bluuebunny/crossref_metadata_2025 huggingface dataset:
Upper bound for the space-charge limiting current of annular electron beams
Authors: Genoni T. C. , Proctor W. A.
Published: March 2009

We report here on a two-dimensional analytical calculation of an upper bound on the space-charge limiting current for a relativistic electron beam in cylindrical geometry. Voronin and co-workers have previously obtained an analytical estimate for the maximum steady-state current that can be propagated in a solid, unneutralized electron beam which completely fills a drift tube immersed in an infinite magnetic guide field. We generalize their method to include annular beams of arbitrary thickness and length, specifying a rigorous upper bound on the limiting current in terms of an eigenvalue of Bessel' s differential equation and separated, homogeneous boundary conditions of the most general form. For the special cases of a thin solid beam in a drift tube of infinite length and a thin annular beam in a drift tube of finite length, we find closed-form analytical expressions for the upper bound which are in good agreement with numerical solutions for the actual space-charge limiting current.
Quasi-linear approach to the propagation of Bernstein waves in an inhomogeneous plasma
Authors: Crescentini A. Airoldi , Orefice A.
Published: March 2009

The quasi-linear equations describing the resonant evolution of a weakly inhomogeneous plasma slab under the action of Bernstein modes resulting from linear conversion of an externally injected extraordinary wave are obtained, together with a tractable form of the pertinent dispersion relation. The coefficients of electron diffusion in velocity space are computed, and their effect is compared to the effect of Coulomb collisions.
Waves in magnetoplasma with a stochastic magnetic field
Authors: Prahalad Y. S. , Mittal M. L.
Published: March 2009

In the present analysis, a normal mode approach is used to study waves in a plasma subjected to a spatially uniform but temporally stochastic magnetic field. The first part deals with the evolution of circularly polarized transverse waves. Making a linear analysis, it is shown that the coherent waves are damped. The nature of the damping is determined by the Kubo number. In the second part, the nonlinear interaction of three coherent waves propagating along the magnetic field is analyzed. The coupling coefficients for the interaction of two circularly polarized waves and a longitudinal one are calculated. It is shown that for coherent waves, the system is equivalent to the interaction of two damped transverse modes with an undamped longitudinal one.
On the validity of a hydrodynamic description of laser-driven fusion
Authors: Lowy D. N. , Kreuzer H. J.
Published: March 2009

The validity of hydrodynamic approximations for non-equilibrium plasmas is examined, with emphasis on applications to laser-driven fusion pellets. Typical density–temperature trajectories of such pellets, as predicted by hydrodynamic calculations in the published literature, are shown to lie sometimes outside the region of validity of hydrodynamic theory, which is an unsatisfactory situation. In view of this, we discuss certain criteria which can be easily used to test the self- consistent validity of any hydrodynamic result. Finally, it is noted that in the low-density, low-temperature plasma region, hydrodynamics initially breaks down because of a breakdown in conventional microscopic linear response theory. A modified microscopic theory is proposed which continues to be valid in this region. This may correspondingly extend the validity of hydrodynamics to plasmas of somewhat lower temperatures and densities.
Local stability of anisotropy-driven modes in diffuse high-beta plasmas
Authors: Goedert J. , Mondt J. P.
Published: March 2009

Finite ion Larmor radius effects (ε ≡ γLi/LΙ< 1 but finite) are found to cause a branching of the Alfvén ion cyclotron mode, whereas the growth rate of the mirror mode is found to be of the order of for ωci for ε≥ 0.1 and rather moderate values of plasma beta and temperature anisotropy. For this regime its growth rate considerably exceeds that of the Alfvén ion cyclotron mode.
Energy loss of relativistic electrons in plasma in accordance with covariant Fokker–Planck formalism
Authors: Ray P. S.
Published: March 2009

A relativistic generalization of the Fokker–Planck formalism has been constructed. This is applied to the study of energy loss of high-energy electrons in plasma. Both the electron–electron and electron–ion scattering have been considered in a relativistic way. The expression obtained for the stopping power differs from that derived with the help of thermodynamic Green's function technique.
On self-consistent waves and their stability in warm plasmas. Part 2. Instability of circularly polarized waves both in the presence and the absence of an ambient magnetic field
Authors: Lee M. A. , Lerche I.
Published: March 2009

