Volume 13, Issue 4, April 2006
 ARTICLES

 Basic Plasma Phenomena, Waves, Instabilities

On the selfheating phenomenon in nonmodal shear flow
View Description Hide DescriptionIn this article, the nonmodal selfheating phenomenon of linear shear flow [A. D. Rogava, Astrophys. Space Sci.293, 189 (2004)] is investigated with an initially excited Alfvénic perturbation focusing on the factors determining the efficiency of the heating process. It is found that to get an efficient selfheating process, the initial Alfvén wave must be at least partially transformed into the fast mode. This is because only the fast mode, among the three types of magnetohydrodynamic modes, can get amplified significantly by the shear flow. This requires the initial wave number along the shear to be positive so that the Spatial Fourier Harmonics can pass through the degeneration region, and also puts constraints on the plasma parameter [, where is the sound (Alfvénic) velocity]. It is shown that the selfheating function, which represents the total energy dissipated at a certain time, decreases monotonically with increasing . In addition, to get efficient heating the viscous coefficient should be in an appropriate range. A smaller viscosity results in an insufficient thermalization of the perturbation energy, while a larger one corresponds to a suppressed nonmodal amplification.

Electrostatic field distribution at the sharp interface between high density matter and vacuum
View Description Hide DescriptionUltrahigh intensity lasers are proven to be particularly suitable for ion acceleration to energies above hundreds of keV and even in the multi MeV range, due to their interaction with either planar thin solid foils, or spherically symmetric targets. With reference to these problems, a quasistationary model is developed, where the Poisson equation for the electrostatic potential distribution at the sharp solid targetvacuum interface is solved for a nonrelativistic Maxwellian distribution of trapped electrons. Analytical solutions are given and ion acceleration in the relevant electrostatic field configurations is discussed.

Invariant imbedding theory of mode conversion in inhomogeneous plasmas. II. Mode conversion in cold, magnetized plasmas with perpendicular inhomogeneity
View Description Hide DescriptionA new version of the invariant imbedding theory for the propagation of coupled waves in inhomogeneous media is applied to the mode conversion of high frequency electromagnetic waves into electrostatic modes in cold, magnetized, and stratified plasmas. The cases where the external magnetic field is applied perpendicularly to the direction of inhomogeneity and the electron density profile is linear are considered. Extensive and numerically exact results for the mode conversion coefficients, the reflectances, and the wave electric and magnetic field profiles inside the inhomogeneous plasma are obtained. The dependencies of mode conversion phenomena on the magnitude of the external magnetic field, the incident angle, and the wave frequency are explored in detail.

Laserexcited shear waves in solid and liquid twodimensional dusty plasmas
View Description Hide DescriptionThe propagation of transverse waves in a twodimensional particle suspension in a plasma is studied in the solid and liquid phase. The different states of the suspension are realized by raising the kinetic temperature of the dust particles with a new laser method. An additional laser beam is used to excite shear waves and the wave is observed by videomicroscopy in terms of the individual velocities of the dust particles. For recovering the spatialwave patterns the method of singular value decomposition is applied and compared with the method of spatialFourier analysis of complex wave numbers. In the solid phase, weakly damped waves are found which follow the expected dispersion relation. In the liquid phase the existence of strongly damped waves is demonstrated. The real part of the wave number is in overall agreement with the predictions of the Quasi Localized Charge Approximation model for a twodimensional system. The damping of the waves is discussed.

Dust confinement and dustacoustic waves in weakly magnetized anodic plasmas
View Description Hide DescriptionExperiments on dustacoustic waves(DAW) in a magnetized anodic plasma are presented for the regime of low collisionality. The dust trapping and the selfexcited and synchronized DAW dynamics are studied. Based on Langmuir and emissive probe measurements the dust confinement is found to be well described with respect to size, stability, and position of the dust cloud by an effective potential well formed by ion drag and Coulomb forces. Moreover, the measurements indicate the necessity for a kinetic model for the wave dispersion. By means of singular value decomposition the local wavelengths and growth rates of the waves are measured systematically. It is found that the measured mean wave number is well described by kinetic theory, while the theoretical growth rates overestimate the experiments. A novel observation for the DAW is a systematic variation of the wavelength inside the dust cloud.

A fluid approach to linear beam plasma electromagnetic instabilities
View Description Hide DescriptionElectromagnetic instabilities found for an arbitrary oriented wave vector are typically difficult to investigate analytically within the framework of kinetic theory. The case of a small density relativistic electron beam interacting with a plasma is considered, and a twofluid theory of the system including a kinetic pressure tensor is developed. The model obtained agrees very well with temperature effects found on oblique instabilities from a kinetic model, and the respective roles of parallel and transverse beam temperatures are correctly reproduced. An analysis of the phase velocities of the unstable waves allows for an explanation of this similarity. Such a formalism could be used to study oblique instabilities in settings where kinetic theory becomes problematic to implement.

