bluuebunny/crossref_metadata_2025 huggingface dataset:
Stability of parallel flow of a multi-component cylindrical plasma to electrostatic perturbations
Authors: Lucas R.
Published: March 2009

Sufficient conditions for the stability of parallel flow of a warm N-component cylindrical plasma to electrostatic perturbations are obtained. In the unperturbed state the jth plasma component is assumed to have axial velocity Vj0(r), r being the radial co-ordinate, and the equilibrium quantities are permitted to be arbitrary functions of r consistent with the zeroth-order equations. The L2-norms of certain system variables are shown to be bounded uniformly in time. Circle theorems are obtained for the complex eigenfrequencies of any normal mode.
Nonlinear electrostatic waves: oblique propagation
Authors: Jackson R. W.
Published: March 2009

The fluid equations for electrostatic wave forms propagating at small angles to a constant magnetic field are investigated. Both ion cyclotron and charge separation effects are included. Numerical results are given for initial conditions which are consistent with soliton formation. These results show a hybrid nonlinear wave form containing oscillations which are identified as short-wavelength fast ion-acoustic waves and long-wavelength slow ion-acoustic waves. An approximate analytic analysis is performed using the Bogoliubov–Krylov–Mitropolskii perturbation method.
A quasi-moment description of the evolution of an electron gas towards a state dominated by a reduced transport equation
Authors: Øien Alf H.
Published: March 2009

For electrons in electric and magnetic fields which collide elastically with neutral atoms or molecules, a minute evolution study is made using the multiple time-scale method. In this study a set of quasi-moment equations is used which is derived from the Boltzmann equation by taking appropriate quasi-moments, i.e. velocity moments where the integration is performed only over velocity angles. In a systematic way we reveal the evolution in a transient regime where processes take place on time-scales related to the electron–atom collision frequency and electron cyclotron frequency and show how the evolution enters a regime where it is governed by a reduced transport equation. This work has relevance to the theory of evolution of gases of charged particles in general and to non-neutral plasmas and partially ionized gases in particular.
The mean electromotive force generated by random Alfvén waves in a coffisionless plasma
Authors: Namikawa Tomikazu , Hamabata Hiromitsu
Published: March 2009

The mean electromotive force and ponderomotive force generated by nonlinear random Alfvén waves propagating along the mean magnetic field and linear random Alfvén waves propagating in arbitrary directions in a collisionless plasma are calculated by use of Fourier analysis methods. It is shown that the a-effect can exist in the interaction between two different waves and that the magnetic turbulent diffusivity can be negative depending on the energy spectrum functions of the initial values of the magnetic and velocity perturbations. The results are applied to the substorms in the Earth's magnetosphere.
Ion turbulence and thermal transport in laser-produced plasmas
Authors: Barr H. C. , Boyd T. J. M.
Published: March 2009

In the interaction of high-intensity lasers with target plasmas the transport of thermal enelgy from the region in which the radiation is absorbed, to the cold dense plasma in the interior of the target, is an issue of central importance. It is also one of great complexity and as such is still largely unresolved. Ion-acoustic turbulence, self-generated magnetic fields and the inadequacy of classical transport theory have all been widely canvassed by way of explaining the observations which show thermal transport much reduced below what would be expected from conventional arguments.

In this paper the role of ion turbulence as a flux limiter is addressed with particular regard to recent experiments in which target plasmas were irradiated by 1·06 µm neodymium laser light at irradiances of 1015W cm−2 and greater. Saturation levels of the ion-acoustic turbulence driven by a combination of a suprathermal electron current and a heat flux have been calculated on the basis of perturbed orbit theory.

The levels of turbulence are found to be markedly lower than those commonly estimated from simple trapping arguments and too low to explain the thermal flux inhibition observed in the experiments used as a basis for the model.
Models of laser-plasma ablation
Authors: Pert G. J.
Published: March 2009

Dimensional analysis is used to predict the functional relationships amongst the characteristic variables of the ablation of a cold dense fluid by an imposed external heat source. From these relations, self-similar limiting forms are identified and evaluated. Numerical simulation is used to investigate the interpolation between these limits. Self-similar forms generalizing well-known existing solutions of relevance to laser-plasma are demonstrated and include a general proof of Nemchinov's hypothesis for the heating of small targets of limited mass.
Effects of particle trapping on distortion of the distribution function of RF-heated minority ions in a tokamak plasma
Authors: Anderson D. , Lisak M.
Published: March 2009

The effect of toroidal geometry upon the distribution function of weakly RF-heated minority ions in a tokamak plasma is considered. An analytic scheme to solve the corresponding bounce-averaged Fokker-Planck equation is developed and explicit solutions are given in the limits of high and low velocities. It is found that trapped-particle effects may significantly reduce the RF-induced anisotropy in the distribution function.
Ohm's law for mean magnetic fields
Authors: Boozer A. H.
Published: March 2009

