Volume 19, Issue 2, February 2012

In this review a plaidoyer is held for a specific form of nonlinearity, the trapping nonlinearity (TN), which arises due to a capture of particles and/or fluid elements in an excited coherent structure. This is of some importance since it appears that TN has not yet taken roots hitherto, neither in turbulence nor in anomalous transport models. The present state of knowledge about wave excitation, seen numerically and experimentally, especially at space craft, however, speaks a different language suggesting that current wave models are constructed too narrowly to reflect reality. The focus is on traveling cnoidal electron holes (CEHs) in electrostatically driven plasmas and the physical world associated with these. As a result a new wave concept emerges, in which the low amplitude dynamics is nonlinearly controlled by TN.
 REVIEW ARTICLE


Cnoidal electron hole propagation: Trapping, the forgotten nonlinearity in plasma and fluid dynamics
View Description Hide DescriptionIn this review a plaidoyer is held for a specific form of nonlinearity, the trapping nonlinearity (TN), which arises due to a capture of particles and/or fluid elements in an excited coherent structure. This is of some importance since it appears that TN has not yet taken roots hitherto, neither in turbulence nor in anomalous transport models. The present state of knowledge about wave excitation, seen numerically and experimentally, especially at space craft, however, speaks a different language suggesting that current wave models are constructed too narrowly to reflect reality. The focus is on traveling cnoidal electron holes (CEHs) in electrostatically driven plasmas and the physical world associated with these. As a result a new wave concept emerges, in which the low amplitude dynamics is nonlinearly controlled by TN.
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 LETTERS


Analysis on the exclusiveness of turbulence suppression between static and timevarying shear flow
View Description Hide DescriptionThe analytical theory of turbulence suppression by shear flow [Y. Z. Zhang and S. M. Mahajan, Phys. Fluids B 4, 1385 (1992)] is extended to analyze the combined actions of flows that have timevarying as well as static components. It is found that each component, appearing alone, may yield the same suppression level. However, when both components coexist, either tends to diminish the suppression caused by the other in certain parameter ranges—a conclusion that agrees with recently published simulation results by Maeyama et al. [Phys. Plasmas 17, 062305 (2010)]. In particular, the mutual exclusiveness is maximized as the strengths of the two components become comparable. The adopted averaging method of the asymptotic theory reveals that it is the coupling between the timevarying shear flow and the induced timevarying relative orbit motion that causes the asymmetry of the two components in turbulence suppression. The numerical results based on a Floquet analysis are also presented for comparison. The implications of the theory to LH transition on tokamaks are discussed, especially, regarding experimental observations of the disappearance of the geodesic acoustic mode in H phases.

Relativistic spherical plasma waves
View Description Hide DescriptionTightly focused laser pulses that diverge or converge in underdense plasma can generate wake waves, having local structures that are spherical waves. Here we study theoretically and numerically relativistic spherical wake waves and their properties, including wave breaking.

An optical analysis tool for avoiding dust formation in veryhigh frequency hydrogen diluted silane plasmas at low substrate temperatures
View Description Hide DescriptionControl of the formation of dust particles in a silane depositionplasma is very important for avoiding electrical shunts in devices, such as thin film silicon solar cells. In this work we present a noninvasive in situ method for identification of the plasma regime, based on optical emission spectroscopy(OES), which can be applied to silane/hydrogen plasmas at low substrate temperatures. By monitoring the OES spectra as a function of the position perpendicular to the plasmaelectrodes we developed a method to identify the transition of a plasma from the dust free to a dusty regime, which was confirmed by TEM images of layers deposited in both regimes. Using this technique we mapped this transition as a function of applied forward veryhigh frequency (VHF) power and hydrogen dilution at different substrate temperatures. The advantage of this technique is that the experiment is insensitive to optical transmission loss at the viewport due to deposition of silicon films. As the transition from the dust free to the dusty regime is substrate temperature dependent and the transition from amorphous to nanocrystalline growth mainly depends on hydrogen dilution, a limited parameter window has been defined in which dustfree amorphous silicon can be deposited at low substrate temperatures. A single simple OES technique can be used for in situ monitoring of amorphous to nanocrystalline transition as well as the onset of the dusty regime in a thin film silicon cell fabrication process.

