bluuebunny/crossref_metadata_2025 huggingface dataset:
Self-consistent treatment of cyclotron resonances in inhomogeneous plasmas
Authors: Harvey B. M. , Laing E. W.
Published: March 2009

The wave differential operator is obtained directly from the perturbed Vlasov equation for an inhomogeneous equilibrium magnetic field including consistently the effects of strong wave damping and linear mode conversion. In the process, conditions on the parallel wavenumber and the magnetic-field gradient for which such a method is valid are obtained. From these equations it is shown that the inclusion of parameter-gradient terms arising from the spatial dependence of the equilibrium magnetic field is important for accurate calculation of mode conversion from fast to ion-Bernstein wave, although the dispersion-relation-based operator can be sufficient to describe transmission and reflection of the fast wave. Finally, the coupled second-order equations used by Fuchs & Bers (1988) are obtained, allowing direct identification of the ‘modes’ referred to in that paper in terms of components of the electric field. By reconciling these two different approaches, some insight is gained into the mode-conversion process.
Scattering of electromagnetic waves by anomalous fluctuations of a magnetized plasma
Authors: Pavlenko V. N. , Panchenko V. G.
Published: March 2009

Fluctuations and scattering of transverse electromagnetic waves by density fluctuations in a magnetized plasma in the presence of parametric decay of the pump wave are investigated. The spectral density of electron-density fluctuations is calculated. It is shown that the differential scattering cross-section has sharp maxima at the ion-acoustic and lower-hybrid frequencies when parametric decay of the lower-hybrid pump wave occurs. We note that scattering at the ion-acoustic frequency is dominant. When the pump-wave amplitude tends to the threshold strength of the electric field the scattering cross-section increases anomalously, i.e. there is critical opalescence.
Higher-order electron modes in a two-electron-temperature plasma
Authors: Mace R. L. , Hellberg M. A.
Published: March 2009

We discuss critical curves that allow us to predict, qualitatively, the topological behaviour of higher-order modes in a two-electron-temperature plasma as wavenumber and hot electron fraction are varied. The relationship of these higher-order modes to the electron-acoustic wave is elucidated.
Oblique stability of circularly polarized MHD waves
Authors: Mjølhus E. , Hada T.
Published: March 2009

The stability of finite-amplitude weakly dispersive circularly polarized MHD wave trains with respect to oblique modulations is investigated. The mathematical model is a multi-dimensional extension of the DNLS equation. We have found that the right-hand-polarized wave, which is stable with respect to parallel modulations, is unstable with respect to certain oblique modulations for most primary wavenumbers.
Two-dimensional generalizations of the Newcomb equation
Authors: Dewar R. L. , Pletzer A.
Published: March 2009

The Bineau reduction to scalar form of the equation governing ideal zero-frequency linearized displacements from a hydromagnetic equilibrium possessing a continuous symmetry is performed in ‘universal co-ordinates’, applicable to both the toroidal and helical cases. The resulting generalized Newcomb equation (GNE) has in general a more complicated form than the corresponding one-dimensional equation obtained by Newcomb in the case of circular cylindrical symmetry, but in this cylindrical case we show that the equation can be transformed to that of Newcomb. In the two-dimensional case there is a transformation that leaves the form of the GNE invariant and simplifies the Frobenius expansion about a rational surface, especially in the limit of zero pressure gradient. The Frobenius expansion about a mode rational surface is developed and the connection with Hamiltonian transformation theory is shown. The derivations of the ideal interchange and ballooning criteria from the formalism are discussed.
Cut-off conditions and existence domains for large-amplitude ion-acoustic solitons and double layers in fluid plasmas
Authors: Baboolal S. , Bharuthram R. , Hellberg M. A.
Published: March 2009

It is shown how existence domains for arbitrary-amplitude ion-acoustic solitons and double layers are determined numerically by cut-off conditions on the corresponding Sagdeev potential. A two-electron-temperature model is considered, and in positive-ion plasmas the cut-off conditions are given in terms of the electron parameters, while for negative-ion plasmas such conditions are described in terms of parameters characterizing the role of the negative ion species.
Anisotropic-ion-beam-plasma interaction: drift parallel to magnetic field
Authors: Singh P. , Bharuthram R.
Published: March 2009

In a plasma in which both the ions and electrons are magnetized we investigate low-frequency electrostatic instabilities driven by an anisotropic ion beam drifting parallel to the external magnetic field. The instability spectrum is found to be dominated by the ion-acoustic and ion-ion two-stream instabilities. Detailed comparisons are made with the isotropie case.
Plasma waves in hot relativistic beam-plasma systems. Part 1. Dispersion relations
Authors: Magneville Alain
Published: March 2009

Dispersion relations of plasma waves in a beam–plasma System are computed in the general case where the plasma and beam temperatures, and the; velocity of the beam, may be relativistic. The two asymptotic temperature cases, and different contributions of plasma or beam particles to wave dispersion are considered.
Theory of magnetosonic wave—plateau shocks driven by upper-hybrid waves
Authors: Rao N. N.
Published: March 2009

