particle drift time scales. Importantly, it is in the absence of any external electric field, additional rotational transform, and/or magnetic fields, which, although not required, in principle, may appear essential particularly due to their role in improving confinement in some of the recent large aspectratio traps. The successful confinement in the small aspectratio limit has also led to several interesting observations: the evolution of the confined plasma is marked by an interesting nonlinear (large amplitude), electrostatic wave activity. Coherent, periodic, double peak oscillations result from a lowfrequency motion of a toroidalvortex in a plasma that closely leans against the inner wall. As many as highly phasecoherent harmonics with dominant power in suggest that the mode is not merely a centerofcharge motion. Rather, a strong coupling of modes leads to a novel nonlinear state. The predominant energy is present in the shaping of the electron cloud and not in the displacement of the center of charge seen in large aspectratio traps. The absence of any powerlaw tail suggests absence of any turbulence, at least on time scales longer than the wallprobe resolution . The frequency, (around at ) shows an unusual shear in time: it reduces as the mode evolves, but later increases as the mode dies.

Generation of suprathermal electrons and Alfvén waves by a high power pulse at the electron plasma frequency
View Description Hide DescriptionThe interaction of a short high power pulse at the electron plasma frequency (, pulse length or , input power ) and a magnetized plasma (, , helium) capable of supporting Alfvén waves has been studied. The interaction leads to the generation of field aligned suprathermal electrons and shear Alfvén waves. The experiment was performed both in ordinary mode ( mode) and extraordinary mode ( mode), for different background magnetic fields and different power levels of the incoming microwaves.

Evanescent wave interference and the total transparency of a warm highdensity plasma slab
View Description Hide DescriptionIt is shown that an overcritical density plasma slab can be totally transparent to a polarized obliquely incident electromagnetic wave. High transparency is achieved due to the interference of the evanescent waves in the subcritical region. The transmission coefficient has the resonant character due to the excitation of a plasmasurface mode (plasmonpolariton). In a warm plasma case, the excitation of the propagating longitudinal (electrostatic) modes becomes possible. It is demonstrated that these longitudinal excitations facilitate the total transparency of an opaque plasma slab creating additional resonances in the transmission property of the system.

Simulation study of spheroidal dust gains charging: Applicable to dust grain alignment
View Description Hide DescriptionThe charging process of nonspherical dustgrains in an unmagnetized plasma as well as in the presence of a magnetic field is studied. It is shown that unlike the spherical dustgrain, due to nonhomogeneity of charge distribution on the spheroidal dustsurface, the resultant electric forces on electrons and ions are different. This process produces some surface charge density gradient on the nonspherical grainsurface. Effects of a magnetic field and other plasma parameters on the properties of the dust particulate are studied. It has been shown that the alignment direction could be changed or even reversed with the magnetic field and plasma parameters. Finally, the charge distribution on the spheroidal grainsurface is studied for different ambient parameters including plasma temperature, neutral collision frequency, and the magnitude of the magnetic field.

Relativistic Landau damping of longitudinal waves in isotropic pair plasmas
View Description Hide DescriptionLandau damping is described in relativistic electronpositron plasmas. Relativistic electronpositron plasma theory contains important new effects when compared with classical plasmas. For example, there are undamped superluminal wave modes arising from both a continuous and discrete mode structure, the former even in the classical limit. We present here a comprehensive analytical treatment of the general case resulting in a compact and useful form for the dispersion relation. The classical pairplasma case is addressed, for completeness, in an appendix.

RankineHugoniot relations of an axial shock in cylindrical nonneutral plasma
View Description Hide DescriptionThe RankineHugoniot relations of an axial shock in cylindrical nonneutral plasma with current, electric and magnetic field are presented. These relations are all dependent on the radius of cylindrical plasma, and markedly different from the onedimensional (i.e., nonradially dependent) case. These twodimensional RankineHugoniot relations cause at least two important new results. First, the radial profiles of the shock downstream parameters are always different from the upstream profiles due to the magnetic effects. Second, the critical Mach number for the shock existence will depend on the shock carried current (i.e., magnetic field). As an example, a set of shock downstream profiles is provided numerically when the upstream profiles are taken as a kind of typical equilibrium profiles of a ZpinchBennett profiles. By comparing the downstream profiles to the corresponding upstream profiles, the dependents of both the amplitudes and profiles of the downstream parameters on the shock carried current are shown.

Entropy conservation in simulations of magnetic reconnection
View Description Hide DescriptionEntropy and mass conservation are investigated for the dynamic field evolution associated with fast magnetic reconnection, based on the “Newton Challenge” problem [Birn et al., Geophys. Res. Lett.32, L06105 (2005)]. In this problem, the formation of a thin current sheet and magnetic reconnection are initiated in a plane Harristype current sheet by temporally limited, spatially varying, inflow of magnetic flux. Using resistive magnetohydrodynamic(MHD) and particleincell(PIC) simulations, specifically the entropy and mass integrated along the magnetic flux tubes are compared between the simulations. In the MHD simulation these should be exactly conserved quantities, when slippage and Ohmic dissipation are negligible. It is shown that there is very good agreement between the conservation of these quantities in the two simulation approaches, despite the effects of dissipation, provided that the resistivity in the MHD simulation is strongly localized. This demonstrates that dissipation is highly localized in the PIC simulation also, and that heat flux across magnetic flux tubes has negligible effect as well, so that the entropy increase on a full flux tube remains small even during reconnection. The mass conservation also implies that the frozenin flux condition of ideal MHD is a good integral approximation outside the reconnection site. This result lends support for using the entropyconserving MHD approach not only before and after reconnection but even as a constraint connecting the two phases.
 Nonlinear Phenomena, Turbulence, Transport

Clebschtype coordinates for nonlinear gyrokinetics in generic toroidal configurations
View Description Hide DescriptionThe nonlinear gyrokinetic equations are frequently used as a basis for simulations of smallscale turbulence in magnetized toroidal plasmas. In this context, fieldaligned coordinates are usually employed in order to minimize the number of necessary grid points. The present work proposes a system of Clebschtype coordinates which does not depend on the existence of flux surfaces. The construction and use of these coordinates is explained, and the corresponding formulation of the nonlinear gyrokinetic equations is accomplished. This setup paves the way toward the investigation of nonaxisymmetric toroidal geometries, also in the region of magnetic islands as well as inside the ergodic layer where flux surfaces cease to exist. For testing purposes, in the axisymmetric, large aspect ratio case, the wellknown expressions are recovered for closed flux surfaces. Moreover, geometric data for a specific stellarator configuration are computed and discussed.

Stability and evolution of onedimensional relativistic solitons on the ion time scale
View Description Hide DescriptionThe onedimensional dynamics of trapped relativistic electromagnetic radiation, which appears during laser plasma interaction, is investigated within a relativistic fluidMaxwell model. The modifications of plasma density due to trapped laser fields are considered for linear as well as circular polarizations. It is shown that standing solitons are stable on the electron time scale. However, the stability region does not agree with the prediction from the VakhitovKolokolov criterion. Ions always drive the standing solitons unstable, irrespective of the polarization. The stability of moving solitons, which have been obtained in the literature as stationary solutions of the fluidMaxwell equations including ion dynamics, is demonstrated. The problem of soliton generation is addressed. The time evolution of the so called postsolitons, which are generated behind a broad laser pulse propagating in underdense plasma, is analyzed. The effect of finite electron and ion temperatures is briefly discussed.