Highfrequency devices with weakly relativistic hollow thinwall electron beams
View Description Hide DescriptionSlowwave devices with hollow electron beams and azimuthally symmetric corrugated operating waveguides can be very effective not only for relativistic but also weakly relativistic particle energies. In the weakly relativistic case, the use of hollow beams permits a significant increase in the diameter of the beam channel and, simultaneously, a drastic decrease in the required current density and heat load at the interaction structure wall in comparison with the conventional devices, which basically exploit thin pencillike beams. Advantages of the hollow beams in the achievement of continuous wave (CW) and longpulse generation can manifest themselves in a wide range from gigahertz to terahertz frequencies. As an example of the concept, a Wband oscillator (orotron) with kilowatt output power in CW regime is discussed in detail. Modification of the microwave system makes it possible to implement highpower frequencytunable BWOs,klystron or TWT amplifiers, and many types of hybrid devices.
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 ARTICLES

 Basic Plasma Phenomena, Waves, Instabilities

Reduced magnetohydrodynamic theory of oblique plasmoid instabilities
View Description Hide DescriptionThe threedimensional nature of plasmoid instabilities is studied using the reduced magnetohydrodynamic equations. For a Harris equilibrium with guide field, represented by , a spectrum of modes are unstable at multiple resonant surfaces in the current sheet, rather than just the null surface of the poloidal field , which is the only resonant surface in 2D or in the absence of a guide field. Here, is the asymptotic value of the equilibrium poloidal field, is the constant equilibrium guide field, and is the current sheet width. Plasmoids on each resonant surface have a unique angle of obliquity . The resonant surface location for angle is , where and the existence of a resonant surface requires . The most unstable angle is oblique, i.e., and , in the constant regime, but parallel, i.e., and , in the nonconstant regime. For a fixed angle of obliquity, the most unstable wavenumber lies at the intersection of the constant and nonconstant regimes. The growth rate of this mode is , in which , is the Alfvén speed, L is the current sheet length, and is the Lundquist number. The number of plasmoids scales as .

Fully kinetic description of the linear excitation and nonlinear saturation of fastiondriven geodesic acoustic mode instability
View Description Hide DescriptionWe show in this paper that geodesic acoustic modes (GAMs) can be efficiently excited by a population of fast ions even when Landau damping on thermal ions is accounted for. We report in particular fully kinetic calculations of the GAM dispersion relation and its complete solution. Written under a variational form, the quasineutrality condition, together with the kinetic Vlasov equation, leads to the density of exchanged energy between particles and the mode. In particular, a linear threshold for the GAMs excitation is derived. Two examples of fast ion distribution have been discussed analytically. It turns out that particles with high perpendicular energy compared to the parallel resonance energy are most responsible for the excitation of the mode. Subsequent numerical simulations of circular plasmas using gysela code have been carried out. In particular, the linear kinetic threshold has been reproduced during the excitation phase, and a nonlinear saturation has been observed. Analysis in the phase space of the evolution of the equilibrium distribution function is presented and the saturation level quantified.

Enhancement of omnidirectional photonic band gaps in onedimensional dielectric plasma photonic crystals with a matching layer
View Description Hide DescriptionIn this paper, we demonstrate by theoretical analysis a novel way to enhance the omnidirectional photonic band gap (OBG) in a type of photonic structure made of dielectric and plasma onedimensional (1D) photonic crystals (1D PCs) by introducing a matching layer. Simulations by the transfer matrix method (TMM) show that such an OBG is insensitive to the incident angle and the polarization of electromagnetic (EM) wave; the frequency range and central frequency of OBG are significantly enlarged by introducing a matching layer in the heterostructure compared to 1D conventional binary dielectricphotonic crystals (DPCs). The photonic band gap(PBG) of both polarizations also can be obviously enlarged as the incident angle is relatively small. The OBG originates from a Bragg gap in contrast to gap or single negative (negative permittivity or negative permeability) gap. From the numerical results, it has been shown that introducing a matching layer in such a heterostructure has a superior feature in the enhancement relative bandwidth of OBG compared with the conventional ternary plasmaphotonic crystals (PPCs); the frequency range of OBG can be notably enlarged by increasing the thickness and density of plasma layer.