The magnetic fields associated with plasmas frequently exhibit small-amplitude MHD fluctuations. It is useful to have equations for the magnetic field averaged over these fluctuations, the so-called mean field equations. Under very general assumptions, it is shown that the effect of MHD fluctuations on a force-free plasma can be represented by one parameter in Ohm's law, which is effectively the coefficient of electric current viscosity.
On the stability of hydromagnetic flow
Authors: Lucas R. J.
Published: March 2009

The linear stability of steady flow of an inhomogeneous, incompressible hydromagnetic fluid is considered. Circle theorems which provide bounds on the complex eigenfrequencies of the unstable normal modes are obtained. Sufficient conditions for stability follow in a number of special cases.
Scattering of relativistic electron beams in a plasma by beam-induced waves and magnetic field errors
Authors: Benford Gregory
Published: March 2009

Relativistic electron beams propagating in plasma broaden as electric and magnetic fields scatter them. We calculate the beam spreading expected from errors in the ambient magnetic field, and from both electrostatic and magnetic waves generated by the beam itself. All these effects can be important in contemplated experimental regimes. Beam expansion can serve to set limits on the strength, size and phase velocity of caviton waves. Beam-driven magnetic waves can scatter beams effectively even if applied field errors are small. This can affect schemes for transport of beams in inertial fusion, and plasma heating schemes.
Electron cyclotron waves: dispersion and accessibility conditions in isotropic and anisotropic plasmas
Authors: Robinson P. A.
Published: March 2009

Dispersion and accessibility conditions for electron cyclotron waves are investigated for arbitrary weakly relativistic plasmas and for specific isotropic and loss-cone distributions. The transition between the cold plasma and vacuum dispersion relations is investigated as a function of temperature and density. The behaviour of mode structure (including mode coupling), cut-offs and resonances are also examined. Generalizations are obtained of earlier results which indicate that access by extraordinary waves to regions nearthe cyclotron layer from the low-field side is easier in weakly relativistic plasmas than predicted by cold plasma theory because of a reduction in the cut-off frequency of the fast extraordinary mode. This effect is found to be more pronounced in loss-cone distributions than in isotropic distributions, permitting access at temperatures considerably lower than those predicted in the isotropic case. Extra loss-cone modes are found to appear near the cyclotron frequency in loss-cone plasmas which also exhibit instabilities near the cyclotron harmonics.
Kelvin-Helmholtz instabilities of supersonic, magnetized shear layers
Authors: Choudhury S. Roy
Published: March 2009

The linear stability of finite-thickness, compressible, ideal magnetohydrodynamic sheared flows along the z direction, with a magnetic field in the (y, z) plane is studied. This paper extends earlier work with the magnetic field parallel to the flow. The present formulation also includes the effects of density and pressure gradients in the equilibrium shear layer. Analytical solutions are obtained for strongly and weakly magnetized shear layers having a vortex sheet profile (where the velocity is a step function). For an equilibrium layer having a linear velocity profile, and uniform pressure and density, contour plots of the real and imaginary parts of the perturbation frequency (corresponding to unstable waves) are numerically generated in (wavenumber, Mach number) plane using a shooting technique. The structure of two distinct regimes of instability (unstable standing modes and unstable travelling modes) is mapped out for various values of the inverse plasma beta, and various angles of propagation of the mode to the flow and the magnetic field.
Acceleration and heating in quasi-linear diffusion
Authors: Rypdal K.
Published: March 2009

Quasi-linear diffusion of charged particles due to a stationary and homogeneous spectrum of electrostatic field fluctuations is investigated via a Fokker-Planck approach. The energy of a given distribution of test particles is found to be conserved whenever the wave spectrum is isotropic and none of the spectral components of the field has a phase speed that equals the speed of any test particle. Quite generally, the energy is monotonically increasing for isotropic spectra. An interesting quantum mechanical interpretation of these results is given, and the special case of beam evolution in an isotropic spectrum of non-dispersive waves is studied in some detail. Conditions for isotropization of directed electron and ion beams from Coulomb collisions and collective oscillations are discussed in the context of the quasi-linear description. Some promising results from a beam-plasma experiment are quoted.
Stimulated Brillouin scattering of an Alfvén wave in low-density plasmas
Authors: Jain K. M. , Bose Mridul , Guha S. , Tewari D. P.
Published: March 2009

The stimulated Brillouin scattering of Alfvén waves is studied in low-density plasmas. It is shown that ion-sound oscillations may be excited by this mechanism under suitable ionospheric conditions and that the presence of negative ions reduces the probability of such excitations.
New terms in MHD equations and their implications for the inertial confinement fusion concept
Authors: Auluck S. K. H.
Published: March 2009

The MHD equations are rederived without neglecting the electron inertia and new terms are obtained. The revised equations predict that strong magnetic fields are spontaneously generated even in an ideally symmetric ICF implosion in contrast to the conventional theory where an ideal ICF implosion is considered to be free of magnetic fields. The dynamics of the implosion is found to be governed by the space-time structure of the magnetic field. Departures from neutrality are taken into account and an explicit equation is obtained for the evolution of the charge density. The complexity of the implosion problem is illustrated with reference to cylindrical and spherical geometries. The existence of this effect has been verified in the case of a Z-pinch. Experiments can be devised to detect it in existing ICF installations. It is suggested that scientific breakeven may be achieved using existing installations if the targets are optimized in accordance with the present theory.
Nonlinear excitation of electron-acoustic waves
Authors: Saleem H. , Murtaza G.
Published: March 2009