The existence as well as the structure of magnetosonic wave-plateau shocks driven by upper-hybrid waves in a two-component electron-ion magnetized plasma is analysed. In the incident region the field quantities have a standing-wave structure, whereas in the evanescent region they monotonically reach constant values. The plasma flow velocity undergoes a transition from submagnetosonic (in the evanescent region) to supermagnetosonic (in the incident region) values via the magnetosonic point. The number density (or the magnetic field) across the shock-front region has a steep gradient and connects a rarefaction (under-dense) wave in the incident region to a shelf-like (over-dense) structure in the evanescent region, where the upper-hybrid electric field drops to zero monotonically. For the case of small- but finite-amplitude shocks the detailed structures of the profiles are obtained analytically. For large-amplitude shocks the profiles are computed using numerical methods. An extension of the present theory as well as some possible applications are pointed out.
A thermal instability in the non-relativistic planar magnetron
Authors: Antani S. N. , Kaup D. J. , Thomas G. E.
Published: March 2009

It is well known that an anisotropic temperature distribution gives rise to thermal instability in many Systems. In their numerical simulations of a two-vane, non-relativistic planar magnetron, Thomaset al.reported a temperature anisotropy and a concomitant formation and growth of a swirling electron cloud bunch (convective cell). In this paper we present an analytic calculation of the shift in the eigenfrequencies by treating the thermal effects as a perturbation, while taking due account of the temperature anisotropy. We find the magnitude of the resulting rate to be of the order of that seen in the simulations.
Linear resonant interaction of an electromagnetic wave with a collisional inhomogeneous plasma
Authors: Lacina J.
Published: March 2009

The time evolution to a steady state of the interaction of an obliquely incident P-polarized wave with an inhomogeneous collisional cold plasma is investigated. The two-dimensional numerical solutions presented show that the rate of energy absorption and the amplitude of the magnetic field do not depend on time during this evolution (after a short transient period). Using this important result, a simple analytical two-dimensional model solution for this evolution has been constructed. It is shown that this solution fuliils the energy conservation law and thus describes the transformation of wave energy into oscillatory and thermal energy during this process. An interesting analogy between this process and that of Landau damping follows from the analytic solution.
Variational approach to Langmuir waves described by the Zakharov equations
Authors: Bhakta J. C.
Published: March 2009

Nonlinear modulational instability and the evolution of a pulse that is initially non-solitonic for Langmuir waves described by the Zakharov equations are considered. The average Lagrangian method has been used to derive the nonlinear dispersion relation for Stokes waves. It is found that the region of instability increases with the amplitude of the perturbed Langmuir field. The propagation of the pulse is studied with the help of the Rayleigh-Ritz optimization method. It is noted that the width of the pulse oscillates rapidly for high initial pulse velocity.
Tearing-mode stability in a cylindrical plasma with equilibrium flows
Authors: Wessen K. P. , Persson M.
Published: March 2009

The effect of a sheared equilibrium mass flow on the resistive tearing mode is studied numerically by calculating Δ′. Both stabilizing and destabilizing effects are found, depending on the velocity and magnetic field profiles. Specifically, when q0 ≈ 1, the flow is strongly stabilizing for centrally peaked current profiles, whereas the flow has a strongly destabilizing effect for flatter current profiles. While the extreme effects are more pronounced for larger flows, a smaller flow may have more influence on marginal stability. The case where the flow speed becomes comparable to the Alfvén speed is also examined. It is found that this may lead to the equations being singular at points other than a rational surface, drastically changing the behaviour of the mode.
Nonlinear acoustic waves in partially ionized collisional plasmas
Authors: Rao N. N. , Kaup D. J. , Shukla P. K.
Published: March 2009

Nonlinear propagation of acoustic-type waves in a partially ionized three-component collisional plasma consisting of electrons, ions and neutral particles is investigated. For bidirectional propagation, we show that the small- but finite-amplitude waves are governed by the Boussinesq equation, which for unidirectional propagation near the acoustic speed reduces to the usual Korteweg de Vries equation. For large-amplitude waves, we demonstrate that the relevant fluid equations are integrable in a stationary frame, and we explicitly obtain the parameter values for the existence of finite-amplitude solutions. In both cases, we take into account the different temperatures of the individual species. The relevance of the results to the earth's ionospheric plasma in the lower altitude ranges is pointed out.
Dissipative magnetohydrodynamic states with non-ideal boundary conditions
Authors: Agim Y. Z. , Montgomery D.
Published: March 2009

A driven dissipative magnetohydrodynamic state is calculated that is consistent with a non-ideal boundary condition relevant to magnetically and mechanically active boundaries of laboratory or astrophysical plasmas. The solution is based on the results from previous analytical and computational investigations of electrically driven states, and is characterized by finite helical distortions and a small flow velocity. It is shown that such a configuration may persist even in the absence of previously assumed rigid perfectly conducting boundaries. It is proposed as a model for an astrophysical ‘flux rope’, and suggests an additional in situ diagnostic for such flux ropes.
Electron plasma oscillations at arbitrary Debye lengths
Authors: Lehnert B.
Published: March 2009

