Volume 19, Issue 12, December 2012

In magnetized plasmas, a turbulent cascade occurs in phase space at scales smaller than the thermal Larmor radius (“subLarmor scales”) [Tatsuno et al., Phys. Rev. Lett. 103, 015003 (2009)]. When the turbulence is restricted to two spatial dimensions perpendicular to the background magnetic field, two independent cascades may take place simultaneously because of the presence of two collisionless invariants. In the present work, freely decaying turbulence of twodimensional electrostatic gyrokinetics is investigated by means of phenomenological theory and direct numerical simulations. A dual cascade (forward and inverse cascades) is observed in velocity space as well as in position space, which we diagnose by means of nonlinear transfer functions for the collisionless invariants. We find that the turbulence tends to a timeasymptotic state, dominated by a single scale that grows in time. A theory of this asymptotic state is derived in the form of decay laws. Each case that we study falls into one of three regimes (weakly collisional, marginal, and strongly collisional), determined by a dimensionless number , a quantity analogous to the Reynolds number. The marginal state is marked by a critical number that is preserved in time. Turbulence initialized above this value become increasingly inertial in time, evolving toward larger and larger ; turbulence initialized below become more and more collisional, decaying to progressively smaller .
 ARTICLES

 Basic Plasma Phenomena, Waves, Instabilities

Gas breakdown driven by L band shortpulse highpower microwave
View Description Hide DescriptionHigh power microwave (HPM) driven gas breakdown is a major factor in limiting the radiation and transmission of HPM. A method that HPM driven gas breakdown could be obtained by changing the aperture of horn antenna is studied in this paper. Changing the effective aperture of horn antenna can adjust the electric field in near field zone, leading to gas breakdown. With this method, measurements of air and SF_{6}breakdowns are carried out on a magnetically insulated transmissionline oscillators, which is capable of generating HPM with pulse duration of 30 ns, and frequency of 1.74 GHz. The typical breakdown waveforms of air and SF_{6} are presented. Besides, the breakdown field strengths of the two gases are derived at different pressures. It is found that the effects of air and SF_{6}breakdown on the transmission of HPM are different: air breakdown mainly shortens the pulse width of HPM while SF_{6}breakdown mainly reduces the peak output power of HPM. The electric field threshold of SF_{6} is about 2.4 times larger than that of air. These differences suggest that gas properties have a great effect on the transmission characteristic of HPM in gases.

Magnetic instability in a dilute circular rarefaction wave
View Description Hide DescriptionThe growth of magnetic fields in the density gradient of a rarefaction wave has been observed in simulations and in laboratory experiments. The thermal anisotropy of the electrons, which gives rise to the magnetic instability, is maintained by the ambipolar electric field. This simple mechanism could be important for the magnetic field amplification in astrophysical jets or in the interstellar medium ahead of supernova remnant shocks. The acceleration of protons and the generation of a magnetic field by the rarefaction wave, which is fed by an expanding circular plasma cloud, is examined here in form of a 2D particleincell simulation. The core of the plasma cloud is modeled by immobile charges, and the mobile protons form a small ring close to the cloud's surface. The number density of mobile protons is thus less than that of the electrons. The protons of the rarefaction wave are accelerated to 1/10 of the electron thermal speed, and the acceleration results in a thermal anisotropy of the electron distribution in the entire plasma cloud. The instability in the rarefaction wave is outrun by a TM wave, which grows in the dense core distribution, and its magnetic field expands into the rarefaction wave. This expansion drives a secondary TE wave.