It is shown that for a plasma with ion temperature greater than electron temperature, an extraordinary electro-magnetic pump wave can parametrically decay into upper-hybrid and electron-acoustic oscillations. The threshold power flux and the growth rate of the instability are obtained. Comparison of our investigation with an earlier work and its possible application to a mirror machine is pointed out.
Nonlinear aspects of collective, electromagnetic interactions in magnetized plasmas with anisotropic protons and isotropic alpha particles
Authors: Cuperman S. , Ofman L. , Dryer M.
Published: March 2009

We use computer simulation experiments to investigate the nonlinear behaviour of plasmas with a mixture of anisotropic protons and isotropie alpha particles, embedded in a static magnetic field. Specifically, we study the linearly predicted ‘stop-band’ for the propagation of the proton-produced electromagnetic ion cyclotron waves in conjunction with the energization of the heavier ions by the same waves. For this, three cases are considered: (1) proton + electron plasma; (2) proton + electron + cold alpha particle plasma, and (3) proton + electron + warm alpha particle plasma. Among the main results obtained we mention the following, (a) In the presence of significant relative He2+ concentrations (either cold or warm) all proton-produced left-polarized waves having frequencies above the alpha-particle gyrofrequency are practically suppressed, during the entire nonlinear evolution of the system, indicating that particle–wave–particle interactions are confined to the low-frequency branch of the waves, (b) The ‘remnant’ wave energy, i.e. that part of the wave energy not transferred to the particles, decreases significantly when going from case 1 to case 3. (c) Nevertheless, in all three cases, the initial proton thermal anisotropy relaxes to the same quasi-equilibrium value (≃ 1·5). (d) The cold alpha particles in case 2 are strongly heated by their non-resonant interaction with the proton-produced ion cyclotron electromagnetic waves, (e) In contrast, the initially warm isotropic alpha particles in case 3 are heated by resonant interaction with the proton-produced waves, resulting in an increase in the perpendicular energy and a decrease in the parallel energy. The physical processes involved in the collisionless interaction of these mixed protons and heavier ions (alpha particles) are discussed.
A model problem for thermal relaxation. Part 2
Authors: Garrett A. J. M.
Published: March 2009

In part 1, a model problem for collisional relaxation in velocity space was constructed, and a series solution suitable for small times was obtained. In the present paper, a series suitable for large times is obtained, and further properties of both series are investigated.
Models of laser-plasma ablation. Part 2. Steady-state theory: self-regulating flow
Authors: Pert G. J.
Published: March 2009

The theory of plasma ablation by laser irradiation of a solid target is considered when thermal conduction is weak and the absorption is dominated by inverse bremsstrahlung (the self-regulating model). Analytic solutions are identified to treat both steady and time-dependent flows in limiting cases. The intermediate behaviour is explored by numerical modelling. The models are presented for planar, cylindrical and spherical geometries with both tight and weak focused beams. A brief investigation of the applicability of analytic models to the heating of thin foil systems is also presented.
Drift instabilities of a relativistic plasma. Part 2. Kinetic theory of low-frequency drift instabilities of a relativistic finite-pressure plasma
Authors: Mikhailovskii A. B. , Onishchenko O. G.
Published: March 2009

The generalization of the kinetic theory of low-frequency long-wavelength drift instabilities (instabilities due to the number density and temperature gradients and an instability of the Kelvin–Helmholtz type) is given for the case of a relativistic plasma. The role of relativistic effects, taking into account the anisotropy of the particle momentum distribution function, is clarified. Particular attention is paid to the investigation of instabilities of these perturbations in a relativistic electron-positron plasma.
Relativistic oblique magnetohydrodynamic shocks
Authors: Webb G. M. , Zank G. P. , McKenzie J. F.
Published: March 2009

Special relativistic magnetohydrodynamic shock waves in a perfect gas of infinite conductivity and constant adiabatic index are analysed. It is shown that the Rankine-Hugoniot equations for such shocks may be reduced to a seventh degree polynomial for the downstream dynamical volume ω, with the polynomial coefficients depending on the upstream state (ω equals the specific volume times the ratio of the energy density of the fluid (omitting electromagnetic terms) to the fluid rest mass energy density). In the non-relativistic limit, the polynomial equation reduces to a relation between the upstream and downstream Alfvénic Mach numbers, previously obtained by Cabannes. The equation for ω classifies in a natural way both shocks in which the electric field may be eliminated by transforming to the de Hoffman–Teller frame, and shocks for which this is not possible. The equation is used to determine the downstream state of relativistic shocks for a given upstream state as specified by the plasma beta, magnetic field obliquity, and flow speed.
Oblique propagation of nonlinear magnetosonic waves
Authors: Shah H. A. , Bruno R.
Published: March 2009