A solution is presented for electron plasma oscillations in a thermalized plasma, at arbitrary ratios of the Debye length AλD and the perturbation wavelength λ. The limit λD≪λ corresponds to the conventional fluid-like theory of small particle excursions, whereas λD≫λ corresponds to the free-streaming limit of strong kinetic phase mixing due to large particle excursions. A strong large-Debye-distance (LDD) effect already appears when λD ≳ λ. The initial amplitude of the fluid-like contribution to the macroscopic density perturbation then becomes small compared with the contribution from the free-streaming part. As a consequence, only a small fraction of the density perturbation remains after a limited number of kinetic damping times of the free-streaming part. The present analysis can be considered as a first exercise in an attempt to tackle the far more difficult problem of large-Larmor-radius (LLR) effects in a magnetized plasma. The analysis further shows that a representation in terms of normal modes of the form exp (— iωt) leads to amplitude factors of these modes that are related to each other and that depend on the combined free-streaming and fluid behaviour of the plasma. Consequently, these modes are coupled and cannot be treated as independent of each other.
Numerical simulations of BGK modes
Authors: Demeio Lucio , Holloway James Paul
Published: March 2009

Solutions of the full nonlinear Vlasov–Poisson system for a one-dimensional unmagnetized plasma that correspond to undamped travelling waves near Maxwellian equilibria are analysed numerically using the splitting scheme algorithm. The numerical results are clearly in favour of the existence of such waves and confirm that there is a critical phase velocity below which they cannot be constructed.
Parametric instabilities of circularly polarized large-amplitude dispersive Alfvén waves: excitation of obliquely-propagating daughter and side-band waves
Authors: Viñas Adolfo F. , Goldstein Melvyn L.
Published: March 2009

We investigate the parametric instabilities of a large-amplitude circularly polarized dispersive parallel-propagating Alfvén wave. Our treatment is more general than that of previous derivations based on the two-fluid equations in that we allow for propagation of the unstable daughter and side-band waves at arbitrary angles to the background (DC) magnetic field. We present the characteristics of the decay and modulational instabilities as functions of propagation angle. We find, in addition to the well-known decay and modulational instabilities, that at oblique and perpendicular propagation there is another parametric instability, namely the filamentation instability, which is characterized by a broad band-width in wavenumber and which satisfies the condition Re (ω) ≪ γ. A second parametric process at oblique and perpendicular angles of propagation, which has not been reported before is also investigated, namely the parametric magneto-acoustic instability. This instability is distinct from the filamentation instability in that it is characterized by density perturbations with large real frequencies that satisfy the condition Re (ω) ≫ γ. Unlike the filamentation instability, the magneto-acoustic instability extends over a broad angular range, but has a very narrow band-width in wavenumber. We report the dispersive characteristics of the filamentation and magneto-acoustic instabilities as functions of plasma β dispersion η and pump amplitude η for arbitrary propagation angles.
Theory of nonlinear interaction of particles and waves in an inverse plasma maser. Part 2. Stationary solution and evolution of initial distributions
Authors: Krivitsky Victor S. , Vladimirov Sergey V.
Published: March 2009

The evolution of the distribution function due to the simultaneous nonlinear interaction of plasma particles with resonant and non-resonant waves is studied. A stationary particle distribution resulting from a balance of the quasi-linear interaction and the nonlinear one is found. The temporal evolution of an initial δ-function-shaped distribution (like a ‘beam’) is examined in the one-dimensional case. General formulae are obtained for stochastic particle acceleration (taking account of the nonlinear interaction studied here).
On the decay of a dipole pump wave to half-harmonics
Authors: Heikkinen J. A. , Pättikangas T. J. H. , Devillers G.
Published: March 2009

Starting from a three-wave interaction coefficient for a homogeneous Vlasov plasma, we show that the parametric decay to half-harmonics has zero growth rate if the wavenumber of the pump wave vanishes. Earlier proofs of this fact for electrostatic decay modes are thus extended for a general case. As a specific example, we study the decay of a fast magnetosonic wave to two slow waves.
Observations of low-frequency oscillations during relativistic-electron-beam-plasma interactions
Authors: Paithankar A. S. , Gupta G. P.
Published: March 2009

During propagation of a relativistic electron beam in hydrogen gas at sub-torr pressures using a foil-less diode, low-frequency oscillations in the megahertz range are observed in the net current wave forms, and continue even after passage of the beam. The novel feature of the experiment is that both beam generation and propagation take place in the same low-pressure regime, and hence the beam parameters are functions of gas pressures. Analysis of the experimental results shows that the low-frequency oscillations result from the resistive-hose instability.
On the existence of ion-acoustic double layers in negative-ion plasmas
Authors: Baboolal S. , Bharuthram R. , Hellberg M. A.
Published: March 2009