Measurements of spatially growing dust acoustic waves in a dc glow discharge plasma
View Description Hide DescriptionIn this paper, an experiment is performed on dust acoustic waves in a dc glow dischargeplasma. Stereoscopic particle image velocimetry (stereoPIV) techniques are used to make measurements of the dust acoustic waves. These stereoPIV measurements reveal the spatial growth of the waves over three to six wavelengths before reaching a saturated level. Experimental measurements are shown to agree with a simple model for spatially varying waves.

Slow magnetohydrodynamic waves in stratified and viscous plasmas
View Description Hide DescriptionThe propagation of slow magnetohydrodynamic waves in vertical thin flux tubes embedded in a vertically stratified plasma in the presence of viscosity is shown here to be governed by the KleinGordonBurgers (KGB) equation, which is solved in two limiting cases assuming an isothermal medium in hydrostatic equilibrium surrounded by a quiescent environment. The results presented here can be applied to, e.g., study the propagation of slow magnetohydrodynamic waves generated by the granular buffeting motion in thin magnetic photospheric tubes. When the variation in the reduced velocity occurs over typical lengths much larger than the gravitational scale height, the KGB equation can be reduced to a KleinGordon equation describing the propagation of an impulse followed by a wake oscillating with the frequency reduced by viscosity and the solution has no spatial or temporal decay. However, in the other limiting case, i.e., typical variations in the reduced velocity occur over characteristic lengths much smaller than the gravitational scale height, waves have a temporal and spatial decay.
 Nonlinear Phenomena, Turbulence, Transport

On the existence of ionacoustic double layers in twoelectron temperature plasmas
View Description Hide DescriptionEarlier Sagdeev pseudopotential treatments of ionacoustic double layers in plasmas with two electron populations were based on a model in which both electron densities were described by isothermal Boltzmann distributions. Using a more recent fluiddynamical approach, with polytropic equations of state indices , one finds analytically that no double layers can be formed for , due to total rarefaction of the cooler electrons or infinite compression of the ions. For , rarefactive double layers occur, but, just below 3/2, at unrealistically small cool electron densities or large Mach numbers. As decreases towards 1, these constraints become less restrictive and go over smoothly to those known from Boltzmann studies. Contrary to what appears in the literature, very weak compressive double layers can also be found for Boltzmann electrons, but only for soliton conditions barely above the existence threshold; i.e., marginally superionacoustic. Any slight increase in the critical Mach number destroys the possibility of having positive double layers, and, within the limits of numerical accuracy, no window could be found for , where compressive double layers exist.

Damping of magnetohydrodynamic disturbances in multiionspecies plasmas
View Description Hide DescriptionThe evolution of macroscopic magnetohydrodynamic disturbances across a magnetic field is studied, with particular attention to the effect of multiple ion species. Analyses are carried out on disturbances where the initial magnetic profiles are sinusoidal. Both the theory and electromagnetic simulations show that, in a singleionspecies plasma, the disturbance is undamped, with its energyoscillating between the magnetic field and ion velocity. In a multiionspecies plasma, however, it is initially damped, owing to the phase mixing of the magnetosonic mode and the modes having ionion hybrid cutoff frequencies. Furthermore, it is found from longtime simulations that the amplitude of the disturbance continues to decrease in a multiionspecies plasma. This is due to nonlinear mode couplings. The magnetic energy is irreversibly transferred to the ions.

Large amplitude relativistic electromagnetic solitons due to strong photoncondensation in intense laser underdense homogeneous collisionless plasma interaction
View Description Hide DescriptionLarge amplitude electromagnetic solitons due to strong photoncondensation, induced by a linearly polarized intense laser interacting with an underdense uniform collisionless plasma, are studied by particle simulations. In homogeneous plasma, both standing and accelerated solitons are observed. It is found that the acceleration of the solitons depends upon not only the laser amplitude but also the plasma length. The electromagnetic frequency of the solitons is between half and one time of the unperturbed electron plasma frequency. The electrostatic field inside the soliton has a onecycle structure in space, while the transverse electric and the magnetic fields have half and onecycle structures, respectively. The acceleration of the solitons is briefly discussed.