We consider obliquely propagating (with respect to the ambient field) nonlinear magnetosonic waves in a hot plasma with arbitrary beta. It is shown that the two-dimensional propagation of both the fast and the slow modes is governed by the Kadomstev–Petiashvilli soliton equation. Explicit expressions are obtained for the various physical quantities involved via the soliton solution.
MHD instabilities of a cylindrical plasma with a realistic energy equation
Authors: Torricelli-Ciamponi Guidetta , Ciampolini Vittorio , Chiuderi Claudio
Published: March 2009

The influence of a realistic energy equation on the stability of a cylindrical magnetized plasma in a force-free magnetic field is discussed. Thermal conduction, heating and line radiation are included in the treatment. Explicit growth rates for the m = 0 and m = 1 modes are derived and compared with the standard adiabatic or incompressible time-scales. Finally, the relevance of these results for laboratory and solar plasmas is discussed.
Turbulent relaxation of a confined magnetofluid to a force-free state
Authors: Dahlburg Jill P. , Montgomery David , Doolen Gary D. , Turner Leaf
Published: March 2009

Three-dimensional, pseudo-spectral computation is used to follow the evolution of a resistive, incompressible magnetofluid. The magnetofluid is confined by rigid, free-slip, perfectly-conducting square boundaries in the x, y directions (‘poloidal’ boundaries), and periodic boundary conditions are assumed in the z direction (‘toroidal’ direction). A constant, uniform d.c. magnetic field B0 is assumed in the z direction and a non-uniform current density j flows along it initially. Starting from a non-equilibrium hollow current profile, the evolution is followed for several tens of Alfvén transit times. Considerable small-scale turbulence develops, which causes energy to decay more rapidly than magnetic helicity. The average toroidal magnetic field at the (x, y) boundary reverses sign spontaneously. The near spatial constancy of the ratio jB/(jB) ≡ cos θ, in the relaxed state at late times, suggests that the state is nearly force-free. However, the ratio j. B/B2 ≡ α is considerably less uniform than is cos θ suggesting more residual disorder than a pure minimum-energy state would display.
Short-wavelength compressive instabilities in cosmic ray shocks and heat conduction flows
Authors: Zank G. P. , Mckenzie J. F.
Published: March 2009

In this paper we discuss the stability of three genetically similar non-uniform flows to compressive disturbances whose wavelengths are much shorter than the length scales characterizing the background flow. The results are relevant to theoretical models of cosmic ray shocks and solar wind type flows involving heat conduction. A JWKB expansion solution yields an equation which determines how the amplitudes of the perturbations may grow (or decay) as they propagate within such structures. It is shown that, in all three of the models considered, the perturbations exhibit spatial growth if the background flow is sufficiently supersonic and decelerating. The associated equations describing the evolution of the wave action are also studied with a view to deciding whether or not the behaviour of this attractive variable can provide an unambiguous answer to the question of stability. In the case of a shock transition dominated by heat conduction, it is shown that the effects of dissipative heating within the transition more than offset those of wave growth, with the result that wave amplification is accompanied by wave action decay. Therefore in general it would appear that the wave action equation alone cannot unambiguously settle stability questions.
Dispersion of electron Bernstein waves including weakly relativistic and electromagnetic effects. Part 2. Extraordinary modes
Authors: Robinson P. A.
Published: March 2009

Extraordinary solutions of the weakly relativistic, electromagnetic dispersion relation are investigated for waves propagating perpendicular to a uniform magnetic field in a Maxwellian plasma. As in a companion paper, which treated ordinary modes, weakly relativistic effects are found to modify dramatically the dispersion predicted by strictly non-relativistic ‘classical’ theory in the neighbourhood of harmonics of the cyclotron frequency Ωe. The infinite families of classical Gross–Bernstein and Dnestrovskii–Kostomarov modes are truncated to include only harmonics s satisfying s ≲ (ω2p mc2/4kB TΩ2e)⅓ and s ≲(ωp/Ωe)⅔/8 respectively where ωp is the plasma frequency and T the temperature. All classical cut-offs and resonances are removed apart from the x– and z– mode cut-offs. The only coupling between large- and small-wave-vector modes is between the z mode and a Gross–Bernstein mode near the upper-hybrid frequency and between the x mode and the second Gross–Bernstein mode near 2Ωe. Dispersion of the weakly relativistic counterpart of the x mode departs only slightly from that predicted by cold plasma theory except near Ωe and 2Ωe.
Single-particle motion under the influence of the perpendicular ponderomotive force
Authors: Festeau-Barrioz M. C. , Sawley M. L. , Václavík J.
Published: March 2009

The motion of a single particle under the influence of the ponderomotive force directed perpendicular to the external magnetostatic field is analysed. By solving the exact equation of motion for a specific applied electromagnetic field, the resultant ponderomotive drift is compared with the prediction of a single-particle theory using the oscillation-centre approximation. The regime of validity of this theory is discussed. It is shown that, for certain values of the amplitude and frequency of the electromagnetic field, the particle motion is unstable and therefore the concept of a single-particle ponderomotive force is meaningless.
On steady-state classical transport in collision-dominated toroidal systems
Authors: Øien Alf H.
Published: March 2009

