Showing papers in "Journal of Plasma Physics in 2014"

25 years of dust acoustic waves

Abstract: The dust acoustic wave (DAW) was first discussed by P. K. Shukla in May of 1989 at the First Capri Workshop on Dusty Plasmas. In the past 25 years, the subsequent publication of the linear and nonlinear properties of the DAW (Rao, N. N., Shukla, P. K. and Yu, M. Y. 1990 Planet. Space Sci.38, 543) has generated and sustained a large body of theoretical and experimental research that has clarified the physics of collective effects in dusty plasmas. A unique feature of the DAW is that it can be observed (literally) using laser illumination and high-speed videography, revealing details of wave-particle interactions at an unprecedented single particle level. This paper attempts to review some of the contributions and extensions of dust acoustic wave physics, as well as identify recent findings that illustrate the potential importance of this dust wave in the agglomeration of dust particles.

Phase space scales of free energy dissipation in gradient-driven gyrokinetic turbulence

Abstract: A reduced four-dimensional (integrated over perpendicular velocity) gyrokinetic model of slab ion temperature gradient-driven turbulence is used to study the phase-space scales of free energy dissipation in a turbulent kinetic system over a broad range of background gradients and collision frequencies. Parallel velocity is expressed in terms of Hermite polynomials, allowing for a detailed study of the scales of free energy dynamics over the four-dimensional phase space. A fully spectral code – the DNA code – that solves this system is described. Hermite free energy spectra are significantly steeper than would be expected linearly, causing collisional dissipation to peak at large scales in velocity space even for arbitrarily small collisionality. A key cause of the steep Hermite spectra is a critical balance – an equilibration of the parallel streaming time and the nonlinear correlation time – that extends to high Hermite number n. Although dissipation always peaks at large scales in all phase space dimensions, small-scale dissipation becomes important in an integrated sense when collisionality is low enough and/or nonlinear energy transfer is strong enough. Toroidal full-gyrokinetic simulations using the Gene code are used to verify results from the reduced model. Collision frequencies typically found in present-day experiments correspond to turbulence regimes slightly favoring large-scale dissipation, while turbulence in low-collisionality systems like ITER and space and astrophysical plasmas is expected to rely increasingly on small-scale dissipation mechanisms. This work is expected to inform gyrokinetic reduced modeling efforts like Large Eddy Simulation and gyrofluid techniques.

Electrostatic shielding in plasmas and the physical meaning of the Debye length

Abstract: This paper examines the electrostatic shielding in plasmas, and resolves inconsistencies about what the Debye length really is. Two different interpretations of the Debye length are currently used: (1) The potential energy approximately equals the thermal energy, and (2) the ratio of the shielded to the unshielded potential drops to 1/e. We examine these two interpretations of the Debye length for equilibrium plasmas described by the Boltzmann distribution, and non-equilibrium plasmas (e.g. space plasmas) described by kappa distributions. We study three dimensionalities of the electrostatic potential: 1-D potential of linear symmetry for planar charge density, 2-D potential of cylindrical symmetry for linear charge density, and 3-D potential of spherical symmetry for a point charge. We resolve critical inconsistencies of the two interpretations, including: independence of the Debye length on the dimensionality; requirement for small charge perturbations that is equivalent to weakly coupled plasmas; correlations between ions and electrons; existence of temperature for non-equilibrium plasmas; and isotropic Debye shielding. We introduce a third Debye length interpretation that naturally emerges from the second statistical moment of the particle position distribution; this is analogous to the kinetic definition of temperature, which is the second statistical moment of the velocity distribution. Finally, we compare the three interpretations, identifying what information is required for theoretical/experimental plasma-physics research: Interpretation 1 applies only to kappa distributions; Interpretation 2 is not restricted to any specific form of the ion/electron distributions, but these forms have to be known; Interpretation 3 needs only the second statistical moment of the positional distribution.

Polarization force for different dusty plasma situations

Abstract: Polarization force (acting on a dust grain) and its modification by polarity of dust, non-isothermal (viz. non-thermal and trapped) ions, adiabaticity of electrons and ions, etc. have been investigated theoretically. It has been found that the polarization force is significantly modified by these effects, i.e. the magnitude of the polarization force is significantly decreased by the presence of non-thermal ions and by the adiabaticity of electrons and ions. On the other hand, it is significantly increased by the presence of trapped ions. It has been also shown that the magnitude of the polarization force is increased (decreased) by electric potential in the case of positively (negatively) charged dust. The relevance of our investigation to some space and astrophysical plasma situations is discussed.