Extraction of coherent bursts from turbulent edge plasma in magnetic fusion devices using orthogonal wavelets
View Description Hide DescriptionA new method to extract coherent bursts from turbulent signals is presented. It uses the wavelet representation which keeps track of both time and scale and thus preserves the temporal structure of the analyzed signal, in contrast to the Fourier representation which scrambles it among the phases of all Fourier coefficients. Using orthogonal wavelets,turbulent signals can be decomposed into coherent and incoherent components, which are orthogonal and whose properties can thus be studied independently. Diagnostics based on the wavelet representation are also introduced to compare the statistical properties of the original signals with their coherent and incoherent components. The waveletbased extraction method is applied to the saturation current fluctuationsmeasuring the plasma densityfluctuations at the edge of the tokamak Tore Supra, Cadarache, France. This procedure disentangles the coherent bursts, which contain most of the density variance, are intermittent and correlated with nonGaussian statistics, from the incoherent background fluctuations, which are much weaker, nonintermittent, noiselike and almost decorrelated with quasiGaussian statistics. We conjecture that the coherent bursts are responsible for turbulent transport, whereas the remaining incoherent fluctuations only contribute to turbulent diffusion.

Nonlinear propagation of modulated ionacoustic plasma waves in the presence of an electron beam
View Description Hide DescriptionTheoretical and numerical studies are presented of the amplitude modulation of ionacoustic waves(IAWs) in a plasma consisting of warm ions, Maxwellian electrons, and a cold electron beam. Perturbations parallel to the carrier IAW propagation direction have been investigated. The existence of four distinct linear ion acoustic modes is shown, each of which possesses a different behavior from the modulational stability point of view. The stability analysis, based on a nonlinear Schrödinger equation (NLSE) reveals that the IAW may become unstable. The stability criteria depend on the IAW carrier wave number, and also on the ion temperature, the beam velocity and the beam electron density. Furthermore, the occurrence of localized envelope structures (solitons) is investigated, from first principles. The numerical analysis shows that the two first modes (essentially IAWs, modified due to the beam) present a complex behavior, essentially characterized by modulational stability for large wavelengths and instability for shorter ones. Darktype envelope excitations (voids, holes) occur in the former case, while brighttype ones (pulses) appear in the latter. The latter two modes are characterized by an intrinsic instability, as the frequency develops a finite imaginary part for small ionic temperature values. At intermediate temperatures, both bright and darktype excitations may exist, although the numerical landscape is intertwined between stability and instability regions.

A twocomponent phenomenology for homogeneous magnetohydrodynamic turbulence
View Description Hide DescriptionA onepoint closure model for energy decay in threedimensional magnetohydrodynamic(MHD)turbulence is developed. The model allows for influence of a largescale magnetic field that may be of strength sufficient to induce Alfvén wave propagation effects, and takes into account components of turbulence in which either the wavelike character is negligible or is dominant. This twocomponent model evolves energy and characteristic length scales, and may be useful as a simple description of homogeneous MHDturbulent decay. In concert with spatial transport models, it can form the basis for approximate treatment of lowfrequency plasma turbulence in a variety of solar, space, and astrophysical contexts.

Structure of the electromagnetic field in threedimensional Hall magnetohydrodynamic turbulence
View Description Hide DescriptionNumerical simulations of freely evolving threedimensional compressible magnetohydrodynamics (MHD) are performed, with and without the Hall term in Ohm’s law. The parameter controlling the presence of the Hall term is the ratio of the ion skin depth to the macroscopic scale of the turbulence. The ion skin depth is set to be slightly larger than the dissipation length scale (controlled by the resistivity) for the Hall MHD simulations, while it is set to zero for nonHall MHD simulations. Small initial cross helicity, hybrid helicity, and magnetic helicity are considered. The system is left to evolve for a few turbulent characteristic times and the magnetic field and electric field are analyzed in real and wavenumber space. Distributions (histograms) of the fields are also computed. It is found that the turbulentmagnetic field (as well as the velocity field) is almost unaffected by the presence of the Hall term, while the electric field is affected at scales smaller than the ion skin depth, that is, close to the dissipation range in these simulations. The importance of each term in Ohm’s law for the electric field is analyzed in wavenumber space. Furthermore, reconnectionlike zones are identified, where the importance of each term in Ohm’s law can be seen in real space. Reconnectionlike zones with magnetic field (or small) and are found within the turbulent state of the system.

Nonplanar dust acoustic waves with transverse perturbation in dusty plasmas with variable dust charge and negative ions
View Description Hide DescriptionA cylindrical KadomstevPetviashvili equation is derived in cylindrical geometry for dust acoustic waves in dusty plasmas consisting of positive ions, negative ions, and adiabatic variable charged dust grains. The effects of negative ions on the dust charge number and dust temperature, as well as the solitonic structures, such as the Nebulon and Wshape soliton, etc., have been investigated. It has also been found that the effect of transverse perturbations is the main factor that determines the formation of the Nebulon.
 Magnetically Confined Plasmas, Heating, Confinement