The stability of a self-consistent, large-amplitude, circularly polarized wave in a warm plasma is investigated. For perturbations to the system propagating normal to the plane of circular polarization, a dispersion relation is derived employing an expansion in the nonlinear wave amplitude and the momentum of the plasma particles in the plane of polarization. Instability results both in the absence and presence of a large-scale magnetic field with a growth rate of the order of the nonlinear wave amplitude.
On the resistive diffusion of force-free magnetic fields
Authors: Low B. C.
Published: March 2009

Reid and Laing recently conjectured on the general behaviour of resistive force- free magnetic fields in a slab model following a numerical study. However, the basic properties of resistive force-free magnetic fields had been established previously. We use and extend some results from the previous work to show that the conjecture of Reid and Laing is incorrect. A general analytic treatment of the problem provides the correct physical properties that Reid and Laing were unable to deduce from their numerical solutions. A criticism is also given of the results presented in another numerical study treating cylindrical resistive forcefree magnetic fields, by the same authors.
The stability of parallel flow of a multi-component plasma
Authors: Lucas R. J.
Published: March 2009

A Liapunov functional is constructed for the plane parallel flow of a multicomponent plasma in an external gravitational field. Sufficient conditions for stability to electrostatic perturbations are obtained. The L2-norms of certain system variables are shown to be bounded uniformly in time.
Langmuir turbulence as a critical phenomenon. Part 1. Destruction of the statistical equilibrium of an interacting-modes ensemble
Authors: Pelletier Guy
Published: March 2009

This paper is the first part of a work concerning a statistical theory of Langmuir turbulence in which the destabilization of an ensemble of plasmons by self- modulation is considered as a critical phenomenon. The first part is devoted to a discussion of the existence of a statistical equilibrium for the ensemble of modes. A transition curve, which separates equilibrium from non-equilibrium, is found. Several properties of the plasma, when the self-modulation instability is saturated, are derived in the neighbourhood of the critical Langmuir energy density Wc. In particular, the Langmuir energy spectrum is found to be proportional to kd-3, the correlation length is found to diverge as üW–Wcü–half, and the anomalous conductivity at the plasma frequency is found to diverge as üW – Wcü-1.
Effect of thermal anisotrophy on the loss-cone produced high-frequency quasi-electrostatic ion cyclotron waves in mixed warm-cold plasmas
Authors: Gomberoff L. , Cuperman S.
Published: March 2009

We show that in the case of generalized loss-cone distribution functions characterized by loss-cone index l, parallel thermal velocity α∥ and perpendicular spread α⊥ sufficiently large anisotropy, (α∥/α⊥), may stabilize the high-frequency electrostatic ion cyclotron instability. The discussion refers to the oblique propagation and includes also a second, cold, ion component (besides warm isotropic electrons). Electromagnetic corrections to the quasi-electrostatic dispersion relation are also considered. Simple analytical expressions for the growth rates are derived and discussed.
An approach to rapid plasma shape diagnostics in tokamaks
Authors: Lee D. K. , Peng Y. K. M.
Published: March 2009

A study is made of a diagnostic procedure which allows one to estimate the plasma boundary shape and location in a tokamak by using numerical values of the poloidal magnetic flux function ψ in the vicinity of the plasma. In the case of the Impurity Study Experiment (ISX-B) tokamak, the magnetic sensor coils located around the periphery of the vacuum chamber provide information on ∂BR/∂t and ∂Bz/∂t, which can be processed to obtain data on ψ (and ∂ψ/∂n) through the relation BR = - R-1∂ψ/∂Z and Bz = R-1∂ψ/∂R. This leads to a Cauchy boundary condition for the Grad-Shafranov equation Δ*ψ = 0 in the region between the contour of the sensor coil locations and the plasma boundary flux surface. Numerical equilibria calculated for the ISX-B with different shapes are used to simulate ψ data along the coil locations. Random errors are added to the data to test the efficacy of two different approaches: global fitting and local fitting. Reasonably accurate results are obtained by the method of global fitting of the boundary values, which is based on the expansion of ψ in terms of eigenfunctions of Δ*ψ = 0 in a toroidal ring co-ordinate system. This approach is found to permit a relatively large random error in poloidal B field values at the sensor coils and appears to have the potential of rapidly displaying the plasma shape and location.
On the ‘non-stationary’ ponderomotive force of a HF field in a plasma
Authors: Tskhakaya Davy D.
Published: March 2009