It is well known that ion-acoustic double layers occur in plasmas containing two-temperature electron species and positive ions. In a recent study Verheest suggested that such structures can occur when there is only one electron species but both negative and positive ion species. There a stationary modified Korteweg de Vries equation was derived to support his deduction. This prediction, however, contradicts our own arbitrary-amplitude studies, which also cover the Verheest parameter regime. Here we resolve the discrepancy by examining both approaches in the pseudo-potential formulation in more relevant detail. The implications of this study extend beyond the realm of the present subject.
The effect of cosmic rays on the instability of a tangential discontinuity
Authors: Chalov S. V.
Published: March 2009

The Kelvin-Helmholtz instability of a tangential velocity discontinuity in a plasma flow when cosmic-ray pressure is taken into account is studied. It is shown that a new unstable mode can exist. This appears when an effective Mach number exceeds some critical value. In the case of strong flow mediation by cosmic rays the wave vectors of the most-unstable waves are directed along the plasma velocity vector for both subsonic and supersonic flows.
Resistive tearing-mode instability in a current sheet with equilibrium viscous stagnation-point flow
Authors: Phan T. D. , Sonnerup B. U.Ö.
Published: March 2009

An analysis is presented of linear stability against tearing modes of a current sheet formed between two oppositely magnetized plasmas forced towards each other in two-dimensional steady stagnation-point flow. The velocity vector in this flow is confined to planes perpendicular to the reversing component of the magnetic field. The unperturbed state is an exact resistive and viscous equilibrium in which the resistive diffusion outwards from the current sheet is exactly balanced by the inward motion associated with the stagnation-point flow. Thus the behaviour of the tearing mode can be examined even when the resistive diffusion time is comparable to or smaller than the growth time of the instability. The linear ordinary differential equation describing the mode structure is integrated numerically. For large Lundquist number S and viscous Reynolds number Re the Furth-Killeen-Rosenbluth scaling of the growth rate is recovered with excellent accuracy. The influence of the stagnation-point flow on the tearing mode is as follows: (i) long-wavelength perturbations are stabilized so that the unstable regime falls between a short-wavelength and a long-wavelength marginal state; (ii) for sufficiently low Lundquist number (S < 12.25) the current sheet is completely stable to tearing-mode perturbations; (iii) the presence of high viscosity reduces the growth rate of the tearing instability. This effect is more important at small wavelength. Finally, application of the results from this study to the problem of solar-wind plasma flow past the earth's magnetosphere is briefly discussed.
Resistive evolution of a force-free plasma to equilibrium
Authors: Gill A. S. , Laing E. W.
Published: March 2009

Using the magnetohydrodynamic model, the evolution of a resistive plasma can be represented as a relaxation through a sequence of force-free equilibrium states. We show, by extending existing work, that this process is equivalent to magnetic field diffusion in a strongly anisotropie static conductor. The latter evolution is easier to simulate numerically, and is carried out for laboratory based plasmas confined in cylinders and toroids. We obtain a variety of universal equilibrium profiles that are consistent with experiment and relaxation theory and that predict the existence of states arising in reversed-field pinches. The existence of a critical axial flux is predicted about which there exist stable modes of operation corresponding to high and low current. We also show the existence of a critical aspect ratio at which it is most desirable to build toroidal devices. This corresponds to the value at which maximum current, for a fixed driving field, can be generated.
Second-harmonic excitation of a Gould—Trivelpiece mode in a beam-plasma system
Authors: Praburam G. , Sharma A. K.
Published: March 2009

A Gould-Trivelpiece mode at significant power levels is excited in a cylindrical beam-plasma system by launching an external signal. The fundamental mode excites a second-harmonic wave in the upper-hybrid mode. When the second-harmonic frequency is close to (where is the upper-hybrid frequency), considerable enhancement in the second-harmonic power level is observed. The results are interpreted using a slab model.
An action principle for the Vlasov equation and associated Lie perturbation equations. Part 1. The Vlasov—Poisson system
Authors: Larsson Jonas
Published: March 2009

A new action principle determining the dynamics of the Vlasov–Poisson system is presented (the Vlasov–Maxwell system will be considered in Part 2). The particle distribution function is explicitly a field to be varied in the action principle, in which only fundamentally Eulerian variables and fields appear. The Euler–Lagrange equations contain not only the Vlasov–Poisson system but also equations associated with a Lie perturbation calculation on the Vlasov equation. These equations greatly simplify the extensive algebra in the small-amplitude expansion. As an example, a general, manifestly Manley–Rowesymmetric, expression for resonant three-wave interaction is derived. The new action principle seems ideally suited for the derivation of action principles for reduced dynamics by the use of various averaging transformations (such as guiding-centre, oscillation-centre or gyro-centre transformations). It is also a powerful starting point for the application of field-theoretical methods. For example, the recently found Hermitian structure of the linearized equations is given a very simple and instructive derivation, and so is the well-known Hamiltonian bracket structure of the Vlasov–Poisson system.
Steady-state self-focusing of rippled laser beams in plasmas: arbitrary nonlinearity
Authors: Sodha M. S. , Konar S. , Maheshwari K. P.
Published: March 2009

