Volume 18, Issue 2, February 2011

The question of electromagnetic wave penetration and screening by a bounded supercritical ( with and being the electronplasma and wave frequencies, respectively) plasma confined in a minimum multicusp field, for waves launched in the mode, is addressed through experiments and numerical simulations. The scale length of radial plasma nonuniformity and magnetostatic field inhomogeneity are much smaller than the free space and guided wavelengths . Contrary to predictions of plane wave dispersion theory and the Clemow–Mullaly–Allis (CMA) diagram, for a bounded plasma a finite propagation occurs through the central plasma regions where and , with being the electron cyclotron frequency. Wave screening, as predicted by the plane wave model, does not remain valid due to phase mixing and superposition of reflected waves from the conducting boundary, leading to the formation of electromagnetic standing wave modes. The waves are found to satisfy a modified upper hybrid resonance (UHR) relation in the minimum field and are damped at the local electron cyclotron resonance (ECR) location.
 LETTERS


Universal asymptotics of poloidal spectra of magnetic perturbations of saddle coils in tokamaks
View Description Hide DescriptionUniversal and generic features of poloidal spectra of external magnetic perturbations created by a set of saddle coils in tokamak plasmas are studied in a vacuum approximation. It is found that the poloidal mode spectra with highaccuracy are described by a linear combination of three universal asymptotical formulas which depend only on the safety factor of the equilibrium plasma and the geometry of perturbation coils. The validity of these formulas is confirmed by numerical calculations of the mode spectra in the DIIID plasma [G. L. Jackson et al., Europhys. Conf. Abstr.27A, P–4 (2007)] and a spherical tokamak, National Spherical Tokamak Experiment [D. A. Gates, et al., Nucl. Fusion49, 104016 (2009)], plasmas perturbed by external control coils.

 ARTICLES

 Basic Plasma Phenomena, Waves, Instabilities

Penetration and screening of perpendicularly launched electromagnetic waves through bounded supercritical plasma confined in multicusp magnetic field
View Description Hide DescriptionThe question of electromagnetic wave penetration and screening by a bounded supercritical ( with and being the electronplasma and wave frequencies, respectively) plasma confined in a minimum multicusp field, for waves launched in the mode, is addressed through experiments and numerical simulations. The scale length of radial plasma nonuniformity and magnetostatic field inhomogeneity are much smaller than the free space and guided wavelengths . Contrary to predictions of plane wave dispersion theory and the Clemow–Mullaly–Allis (CMA) diagram, for a bounded plasma a finite propagation occurs through the central plasma regions where and , with being the electron cyclotron frequency. Wave screening, as predicted by the plane wave model, does not remain valid due to phase mixing and superposition of reflected waves from the conducting boundary, leading to the formation of electromagnetic standing wave modes. The waves are found to satisfy a modified upper hybrid resonance (UHR) relation in the minimum field and are damped at the local electron cyclotron resonance (ECR) location.

Magnetic field effect on stimulated Raman scattering of electromagnetic waves from nanoparticle lattice
View Description Hide DescriptionThe influence of a static magnetic field on the Raman scattering of a millimeter pump wave propagating through periodic nanoparticles is studied. Formulas for the growth rate of the scatteredelectromagnetic wave and the electrostatic wave are derived and analyzed. It is found that the growth rate for the backscattering case is larger than that of forward scattering and the growth rate is increased by the static magnetic field. A resonance in the dispersion relation of the electromagnetic wave is found as a combination of the cyclotron and plasma frequency. However, no instability was found for this lower branch of the dispersion curve.

Fast numerical treatment of nonlinear wave equations by spectral methods
View Description Hide DescriptionA method is presented that accelerates spectral methods for numerical solution of a broad class of nonlinear partial differential wave equations that are first order in time and that arise in plasma wave theory. The approach involves exact analytical treatment of the linear part of the wave evolution including growth and damping as well as dispersion. After introducing the method for general scalar and vector equations, we discuss and illustrate it in more detail in the context of the coupling of high and lowfrequency plasma wave modes, as modeled by the electrostatic and electromagnetic Zakharov equations in multiple dimensions. For computational efficiency, the method uses eigenvector decomposition, which is particularly advantageous when the wave damping is modedependent and anisotropic in wavenumber space. In this context, it is shown that the method can significantly speed up numerical integration relative to standard spectral or finite difference methods by allowing much longer time steps, especially in the limit in which the nonlinear Schrödinger equation applies.