A general expression is obtained for the ponderomotive force of a HF field in a plasma. This expression is valid for both transverse and longitudinal HF fields. The conditions are discussed under which the ponderomotive force contains a term proportional to the time derivative of the HF field amplitude. This part of the ponderomotive force is termed ‘non-stationary’ ponderomotive force.
Electron oscillations of a collisionless plasma in a static electric field
Authors: Wahlberg Christer
Published: March 2009

The influence of a static electric field on electron oscillations of (i) a cold beam of electrons and (ii) a hot non-drifting plasma is investigated. The importance of the relative strength of the field is emphasized. In the weak field limit the oscillations are adiabatic, manifested by the existence of adiabatic invariants, preservation of eigenmodes and absence of reflexion. If the field is strong, however, interesting new features, such as mutual coupling of eigenmodes and wave reflexion, appear. Possible stability properties of a monotonic electrostatic transition (shock, double layer) are also discussed.
Non-spherical implosion of a dense thermonuclear plasma
Authors: Winterberg F.
Published: March 2009

In contrast to the electronic heat conduction losses which for a tamped thermonuclear micro-explosion are minimized by a spherical target shape, the adiabatic temperature rise can be larger for a non-spherical implosion geometry, whereas for a given plasma volume and density the bremsstrahlung losses are independent of the particular geometry. The enhancement of the adiabatic temperature rise results from the ‘scissors effect’ in non-spherical implosions by which a cavity wedge can assume a larger geometric implosion velocity than the physical implosion velocity of the cavity wall. The net effect of the enhanced adiabatic temperature rise by the 'scissors effect' and enhanced electronic heat conduction losses for non-spherical cavity shapes results in an optimal non-spherical implosion geometry. For the special case of an imploding oblate ellipsoid the optimal eccentricity is derived from an exact analytical solution. The predicted effect leads to a reduction in required beam power density, permitting less beam focusing than is necessary for spherical targets, which is of special importance for electron- and ion-beam induced micro-explosions, and may even make possible the attainment of thermonuclear temperatures by chemical explosives.
Slowly varying nonlinear waves in a cold plasma stream
Authors: Gribben R. J. , Parkes E. J.
Published: March 2009

This paper is concerned with the propagation of one-dimensional nonlinear waves in the relatively simple physical situation of a cold, collisionless, field-free, slightly non-uniform plasma comprising a stream of oscillating electrons and a stream of ions whose oscillatory motion is neglected. The waves are considered as a small perturbation from the corresponding uniform periodic solution. The equations which govern the slow variation of certain gross quantities associated with the waves are obtained by applying the ‘two-timing’ technique to the basic plasma equations. The properties of the resulting modulation equations are discussed and an exact solution of an initial value problem for them is given.
Three component non-symmetric counter-streaming instabilities: longitudinal electron plasma modes
Authors: Cuperman S. , Gomberoff L. , Roth I.
Published: March 2009

The counter-streaming instabilities arising in three-component electron plasmas are investigated analytically and numerically in the general non-symmetric case, i.e. whenHere n1n2and narepresent the electron particle density in the first and second beams and in the background (ambient) stationary plasma, respectively; U1and U2represent the streaming velocities of the two counter-streaming electron beams. No magnetic or temperature effects are considered; consequently the three components interact only through the electric collective fields and only longitudinal modes are present. The positive ions here represent a stationary neutralizing background. Combined analytical and numerical solutions of the dispersion equation indicate that the basic properties of the unstable plasma modes may change significantly, depending on the values of the dimensionless parameters e, a and g. Thus, the standing wave spectrum (Re ω = 0) which occurs in the symmetric case (ε = a = 1) without background (gr = 0) may be replaced by a mixed travellingstanding wave spectrum having a rather complex structure; the maximum growth rate could be also strongly affected. The transformation of the instability from ‘absolute’ into mixed ‘convective and absolute’ may have significant physical implications, especially for finite size plasma systems or finite length unstable interaction regions. The results are relevant for laboratory and (especially) astrophysical situations in which counter-streaming electron beams having unequal streaming velocities (and particle densities) penetrate plasma regions with significant relative particle concentration.
Stability of a stratified partially ionized plasma in a vertical magnetic field
Authors: Maheshwari S. L. , Bhatia P. K.
Published: March 2009

