Volume 20, Issue 3, March 2013

In the past, longtime evolution of an initial perturbation in collisionless Maxwellian plasma (q = 1) has been simulated numerically. The controversy over the nonlinear fate of such electrostatic perturbations was resolved by Manfredi [Phys. Rev. Lett. 79, 2815–2818 (1997)] using longtime simulations up to . The oscillations were found to continue indefinitely leading to BernsteinGreeneKruskal (BGK)like phasespace vortices (from here on referred as “BGK structures”). Using a newly developed, high resolution 1D VlasovPoisson solver based on piecewiseparabolic method (PPM) advection scheme, we investigate the nonlinear Landau damping in 1D plasma described by toy qdistributions for long times, up to . We show that BGK structures are found only for a certain range of qvalues around q = 1. Beyond this window, for the generic parameters, no BGK structures were observed. We observe that for values of where velocity distributions have long tails, strong Landau damping inhibits the formation of BGK structures. On the other hand, for where distribution has a sharp fall in velocity, the formation of BGK structures is rendered difficult due to high wave number damping imposed by the steep velocity profile, which had not been previously reported. Wherever relevant, we compare our results with past work.
 LETTERS


Measurement of energeticparticledriven core magnetic fluctuations and induced fastion transport
View Description Hide DescriptionInternal fluctuations arising from energeticparticledriven instabilities, including both density and radial magnetic field, are measured in a reversedfieldpinch plasma. The fluctuations peak near the core where fast ions reside and shift outward along the major radius as the instability transits from the n = 5 to n = 4 mode. During this transition, strong nonlinear threewave interaction among multiple modes accompanied by enhanced fastion transport is observed.
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 ARTICLES

 Basic Plasma Phenomena, Waves, Instabilities

Linear mode conversion of Langmuir/zmode waves to radiation: Scalings of conversion efficiencies and propagation angles with temperature and magnetic field orientation
View Description Hide DescriptionLinear mode conversion (LMC) is the linear transfer of energy from one wave mode to another in an inhomogeneous plasma. It is relevant to laboratory plasmas and multiple solar system radio emissions, such as continuum radiation from planetary magnetospheres and type II and III radio bursts from the solar corona and solar wind. This paper simulates LMC of waves defined by warm, magnetized fluid theory, specifically the conversion of Langmuir/zmode waves to electromagnetic (EM) radiation. The primary focus is the calculation of the energy and power conversion efficiencies for LMC as functions of the angle of incidence θ of the Langmuir/zmode wave, temperature , adiabatic index γ, and orientation angle ϕ between the ambient density gradient and ambient magnetic field in a warm, unmagnetized plasma. The ratio of these efficiencies is found to agree well as a function of θ, γ, and β with an analytical relation that depends on the group speeds of the Langmuir/z and EM wave modes. The results demonstrate that the energy conversion efficiency ϵ is strongly dependent on , ϕ and θ, with and . The power conversion efficiency , on the other hand, is independent of but does vary significantly with θ and ϕ. The efficiencies are shown to be maximum for approximately perpendicular density gradients ( ) and minimal for parallel orientation ( ) and both the energy and power conversion efficiencies peak at the same θ.

Magnetorotational instability in plasmas with mobile dust grains
View Description Hide DescriptionThe magnetorotational instability of dusty plasmas is investigated using the multifluid model and the general dispersion relation is derived based on local approximation. The dust grains are found to play an important role in the dispersion relation in the lowfrequency mode and exhibit destabilizing effects on the plasma. Both the instability criterion and growth rate are affected significantly by the dust and when the dust is heavy enough to be unperturbed, the reduced dispersion relations are obtained. The instability criteria show that the dust grains have stabilizing effects on the instability when the rotation frequency decreases outwards and conversely lead to destabilizing effects when the rotation frequency increases outwards. The results are relevant to accession and protoplanetary disks.

Ion heating and short wavelength fluctuations in a helicon plasma source
View Description Hide DescriptionFor typical helicon source parameters, the driving antenna can couple to two plasma modes; the weakly damped “helicon” wave, and the strongly damped, short wavelength, slow wave. Here, we present direct measurements, obtained with two different techniques, of few hundred kHz, short wavelength fluctuations that are parametrically driven by the primary antenna and localized to the edge of the plasma. The short wavelength fluctuations appear for plasma source parameters such that the driving frequency is approximately equal to the lower hybrid frequency. Measurements of the steadystate ion temperature and fluctuation amplitude radial profiles suggest that the anomalously high ion temperatures observed at the edge of helicon sources result from damping of the short wavelength fluctuations. Additional measurements of the time evolution of the ion temperature and fluctuation profiles in pulsed helicon source plasmas support the same conclusion.