A model of onedimensional current sheet with parallel currents and normal component of magnetic field
View Description Hide DescriptionWe develop a model of a current sheet including fieldaligned currents and a finite value of the normal component of magnetic field. The model is based on the conservation of a quasiadiabatic invariant of ion motion, while for electrons a fluid approach is used. A part of the current becomes parallel to the magnetic field due to the magnetic field shear, however the perpendicular component of the current is also present. The difference in the plasma pressure between the current sheet center and its boundaries decreases is only half of the value of the model free of parallel currents. We discuss the possible application of the model developed in this paper.

Magnetohydrodynamic structure of a plasmoid in fast reconnection in lowbeta plasmas
View Description Hide DescriptionPlasmoid structures in fast reconnection in lowbeta plasmas are investigated by twodimensional magnetohydrodynamic simulations. A highresolution shockcapturing code enables us to explore a variety of shock structures: vertical slow shocks behind the plasmoid, another slow shock in the outerregion, and the shockreflection in the front side. The Kelvin–Helmholtzlike turbulence is also found inside the plasmoid. It is concluded that these shocks are rigorous features in reconnection in lowbeta plasmas, where the reconnection jet speed or the upstream Alfvén speed exceeds the sound speed.

The magnetic Rayleigh–Taylor instability and flute waves at the ion Larmor radius scales
View Description Hide DescriptionThe theory of flutewaves (with arbitrary spatial scales compared to the ion Larmor radius) driven by the Rayleigh–Taylor instability(RTI) is developed. Both the kinetic and hydrodynamic models are considered. In this way we have extended the previous analysis of RTI carried out in the long wavelength limit. It is found that complete finite ion Larmor radius stabilization is absent when the ion diamagnetic velocity attains the ion gravitation drift velocity. The hydrodynamic approach allowed us to deduce a new set of nonlinear equations for flutewaves with arbitrary spatial scales. It is shown that the previously deduced equations are inadequate when the wavelength becomes of the order of the ion Larmor radius. In the linear limit a Fourier transform of these equations yields the dispersion relation which in the socalled Padé approximation corresponds to the results of the fully kinetic treatment. The development of such a theory gives us enough grounds for an adequate description of the RTI stabilization by the finite ion Larmor radius effect.

Wave propagation and noncollisional heating in neutral loop and helicon discharges
View Description Hide DescriptionHeating mechanisms in two types of magnetized low pressure rf (13.56 MHz) discharges are investigated: a helicon discharge and a neutral loop discharge. Radial Bdot probe measurements demonstrate that the neutral loop discharge is sustained by helicon waves as well. Axial Bdot probe measurements reveal standing wave and beat patterns depending on the dc magnetic field strength and plasma density. In modes showing a strong wave damping, the plasma refractive index attains values around 100, leading to electronwave interactions. In strongly damped modes, the radial plasma density profiles are mainly determined by power absorption of the propagating helicon wave, whereas in weakly damped modes, inductive coupling dominates. Furthermore, an azimuthal diamagnetic drift is identified. Measurements of the helicon wave phase demonstrate that initial plane wave fronts are bent during their axial propagation due to the inhomogeneous density profile. A developed analytical standing wave model including Landau damping reproduces very well the damping of the axial helicon wave field. This comparison underlines the theory whereupon Landau damping of electrons traveling along the field lines at speeds close to the helicon phase velocity is the main damping mechanism in both discharges.

Modulational instability of ionacoustic waves in a plasma with a nonextensive electron velocity distribution
View Description Hide DescriptionThe modulational instability (MI) of ionacoustic waves(IAWs) in a twocomponent plasma is investigated in the context of the nonextensive statistics proposed by Tsallis [J. Stat. Phys.52, 479 (1988)]. Using the reductive perturbation method, the nonlinear Schrödinger equation (NLSE) which governs the MI of the IAWs is obtained. The presence of the nonextensive electron distribution is shown to influence the MI of the waves. Three different ranges of the nonextensive parameter are considered and in each case the MI sets in under different conditions. Furthermore, the effects of the parameter on the growth rate of MI are discussed in detail.

Combined effect of viscosity and vorticity on single mode Rayleigh–Taylor instability bubble growth
View Description Hide DescriptionThe combined effect of viscosity and vorticity on the growth rate of the bubble associated with single mode Rayleigh–Taylor instability is investigated. It is shown that the effect of viscosity on the motion of the lighter fluid associated with vorticity accumulated inside the bubble due to mass ablation may be such as to reduce the net viscousdrag on the bubble exerted by the upper heavier fluid as the former rises through it.