Starting from classical transport theory, equations for particle density, particle momentum and electron and ion temperatures are derived for steady-state, toroidal plasma configurations in a parameter regime like that of ACT-I. A set of simplified equations for particle density and electron and ion temperatures are solved numerically. Radial density and temperature profiles are shown and compared with experiments.
Dynamics of kink instability in a non-uniform magnetoplasma
Authors: Bharuthram R. , Shukla P. K.
Published: March 2009

Accounting for an external electron current gradient, a set of nonlinear fluid equations governing the dynamics of kink instability in an inhomogeneous magnetized plasma has been derived. In the linear regime, the dispersion relation is analysed and the variation of the growth rate is graphically shown. In the nonlinear regime, it is shown that a quasi-stationary solution of the mode coupling equations can be represented as a dipolar vortex. Conditions under which the latter arises are given.
Fokker-Planck calculations on heat flow in plasmas
Authors: Jorna S. , Wood L.
Published: March 2009

This paper deals with the application of a Fokker–Planck code to the problem of heat conduction down steep thermal gradients. The results are compared with those obtained with other codes based on the Fokker–Planck equation in which various simplifying assumptions are made in the calculation of the Rosenbluth potentials. The particular problem considered is that of heat flow between spherical shells at different temperatures. The difference between the heat flows resulting from isotropic and anisotropic distributions is specially emphasized. The results show that, for calculating temperature, the usual Legendre polynomial expansion for the angular dependence of the distribution function gives reasonable results even when it is limited to two terms. However, the heat fluxes can differ by a factor of two when the Rosenbluth potentials are calculated from angular averages of the distribution function even when in the rest of the calculation the Legendre expansion is retained to all orders.
Nonlinear stage of the modulational instability of a whistler wave. Part 2
Authors: Karpman V. I. , Shagalov A. G.
Published: March 2009

Nonlinear structures in the developed stage of the two-dimensional modulational instability of a whistler wave are investigated. On the basis of the results obtained, some suggestions are made regarding the nonlinear dynamics of three-dimensional modulational instability and three-dimensional whistler solitons.
Field-driven ion migration against dead-stop collisional braking
Authors: Grzesik J. A.
Published: March 2009

The steady-state migration of ions, driven by a uniform electric field against full-stop collisions, is investigated in some detail. The required phase-space distribution is obtained very easily from Boltzmann's equation together with explicit recognition of energy conservation and population balance for the stagnant ion pool. We go on to decompose this aggregate solution into ion tiers classified by the number of background impacts previously endured. Such a decomposition permits us to detect the presence of Poisson statistics (as to collision number) lurking within the composite, thermalized Maxwellian, and likewise also a multiple-scattering hierarchy having the maiden, first-flight distribution for its natural kernel. Scattering-sequence accounting, in particular, allows a quantitative (even though unwieldy) distinction to be made between ions of varying residence times. A model of this sort is motivated by the technique of ion implantation through sample immersion within a plasma at higher electric potential. Numerical consequences of the solution obtained here reveal that both ion density and average kinetic energy relax to their terminal values within just a few mean free-path lengths. Such modest scaling of plasma-sheath extent evidently carries a beneficial implication for the technological ease with which surface properties (such as metal corrosion resistance and hardness) remain open to improvement via ion bombardment.
Ion-acoustic solitons in multi-component plasmas including negative ions at critical densities
Authors: Verheest Frank
Published: March 2009

Ion-acoustic solitons in a plasma with different adiabatic ion constituents and isothermal electrons are studied via a reductive perturbation method. The basic fluid equations then give rise to KdV or modified KdV equations, depending upon the relative ion densities. At critical densities, rarefactive and compressive fast ion-acoustic solitons are possible. Explicit stationary solutions are discussed in the special case of cold ions, in a plasma containing two species of negative ions and one of positive ions. The inclusion of heavier ions, even at low densities, increases the amplitudes of the critical solitons.
Hamiltonian theory of the generalized oscillation-centre transformation
Authors: Weyssow B. , Balescu R.
Published: March 2009

The theory of the slow reaction of a charged particle in the combined presence of a strong quasi-static magnetic field and a high-frequency electromagnetic field (generalized oscillation-centre motion) is constructed by using a Hamiltonian formalism with non-canonical variables and pseudo-canonical transformations. The theory combines the features studied in our previous works for the case in which only one of the previously mentioned fields is present. The new averaging transformation is based on the fact that the Larmor frequency of the quasi-static field is of the same order as the external frequency of the high-frequency field. Our theory is manifestly gauge-invariant and involves only physical quantities (particle velocity and electromagnetic fields). Explicit expressions for the drift velocity of the oscillation centre and for the ponderomotive force are derived.
Nonlinear excitation of convective cell by drift wave and spectrum cascade process in finite ion temperature plasma
Authors: Majumdar D.
Published: March 2009