Effect of q -non-extensive distribution of electrons on the plasma sheath floating potential

Abstract: first published online 9 April 2014) In this paper, a collisionless unmagnetized plasma sheath consisting of electrons following non-extensive q-distribution, and cold mobile inertial ions is studied in the stationary state. In this type of plasma with non-Maxwellian electron distribution (Tsallis statistical mechanics), the effective electron temperature (Te,eff ) and electron screening temperature (Te,∗) are evaluated. The other plasma sheath phenomena such as the Bohm sheath criterion, Debye shielding, floating potential, and sheath length are investigated in the presence of q-non-extensive velocity-distributed electrons. It is observed that above-mentioned phenomena depend significantly on the non-extensive parameter q.

Non-extensive effects on the characteristics of dust-acoustic solitary waves in magnetized dusty plasma with two-temperature isothermal ions

Abstract: The nonlinear Zakharov–Kuznetsov and the modified Zakharov–Kuznetsov equations are derived for dust-acoustic solitary waves (DASWs) in a magnetized four-component dusty plasma system comprising negatively charged cold dust, non-extensive electrons, and two-temperature thermal ions using standard reductive perturbation method. The combined effects of electron non-extensivity, strength of magnetic field, and its obliqueness on the DASWs profile are analyzed. Different ranges of non-extensive q -parameter are considered. Our results show that solitary waves, that their amplitude and width of which depend sensitively on the q -non-extensive parameter, can exist. Due to electron non-extensivity, our dusty plasma model can admit positive potential as well as negative potential solitons. The strength of magnetic field has no effect on the amplitude of solitary waves, whereas its obliqueness affects both amplitude and width of the solitary waves structure. Results show that the amplitude of soliton increases with increasing the velocity of soltion. For any magnitude of q there is an extremum for the direction of the magnetic field at which the width of soliton is maximum.

Bifurcations of ion acoustic solitary and periodic waves in an electron-positron-ion plasma through non-perturbative approach

Abstract: Ion acoustic solitary waves and periodic waves in an unmagnetized plasma with superthermal (kappa-distributed) electrons and positrons are investigated through a non-perturbative approach. Model equations are transformed to a planar dynamical system. Then by using the bifurcations of phase portraits of this planar dynamical system, we have established that our model has solitary wave and periodic wave solutions. We have obtained two analytical solutions for these solitary and periodic waves depending on the parameters. From these solitary wave and periodic wave solutions, we have shown the combined effects of temperature ratio (σ) of electrons and positrons, spectral index (κ), speed of the traveling wave (v), and density ratio (p) of positrons and electrons on the characteristics of ion acoustic solitary and periodic waves. The spectral index, density ratio, speed of the traveling wave, and temperature ratio significantly affect the characteristics of ion acoustic solitary and periodic structures. The present study might be helpful to understand the salient features of nonlinear ion acoustic solitary and periodic structures in the interstellar medium.

Preliminary characteristics of magnetic field and plasma performance in the Magnetized Dusty Plasma Experiment (MDPX)

Abstract: The Magnetized Dusty Plasma Experiment (MDPX) device is a newly constructed research instrument for the study of dusty (complex) plasmas. The MDPX device is envisioned as an experimental platform in which the dynamical behavior of all three charged plasma components, the electrons, ions, and charged microparticles (i.e., the ‘dust’) will be significantly influenced by the magnetic force. This brief paper will provide a short overview of the design, magnetic performance, and initial plasma measurements in the MDPX device.

Dusty plasmas over the Moon

Abstract: The results on dusty plasmas over the Moon are reviewed. The problems concerning the dusty plasma over the lunar surface are formulated.