Plasma equilibrium in a semiclassical plasma due to nonresonant wave particle interactions
View Description Hide DescriptionA nonresonant perturbative approach has been utilized to probe the modification of the equilibrium plasma distribution function due to plasma interaction with externally launched highfrequency largeamplitude RF waves in the presence of quantum effects. The quantum distribution function from the complete Wigner equation has been obtained for a highfrequency wave with constant amplitude. For waves with weak spatial or temporal modulation, the equilibrium distribution function has been obtained by solving the Wigner equation as an initial or boundaryvalue problem and retaining only lowestorder quantum effects. In the dipole approximation, a higher order diffusion has been identified in addition to quantum modified ponderomotive and quasilinear diffusion effects. Additional terms of the Wigner equation give the impression of higher order diffusion effects in the system.

Lowfrequency electromagnetic field in a Wigner crystal
View Description Hide DescriptionLongwave lowfrequency oscillations are described in a Wigner crystal by generalization of the reverse continuum model for the case of electronic lattice. The internal selfconsistent longwave electromagnetic field is used to describe the collective motions in the system. The eigenvectors and eigenvalues of the obtained system of equations are derived. The velocities of longitudinal and transversal sound waves are found.

Nonlinear Landau damping and formation of BernsteinGreeneKruskal structures for plasmas with qnonextensive velocity distributions
View Description Hide DescriptionIn the past, longtime evolution of an initial perturbation in collisionless Maxwellian plasma (q = 1) has been simulated numerically. The controversy over the nonlinear fate of such electrostatic perturbations was resolved by Manfredi [Phys. Rev. Lett. 79, 2815–2818 (1997)] using longtime simulations up to . The oscillations were found to continue indefinitely leading to BernsteinGreeneKruskal (BGK)like phasespace vortices (from here on referred as “BGK structures”). Using a newly developed, high resolution 1D VlasovPoisson solver based on piecewiseparabolic method (PPM) advection scheme, we investigate the nonlinear Landau damping in 1D plasma described by toy qdistributions for long times, up to . We show that BGK structures are found only for a certain range of qvalues around q = 1. Beyond this window, for the generic parameters, no BGK structures were observed. We observe that for values of where velocity distributions have long tails, strong Landau damping inhibits the formation of BGK structures. On the other hand, for where distribution has a sharp fall in velocity, the formation of BGK structures is rendered difficult due to high wave number damping imposed by the steep velocity profile, which had not been previously reported. Wherever relevant, we compare our results with past work.

Electron and ion kinetic effects on nonlinearly driven electron plasma and ion acoustic waves
View Description Hide DescriptionFully nonlinear kinetic simulations of electron plasma and ion acoustic waves (IAWs) have been carried out with a new multispecies, parallelized Vlasov code. The numerical implementation of the Vlasov model and the methods used to compute the wave frequency are described in detail. For the first time, the nonlinear frequency of IAWs, combining the contributions from electron and ion kinetic effects and from harmonic generation, has been calculated and compared to Vlasov results. Excellent agreement of theory with simulation results is shown at all amplitudes, harmonic generation being an essential component at large amplitudes. For IAWs, the positive frequency shift from trapped electrons is confirmed and is dominant for the effective electrontoion temperature ratio, Z with Z as the charge state. Furthermore, numerical results demonstrate unambiguously the dependence [R. L. Dewar, Phys. Fluids 15, 712 (1972)] of the kinetic shifts on details of the distribution of the trapped particles, which depends in turn on the conditions under which the waves were generated. The trapped particle fractions and energy distributions are derived and, upon inclusion of harmonic effects, shown to agree with the simulation results, completing a consistent picture. Fluid models of the wave evolution are considered but prove unable to capture essential details of the kinetic simulations. Detrapping by collisions and sideloss is also discussed.

A simplified approach to calculate atomic partition functions in plasmas
View Description Hide DescriptionA simplified method to calculate the electronic partition functions and the corresponding thermodynamic properties of atomic species is presented and applied to C(I) up to C(VI) ions. The method consists in reducing the complex structure of an atom to three lumped levels. The ground level of the lumped model describes the ground term of the real atom, while the second lumped level represents the low lying states and the last one groups all the other atomic levels. It is also shown that for the purpose of thermodynamic function calculation, the energy and the statistical weight of the upper lumped level, describing highlying excited atomic states, can be satisfactorily approximated by an analytic hydrogenlike formula. The results of the simplified method are in good agreement with those obtained by direct summation over a complete set (i.e., including all possible terms and configurations below a given cutoff energy) of atomic energy levels. The method can be generalized to include more lumped levels in order to improve the accuracy.