A nonlinear drift mode equation for finite ion temperature plasma is derived. Possibilities of explosive instabilities for the drift wave are obtained. To discuss the modulational instability of drift wave, a nonlinear evolution equation for the drift mode is deduced from a third-order secularity elimination condition using the multiple time and space scales technique. The effect of low-frequency localized structure on particle transport has been investigated and the diffusion tensor is calculated using Ficks law.
Solitons in an ion-beam plasma
Authors: Zank G. P. , McKenzie J. F.
Published: March 2009

It is shown that the conservation law for total momentum of an ion-beam plasma system can be cast in the form of a classical energy integral of a particle in a potential well. By using boundary conditions appropriate to a solitary pulse, we derive conditions for the existence of finite-amplitude solitons propagating in the system. Under suitable conditions, as many as three forward-propagating solitary waves can exist. It is interesting to note that the criterion for their existence is intimately related to the absence of convective instabilities in an ion-beam plasma. Exact ‘sech2’ type solutions are available in the weakly nonlinear regime. Solitary-wave profiles for the general case are obtained numerically.
Nonlinear interactions of two compressional hydromagnetic waves
Authors: Ghosh B. , Das K. P.
Published: March 2009

Nonlinear interactions of two azimuthally symmetric compressional hydromagnetic waves propagating in a cylindrical waveguide filled with cold magnetized plasma are investigated. Two cases are considered: the nonlinear interaction of two identical oppositely propagating compressional waves and the nonlinear interaction of two compressional waves propagating with equal group velocities. In the first case the second-order perturbation fields generated through self- and mutual interactions of the waves are calculated and their effect on the otherwise-formed simple linear standing-wave pattern is studied. The possibility of observing a resonant nonlinear interaction is shown. In the second case, in order to describe the nonlinear evolution of the wave amplitudes, two coupled nonlinear Schrödinger (NLS) equations are presented. When excited individually, both the waves are seen to be modulationally stable; but when excited simultaneously, a strong nonlinear wave-wave coupling comes into play, which makes the waves modulationally unstable. The corresponding growth rate of the instability is also calculated.
Nonlinear dispersion relation for nonlinear Schrödinger equation
Authors: Bhakta J. C.
Published: March 2009

By using the average-Lagrangian method (average variational principle), a nonlinear dispersion relation has been derived for the cubic nonlinear Schrödinger equation. It is found that the size of the instability region in wavenumber space decreases with increasing field amplitude in comparison with the linear theory.
Full-wave calculations of the O-X mode conversion process
Authors: Hansen F. R. , Lynov J. P. , Maroli C. , Petrillo V.
Published: March 2009

A two-point boundary-value problem has been formulated that describes the conversion between ordinary (O) and extraordinary (X) wave modes in a cold inhomogeneous plasma. Numerical solutions to this problem have been obtained for various values of the WKB parameter k0L; where k0 is the vacuum wavenumber and L the density-gradient scale length. The results are compared with three different theoretical expressions for the O-X mode conversion efficiency derived by others in the WKB limit of k0 L ≫ l. Most of the results presented in this paper are obtained for a collisionless plasma with finite density near the plasma cut-off density. However, some examples are also given of wave propagation from vacuum. In these examples, collision effects are added to the equations in order to remove the singularity otherwise present at the position of the upper hybrid resonance layer.
Pulse shapes for absolute and convective free-electron-laser instabilities
Authors: Davies John A. , Davidson Ronald C. , Johnston George L.
Published: March 2009

This paper contains an analysis of pulse shapes produced by a delta-function disturbance of the equilibrium state of a relativistic electron beam propagating through a constant-amplitude, helical magnetic wiggler field. Pulse shapes are determined by using the relativistic pinch-point techniques developed by Bers, Ram and Francis. Two pulses are produced corresponding to a convective upshifted pulse (representing the production of the high-frequency radiation desired in a free electron laser) and a downshifted pulse. The downshifted instability may be convective or absolute, depending upon the beam density and momentum spread. Parameter regimes in which the downshifted instability is convective are investigated. It is found that momentum spreads sufficiently large to suppress the absolute instability reduce the growth rate of the upshifted pulse to negligible values. Pulse shapes computed by using the Raman and Compton approximations are compared with exact pulse shapes. It is found that the Raman approximation should be applied to the downshifted regime for most systems of practical interest.
Drift waves and magnetic field oscillations in cylindrical plasmas
Authors: Aebischer H. A. , Sayasov Yu. S.
Published: March 2009