Dust-acoustic shock waves in a magnetized non-thermal dusty plasma

Abstract: A theoretical investigation is carried out to study the basic properties of dust-acoustic (DA) shock waves propagating in a magnetized non-thermal dusty plasma (containing cold viscous dust fluid, non-thermal ions, and non-thermal electrons). The reductive perturbation method is used to derive the Korteweg–de Vries–Burgers equation. It is found that the basic properties of DA shock waves are significantly modified by the combined effects of dust fluid viscosity, external magnetic field, and obliqueness (angle between external magnetic field and DA wave propagation direction). It is shown that the dust fluid viscosity acts as a source of dissipation, and is responsible for the formation of DA shock structures in the dusty plasma system under consideration. The implications of our results in some space and laboratory plasma situations are briefly discussed.

Effect of plasma-β on the onset of plasmoid instability in Sweet–Parker current sheets

Abstract: Abstract A numerical study of magnetic reconnection in two-dimensional resistive magnetohydrodynamics for Sweet–Parker current sheets that are subject to plasmoid instability is carried out. The effect of the initial upstream plasma-β on the critical Lundquist number Sc for the onset of plasmoid instability is studied. Our results indicate a weak dependence, with a value of Sc ≃ 1.5 × 104 in the limit of zero β, and a value of Sc ≃ 1 × 104 in the opposite high β regime (β ≫ 1). A similar dependence was previously obtained (Ni et al. 2012 Phys. Plasm. 19, 072902), but with a somewhat much larger variation, that can be largely attributed to the different configuration setup used in their study, and also to the definition of the Lundquist number. This conclusion does not depend significantly on the equilibrium used, i.e. both initial configurations with either plasma density or temperature spatial variations lead to very similar results. Finally, we show that the inner plasmoid structure appears as an under-dense hotted magnetic island, with a local temperature increase that is noticeably strengthened for low β cases.

Dust acoustic shock waves in dusty plasma of opposite polarity with non-extensive electron and ion distributions

Abstract: A theoretical investigation has been made of obliquely propagating nonlinear electrostatic shock structures. The reductive perturbation method has been used to derive the Korteweg-de Vries-Burger (KdV-Burger) equation for dust acoustic shock waves in a homogeneous system of a magnetized collisionless plasma comprising a four-component dusty plasma with massive, micron-sized, positively, negatively dust grains and non-extensive electrons and ions. The effect of dust viscosity coefficients of charged dusty plasma of opposite polarity and the non-extensive parameters of electrons and ions have been studied. The behavior of the oscillatory and monotonic shock waves in dusty plasma has been investigated. It has been found that the presence of non-extensive parameters significantly modified the basic properties of shock structures in space environments.

High-informative version of nonlinear transformation of Langmuir waves to electromagnetic waves

Abstract: The concept of informativeness of nonlinear plasma physical scenario is discussed. Basic principles for heightening the informativeness of plasma kinetic models are explained. Former high-informative correlation analysis of plasma kinetics (Erofeev, V. 2011 High-Informative Plasma Theory, Saarbrucken: LAP) is generalized for studies of weakly turbulent plasmas that contain fields of solenoidal plasma waves apart from former potential ones. Respective machinery of plasma kinetic modeling is applied to an analysis of fusion of Langmuir waves with transformation to electromagnetic waves. It is shown that the customary version of this phenomenon (Terashima, Y. and Yajima, N. 1963 Prog. Theor. Phys. 30, 443; Akhiezer, I. A., Danelia, I. A. and Tsintsadze, N. L. 1964 Sov. Phys. JETP19, 208; Al'tshul', L. M. and Karpman, V. I. 1965 Sov. Phys. JETP20, 1043) substantially distorts the picture of merging of Langmuir waves with long wavelengths (λ ≳ c/ωpe).

Exact Riemann solver for ideal magnetohydrodynamics that can handle all types of intermediate shocks and switch-on/off waves

Abstract: We have built a code to obtain the exact solutions of Riemann problems in ideal magnetohydrodynamics (MHD) for an arbitrary initial condition. The code can handle not only regular waves but also switch-on/off rarefactions and all types of non-regular shocks: intermediate shocks and switch-on/off shocks. Furthermore, the initial conditions with vanishing normal or transverse magnetic fields can be handled, although the code is partly based on the algorithm proposed by Torrilhon (2002) (Torrilhon, M. 2002 Exact solver and uniqueness condition for Riemann problems of ideal magnetohydrodynamics. Research report 2002-06, Seminar for Applied Mathematics, ETH, Zurich, Switzerland), which cannot deal with all types of non-regular waves nor the initial conditions without normal or transverse magnetic fields. Our solver can find all the solutions for a given Riemann problem, and hence, as demonstrated in this paper, one can investigate the structure of the solution space in detail. Therefore, the solver is a powerful instrument to solve the outstanding problem of existence and uniqueness of solutions of MHD Riemann problems. Moreover, the solver may be applied to numerical MHD schemes like the Godunov scheme in the future.