The dynamic stability of a stratified layer of partially ionized compressible plasma is discussed to investigate the effects of finite electrical conductivity and ion viscosity. The prevailing magnetic field is assumed to be uniform and vertical. For a semi-infinite plasma having a one-dimensional exponential density gradient along the vertical, the dispersion relation has been obtained by variational methods. It is found that the ion viscosity and ion–neutral collisions, whether included jointly or separately, do not change the stability criterion of the perfectly conducting system. Their inclusion, however, has a tendency to reduce the growth rate of the unstable perturbations showing that they have a stabilizing influence. On the other hand the inclusion of the effects of finite resistivity and compressibility of the medium is found to be destabilizing as the wavenumber range over which the plasma would otherwise be stable, becomes unstable.
Numerical simulation of plasma double layers
Authors: Joyce Glenn , Hubbard Richard F.
Published: March 2009

The results of a numerical simulation of a plasma double layer are presented. The model is of a finite, one-dimensional plasma with a specified potential difference across the system. Initially a single pulse is formed which traverses the system with constant velocity. This stage is followed by the formation of a potential drop across a limited region of the plasma. The relation between the spatial extent of the double layer and the potential drop is given approximately by L = 6(edgr;φ/kTe)½. The double layer causes electron and ion beams which tend to lead to instabilities in the upstream and downstream regions.
Stability criterion for symmetric MHD equilibria by minimizing the potential energy
Authors: Edenstrasser Johann W.
Published: March 2009

The potential energy of an ideal static MHD plasma is minimized using the invariants of motion as variational constraints and assuming a general symmetry (dependence on two space variables only). For simplicity only the plasma-on- the-wall case is considered. The first variation yields a generalized Shafranov equation, the second the desired stability criterion. It is found that equilibria with a longitudinal current increasing monotonicaily towards the boundary are always stable with respect to symmetric modes. For equilibria with an outwardly decreasing current a sufficient criterion (for symmetric modes) is derived, which only requires the solution of a linear eigenvalue problem. The theory is applied to the straight circular cylinder and to the axisymmetric torus.
Solitary Alfvén waves in inhomogeneous streaming plasma
Authors: Buti B.
Published: March 2009

Large-amplitude Alfvén waves, propagating along the magnetic field in an inhomogeneous plasma with non-uniform streaming, are shown to be governed by the DNLS equation modified by the inhomogeneity and the streaming. For weak but arbitrary inhomogeneity this modified DNLS leads to accelerated solitary Alfvén waves. The acceleration is modified further owing to streaming. For certain values of the plasma β, streaming can change the accelerating solitons into decelerating solitons, and vice versa.
Time scales and efficiency of resonant absorption in periodically driven resistive plasmas
Authors: Poedts Stefaan , Kerner Wolfgang
Published: March 2009

The time scales and efficiency of plasma heating by resonant absorption of Alfvén waves are studied in the framework of linearized compressible and resistive magnetohydrodynamics. The configuration considered consists of a straight cylindrical axisymmetric plasma column surrounded by a vacuum region and a perfectly conducting shell. The plasma is excited periodically by an external source, located in the vacuum region. The temporal evolution of this driven system is simulated numerically. It is shown that the so-called ‘ideal quasi-modes’ (or ‘collective modes’) play a fundamental role in resonant absorption, and affect both the temporal evolution of the driven system and the efficiency of this heating mechanism considerably. The variation of the energetics in periodically driven resistive systems is analysed in detail for three different choices of the driving frequency, viz an arbitrary continuum frequency, the frequency of an ideal ‘quasi-mode’, and a discrete Alfvén wave frequency. The consequences for Alfvén wave heating of both laboratory plasmas and solar coronal loops are discussed.
Free-electron lasing in the wake field of an elliptical pill-box cavity
Authors: Kim S. H.
Published: March 2009