Photonic band gaps in onedimensional magnetized plasma photonic crystals with arbitrary magnetic declination
View Description Hide DescriptionIn this paper, the properties of photonic band gaps and dispersion relations of onedimensional magnetized plasma photonic crystals composed of dielectric and magnetized plasma layers with arbitrary magnetic declination are theoretically investigated for TM polarized wave based on transfer matrix method. As TM wave propagates in onedimensional magnetized plasma photonic crystals, the electromagnetic wave can be divided into two modes due to the influence of Lorentz force. The equations for effective dielectric functions of such two modes are theoretically deduced, and the transfer matrix equation and dispersion relations for TM wave are calculated. The influences of relative dielectric constant,plasma collision frequency, incidence angle, plasma filling factor, the angle between external magnetic field and +z axis, external magnetic field and plasma frequency on transmission, and dispersion relation are investigated, respectively, and some corresponding physical explanations are also given. From the numerical results, it has been shown that plasma collision frequency cannot change the locations of photonic band gaps for both modes, and also does not affect the reflection and transmission magnitudes. The characteristics of photonic band gaps for both modes can be obviously tuned by relative dielectric constant, incidence angle, plasma filling factor, the angle between external magnetic field and +z axis, external magnetic field and plasma frequency, respectively. These results would provide theoretical instructions for designing filters, microcavities, and fibers, etc.

Global gyrokinetic particleincell simulations of internal kink instabilities
View Description Hide DescriptionInternal kink instabilities have been studied in straight tokamak geometry employing an electromagnetic gyrokineticparticleincell(PIC) code. The idealMHD internal kink mode and the collisionless tearing mode have been successfully simulated with the PIC code. Diamagnetic effects on the internal kink modes have also been investigated.

Effect of viscosity and shear flow on the nonlinear two fluid interfacial structures
View Description Hide DescriptionA nonlinear formulation is presented to deal with the combined action of RayleighTaylor and KelvinHelmholtz instabilities as well as combined RicthmyerMeshkov and KelvinHelmholtz instabilities at the two fluid interface under the influence of viscosity and consequent shear flow. Using Layzer's model, the development of the interfacial structures like bubbles is investigated analytically and numerically. It is found that the growth and normal velocity of the structures are dependent on the relative velocity shear and the kinematic coefficient of viscosity of both the fluids. Both the bubble growth and growth rate are reduced significantly for fluids of higher viscosity coefficient with small velocity shear difference. It is also observed that, for viscous fluids, the transverse velocity of the perturbed interface becomes slower under certain conditions.

Study of second harmonic generation by high power laser beam in magneto plasma
View Description Hide DescriptionThis paper examines the problem of nonlinear generation of second harmonic of a high power laser pulse propagating in magnetized plasma. The propagation of strong laser beam is proposed in the direction perpendicular to a relatively weak static magnetic field. The laser pulse is taken to be linearly polarized, with the orientation of its electric field that corresponds to an ordinary electromagnetic wave. Besides the standard ponderomotive nonlinearity, the appropriate wave equation also contains the nonlinearity that arises from the relativistic electron jitter velocities. During its propagation, the laser beam gets filamented on account of relativistic and pondermotive nonlinearities present in the plasma. The generatedplasma wave gets coupled into the filamentary structures of the pump beam. Due to the expected presence of the beam filamentation, the work has been carried out by considering modified paraxial approximation (i.e., beyond the standard paraxial approximation of a very broad beam). It is found that the power of the plasma wave is significantly affected by the magnetic field strength in the presence of both relativistic and pondermotive nonlinearities. It is investigated that the second harmonic generation is also considerably modified by altering the strength of magnetic field. To see the effect of static magnetic field on the harmonic generation, a key parameter, i.e., the ratio of the cyclotron frequency over the laser frequency has been used, where c is the velocity of light, m and e are the mass and charge of the electron and B_{0} is the externally applied magnetic field.

Modulation instability of an intense laser beam in the hot magnetized electronpositron plasma in the quasineutral limit
View Description Hide DescriptionThe aim of the present study is to investigate the problem of modulation instability of an intense laser beam in the hot magnetized electronpositron plasma. Propagation of the intense circularly polarized laser beam along the external magnetic field is studied using a relativistic fluid model. A nonlinear equation describing the interaction of the laser pulse with the magnetized hot pair plasma is derived based on the quasineutral approximation, which is valid for the hot plasma. Also, the nonlinear dispersion equation for the hot plasma is obtained. The growth rate of the instability is calculated and its dependence on temperature and external magnetic field are considered.