A general investigation of linear drift-wave phenomena in cylindrically bounded plasmas, immersed in a magnetic field without shear and curvature, is performed within the two-fluid hydrodynamical approximation, taking into account electron-temperature oscillations and inhomogeneous radial distributions of the undisturbed electron density and temperature. For plasmas in which the electron temperature strongly exceeds the ion temperature the problem is reduced to an ordinary complex second-order differential equation describing the radial distribution of the oscillating electric potential. It is shown that the presence of electron-temperature oscillations (which must always exist in order to satisfy electron-energy conservation) and of radial gradients in the undisturbed electron temperature (which must always exist owing to cooling of the plasma at the boundary) leads to an important modification of the theory of drift waves in cylindrical plasmas (with regard to their stability and the radial distribution of the oscillating quantities) compared with previous papers in which these phenomena were disregarded. A numerical program for solving the corresponding complex-eigenvalue problem has been derived that allows a realistic calculation of all the quantities pertaining to drift-wave phenomena. It has been applied, in particular, to the calculation of the radial distribution of the oscillating coherent magnetic fields accompanying the coherent drift waves. The numerical results prove to be in good agreement with experiments performed with a helium plasma.
The α-effect generated by standing Alfvén waves
Authors: Namikawa Tomikazu , Hamabata Hiromitsu
Published: March 2009

The mean electromotive force generated by nonlinear standing Alfvén waves propagating along the mean magnetic field is investigated. It is shown that the α-effect can exist owing to the interaction between oppositely propagating two waves, provided that the initial fields have non-zero helicity. The result is discussed in the context of field-aligned currents and periodic particle flux variations in the earth's magnetosphere.
Linear stability of Vlasov–Poisson electron plasma in crossed fields. Perturbations propagating parallel to the magnetic field
Authors: Lee Hee-Jae , Kaup D. J. , Thomas Gary E.
Published: March 2009

It is shown that electrostatic Vlasov–Poisson perturbations that propagate parallel to the magnetic field in a planar magnetron are stable for both an isotropic and also for a particular anisotropic (Ty = 3Tx) temperature distribution. The inhomogeneity of the electron density is fully incorporated in the analysis. The proof makes use of only the dispersion relation of Trivelpiece–Gould type, without actually solving the eigenvalue equation. These results suggest, not unexpectedly, that these modes should be stable for all such anisotropic velocity distributions.
Generation and radiation of third harmonics by s-polarized electromagnetic waves incident on a narrow inhomogeneous magnetoactive plasma layer
Authors: Hussein A. M.
Published: March 2009

An investigation is made of wave generation and radiation of third harmonics by s-polarized electromagnetic waves incident on a narrow inhomogeneous layer of a magnetoactive plasma. The amplitudes of the radiated third-harmonic waves are calculated. In contrast with second harmonics, third harmonics are radiated for the case of normally incident waves on an unmagnetized plasma.
Three-wave coupling coefficients for magnetized plasmas with pressure anisotropy
Authors: Brodin G. , Stenflo L.
Published: March 2009

In order to find the equations for the nonlinear energy exchange between low-frequency waves in magnetized plasmas in the presence of pressure anisotropy, we start from the Chew–Goldberger–Low equations, the isothermal MHD equations, as well as a new hybrid system of equations. The coupling coefficients describing the interaction between two Alfvén waves and one magnetosonic wave as well as the interaction between two magnetosonic waves and one Alfvén wave are deduced.
Influence of dispersion on the modulational instability of a whistler wave
Authors: Karpman V. I. , Shagalov A. G.
Published: March 2009

The modulational instability of a whistler wave propagating along an external magnetic field is investigated, taking into account the dispersion of the low-frequency modulations. The dispersive effects are significant if the modulation frequencies Ω are comparable to or greater than the ion cyclotron frequency ωci. It is shown that in this case there are four unstable branches: the long-wave modulational instability and three others with much larger growth rates. At Ω≪ωci the latter correspond to fast magnetic sound, Alfvén and slow magnetic sound branches.
On the higher-order corrections to the ion-acoustic cnoidal waves in a relativistic plasma with cold ions and two-temperature electrons
Authors: Chowdhury A. Roy , Pakira G. , Paul S. N.
Published: March 2009

We have considered the effect due to the presence of two-temperature electrons on the formation and propagation of cnoidal waves in a weak relativistic plasma. Since the cnoidal wave is equivalent to an infinite series of solitary waves, it is worthy of study for the situation where more than one solitary wave is important. The phase velocity of the modulated periodic wave is plotted as a function of the amplitude. The form of the wave for small values of ellipticity of the cnoidal wave shows up as a series of harmonics. Such cnoidal excitations are important in determining the anomalous transport coefficients of a plasma.
Large-Debye-distance effects in a homogeneous plasma
Authors: Scheffel Jan , Lehnert Bo
Published: March 2009

The classical phenomenon of electron plasma oscillations has been investigated from new aspects. The applicability of standard normal-mode analysis of plasma perturbations has been judged from comparisons with exact numerical solutions to the linearized initial-value problem. We consider both Maxwellian and non-Maxwellian velocity distributions. Emphasis is on perturbations for which αλD is of order unity, where α is the wavenumber and λD the Debye distance. The corresponding large-Debye-distance (LDD) damping is found to substantially dominate over Landau damping. This limits the applicability of normal-mode analysis of non-Maxwellian distributions. The physics of LDD damping and its close connection to large-Larmor-radius (LLR) damping is discussed. A major discovery concerns perturbations of plasmas with non-Maxwellian, bump-in-tail, velocity distribution functions f0(ω). For sufficiently large αλD (of order unity) the plasma responds by damping perturbations that are initially unstable in the Landau sense, i.e. with phase velocities initially in the interval where df0/dw > 0. It is found that the plasma responds through shifting the phase velocity above the upper velocity limit of this interval. This is shown to be due to a resonance with the drifting electrons of the bump, and explains the Penrose criterion.
A perturbation theory for the solitary-drift-vortex solutions of the Hasegawa-Mima equation
Authors: Swaters Gordon E.
Published: March 2009