It is shown using the photon concept that free-electron lasing (or net stimulated bremsstrahlung) is unrelated to the electron phase with respect to the laser wave, while the net acceleration (or net two-photon absorption) in an RF acceleration cavity depends on the electron phase with respect to the RF wave. The gain formula for the free-electron laser using a magnetic wiggler (MFEL) derived using the recently developed quantum-augmented classical theory in which the electron phase is ignored is in excellent agreement with that obtained quantum-mechanically. It is found by means of this theory that if an electric wiggler is added to a MFEL, the synchronization between the transverse velocity and the laser wave, which is required for coherence of the laser light, is not affected, while the laser gain is enhanced owing to the increase in the amplitude of the energy modulation by the electric wiggler. As a configuration of this turbo-MFEL, a two-beam elliptical wake-field cavity is proposed. An electron beam injected in the antiparallel direction along the lasing-beam path in this cavity lases through transverse wiggling by the transverse wake field and energy modulation by the longitudinal wake produced by relativistic drivingbeam bunches. This laser (WFEL) becomes of greater advantage compared with the MFEL as the laser wavelength is made shorter. It is also shown that the amplification of the WFEL is much greater than that of the present MFEL if we can produce a wake field whose longitudinal component has field strength greater than 1 MV m–1.
The propagation of a plasma wave with trapped particles in a weakly inhomogeneous plasma
Authors: Krasovsky V. L.
Published: March 2009

The propagation of a Langmuir wave with a small group of trapped particles in a weakly non-uniform plasma along a density gradient is considered. The dynamics of trapped electrons accelerated by the wave is investigated in the adiabatic approximation, including the relativistic case. The set of equations describing the self-consistent spatial evolution of the wave—trapped-particles system is obtained and analysed. It is shown that the possibility exists of wave transmission through a classically forbidden barrier as a consequence of the reversibility of the wave—particle interaction. The conditions of validity of the theory developed are also discussed.
Stabilization of collisional drift waves by kinetic Alfvén waves
Authors: Kar C. , Majumdar S. K. , Iyengar A. N. Sekar
Published: March 2009

We have investigated a mode-coupling mechanism between kinetic Alfvén waves and a collisional drift wave in an inhomogeneous cylindrical plasma. Drift waves satisfying the condition k⊥D > 1/r0 (where r0 is the radius of the plasma cylinder) are stabilized by the low-frequency ponderomotive force generated by the kinetic Alfvén waves. For typical plasma parameters and a moderate level of Alfven-wave intensity the stabilization factor is comparable to the destabilization mechanism due to collisions.
Toroidal equilibrium of a non-neutral plasma with toroidal current, inertia and pressure
Authors: Bhattacharyya S. N. , Avinash K.
Published: March 2009

Equilibrium of non-neutral clouds in a toroidal vessel with toroidal magnetic field is demonstrated in the presence of a toroidal current, finite mass and finite pressure. With a toroidal current, it is shown that in a large-aspect-ratio conducting torus the equilibrium is governed by competition between forces produced by image charges and image currents. When (where Er and Bθ are the self electrostatic and self magnetic fields of the cloud), the confinement is electrostatic and plasma shifts inwards; when the confinement is magnetic and plasma shifts outwards. For there is no equilibrium. With finite mass or finite pressure, it is shown, in a large-aspectratio approximation, that the fluid drift surfaces and equipotential surfaces are displaced with respect to each other. In both cases the fluid drift surfaces are shifted inwards from the equipotential surfaces.
Nonlinear drift phase-space structures
Authors: Rath Sharadini , Kaw P. K.
Published: March 2009

The collisionless Vlasov–Poisson system in the drift approximation is examined for the existence of maximum-entropy nonlinear coherent solutions in the steady state. Two major nonlinear effects are taken into account. The first is the velocity-space trapping of particles, leading to closed trajectories in phase space. The second is the physical-space trapping of particles, leading to closed trajectories in the plane perpendicular to the magnetic field. The regions of validity of these nonlinearities are discussed and their relative importance demonstrated. Numerical solutions of the equations describing the nonlinear stationary states in one and two dimensions are presented.
Drift-dissipative instability of the electromagnetic convection mode in a low-temperature plasma
Authors: Saleem Hamid , Yu M. Y.
Published: March 2009