Spontaneous electromagnetic fluctuations in unmagnetized plasmas. III. Generalized Kappa distributions
View Description Hide DescriptionIn the first two papers of this series, the general expressions for the spontaneous fluctuations spectra (electric and magnetic field,charge and current densities) from uncorrelated plasma particles are derived and illustrated for a Maxwellian (relativistic or nonrelativistic) plasma close to thermal equilibrium. In this paper, the results are illustrated for the nonideal case of a plasma out of thermal equilibrium and described by the generalized Kappa (powerlaw) particle distribution function in the nonrelativistic limit. The suprathermal fluctuations of weakly amplified modes and aperiodic modes are provided. Thus, it is shown for the first time the existing finite level of noncollective fluctuations, which are particularly important in the context of plasma fluctuations (collective or noncollective) as the best agent in the energy dissipation and transfer to suprathermal populations. The results obtained in the first paper for an equilibrium plasma are recovered only in the limit of a very large power index .

Electron temperature anisotropy instabilities represented by superposition of streams
View Description Hide DescriptionThe generation of magnetic field, together with the electrostatic activity met in the saturation regime of the Weibel instability (WI), is investigated by means of an analytical multistream model in a Hamiltonian framework. Taking advantage from the invariance of the generalized canonical momentum, the model allows to reduce the full kinetic 1D2V Vlasov equation into several 1D1V equations while keeping its kinetic character. The multistream model provides a more complete and accurate picture of the Weibel instability, because it is possible to separate the specific contribution of each stream during the development of the Weibel instability. An interesting result for the multistream mode is a lower cost in the perpendicular treatment of the p_{y} momentum component since no differential operator associated with some approximate numerical scheme has to be carried out on this variable. Indeed, a small number of streams or particle classes are sufficient to correctly describe the magnetic field generation and the mixed electrostatic electromagnetic nature of the instability.

Power loss of an oscillating electric dipole in a quantum plasma
View Description Hide DescriptionA system of linearized quantum plasmaequations (quantum hydrodynamic model) has been used for investigating the dispersionequation for electrostatic waves in the plasma. Furthermore, dispersion relations and their modifications due to quantum effects are used for calculating the power loss of an oscillating electric dipole. Finally, the results are compared in quantum and classical regimes.

A computational approach to continuum damping of Alfvén waves in two and threedimensional geometry
View Description Hide DescriptionWhile the usual way of calculating continuum damping of global Alfvén modes is the introduction of a small artificial resistivity, we present a computational approach to the problem based on a suitable path of integration in the complex plane. This approach is implemented by the Riccati shooting method and it is shown that it can be transferred to the Galerkin method used in threedimensional ideal magnetohydrodynamics (MHD) codes. The new approach turns out to be less expensive with respect to resolution and computation time than the usual one. We present an application to large aspect ratio tokamak and stellarator equilibria retaining a few Fourier harmonics only and calculate eigenfunctions and continuum damping rates. These may serve as an input for kinetic MHD hybrid models making it possible to bypass the problem of having singularities on the path of integration on one hand and considering continuum damping on the other.

The stability and the growth rate of the electron acoustic traveling wave under transverse perturbations in a magnetized quantum plasma
View Description Hide DescriptionTheoretical and numerical studies are carried out for the stability of the electron acoustic waves under the transverse perturbation in a magnetized quantum plasma. The ZakharovKuznetsov (ZK) equation of the electronacoustic waves(EAWs) is given by using the reductive perturbation technique. The cutoff frequency is obtained by applying a transverse sinusoidal perturbation to the plane soliton solution of the ZK equation. The propagation velocity of solitary waves, the real cutoff frequency, as well as the growth rate of the higher order perturbation to the traveling solitary wave are obtained.