Coupling of Kelvin–Helmholtz instability and buoyancy instability in a thermally laminar plasma
View Description Hide DescriptionThermal convective instability is investigated in a thermally stratified plasma in the presence of shear flow, which is known to give rise to the Kelvin–Helmholtz (KH)instability. We examine how the KH instability and magnetothermal instability (MTI) affect each other. Based on the sharp boundary model, the KH instability coupled with the MTI is studied. We present the growth rate and instability criteria. The shear flow is shown to significantly alter the critical condition for the occurrence of thermal convective instability.

Filamentation of laser in an inhomogeneous plasma
View Description Hide DescriptionFilamentation of an intense short pulse laser in an inhomogeneous plasma is investigated when laser propagates along the direction of density gradient and nonlinearity arises due to the relativistic mass variation and ponderomotive force. The ion motion is neglected; however, the effect of dielectric swelling is included. The inhomogeneity in the density profile introduces dielectric swelling of the pump intensity enhancing the plasmapermittivity and the growth rate of the instability. The perturbation in laser amplitude grows faster than exponential as the laser penetrates deeper into the denser plasma.

Ionic electrostatic excitations along biological membranes
View Description Hide DescriptionA theoretical analysis of ionic electrostatic excitations of a charged biological membrane is presented within the framework of the fluid theory for surface ions inside and outside the cell, in conjunction with the Poisson’s equation. General expressions of dispersion relations are obtained for electrostatic oscillations of intrinsic cellular with different shapes and symmetries.
 Nonlinear Phenomena, Turbulence, Transport

Simulation of low frequency Buneman instability of a currentdriven plasma by particle in cell method
View Description Hide DescriptionThe nonlinear dynamics of low frequency Buneman instability in a currentdriven cold unmagnetized plasma are studied using particle in cell simulation. Simulations of the Buneman instability show that the electron density profile has sharp peaks and the amplitude of the peaks changes with time. Also, the nonlinear evolution of this instability and saturation time is investigated by the time variation of the electric potential energy in the plasma. Moreover, the electron trapping phenomena and the formation of phase space electron holes are presented by considering the phase space diagram and electron distribution function. Finally, the ion mass effect on saturation time is investigated and it is found that the saturation time increases by increasing the ion mass and the saturation level is not very sensitive to the ion mass.

Time sequence of energetic particle spectra in quasiparallel shocks in large simulation systems
View Description Hide DescriptionWe have performed collisionless shock simulations using a onedimensional hybrid particleincell method to investigate the energy spectra of the differential intensity around the quasiparallel shocks. The system size is sufficiently large (200 000 ion inertia length) in order to eliminate the unphysical effect caused by the upstream boundary. The obtained spectrum of the differential intensity have the shape of the powerlaw with exponentially falling off in higher energy as predicted in previous simulations, however, the powerlaw indices and folding energy do not depend on the shock parameters, the shock Mach number (7.1–11.7) and the shock angle (10°–40°). The powerlaw index is . This number is close to the prediction by the standard diffusive shock acceleration theory. However, the reason for the agreements between the values is not clear because an additional acceleration process is also observed in the present runs; this process was reported in [Sugiyama and Terasawa, Adv. Space Res.24, 73 (1999)] and [Sugiyama et al., J. Geophys. Res.106, 21657 (2001)]. The folding energy linearly increases in time for all runs. One of the reasons for these independent profiles on shock parameters is that the pitch angle distribution in the upstream region shows similar profiles in each run.

Shocks, explosions, and vortices in twodimensional homogeneous quantum magnetoplasma
View Description Hide DescriptionUsing the quantum hydrodynamic model for a uniform quantum magnetoplasma, and considering that the collision between ions and neutrals is dominant, a twodimensional nonlinear system is derived. The linear dispersion relation is obtained and thus the variations of the dispersion relation with the obliqueness angle and density are discussed in detail. Shock, explosion, and vortex solutions of the nonlinear system are obtained. It is found that increasing the plasma density may enhance the strength of the shock and the width of the explosion. However, the higher the collision frequency is, the weaker the shock and the narrower the explosion will be. The temporal and spatial distributions for the vortex potential are studied. Spatially, it forms a periodic vortex street. Temporally, the vortex street may evolve in various ways owing to the arbitrary function of time.