2.5D magnetohydrodynamic simulation of the KelvinHelmholtz instability around Venus—Comparison of the influence of gravity and density increase
View Description Hide DescriptionWe present a numerical study of the 2.5D KelvinHelmholtz instability and its vortices, where an initial plasma configuration appropriate for the situation around unmagnetized planets is assumed. We solve the set of ideal magnetohydrodynamic equations numerically with the total variation diminishing LaxFriedrichs algorithm. Our density profile is such that the mass density increases toward the planet. A high density leads to smaller growth rates of the instability and, thus, has a stabilizing effect for the boundary layer. Moreover, we include source terms in the equations, enabling us to study the influence of gravity. Our results show that gravity affects the evolution of the KelvinHelmholtz instability. However, the effect is not very significant. We thus conclude that the density increase toward the planet stabilizes the boundary layer around Venus more than gravity does.

Spontaneous electromagnetic fluctuations in unmagnetized plasmas I: General theory and nonrelativistic limit
View Description Hide DescriptionUsing the system of the Klimontovich and Maxwell equations, general expressions for the electromagneticfluctuation spectra (electric and magnetic field, charge and current densities) from uncorrelated plasma particles are derived, which are covariantly correct within the theory of special relativity. The general expressions hold for arbitrary momentum dependences of the plasmaparticle distribution functions and for collective and noncollective fluctuations. In this first paper of a series, the results are illustrated for the important special case of nonrelativistic isotropic Maxwellianparticle distribution functions providing in particular the thermal fluctuations of weakly amplified modes and aperiodic modes.

Thermal force drift wave
View Description Hide DescriptionA drift instability of a collisional magnetized plasma, unstable due to the Braginskii thermal force but not requiring any direct dissipation such as resistivity or electron inertia, is examined. Unlike conventional driftmodes, the maximum growth rate of the thermal force drift wave (TFDW) is of order the drift frequency, making for a strongly turbulent nonlinear state. A 3D, magnetized twofluid code is developed to allow the study of both ideal MHD modes as well as lower frequency drift modes. The governing equations are essentially the ideal MHD equations with the inclusion of Hall and thermal force terms in Ohm’s law. This set of equations is reduced in a finite β, long parallel wavelength, and small but significant Larmor radius ordering and tested for shear Alfven waves, parallel sound waves, and drift modes. The code is employed to recover the TFDW instability, to verify the code against the mode’s analytic linear characteristics, and to study the nonlinear behavior of the TFDW. The TFDW growth is strongly suppressed by parallel thermal conduction and thus this mode is more likely to be observed in low temperature plasmas.

Modeling the Parker instability in a rotating plasma screw pinch
View Description Hide DescriptionWe analytically and numerically study the analogue of the Parker (magnetic buoyancy) instability in a uniformly rotating plasmascrew pinch confined in a cylinder. Uniform plasma rotation is imposed to create a centrifugal acceleration, which mimics the gravity required for the classical Parker instability. The goal of this study is to determine how the Parker instability could be unambiguously identified in a weakly magnetized, rapidly rotating screw pinch, in which the rotation provides an effective gravity and a radially varying azimuthal field is controlled to give conditions for which the plasma is magnetically buoyant to inward motion. We show that an axial magnetic field is also required to circumvent conventional current driven magnetohydrodynamic(MHD)instabilities such as the sausage and kink modes that would obscure the Parker instability. These conditions can be realized in the Madison plasma Couette experiment (MPCX). Simulations are performed using the extended MHD code NIMROD for an isothermal compressible plasma model. Both linear and nonlinear regimes of the instability are studied, and the results obtained for the linear regime are compared with analytical results from a slab geometry. Based on this comparison, it is found that in a cylindrical pinch, the magnetic buoyancy mechanism dominates at relatively large Mach numbers (M > 5), while at low Mach numbers (M < 1), the instability is due to the curvature of magnetic field lines. At intermediate values of Mach number (1 < M < 5), the Coriolis force has a strong stabilizing effect on the plasma. A possible scenario for experimental demonstration of the Parker instability in MPCX is discussed.