Analysis of metallic impurity density profiles in low collisionality Joint European Torus Hmode and Lmode plasmas
View Description Hide DescriptionThis paper describes the behavior of nickel in low confinement (Lmode) and high confinement (Hmode) Joint European Torus (JET) discharges [P. J. Lomas, Plasma Phys. Control. Fusion 31, 1481 (1989)] characterized by the application of radiofrequency (rf) power heating and featuring ITER (International Thermonuclear Experimental Reactor) relevant collisionality. The impurity transport is analyzed on the basis of perturbative experiments (laser blow off injection) and is compared with electron heat and deuterium transport. In the JET plasmas analyzed here, ion cyclotron resonance heating (ICRH) is applied either in mode conversion (MC) to heat the electrons or in minority heating (MH) to heat the ions. The two heating schemes have systematically different effects on nickel transport, yielding flat or slightly hollow nickel density profiles in the case of ICRH in MC and peaked nickel density profiles in the case of rf applied in MH. Accordingly, both diffusion coefficients and pinch velocities of nickel are found to be systematically different. Linear gyrokinetic calculations by means of the code GS2 [M. Kotschenreuther, G. Rewoldt, and W.M. Tang, Comput. Phys. Commun. 88, 128 (1995)] provide a possible explanation of such different behavior by exploring the effects produced by the different microinstabilities present in these plasmas. In particular, trapped electron modes driven by the stronger electron temperature gradients measured in the MC cases, although subdominant, produce a contribution to the impurity pinch directed outwards that is qualitatively in agreement with the pinch reversal found in the experiment. Particle and heat diffusivities appear to be decoupled in MH shots, with and , and are instead quite similar in the MC ones. In the latter case, nickel transport appears to be driven by the same turbulence that drives the electron heat transport and is sensitive to the value of the electron temperature gradient length. These findings give ground to the idea that in ITER it should be possible to find conditions in which the risk of accumulation of metals such as nickel can be contained.

Toroidally localized soft xray expulsion at the termination of the improved confinement regime in the TPERX reversedfield pinch experiment
View Description Hide DescriptionThe pulsed poloidal current drive technique reduces the magnetic chaos that characterizes reversedfield pinch configurations and produces a regime with an improved confinement. In this paper, we describe that, in TPERX [Y. Yagi et al., Fusion Eng. Des.45, 409 (1999)], the termination phase of this regime is due to the increase of the slinky structure that creates a stochastic region and produces the expulsion of energy in a localized toroidal position. Before the plasma reaches the improved confinement regime, the slinky distorts the chain of islands on the reversal surface. During this regime, the magnetic activity and the phase locking decrease, the distortion in the island chain disappears, and the confinement increases. At the termination of this regime the magnetic activity markedly increases, as well as the phase locking, recreating the distortion in the magnetic island chain. As a consequence, at the position of the distortion the plasma region inside the reversal surface is characterized by a rapid energy loss, and outside the reversal surface a toroidally localized energy expulsion is induced.

Collective electric field effects on the confinement of fast ions in tokamaks
View Description Hide DescriptionThe injection of neutral particle beams counter to the plasmacurrent direction in the MegaAmpère Spherical Tokamak (MAST) [A. Sykes, R. J. Akers, L. C. Appel et al., Nucl. Fusion, 41, 1423 (2001)] leads to substantial losses of energetic beam ions and also rapid toroidal rotation. The electrodynamic consequences of energetic ion loss on tokamakplasmas are explored in light of results from the MAST counterinjection experiments and test particle calculations of the current density due to escaping ions. Previous authors have noted that there are two possible consequences of such a current: either a compensating bulk plasma return current is set up, or the plasma behaves as an insulator, with the energetic ion current balanced by a displacement current rather than a conduction current. Radial electric fields and hence toroidalflows occur in both cases, but higher fields are predicted in the insulating case. Such fields are important because they can confine both fast ions and bulk plasma (via the suppression of turbulent transport). The return current scenario, which appears to be operative during counterinjection in MAST, is shown to be applicable if there is a sufficiently high level of momentum transport in the bulk ions; electrons cannot carry the return current, although they contribute to an ambipolar particle flux on the plasma confinement time scale. The insulating scenario may be applicable to high confinement regimes in burning tokamakplasmas.

Nonlinearly driven second harmonics of Alfvén cascades
View Description Hide DescriptionIn recent experiments on Alcator CMod [J. A. Snipes et al., Phys. Plasmas12, 056102 (2005)], measurements of density fluctuations with phase contrast imaging through the plasma core show a second harmonic of the basic Alfvén cascade (AC) signal. The present paper presents a theory that describes the secondharmonic perturbation as a nonlinear sideband produced by the ACeigenmode via quadratic terms in the magnetohydrodynamic equations. It is shown that in a lowpressure plasma the nonlinear coupling to compressional Alfvén and acoustic perturbations can be neglected when calculating the secondharmonic density. The derived expressions for this density perturbation can potentially be used together with experimental measurements to determine the AC amplitude inside the plasma, rather than just at the edge as with magnetic probes.