This paper presents an analysis of the self-focusing of a rippled Gaussian laser beam in a plasma when the nonlinear part of the effective dielectric constant is arbitrarily large. Considering the nonlinearity to arise from ponderomotive, collisional or thermal-conduction phenomena and following the approach of Akhmanov, Sukhorukov and Khokhlov (which is based on the WKB and paraxial-ray approximation) the phenomenon of self-focusing of rippled laser beams is studied for arbitrary magnitude of nonlinearity. For ponderomotive and collisional nonlinearities, the present theory leads to two values of the critical power for self-focusing of the beam, Pcrl and Pcr2, which depend on the amplitudes and phase difference of the main beam and the ripple. When the beam power P lies between the two critical values (i.e. Pcr1 < P < Pcr2), the medium behaves as an oscillatory waveguide; the beam first converges and then diverges, again converges, and so on. For P < Pcr2, the beam first diverges, then converges, then diverges, and so on. When thermal conduction is the dominant mechanism of nonlinearity of the dielectric constant, only one value of the threshold critical power Pcr for self-focusing of the beam exists. When the beam power P < Pcr, the medium behaves as an oscillatory waveguide.
On driven, dissipative, energy-conserving magnetohydrodynamic equilibria
Authors: Goodman† Michael L.
Published: March 2009

A cylindrically symmetric, electrically driven, dissipative, energy-conserving magnetohydrodynamic equilibrium model is considered. The high-magnetic-field Braginskii electron electrical resistivity η parallel to a constant axial magnetic field B and ion thermal conductivity ĸ perpendicular to B are included in an energy equation and in Ohm's law. The expressions for η and ĸ depend on number density and temperature, which are functions of radius that are obtained as part of the equilibrium solution. The model has plasma-confining solutions, by which are meant solutions characterized by the separation of the plasma into two regions separated by a relatively thin transition region that is an internal boundary layer across which temperature and current density vary rapidly. The inner region has a temperature, pressure and current density that are much larger than in the outer region. The number density and thermal conductivity attain their minimum values in the transition region. The model has an intrinsic value of β, about 6.6%, which must be exceeded in order that a plasma-confining solution exist. The model has an intrinsic length scale, which, for plasma-confining solutions, is a measure of the thickness of the transition region separating the inner and outer regions of plasma. A larger class of transport coefficients is modelled by artificially changing η and ĸ by changing the constant coefficients ηO and ĸO that occur in their expressions. Increasing ĸO transforms a state that does not exhibit confinement into one that does, improves the confinement in a state that already exhibits it, and leads to an increase in ĸ in the confined region of plasma. The improvement in confinement consists in a decrease in the thickness of the transition region. Decreasing ηO subject to certain constraints, also transforms a state that does not exhibit confinement into one that does, improves the confinement in a state that already exhibits it, and leads to a decrease in η in the confined region of plasma. Increasing ηO up to a critical point increases the current, temperature, and volume of the confined region of plasma, and causes the thickness of the transition region to increase. If ηO is increased beyond the critical point, a plasma-confining state cannot exist. In all cases it is found that an increase in ĸ and a decrease in η in the confined region of plasma are associated with an improvement in the confinement properties of the equilibrium state. If the pressure and temperature are given on the cylinder wall, the equilibrium bifurcates when the electric field decreases below a critical value. The equilibrium can bifurcate into a state that exhibits confinement and a state that does not.
Effect of large Larmor radius on the stability of an infinitely conducting inhomogeneous plasma
Authors: Kumar Nagendra , Srivastava Krishna M. , Kumar Vinod
Published: March 2009

The effect of a large Larmor radius on the stability of an infinitely conducting infinitely extended inhomogeneous plasma with two-dimensional magnetic field has been studied. A dispersion relation is obtained for the homogeneous system, and it is found that it is stable and MHD waves propagate. For an inhomogeneous plasma, a dispersion relation is also obtained and discussed for disturbances propagating transverse to inhomogeneity in (a) a cold plasma and (b) an incompressible plasma. It is found that the inhomogeneous system is unstable in both the cases, in agreement with the results of Lee and Roberts. The values of ωr and ωi are computed numerically, and the variations of ωi>0 and the corresponding ωr with the large-Larmor-radius parameter are shown graphically.
Lagrangian description and entropy of magnetic Vlasov systems
Authors: Minardi E.
Published: March 2009

In this paper we study the relation between the collective magnetic entropy of the Vlasov systems, introduced previously on a phenomenological basis, and the Lagrangian description of the motion of a system of independent particles in a magnetic field, subject to a constraint that introduces collective behaviour. The main result is the equivalence of the first variations of the action integral and of the collective entropy with respect to a certain family of variations of the Lagrangian co-ordinates corresponding to reversible variations of the collective system considered as isolated. In the case of irreversible transformations the collective entropy is not determined dynamically, but acquires its meaning through the procedure of maximum probability assignment according to the standard formalism of information theory, under the requirement of macroscopic reproducibility.
Second-order oscillations of a Vlasov–Poisson plasma in Fourier-transformed velocity space
Authors: Sedláček Zdeněk , Nocera Luigi
Published: March 2009