The convection mode in a collisional plasma is investigated, with the inclusion of electromagnetic effects. It is shown that a dissipative instability can occur. The relationship to several well-known modes as well as applications to typical low-temperature plasmas are discussed.
Phase-space description of plasma waves. Part 1. Linear theory
Authors: Biro T. , Rönnmark K.
Published: March 2009

We develop an (r, k) phase-space description of waves in plasmas by introducing Gaussian window functions to separate short-scale oscillations from long-scale modulations of the wave fields and variations in the plasma parameters. To obtain a wave equation that unambiguously separates conservative dynamics from dissipation in an inhomogeneous and time-varying background plasma, we first discuss the proper form of the current response function. In analogy with the particle distribution function f(v, r, t), we introduce a wave density N(k, r, t) on phase space. This function is proved to satisfy a simple continuity equation. Dissipation is also included, and this allows us to describe the damping or growth of wave density along rays. Problems involving geometric optics of continuous media often appear simpler when viewed in phase space, since the flow of N in phase space is incompressible.
Effect of finite spectral width on the modulational instability of Alfvén waves
Authors: Roy P. C. , Bhakta J. C.
Published: March 2009

The effect of finite spectral width on the modulational instability of Alfvén waves described by the derivative nonlinear Schrodinger equation is investigated using a method developed by Alber to derive a transport equation for the spectral density. The dispersion relation for a monochromatic wave is regained for a delta spectrum. It is shown that the growth rate and domain of modulational instability diminish as the spectral width increases for both the Gaussian and uniform spectrums.
Decay instability of cirularly polarized waves into cirularly polarized and Langmuir waves in a magnetized plasma
Authors: Lee Kai Fong
Published: March 2009

A study is made of a parametric instability in a magnetized plasma in which an electromagnetic pump wave of either right- or left-hand circular polarization decays into a Langmuir wave and another circularly polarized wave, all with wave vectors colinear with the external magnetic field. The analysis is based on a multiple-time-scale perturbation expansion of the fluid equations, incorporating the effects of temperature, collisions, and the spatial variation of the pump wave. The threshold values of the pump field intensity required for instability and the growth rates above threshold are calculated.
Low-frequency surface waves on bounded warm magneto-active plasma
Authors: Zhelyazkov I. , Nenovski P.
Published: March 2009

The spectra of low-frequency surface waves propagating along a warm magneto- plasma layer bounded by dielectric are investigated, using a two-fluid hydrodynamic plasma model. It is shown that such propagation is possible only for some definite directions of the external magnetic field B0, with respect to the plasma-dielectric interfaces. The spectra obtained for a thick plasma layer correspond to the well-known results for a magneto-active plasma, bounded on one side by a vacuum, derived in the limit of one-fluid hydrodynamics.
Wave propagation in a moving plasma. Part 1. Wave propagation normal to the magnetic field and motion of the plasma along the magnetic field
Authors: Srivastava D. N.
Published: March 2009

The dispersion relation for a collisionless moving electron plasma, when the direction of motion is along the magnetic field, and that of the wave propagation normal to the magnetic field, is analysed. It is shown that in small magnetic fields the ordinary wave develops a new band of backward waves below the plasma frequency. When the frequency of the wave is higher than the plasma frequency, the effect of the motion of the plasma is identical to a deviation of the direction of propagation.
Electron temperature resonances of a plasma column described to full first order in the temperature
Authors: Koch R. , Vandenplas P. E.
Published: March 2009