Terahertz wave generation by the upper hybrid wave
View Description Hide DescriptionThis paper investigates the excitation of terahertz radiation (in the form of a magnetosonic wave) by the interaction of the upper hybrid (pump) wave and the extraordinary wave (laser). The ponderomotive force due to the nonlinear interaction between the pump wave and the extraordinary wave (laser) generates a nonlinear current at the difference frequency. If the appropriate phase matching conditions are satisfied and the frequency of the pump is appropriate, then this difference frequency can be brought in the terahertz range. The extraordinary wave propagates perpendicular to the static magnetic field and is polarized perpendicular to the static magnetic field. The expressions for the coupling coefficients of the threewave interaction have been derived. The analytical expression for the electric vector of the terahertz wave has been obtained. By changing the strength of the magnetic field, one can enhance or suppress the terahertz emission. For the typical laser plasma parameters used here (plasma density, pump wave frequency , normalized pump wave amplitude , and applied magnetic field, 150, and 205 kG for ), the generatedterahertz emission can be at the power level of gigawatts. The power spectrum of the generatedradiations is also given. The expression for growth rate of this decay instability is also calculated; we have found that the value of decay growth rate comes out to be of the order of .

Higherorder energyconserving gyrokinetic theory
View Description Hide DescriptionA higherorder selfconsistent energyconserving gyrokinetic system of equations is derived. It is shown that additional terms appear in the quasineutrality condition. These terms are nonlinear in the electric field. The derivation includes higherorder terms in the gyrokinetic Hamiltonian (needed for the energy conservation) and employs a variational principle that automatically provides all the conservation laws through the Noether theorem. The equations derived here can be applied in certain transition layers such as the stellarator transport barriers caused by the transition between the electron and ion root regimes. The theory may also be of interest for the edge plasma, where the nonlinear terms in the quasineutrality equation could be relevant. The equations derived are simple enough and can readily be used in gyrokinetic codes.

Comparison of scrapeoff layer turbulence simulations with experiments using a synthetic gas puff imaging diagnostic
View Description Hide DescriptionA synthetic gas puff imaging (GPI) diagnostic has been added to the scrapeoff layer turbulence (SOLT) simulation code, enabling comparisons with GPI data from the National Spherical Torus Experiment (NSTX) [M. Ono et al. , Nucl. Fusion40, 557 (2000)]. The edge and scrapeoff layer are modeled in the radial and poloidal (bidirectional) dimensions of the outboard midplane region of NSTX. A lowconfinement mode discharge is simulated by choosing reference parameters, including radial density and temperature profiles, to be consistent with those of the shot (no. 112825). NSTX and simulation GPI data are submitted to identical analyses. It is demonstrated that the level of turbulent fluctuations in the simulation may be adjusted to give synthetic GPI radial intensity profiles similar to those of the experiment; for a “bestcase” simulation, SOLT and NSTX probability distribution functions of blob radial locations, widths, and GPI image velocities are compared. For the simulation, synthetic GPI image velocity and fluid convection velocity are compared and contrasted.

Generation of coherent magnetic fields in sheared inhomogeneous turbulence: No need for rotation?
View Description Hide DescriptionCoherent magnetic fields are often believed to be generated by the combination of stretching by differential rotation and turbulent amplification of magnetic field, via the socalled effect. The latter is known to exist in helical turbulence, which is envisioned to arise due to both rotation and convection in solartype stars. In this contribution, a turbulent flow driven by a nonhelical inhomogeneous forcing and its kinematic dynamo action are studied for a uniform magnetic field in the background of a linear shear flow. By using a quasilinear analysis and a nonperturbative method utilizing a timedependent wave number, turbulence property and electromotive force are computed for arbitrary shear strength. Due to the largescale shear flow, the turbulence is highly anisotropic, as a consequence, so is the electromotive force. The latter is found to exist even without rotation due to the combined effect of shear flow and inhomogeneous forcing, containing not only the effect but also magnetic pumping (the effect representing a transport of magnetic flux by turbulence). Specifically, without shear, only the magnetic pumping exists, aligned with the direction of inhomogeneity. For a weak but nonzero shear, the combined effects of shear and inhomogeneous forcing modify the structure of the magnetic pumping when the inhomogeneity is in the plane of the shear flow, the magnetic pumping becoming bidimensional in that plane. It also induces an tensor which has nondiagonal components. When the inhomogeneity is perpendicular to the plane of the shear flow, the effect has three nonzero diagonal components and one offdiagonal component. However, for a sufficiently strong shear, the and effects are suppressed due to shear stabilization which damps turbulence. A simplified dynamo model is then proposed where a largescale dynamo arises due to the combined effect of shear flow and inhomogeneous forcing. In particular, the growth of a largescale axisymmetric magnetic field is demonstrated in case of an inhomogeneity which is perpendicular to the plane of the shear flow. Interesting implications of these results for the structure of magnetic fields in star with slow rotation are discussed.