Nonlocal theory of electromagnetic wave decay into two electromagnetic waves in a rippled density plasma channel
View Description Hide DescriptionParametric decay of a large amplitude electromagnetic wave into two electromagnetic modes in a rippled density plasma channel is investigated. The channel is taken to possess step density profile besides a density ripple of axial wave vector. The density ripple accounts for the momentum mismatch between the interactingwaves and facilitates nonlinear coupling. For a given pump wave frequency, the requisite ripple wave number varies only a little w.r.t. the frequency of the low frequency decay wave. The radial localization of electromagnetic wave reduces the growth rate of the parametric instability. The growth rate decreases with the frequency of low frequency electromagnetic wave.

Group velocity of extraordinary waves in superdense magnetized quantum plasma with spin1/2 effects
View Description Hide DescriptionBased on the one component plasma model, a new dispersion relation and group velocity of elliptically polarized extraordinary electromagnetic waves in a superdense quantum magnetoplasma are derived. The group velocity of the extraordinary wave is modified due to the quantum forces and magnetization effects within a certain range of wave numbers. It means that the quantum spin1/2 effects can reduce the transport of energy in such quantum plasma systems. Our work should be of relevance for the dense astrophysical environments and the condensed matter physics.

The modulational instability in the extended HasegawaMima equation with a finite Larmor radius
View Description Hide DescriptionThe effects of the finite Larmor radius on the generation of zonal flows by the fourwave modulational instability are investigated using an extended form of the HasegawaMima equation. Growth rates of the zonal mode are quantified using analytical predictions from a fourmode truncated model, as well as from direct numerical simulation of the nonlinear extended HasegawaMima equation. We not only consider purely zonal flows but also examine the generic oblique case and show that, for small Larmor radii, offaxis modes may become dominant. We find a key parameter which characterises the behaviour of the system due to changes in the Larmor radius. We find that, similarly to previous results obtained by changing the driving wave amplitude, two separate dynamical regimes can be accessed. These correspond to oscillatory energy transfer between zonal flows and a driving wave and the fully saturated zonal flow.

Development of highpower gyrotrons with gradually tapered cavity
View Description Hide DescriptionIn high power gyrotrons, the parasitic modes coupled with the operating mode cannot be avoided in the beamwave interaction. These parasitic modes will decrease the efficiency of the gyrotrons. The purity of the operating mode affected by different tapers should be carefully studied. The steadystate selfconsistent nonlinear theory for gyrotron with gradually tapered cavity is developed in this paper. A steadystate calculation code including “cold cavity” and “hot cavity” is designed. By comparison, a timedomain model analysis of gyrotron operation is also studied by particleincell(PIC). It is found that the tapers of gyrotron have different influences on the modes coupling between the operating mode and the parasitic modes. During the study, an example of 94 GHz gyrotron with pure operating mode TE_{03} has been designed. The purity of the operating mode in the optimized cavity is up to −77 dB, and in output waveguide of the cavity is up to −76 dB. At the same time, the beamwave interaction in the designed cavity has been simulated, too. An output power of 120 kW, corresponding to 41.6% efficiency and an oscillation frequency of 94.099 GHz have been achieved with a 50 kV, 6 A helical electron beam at a guiding magnetic field of 3.5485 T. The results show that the power in spurious modes of the optimized cavity may be kept far below than that of the traditional tapered cavity.
 Nonlinear Phenomena, Turbulence, Transport

Existence domains of arbitrary amplitude nonlinear structures in twoelectron temperature space plasmas. II. Highfrequency electronacoustic solitons
View Description Hide DescriptionA threecomponent plasma model composed of ions, cool electrons, and hot electrons is adopted to investigate the existence of large amplitude electronacoustic solitons not only for the model for which inertia and pressure are retained for all plasma species which are assumed to be adiabatic but also neglecting inertial effects of the hot electrons. Using the Sagdeev potential formalism, the Mach number ranges supporting the existence of large amplitude electronacoustic solitons are presented. The limitations on the attainable amplitudes of electronacoustic solitons having negative potentials are attributed to a number of different physical reasons, such as the number density of either the cool electrons or hot electrons ceases to be real valued beyond the upper Mach number limit, or, alternatively, a negative potential double layer occurs. Electronacoustic solitons having positive potentials are found to be supported only if inertial effects of the hot electrons are retained and these are found to be limited only by positive potential double layers.