We study the Vlasov–Poisson system of equations in Fourier-transformed velocity space. First we reformulate some results of the linear theory: in the new representation the van Kampen–Case eigenmodes are found to be ordinary functions with convenient continuity properties. We give a transparent derivation of the free-streaming temporal echo in terms of the kinematics of wave packets in Fourier-transformed velocity space. We further extend this analysis to include Coulomb interactions, which allows us to establish a connection between the echo theory, the second-order oscillations of Best and the phenomenon of linear side bands. The calculation of the time evolution of the global second-order electric field is performed in detail in the case of a Maxwellian equilibrium distribution function. We conclude that the phenomenon of linear side bands may be properly explained in terms of the intrinsic features of the equilibrium distribution function.
Generation of large-amplitude plasma wakefields with low phase velocities by an intense short laser pulse
Authors: Murusidze I. G. , Tsintsadze L. N.
Published: March 2009

The generation of nonlinear plasma waves with arbitrary phase velocities by an intense laser pulse is considered in order to determine the dependence of the maximum amplitude of driven waves on the group velocity of the laser pulse (or the phase velocity of excited wakefields). Analytical as well as numerical studies of the problem are carried out within the so-called quasi-static approximation. In the case of square-shaped laser pulses the analytical expression for the maximum amplitude as a function of the pump amplitude and the phase velocity is derived. The numerical analysis in the case of Gaussian pulses confirms the result that follows from the analytical formula: the lower the phase velocity of the wakefleld, the greater is its maximum amplitude for a given amplitude of the driving pulse.
A time-dependent model of magnetic field annihilation
Authors: Heyn Martin F. , Pudovkin Mikhail I.
Published: March 2009

Quasi-periodic variations in the electric field intensity near the dayside magnetopause are studied within a planar, dissipative MHD model of a stagnation-line flow embedded in a rectilinear magnetic field. The model is based on an exact time-dependent solution of the resistive MHD equations applied to a Parker-type diffusion region of field-line merging. The results lead to the prediction of certain relations between physical parameters of the solar- wind plasma, and these are compared with actual measurements.
Effect of collisions on the nonlinear mixing of electromagnetic waves in plasmas
Authors: Stenflo L.
Published: March 2009

We consider the plasma heating nonlinearities that are important in many wave-interaction processes. By means of some simple examples, we analyse the nonlinear terms originating from the collision integral for a weakly collisional plasma. As a result, it turns out to be necessary to generalize the collisional Zakharov equations by including the contribution from the non-diagonal part of the pressure tensor. A new system of equations is thus presented.
An action principle for the Vlasov equation and associated Lie perturbation equations. Part 2. The Vlasov–Maxwell system
Authors: Larsson Jonas
Published: March 2009

An action principle for the Vlasov–Maxwell system in Eulerian field variables is presented. Thus the (extended) particle distribution function appears as one of the fields to be freely varied in the action. The Hamiltonian structures of the Vlasov–Maxwell equations and of the reduced systems associated with small-ampliltude perturbation calculations are easily obtained. Previous results for the linearized Vlasov–Maxwell system are generalized. We find the Hermitian structure also when the background is time-dependent, and furthermore we may now also include the case of non-Hamiltonian perturbations within the Hamiltonian-Hermitian context. The action principle for the Vlasov–Maxwell system appears to be suitable for the derivation of reduced dynamical equations by expanding the action in various small parameters.
The drift-wave dispersion equation revisited
Authors: Balescu R. , Eijnden E. Vanden , Weyssow B.
Published: March 2009

In view of some difficulties that appeared in previous work, the drift-wave dispersion equation has been studied in great detail by stressing some features that are not discussed in the usual textbook presentations. It is shown that any analytical approximation of a plasma dispersion equation leads to a singular perturbation problem for the roots of an algebraic equation. This property is associated with a number of parasitic roots, which can be identified and eliminated from the start. The behaviour of the remaining physical roots is discussed in detail by defining characteristic regions in the parameter space spanned by the gradients of density, electron and ion temperatures. Whereas in a large domain the usual behaviour predicted by elementary drift-wave theory is recovered, it is shown that there exists a region (whose existence is not predicted by elementary theory), where the conditions of existence of a drift wave are violated, thus causing the appearance of the (spurious) singularity previously found by Balescu. The explanation of this paradoxical situation is discussed in detail. The smooth connection of these results with the limit of a spatially homogeneous plasma is considered in an appendix.
Higher harmonics and longitudinal momentum in the stochastic interaction of magnetized electrons and ordinarily polarized modes
Authors: Corso G. , Rizzato F. B.
Published: March 2009