Solution of Grad–Shafranov equation by the method of fundamental solutions

Abstract: In this paper we have used the Method of Fundamental Solutions (MFS) to solve the Grad–Shafranov (GS) equation for the axisymmetric equilibria of tokamak plasmas with monomial sources. These monomials are the individual terms appearing on the right-hand side of the GS equation if one expands the nonlinear terms into polynomials. Unlike the Boundary Element Method (BEM), the MFS does not involve any singular integrals and is a meshless boundary-alone method. Its basic idea is to create a fictitious boundary around the actual physical boundary of the computational domain. This automatically removes the involvement of singular integrals. The results obtained by the MFS match well with the earlier results obtained using the BEM. The method is also applied to Solov'ev profiles and it is found that the results are in good agreement with analytical results.

Ion acoustic traveling waves

Abstract: Models for traveling waves in multi-fluid plasmas give essential insight into fully nonlinear wave structures in plasmas, not readily available from either numerical simulations or from weakly nonlinear wave theories. We illustrate these ideas using one of the simplest models of an electron–proton multi-fluid plasma for the case where there is no magnetic field or a constant normal magnetic field present. We show that the traveling waves can be reduced to a single first-order differential equation governing the dynamics. We also show that the equations admit a multi-symplectic Hamiltonian formulation in which both the space and time variables can act as the evolution variable. An integral equation useful for calculating adiabatic, electrostatic solitary wave signatures for multi-fluid plasmas with arbitrary mass ratios is presented. The integral equation arises naturally from a fluid dynamics approach for a two fluid plasma, with a given mass ratio of the two species (e.g. the plasma could be an electron–proton or an electron–positron plasma). Besides its intrinsic interest, the integral equation solution provides a useful analytical test for numerical codes that include a proton–electron mass ratio as a fundamental constant, such as for particle in cell (PIC) codes. The integral equation is used to delineate the physical characteristics of ion acoustic traveling waves consisting of hot electron and cold proton fluids.

Wave theories of non-laminar charged particle beams: from quantum to thermal regime

Abstract: The standard classical description of non-laminar charged particle beams in paraxial approximation is extended to the context of two wave theories. The first theory that we discuss (Fedele R. and Shukla, P. K. 1992 Phys. Rev. A45, 4045. Tanjia, F. et al. 2011 Proceedings of the 38th EPS Conference on Plasma Physics, Vol. 35G. Strasbourg, France: European Physical Society) is based on the Thermal Wave Model (TWM) (Fedele, R. and Miele, G. 1991 Nuovo Cim. D13, 1527.) that interprets the paraxial thermal spreading of beam particles as the analog of quantum diffraction. The other theory is based on a recently developed model (Fedele, R. et al. 2012a Phys. Plasmas19, 102106; Fedele, R. et al. 2012b AIP Conf. Proc.1421, 212), hereafter called Quantum Wave Model (QWM), that takes into account the individual quantum nature of single beam particle (uncertainty principle and spin) and provides collective description of beam transport in the presence of quantum paraxial diffraction. Both in quantum and quantum-like regimes, the beam transport is governed by a 2D non-local Schrodinger equation, with self-interaction coming from the nonlinear charge- and current-densities. An envelope equation of the Ermakov–Pinney type, which includes collective effects, is derived for both TWM and QWM regimes. In TWM, such description recovers the well-known Sacherer's equation (Sacherer, F. J. 1971 IEEE Trans. Nucl. Sci.NS-18, 1105). Conversely, in the quantum regime and in Hartree's mean field approximation, one recovers the evolution equation for a single-particle spot size, i.e. for a single quantum ray spot in the transverse plane (Compton regime). We demonstrate that such quantum evolution equation contains the same information as the evolution equation for the beam spot size that describes the beam as a whole. This is done heuristically by defining the lowest QWM state accessible by a system of non-overlapping fermions. The latter are associated with temperature values that are sufficiently low to make the single-particle quantum effects visible on the beam scale, but sufficiently high to make the overlapping of the single-particle wave functions negligible. This lowest QWM state constitutes the border between the fundamental single-particle Compton regime and the collective quantum and thermal regimes at larger (nano- to micro-) scales. Comparing it with the beam parameters in the existing accelerators, we find that it is feasible to achieve nano-sized beams in advanced compact machines.