Kinetic equilibrium for an asymmetric tangential layer
View Description Hide DescriptionFinding kinetic (Vlasov) equilibria for tangential current layers is a long standing problem, especially in the context of reconnection studies, when the magnetic field reverses. Its solution is of pivotal interest for both theoretical and technical reasons when such layers must be used for initializing kinetic simulations. The famous Harris equilibrium is known to be limited to symmetric layers surrounded by vacuum, with constant ion and electron flow velocities, and with current variation purely dependent on density variation. It is clearly not suited for the “magnetopauselike” layers, which separate two plasmas of different densities and temperatures, and for which the localization of the current density is due to the localization of the electrontoion velocity difference and not of the density n. We present here a practical method for constructing a Vlasov stationary solution in the asymmetric case, extending the standard theoretical methods based on the particle motion invariants. We show that, in the case investigated of a coplanar reversal of the magnetic field without electrostatic field, the distribution function must necessarily be a multivalued function of the invariants to get asymmetric profiles for the plasma parameters together with a symmetric current profile. We show also how the concept of “accessibility” makes these multivalued functions possible, due to the particle excursion inside the layer being limited by the Larmor radius. In the presented method, the current profile across the layer is chosen as an input, while the ion density and temperature profiles in between the two asymptotic imposed values are a result of the calculation. It is shown that, assuming the distribution is continuous along the layer normal, these profiles have always a more complex profile than the profile of the current density and extends on a larger thickness. The different components of the pressure tensor are also outputs of the calculation and some conclusions concerning the symmetries of this tensor are pointed out.

Pinching of ablation streams via magnetic field curvature in wirearray Zpinches
View Description Hide DescriptionIn this paper, the shapes of the ablation streams in nonimploding cylindrical wirearray Zpinches are investigated. Experimental observations using axial X pinch imaging show an azimuthal pinching of the streams that appear to depend on the topology of the global magnetic field. With fewer wires and increased interwire spacing, the radial component of the global field is increased; resulting in a stronger pinching of the streams. Computer simulations are used to model the magnetic field development and show that the sparser array has a significantly stronger azimuthal force.

The structure of the magnetic reconnection exhaust boundary
View Description Hide DescriptionThe structure of shocks that form at the exhaust boundaries during collisionless reconnection of antiparallel fields is studied using particleincell(PIC) simulations and modeling based on the anisotropic magnetohydrodynamic equations. Largescale PIC simulations of reconnection and companion Riemann simulations of shock development demonstrate that the pressureanisotropy produced by counterstreaming ions within the exhaust prevents the development of classical Petschek switchoffslow shocks (SSS). The shock structure that does develop is controlled by the firehose stability parameter through its influence on the speed order of the intermediate and slow waves. Here, and are the pressure parallel and perpendicular to the local magnetic field. The exhaust boundary is made up of a series of two shocks and a rotational wave. The first shock takes from unity upstream to a plateau of 0.25 downstream. The condition is special because at this value, the speeds of nonlinear slow and intermediate waves are degenerate. The second slow shock leaves unchanged but further reduces the amplitude of the reconnectingmagnetic field. Finally, in the core of the exhaust, drops further and the transition is completed by a rotation of the reconnecting field into the outofplane direction. The acceleration of the exhaust takes place across the two slow shocks but not during the final rotation. The result is that the outflow speed falls below that expected from the Walén condition based on the asymptotic magnetic field. A simple analytic expression is given for the critical value of within the exhaust below which SSSs no longer bound the reconnection outflow.

Nonlinear theory of mode conversion at plasma frequency
View Description Hide DescriptionAn electromagnetic (EM) wave at the mode conversion layer transfers its energy to the electrostatic (ES) wave whose amplitude can be greatly enhanced due to its slow group velocity near the cut off layer. The large amplitude ES wave produces the density compression, indispensable for the nonlinear coupling in the EM wave, leading to the localized vortex flow. A dc magnetic field, tantamount to the vorticity, is generated as a result of the conservation of canonical momentum.
 Nonlinear Phenomena, Turbulence, Transport