In this work we investigate the nonlinear dynamical interaction of magnetized electrons and ordinarily polarized electromagnetic modes. We show that when either the mode amplitude is sufficiently large or the electronic longitudinal momentum along the external magnetic field is sufficiently small, non-integer harmonics originating from higher-order terms in the expansion of the Hamiltoniari in powers of the electromagnetic field become important, and the relevant action-angle phase space ceases to be well described by standard nonlinear pendulum approximations. We develop appropriate resonance overlap studies in order to determine the conditions to be satisfied at the transition from regular to chaotic orbits, checking the accuracy of the results with numerical integrations of the full dynamical equations. We verify that chaotic orbits occur within a ‘window’ among the possible values of the longitudinal momentum. The width of this window and the degree of overlap between neighbouring resonances within it are both shown to grow with particle action and wave frequency. We also show that once overlap has occurred for a particular value of the action, it persists for larger values of this quantity, a circumstance that leads to a large amount of particle energization.
Conditions for the existence of strong double layers
Authors: Jelić N. , Čerček M. , Stanojević M. , Gyergyek T.
Published: March 2009

We present the results of a theoretical investigation of the conditions for the existence of a stationary, strong, monotonic double layer. A model that includes finite temperatures both of the particle species accelerated by the double layer and of those reflected by it is developed on the basis of the general theory of double layers due to Andrews and Allen. A numerical solution of the model equations is presented and analysed. Explicit approximate formulae for the electron-to-ion current ratio (i.e. the Langmuir factor) and for the initial velocities (i.e. directional energies of the accelerated particles at the double-layer boundaries before acceleration) are also derived that fit almost exactly the exact numerical solution over a wide range of double-layer potentials. It is shown that in the cases in which the standard results of Langmuir and Bohm are an oversimplification, approximate formulae may be used instead of exact numerical solutions to obtain quite accurate results in a simple manner.
Relaxation of collisionless plasmas
Authors: Wiechen H. , Ziegler H. J.
Published: March 2009

We present a new theory for the relaxation of two-dimensional collisionless quasi-neutral plasmas by mixing in phase space. In general, mixing in phase space does not lead to equilibrium states in the framework of exact, collisionless theory. However, filamentation on smaller and smaller scales can result in stationary states from a macroscopic (coarse-grained) point of view. In a first step we discuss a general technique to calculate suitably stable equilibria of collisionless plasmas. In a second step we develop a model relaxation that yields a simple transition to a description on macroscopic scales without following the details of the complicated mixing dynamics. Combination of both results allows calculation of final states of collisionless relaxation. We illustrate our approach with the help of a one-dimensional sheet configuration as a simple example.
Nonlinear wave interactions in two-electron-temperature plasmas
Authors: Hanssen A. , Pécseli H. L. , Stenflo L. , Trulsen J.
Published: March 2009

Dynamical equations are derived for the evolution of weakly nonlinear electron plasma waves when the electron distributions are characterized by more than one temperature component. The presence of electron-acoustic modes in multi- temperature plasmas opens a new decay channel. By considering an explicit example, it is demonstrated that these distributions imply significant modifications of the standard models for the decay spectrum of electron plasma waves. In particular, long-wavelength Langmuir waves can decay to shorter wavelengths. The results can have implications for ionospheric heating experiments.
Possible beneficial ponderomotive force effects on fast-wave coupling in tokamaks
Authors: Petržílka V. A.
Published: March 2009

At lower-hybrid frequencies in tokamaks, ponderomotive forces at fast-wave launching typically lead in the vicinity of the launching structure to a boundary plasma density increase. This results in a decrease in the reflection coefficient, and, in detached plasmas, to the appearance of a local electric field maximum at several centimetres from the launching grill structure; this electric field maximum is connected to the reversal of the plasma density gradient near the grill mouth because of ponderomotive force effects.
Nonlinear Kelvin—Helmholtz instability in magnetic fluids of finite thickness: effects of a tangential magnetic field
Authors: Elhefnawy Abdel Raouf F.
Published: March 2009

The nonlinear stability of a horizontal interface separating two streaming magnetic fluids of finite thickenss is investigated in two dimensions. The fluids are considered to be inviscid and incompressible. The magnetic field is applied along the direction of streaming. The method of multiple scales, in both space and time, is used to examine the stability properties of the system arising from second-harmonic resonance. A pair of partial differential equations for the amplitude of the wave and its second harmonic are derived. These describe the evolution of the wave train up to cubic order, and may be regarded as the counterparts of the single nonlinear Schrödinger equation that occurs in the non-resonant case. The stability condition of this equation is discussed both analytically and numerically, and stability diagrams are obtained. Regions of stability and instability are identified. The nonlinear cut-off wavenumber separating the regions of stability from those of instability is obtained. The equation governing the evolution of the amplitude at the critical point is also obtained, which leads to a nonlinear Klein—Gordon equation.
Tokamak divertor maps
Authors: Punjabi Alkesh , Verma Arun , Boozer Allen
Published: March 2009