Numerical simulations of dust charging and wakefield effects

Abstract: Charging of dust grains and related phenomena are fundamental problems in the physics of complex plasmas. The relative motion of grains and plasma breaks the symmetry in dust charging and gives rise to the wake in plasma density and potential, which can significantly influence the dynamics of other grains. This paper gives an overview of dust charging in two- and multi-component plasma flows and related wake effects, and presents recent results from self-consistent particle-in-cell (PIC) simulations. The role of wakefields is considered in the context of charging of downstream grains.

Collective dynamics in strongly coupled dusty plasma medium

Abstract: A simplified description of dynamical response of strongly coupled medium is desirable in many contexts of physics. The dusty plasma medium can play an important role in this regard due to its uniqueness, as its dynamical response typically falls within the perceptible grasp of human senses. Furthermore, even at room temperature and normal densities it can be easily prepared to be in a strongly coupled regime. A simplified phenomenological fluid model based on the visco - elastic behaviour of the medium is often invoked to represent the collective dynamical response of a strongly coupled dusty plasma medium. The manuscript reviews the role of this particular Generalized Hydrodynamic (GHD) fluid model in capturing the collective properties exhibited by the medium. In addition the paper also provides new insights on the collective behaviour predicted by the model for the medium, in terms of coherent structures, instabilities, transport and mixing properties.

Unperturbed state and solitary structures in an electron-positron plasma having dust impurity and density inhomogeneity

Abstract: An electron–positron pair plasma having dust impurity and density non-uniformity is studied for its unperturbed state and evolution of solitary structures under the effect of either positively charged or negatively charged dust grains. Zeroth-order equations are solved to examine the unperturbed state of the plasma via unperturbed potential φ0, drift velocities of the electrons and positrons (ve0 and vp0), and plasma (positron) density gradient np0η. It is observed that the dust distribution affects the gradient np0η significantly, which increases very sharply with a small increment in the dust density gradient nd0η. With relation to the solitary structures, a modified form of Korteweg–deVries equation (mKdV equation) is realized in the said plasma, which reveals that a tailing structure is associated with the soliton (sech 2 structure). This tail is less prominent in the present pair plasma, contrary to the observation made in ordinary plasmas having only ions and electrons. The dust impurity is found to influence the solitary structure much significantly and its presence suppresses the rarefactive solitons, which are generally observed in multi-component species plasmas.

Multi-symplectic magnetohydrodynamics

Abstract: A multi-symplectic formulation of ideal magnetohydrodynamics (MHD) is developed based on the Clebsch variable variational principle in which the Lagrangian consists of the kinetic minus the potential energy of the MHD fluid modified by constraints using Lagrange multipliers that ensure mass conservation, entropy advection with the flow, the Lin constraint, and Faraday's equation (i.e. the magnetic flux is Lie dragged with the flow). The analysis is also carried out using the magnetic vector potential A where α=A⋅dx is Lie dragged with the flow, and B=∇×A. The multi-symplectic conservation laws give rise to the Eulerian momentum and energy conservation laws. The symplecticity or structural conservation laws for the multi-symplectic system corresponds to the conservation of phase space. It corresponds to taking derivatives of the momentum and energy conservation laws and combining them to produce n(n−1)/2 extra conservation laws, where n is the number of independent variables. Noether's theorem for the multi-symplectic MHD system is derived, including the case of non-Cartesian space coordinates, where the metric plays a role in the equations.