Experimental investigation of geodesic acoustic mode spatial structure, intermittency, and interaction with turbulence in the DIIID tokamak
View Description Hide DescriptionGeodesic acoustic modes (GAMs) and zonal flows are nonlinearly driven, axisymmetric flows, which are thought to play an important role in establishing the saturated level of turbulence in tokamaks. Results are presented showing the GAM’s observed spatial scales, temporal scales, and nonlinear interaction characteristics, which may have implications for the assumptions underpinning turbulence models towards the tokamak edge (). Measurements in the DIIID tokamak [Luxon, Nucl. Fusion 42, 614 (2002)] have been made with multichannel Doppler backscattering systems at toroidal locations separated by ; analysis reveals that the GAM is highly coherent between the toroidally separated systems () and that measurements are consistent with the expected structure. Observations show that the GAM in Lmodeplasmas with MW auxiliary heating occurs as a radially coherent eigenmode, rather than as a continuum of frequencies as occurs in lower temperature discharges; this is consistent with theoretical expectations when finite ion Larmor radius effects are included. The intermittency of the GAM has been quantified, revealing that its autocorrelation time is fairly short, ranging from about 4 to about 15 GAM periods in cases examined, a difference that is accompanied by a modification to the probability distribution function of the velocity at the GAM frequency. Conditionallyaveraged bispectral analysis shows the strength of the nonlinear interaction of the GAM with broadband turbulence can vary with the magnitude of the GAM. Data also indicate a wavenumber dependence to the GAM’s interaction with turbulence.

Simulation studies of positron acceleration in a shock wave in a nonuniform external magnetic field
View Description Hide DescriptionPositron acceleration in a shock wave in an electronpositronion plasma is studied with onedimensional, fully kinetic, electromagnetic particle simulations, with particular attention paid to the effect of inhomogeneity of external magnetic fieldB _{0}. First, acceleration to γ ∼ 10^{4}, where γ is the Lorentz factor, is demonstrated for a shock wave in a uniform B _{0} with the shock speed _{sh} close to c cos θ, where c is the speed of light and θ is the angle between B _{0} and the wave normal. The acceleration is not saturated till the end of the simulation run. Then, the effect of nonuniformity of B _{0} is investigated: Comparisons are made between the case in which the difference ( _{sh} − c cos θ) at the shock front changes from negative to positive values as the shock wave propagates and the case with this relation reversed. The latter is found to create a greater number of highenergy particles than the former.

Nonlinear entropy transfer via zonal flows in gyrokinetic plasma turbulence
View Description Hide DescriptionNonlinear entropy transfer processes in toroidalion temperature gradient(ITG) and electron temperature gradient (ETG) driven turbulence are investigated based on the gyrokineticentropy balance relations for zonal and nonzonal modes, which are coupled through the entropy transfer function regarded as a kinetic extension of the zonalflow production due to the Reynolds stress. Spectral analyses of the “triad” entropy transfer function introduced in this study reveal not only the nonlinear interactions among the zonal and nonzonal modes, but also their effects on the turbulenttransport level. Different types of the entropy transfer processes between the ITG and ETG turbulence are found: the entropy transfer from nonzonal to zonal modes is substantial in the saturation phase of the ITGinstability, while, once the strong zonal flow is generated, the entropy transfer to the zonal modes becomes quite weak in the steady turbulence state. Instead, the zonal flows mediate the entropy transfer from nonzonal modes with low radialwavenumbers (with contribution to the heat flux) to the other nonzonal modes with higher radialwavenumbers (but with less contribution to the heat flux) through the triad interaction. The successive entropy transfer processes to the higher radialwavenumber modes are associated with transport regulation in the steady turbulence state. In contrast, in both the instabilitysaturation and steady phases of the ETG turbulence, the entropy transfer processes among lowwavenumber nonzonal modes are dominant rather than the transfer via zonal modes.

Nonplanar electron acoustic shock waves in a plasma with electrons featuring Tsallis distribution
View Description Hide DescriptionThe properties of cylindrical and spherical electron acoustic shock waves (EASWs) in an unmagnetized plasma consisting of cold electrons, immobile ions, and hot electrons featuring Tsallis statistics are investigated by employing the reductive perturbation technique. A Kortewegde Vries Burgers (KdVB) equation is derived and its numerical solution is obtained. The effects of electron nonextensivity and electron kinematicviscosity on the basic features of EA shock waves are discussed in nonplanar geometry. It is found that nonextensive nonplanar EA shock waves behave quite differently from their planar counterpart. Deviations from a pure planar geometry are significant only for times shorter that the inverse of the cold electron plasma frequency. Given that the hot electron dynamics is the most interesting one, and that in many astrophysical scenarios the cold electrons can be significantly rarefied, this restriction is not too limiting for the applicability of our model.