A multiple-scales adiabatic perturbation theory is presented describing the adiabatic dissipation of the solitary vortex-pair solutions of the Hasegawa-Mima equation. The vortex parameter transport equations are derived as solvability conditions for the asymptotic expansion and are identical with the transport equations previously derived by Aburdzhaniya et al. (1987) using an energy- and enstrophy-conservation balance procedure. The theoretical results are compared with high-resolution numerical simulations. Global properties such as the decay in the enstrophy and energy are accurately reproduced. Local properties such as the position of the centre of the vortex pair, decay of the extrema in the vorticity and stream-function fields, and the dilation of the vortex dipole are also in good agreement. In addition, time series of vorticity–stream-function scatter diagrams for the numerical simulations are presented to verify the adiabatic ansatz.
Compressible models of fast steady-state magnetic reconnection
Authors: Jardine M. , Priest E. R.
Published: March 2009

We investigate the effects of compressibility on magnetic reconnection, using as a basis the incompressible models of Priest & Forbes and Jardine & Priest. Our results show that compressibility modifies the reconnection process, without changing its essential character. In the region of inflowing plasma, compressibility tends to increase the convergence or divergence of the flow. Also, for regimes with a compression in the inflow the maximum rate of reconnection is increased, while for regimes with an expansion in the inflow the magnetic Mach number at the entrance to the diffusion region is increased. In the region of outflowing plasma the main effects of compressibility are to produce faster and narrower outflow jets, with a lower magnetic field strength.
Effects of non-uniformities on electrical conduction in weakly ionized plasmas
Authors: Numano M. , Murakami Y. , Nitta T.
Published: March 2009

The effect of non-uniformities on the flow of electric current in weakly ionized plasmas is investigated by taking into account the ion slip as well as the Hall current. An Ohm's law for a non-uniform plasma is derived, from which the formula previously obtained by Numano, i.e. an extension of Rosa's equation, is obtainable as a special case. Making use of this new Ohm's law, the effective electrical conductivity and the effective Hall parameter are determined for isotropically turbulent plasmas. It is found that when the ion-slip effect is absent they are in good agreement with the results obtained previously.
Three-wave interaction between transverse and longitudinal waves
Authors: Brodin G. , Stenflo L.
Published: March 2009

We consider the resonant interaction between two transverse waves and one longitudinal wave in a plasma. In particular, we discuss coupling phenomena involving long-wavelength modes that have been overlooked by previous authors.
Exact nonlinear wave solutions of the incompressible magnetohydrodynamic equations in a non-uniform magnetic field
Authors: Hamabata Hiromitsu , Namikawa Tomikazu
Published: March 2009

Exact wave solutions of the nonlinear magnetohydrodynamic equations for a highly conducting incompressible fluid within an axisymmetric container are obtained. It is shown that there are four types of exact wave solutions with large amplitude in a non-uniform magnetic field. These solutions are very useful because they can be expressed in terms of arbitrary scalar functions and they are applicable to astrophysical and laboratory plasmas as well as the earth's core. The solutions also include as special cases the nonlinear Alfvén waves in a uniform magnetic field and in a circular magnetic field found respectively by Walén (1944) and by Namikawa & Hamabata (1987, 1988).
Spectral laws for energy and enstrophy cascades in electrostatic turbulence
Authors: Shivamoggi Bhimsen K.
Published: March 2009

In this paper we develop spectral laws for the small- and large-wavenumber regimes of the energy and enstrophy cascades in electrostatic turbulence and discuss how these spectra differ, owing to compressibility effects, from those for two-dimensional hydrodynamic turbulence. We also show that the compressibility effects on the scaling laws can be described as intermittency corrections formulated according to the log-normal model of Obukhov and Kolmogorov.
Mode conversion and transmission in spatially cyclic fields
Authors: Diver D. A. , Laing E. W.
Published: March 2009

In a cold plasma, the 0 and X modes are determined by the orientation of the first-order electromagnetic fields with respect to the equilibrium magnetic field B0. In the particular case where the direction of B0 is a function of position the distinction between these types of waves is lost. In this paper, two semi-infinite regions of homogeneous cold plasma are connected by a finite zone in which the equilibrium magnetic field has a spatially periodic shear. This system is studied self-consistently to reveal the mode-con version and transmission characteristics of plasmas containing field structures of this kind, and preliminary calculations of the full coefficients are presented. The results thus obtained are directly relevant to situations where magnetic shear is important.