Lifting particle coordinate changes of magnetic moment type to VlasovMaxwell Hamiltonian dynamics
View Description Hide DescriptionTechniques for coordinate changes that depend on both dependent and independent variables are developed and applied to the MaxwellVlasov Hamiltonian theory. Particle coordinate changes with a new velocity variable dependent on the magnetic field, with spatial coordinates unchanged, are lifted to the field theoretic level, by transforming the noncanonical Poisson bracket and Hamiltonian structure of the VlasovMaxwell dynamics. Several examples are given including magnetic coordinates, where the velocity is decomposed into components parallel and perpendicular to the local magnetic field, and the case of spherical velocity coordinates. An example of the lifting procedure is performed to obtain a simplified version of gyrokinetics, where the magnetic moment is used as a coordinate and the dynamics is reduced by elimination of the electric field energy in the Hamiltonian.

Laboratory studies of the dynamic of resonance cones formation in magnetized plasmas
View Description Hide DescriptionThe paper is devoted to experimental studies of formation of resonance cones in magnetized plasmas by pulsed RF source in the lowerhybrid (whistler) and the upperhybrid frequency ranges. It is shown that in both frequency ranges, resonance cones exhibit similar dynamics after switchingon the RF source: at first, wide maxima of radiation are formed in nonresonance directions, which then become narrower, with their direction approaching the resonance one. While the resonance cones are being formed, one observes a fine structure in the form of secondary radiation maxima. It is shown that the characteristic formation time of stationary resonance cones is determined by the minimal value of the group velocity of the quasielectrostatic waves excited by the antenna. In the lowtemperature plasma, this value is limited in the lowerhybrid frequency range by the spatial spectrum of the emitting antenna and in the upperhybrid range, by the effects of spatial plasma dispersion.

Waves generated in the plasma plume of helicon magnetic nozzle
View Description Hide DescriptionExperimental measurements have shown that the plasma plume created in a helicon plasma device contains a conical structure in the plasma density and a Ushaped double layer (USDL) tightly confined near the throat where plasma begins to expand from the source. Recently reported twodimensional particleincell simulations verified these density and USDL features of the plasma plume. Simulations also showed that the plasma in the plume develops nonthermal feature consisting of radial ion beams with large densities near the conical surface of the density structure. The plasma waves that are generated by the radial ion beams affecting the structure of the plasma plume are studied here. We find that most intense waves persist in the highdensity regions of the conical density structure, where the transversely accelerated ions in the radial electric fields in the plume are reflected setting up counterstreaming. The waves generated are primarily ion Bernstein modes. The nonlinear evolution of the waves leads to magnetic fieldaligned striations in the fields and the plasma near the conical surface of the density structure.

Modified Kortewegde Vries soliton reflection in a magnetized plasma with dust grains and trapped electrons
View Description Hide DescriptionThis article aims at studying the reflection of solitons in an inhomogeneous magnetized warm plasma having dust grains with positive or negative charge and trapped electrons (low temperature nonisothermal electrons). In order to study the soliton reflection, a coupled modified Kortewegde Vries equation is derived and solved along with the use of incident soliton solution. The expressions for the reflected soliton amplitude, width, and reflection coefficient are obtained, and examined under different parameter regimes. The combined effect of the dust grain density with their charge polarity and trapping of the electrons is largely studied on the soliton reflection characteristics under the influence of magnetic field.

Effects of the background plasma temperature on the current filamentation instability
View Description Hide DescriptionThe effects of thermal anisotropy of background plasma on the currentfilamentation instability (CFI) in an asymmetric counterstreaming system are investigated with a fully relativistic kinetic model. It is found that both the temperature and the thermal anisotropy of the background plasma play important roles in the development of the CFI. It is also pointed out that the thermal anisotropy of the background plasma dominates over the space charge effect in suppressing the CFI. A parametric study of the CFI is presented in the context of fast ignition. A new way to suppress CFI and its detrimental effects on the fast electron beam divergence has been proposed. The results of the analytical estimations are verified by 2D3V particleincell simulations.

Resistive magnetohydrodynamic model for cylindrical plasma expansion in a magnetic field
View Description Hide DescriptionThe study of hot plasma expansion in a magnetic field is of interest for many laboratory and astrophysical applications. In this paper, an exactly solvable analytical model is proposed for an expanding resistive plasma in an external magnetic field in the regime in which the magnetic field does not perturb the plasma motion. The model is based on a class of exact solutions for the purely radial expansion of the plasma in the absence of a magnetic field. This approximation permits the reduction of the electromagnetic problem to consideration of a diffusion equation for the magnetic field. Explicit solutions are derived for a resistive cylindrical plasma expanding into a uniform ambient magnetic field. Some numerical examples related to the laserproduced plasma experiments are presented.