On physical interpretation of two dimensional timecorrelations regarding time delay velocities and eddy shaping
View Description Hide DescriptionTime delay estimation (TDE) techniques are frequently used to estimate the flowvelocity from fluctuatingmeasurements. Tilted structures carried by the flow lead to misinterpretation of the time delays in terms of velocity direction and amplitude. It affects TDE measurements from probes, and is also intrinsically important for beam emission spectroscopy and gas puff imaging measurements. Local eddy shapes estimated from 2D fluctuating field are necessary to gain a more accurate flow estimate from TDE, as illustrated by Langmuir probe array measurements. A least square regression approach is proposed to estimate both flow field and shaping parameters. The technique is applied to a test case built from numerical simulation of interchange fluctuations. The local eddy shape does not only provide corrections for the velocity field but also quantitative information about the statistical interaction mechanisms between local eddies and flow shear. The technique is then tested on gaz puff imaging data collected at the edge of EAST tokamak plasmas. It is shown that poloidal asymmetries of the fluctuation fields—velocity and eddy shape—are consistent at least qualitatively with a ballooning type of turbulence immersed in a radially sheared equilibrium flow.

Plasma turbulence driven by transversely largescale standing shear Alfvén waves
View Description Hide DescriptionUsing twodimensional particleincell simulations, we study generation of turbulence consisting of transversely smallscale dispersive Alfvén and electrostatic waves when plasma is driven by a largescale standing shear Alfvén wave (LSSAW). The standing wave is set up by reflecting a propagating LSSAW. The ponderomotive force of the standing wave generates transversely largescale density modifications consisting of density cavities and enhancements. The drifts of the charged particles driven by the ponderomotive force and those directly caused by the fields of the standing LSSAW generate nonthermal features in the plasma. Parametric instabilities driven by the inherent plasma nonlinearities associated with the LSSAW in combination with the nonthermal features generate smallscale electromagnetic and electrostatic waves, yielding a broad frequency spectrum ranging from below the source frequency of the LSSAW to ion cyclotron and lower hybrid frequencies and beyond. The power spectrum of the turbulence has peaks at distinct perpendicular wave numbers (k_{⊥}) lying in the range d_{e} ^{−1}6d_{e} ^{−1}, d_{e} being the electron inertial length, suggesting nonlocal parametric decay from small to large k_{⊥}. The turbulence spectrum encompassing both electromagnetic and electrostaticfluctuations is also broadband in parallel wave number (k_{}). In a standingwave supported density cavity, the ratio of the perpendicular electric to magnetic field amplitude is R(k_{⊥}) = E_{⊥}(k_{⊥})/B_{⊥}(k_{⊥}) ≪ V_{A} for k_{⊥}d_{e} < 0.5, where V_{A} is the Alfvén velocity. The characteristic features of the broadband plasma turbulence are compared with those available from satellite observations in space plasmas.

Magnetic turbulence suppression by a helical mode in a cylindrical geometry
View Description Hide DescriptionTo study processes involved in a helical structure formation in reversed field pinch devices, the scaling of a turbulent boundary layer width associated with a vortex structure having large shears of magnetic field and flow is obtained for reduced magnetohydrodynamics. The coherent vortex, with its flow and magnetic shears, interacts with Alfvén turbulence, forming a turbulent boundary layer at the edge of the vortex. The layer arises from the balance between turbulencediffusion rates and shearing rates and suppresses the turbulence in the structure. The suppression of turbulence impedes relaxation of the coherent vortex profiles, leading to long coherence times. The scaling of the boundary layer width reveals that both magnetic shear and flow shear can effectively suppress magnetic turbulence.