Kelvin-Helmholtz instability in dusty plasma medium: Fluid and particle approach

Abstract: The Kelvin-Helmholtz (KH) instability is studied in a two dimensional strongly coupled dusty plasma medium using a fluid approach as well as through a molecular dynamic (MD) simulation. For the fluid description the generalized hydrodynamic (GH) model which treats the strongly coupled dusty plasma as a visco-elastic fluid is adopted. For the MD studies the ensemble of particles are assumed to interact through a Yukawa potential. Both the approaches predict a stabilization of the KH growth rate with an increase in the strong coupling parameter. The present study also delineates the temporal evolution and the interaction of transverse shear waves with the collective dynamics of the dusty plasma medium within the framework of both these approaches.

Behavior of dust particles in cylindrical discharges: Structure formation, mixture and void, effect of gravity

Abstract: Theoretical and numerical works on dusty plasmas with cylindrical symmetry are presented. The main purpose has been to investigate behavior of dust particles in strongly coupled dusty plasmas which are expected to be realized in the planned experiments by PK-4 on the International Space Station and experiments by PK-4J, a similar apparatus constructed in Japan. The distribution of dust particles is analyzed on the basis of the drift-diffusion equations and, with the effect of discreteness taken into account, structure formations are numerically simulated.

Exact equilibria for nonlinear force-free magnetic fields with its applications to astrophysics and fusion plasmas

Abstract: Knowledge of the structure of coronal magnetic field originating from the photosphere is relevant to the understanding of many solar activity phenomena, e.g. flares, solar prominences, coronal loops, and coronal heating. In most of the existing literature, these loop-like magnetic structures are modeled as force-free magnetic fields (FFMF) without any plasma flow. In this paper, we present several exact solution classes for nonlinear FFMF, in both translational and axisymmetric geometries. The solutions are considered for their possible relevance to astrophysics and solar physics problems. These are used to illustrate arcade-type magnetic field structures of the photosphere and twisted magnetic flux ropes through the coronal mass ejections (CMEs), as well as magnetic confinement fusion plasmas.

Electrostatic nonlinear supersolitons in dusty plasmas

Abstract: Using the Sagdeev pseudopotential method, the properties of negative dust-acoustic supersolitons are investigated in a plasma comprising cold negative dust and Boltzmann and Cairns non-thermal positive ions Supersolitons have electric field profiles with additional wiggles on traditional bipolar structures, and their existence requires pseudopotentials having two sub-wells before a root is reached Once the existence ranges are determined in parameter space, typical pseudopotential, supersoliton and electric field profiles can be easily generated Their characteristics are very robust and yield dust and dust-ion-acoustic supersolitons in a wide range of compositional models and parameter ranges

Modulational stability of electron plasma wave spectra

Abstract: Analytical models for weakly nonlinear electron plasma waves are considered in order to obtain dynamic equations for the space-time evolution of their local power spectra. The model contains the wave kinetic equation as a limiting case for slow, long wavelength modulations. It is demonstrated that a finite spectral width in wavenumbers has a stabilizing effect on the modulational instability. The results invite a simple heuristic relation between the spectral width and the root-mean-square amplitude of stable stationary turbulent Langmuir wave spectra. A non-local average dispersion relation is derived as a limiting form by using the formalism developed for the spectral dynamics.

Nanoparticles in direct-current discharges: Growth and electrostatic coupling

Abstract: The formation of nanoparticles from the sputtering of graphite and tungsten cathodes in direct-current discharges is investigated. The successive phases of growth present specificities according to the cathode material. The evolution of the discharge and plasma parameters during the growth phases accounts for the nanoparticle-plasma electrostatic coupling. This evolution also presents strong differences as a function of the cathode material. Features characterising each case are discussed.

Examining the range of validity of the Bohm criterion

Abstract: This work shows that there is no such thing as a formulation of the Bohm criterion for the case of a collisional plasma. It examines critically the work of several authors who have sought to promote their own version of what has come to be called a collisionally modified Bohm criterion.

Three-wave interaction and Manley-Rowe relations in quantum hydrodynamics

Abstract: The theory for nonlinear three-wave interaction in magnetized plasmas is reconsidered using quantum hydrodynamics. The general coupling coefficients are calculated for the generalized Bohm de Broglie term. It is found that the Manley–Rowe relations are fulfilled only if the form of the particle dispersive term coincides with the standard expression. The implications of our results are discussed.