The mixed Wentzel–Kramers–Brillouinfullwave approach and its application to lower hybrid wave propagation and absorption
View Description Hide DescriptionThe mixed Wentzel–Kramers–Brillouin (WKB)fullwave approach for the calculation of the 2D mode structure in tokamak plasmas is further developed based on our previous work [A. Cardinali and F. Zonca, Phys. Plasmas 10, 4199 (2003) and Z. X. Lu et al., Phys. Plasmas 19, 042104 (2012)]. A new scheme for theoretical analysis and numerical implementation of the mixed WKBfullwave approach is formulated, based on scale separation and asymptotic analysis. Besides its capability to efficiently investigate the initial value problem for 2D mode structures and linear stability, in this work, the mixed WKBfullwave approach is extended to the investigation of radio frequency wave propagation and absorption, e.g., lower hybrid waves. As a novel method, its comparison with other approaches, e.g., WKB and beam tracing methods, is discussed. Its application to lower hybrid wave propagation in concentric circular tokamak plasmas using typical FTU discharge parameters is also demonstrated.

Unified onedimensional model of bounded plasma with nonzero ion temperature in a broad pressure range
View Description Hide DescriptionA onedimensional model for steady state plasmas bounded either between large parallel walls, or by a cylinder or a sphere, valid in a wide range of gas pressures, is considered. The model includes nonzero ion temperature, inertial terms in the ion momentum equations, and allows one to calculate the plasma electron temperature and ion current density reaching the wall, as well as the spatial distributions of the ion fluid velocity, plasma density, and plasma potential in the plasma bulk. In addition, the effect of electron inertia is analyzed. The model includes as particular cases several earlier models that were based on a similar set of differential equations, but that are restricted to a specific pressure regime (low, intermediate, or high). Analytical solution is found in planar geometry, and numerical solution is given in cylindrical and spherical geometry. The results obtained are compared with those of earlier models and the differences are analyzed.

KelvinHelmholtz instability in a currentvortex sheet at a 3D magnetic null
View Description Hide DescriptionWe report here, for the first time, an observed instability of a KelvinHelmholtz nature occurring in a fully threedimensional (3D) currentvortex sheet at the fan plane of a 3D magnetic null point. The currentvortex layer forms selfconsistently in response to foot point driving around the spine lines of the null. The layer first becomes unstable at an intermediate distance from the null point, with the instability being characterized by a rippling of the fan surface and a filamentation of the current density and vorticity in the shear layer. Owing to the 3D geometry of the shear layer, a branching of the current filaments and vortices is observed. The instability results in a mixing of plasma between the two topologically distinct regions of magnetic flux on either side of the fan separatrix surface, as flux is reconnected across this surface. We make a preliminary investigation of the scaling of the system with the dissipation parameters. Our results indicate that the fan plane separatrix surface is an ideal candidate for the formation of currentvortex sheets in complex magnetic fields and, therefore, the enhanced heating and connectivity change associated with the instabilities of such layers.

Analysis of photonic band gap in dispersive properties of tunable threedimensional photonic crystals doped by magnetized plasma
View Description Hide DescriptionIn this paper, the magnetooptical effects in dispersive properties for two types of threedimensional magnetized plasma photonic crystals (MPPCs) containing homogeneous dielectric and magnetized plasma with diamond lattices are theoretically investigated for electromagnetic (EM) wave based on plane wave expansion (PWE) method, as incidence EM wave vector is parallel to the external magnetic field. The equations for two types of MPPCs with diamond lattices (dielectric spheres immersed in magnetized plasma background or vice versa) are theoretically deduced. The influences of dielectric constant, plasma collision frequency, filling factor, the external magnetic field, and plasma frequency on the dispersive properties for both types of structures are studied in detail, respectively, and some corresponding physical explanations are also given. From the numerical results, it has been shown that the photonic band gaps (PBGs) for both types of MPPCs can be manipulated by plasma frequency, filling factor, the external magnetic field, and the relative dielectric constant of dielectric, respectively. Especially, the external magnetic field can enlarge the PBG for type2 structure (plasma spheres immersed in dielectric background). However, the plasma collision frequency has no effect on the dispersive properties of two types of threedimensional MPPCs. The locations of flatbands regions for both types of structures cannot be tuned by any parameters except for plasma frequency and the external magnetic field. The analytical results may be informative and of technical use to design the MPPCs devices.
 Nonlinear Phenomena, Turbulence, Transport

Adiabatic trapping in coupled kinetic Alfvénacoustic waves
View Description Hide DescriptionIn the present work, we have discussed the effects of adiabatic trapping of electrons on obliquely propagating Alfvén waves in a low plasma. Using the two potential theory and employing the Sagdeev potential approach, we have investigated the existence of arbitrary amplitude coupled kinetic Alfvénacoustic solitary waves in both the sub and super Alfvénic cases. The results obtained have been analyzed and presented graphically and can be applied to regions of space where the low assumption holds true.