A mapping method is developed to investigate the problem of determination and control of heat-deposition patterns on the plates of a tokamak divertor. The deposition pattern is largely determined by the magnetic field lines, which are mathematically equivalent to the trajectories of a single-degree-of-freedom time-dependent Hamiltonian system. Maps are natural tools to study the generic features of such systems. The general theory of maps is presented, and methods for incorporating various features of the magnetic field and particle motion in divertor tokamaks are given. Features of the magnetic field include the profile of the rotational transform, single- versus double-null divertor, reverse map, the effects of naturally occurring low M and N, and externally imposed high-M, high-N perturbations. Particle motion includes radial diffusion, pitch angle and energy scattering, and the electric sheath at the plate. The method is illustrated by calculating the stochastic broadening in a single- null divertor tokamak. Maps provide an efficient, economic and elegant method to study the problem of motion of plasma particles in the stochastic scrape-off layer.
Toroidal equilibrium of rotating plasma with adiabatic constraints
Authors: Gałkowski A. , Żelazny R.
Published: March 2009

A numerical technique, alternative to Grad's well-known ADM method has been proposed to deal with the slow adiabatic evolution of a toroidal plasma with flow. The equilibrium problem with prescribed adiabatic constraints may be solved by simultaneous calculations of flux surface geometry and original profile functions. Implications for the problem of bifurcation due to nonlinearity of the governing equations are discussed. In the case of field-aligned sub-Alfvénic flow the system is in the second elliptic regime if β <A2/(1 –A2) at the magnetic axis, whereAis the Mach Alfvén number of the flow. Super-Alfvénic flows do not satisfy the local firehose stability criterion.
A Fourier-space description of oscillations in an inhomogeneous plasma. Part 2. Discrete approach
Authors: Cally P. S. , Sedláček Z.
Published: March 2009

The process of phase mixing in inhomogeneous MHD or cold plasmas is interpreted as one of energy propagation in discrete Fourier space. Three instructive scenarios are examined: (i) an isolated inhomogeneity with zero boundary conditions; (ii) a periodic inhomogeneity; and (iii) a monotonic inhomogeneity sandwiched between two semi-infinite uniform regions. In each case the coefficients of the associated wave equation in Fourier space for an appropriately chosen dependent variable are very nearly constant almost everywhere, so the propagation is like that of a free unreflected wave. An exception may arise in the coupling of the lowest modes, which can be highly reflective. It is argued that Fourier space is the simplest and most natural context in which to discuss the development of fine-scale oscillations.
Axial structure of surface-wave-sustained discharges influenced by local plasma resonances
Authors: Aliev Yu. M. , Maximov A. V. , Schlüter H. , Shivarova A.
Published: March 2009

The influence of absorption of wave energy in regions of local plasma resonances in inhomogeneous (in the transverse direction) plasmas on the axial structure of discharges sustained by surface waves is studied analytically. The two regimes of charged-particle loss, namely diffusion- and recombinationcontrolled regimes, are considered. First, to extract the basic features of the phenomena, the discharge is modelled by a slab configuration and the case of slow surface-wave propagation is investigated. It is shown that it is resonant absorption that determines the properties of the discharge in the region towards its end. In the case of a cylindrical waveguide, which is the real configuration in experiments, the influence of the mechanism of resonant absorption is studied in both regions of fast and slow surface-wave propagation. With respect to the discharge behaviour, these cases correspond respectively to the regions at the beginning of the discharge close to the surface-wave launcher and at the discharge end.
Anomalous temperature relaxation and particle transport in a strongly non-unifrom, fully in ionized Plasma in a stromg mangnetic field
Authors: Øien Alf H.
Published: March 2009

In classical kinetic and transport theory for a fully ionized plasma in a magnetic field, collision integrals from a uniform theory without fields are used. When the magnetic field is so strong that electrons may gyrate during electron—electron and electron—ion interactions, the form of the collision integrals will be modified. Another modification will stem from strong non-uniformities transverse to the magnetic field B. Using collision terms that explicitly incorporate these effects, we derive in particular the temperature relaxation between electrons and ions and the particle transport transverse to the magnetic field. In both cases collisions between gyrating electrons, which move along the magnetic field, and non-gyrating ions, which move in arbitrary directions at a distance transverse to B from the electrons larger than the electron Larmor radius but smaller than the Debye length, give rise to enhancement factors in the corresponding classical expressions of order In (mion/mel).
Simple magnetohydrodynamic waves
Authors: Mann G.
Published: March 2009

Large-amplitude magnetic field fluctuations often accompanied by density variations are frequently observed in front of the earth's bow shock and in the vicinity of comets by extraterrestrial in situ measurements. They are identified as a manifestation of magnetohydrodynainic (MHD) waves in space plasmas. Because of their large amplitudes (i.e. because the magnetic field amplitude is of the order of the ambient magnetic field, for instance), these fluctuations cannot be satisfactorily described by linear wave theory. In this paper the properties of one-dimensional MHD waves of arbitrary amplitude, i.e. so-called simple MHD waves, are investigated, and a relationship is derived between the enhancement of the magnetic field and the density as well as the propagation velocity. Fast large-amplitude magnetosonic waves exhibit wave steepening. Here the dependence of the steepening time on the wave amplitude is derived and illustrated numerically.