An inhomogeneous plasma column surrounded by a glass wall is described through full first order in temperatures Te and Ti using a complete electromagnetic treatment. We study the response of this system to a purely TE wave with K perpendicular to the axis. Comparison with existing theories and experimental results is made in the electron–wave domain (ions play no role) with zero steady magnetic field, i.e. in the case of temperature (Tonks-Dattner) resonances. Perhaps surprising at first sight, there is poor agreement with experiment at low density, the classic T½e theory (scalar perturbed pressure approximation) giving far better results. Simple arguments concerning the different levels of approximation in the description of the longitudinal k2 enable us to distinguish the crucial difference existing between a scalar pressure and a complete T description and to understand this result. We generalize these findings, demoastrating that a description is always more realistic than a one in the range ωpe<ω.
Generation and radiation of second harmonics by s-polarized electromagnetic waves incident on a narrow inhomogeneous plasma layer
Authors: Dolgopolov V. V. , El-Siragy N. M. , Sayed Y. A.
Published: March 2009

We investigate radiation of waves at double the frequency from an arbitrary inhomogeneous, isotropic plasma layer, when 8-polarized electromagnetic waves are obliquely incident on it and their lengths are considerably greater than the width of the layer. We calculate the amplitudes of the radiated waves. We show that, in general, the second harmonics are radiated in the direction of propagation of both the reflected and the transmitted wave being at the basic frequency. At small plasma densities, the second harmonics are emitted practically only in the direction of propagation of the reflected wave at the basic frequency. For normal incidence, there is no wave radiation at double the frequency of the incident wave.
Effect of Hall current on the instability of an anisotropic plasma jet
Authors: Srivastava K. M.
Published: March 2009

The modified Chew—Goldberger—Low (CGL) equations are applied to the effect of Hall current on the instability of an incompressible plasma jet surrounded by non-conducting, compressible matter. The dispersion relation is obtained and discussed. The following is found. (i) When λ (the ratio of plasma density to the density of surrounding medium) is much greater than unity, the plasma jet is unstable for all wavenumbers for which k* = Küα < [(4R22 – 1)ü(1 + V2α)], where R2 = p∥/p⊥, V2α = H2/4αρ, K = (l2 + α2)½. Also, the jet is unstable for R2 > 1 + V2α. (ii) When λ ≪ 1, the critical wavenumber ratio for the instability to set in is k* < [(V2α + 3R2)ü(1 + V2α)½. Also, the jet becomes unstable for R2 < ⅓. (iii) When either l = 0 or α= 0, we must have R2 > 1 + V2α for instability. It is established that the Hall current has a destabilizing effect for certain wave- numbers. The dispersion relation for the incompressible plasma jet in cylindrical geometry is solved numerically on a computer.
Nonlinear waves in a cold plasma by Lorentz transformation
Authors: Clemmow P. C.
Published: March 2009

Wave propagation in a cold, collisionless, two-component plasma is analyzed by considering, first, the frame of reference in which the field has no space dependence, and then applying a Lorentz transformation to obtain a wave whose space-time dependence is a function of t — nz / c only, where n is a constant. Exact (nonlinear, relativistic) results for known special cases, and some others, are given; and it is shown that, when there is no ambient magnetic field, the general problem in essence reduces to the solution of one second-order, nonlinear differential equation. The desirabifity of introducing a free parameter representing a stream velocity in the direction of wave propagation is emphasized; and the significance of the choice of this parameter is discussed.
Plasma flows in a converging and diverging configuration and the associated plasma particle acceleration: kinetic approach
Authors: Fridman M.
Published: March 2009

Transport laws in collisionless systems must be derived from the one-particle Liouville equation. The simplest cases are those of the CGL invariants along the magnetic field lines, together with the resulting equations of continuity and motion, in circumstances where a supersonic particle flux is parallel to a diminishing magnetic field. We give functional expressions for the two contributions to the parallel heat flux, with integrated forms of kinetic theory. The general expressions, corresponding to the moments of greater order, coincide with those obtained by series development of the differential equation of moments. Moreover, we illustrate a case of both parallel and convergent flux, for which the equation of continuity gives considerable acceleration to the precipitation flux average velocity in the absence of any important electric field, because that acceleration is important in understanding the relationship between the plasmasheet and the ionosphere.
Second harmonic generation using spatially varying static electron number density in a magnetoplasma
Authors: Chakrabarti N. B. , Basu B. N.
Published: March 2009

The Boltzmann transfer equation for electrons in an r.f. discharge plasma immersed in a stationary magnetic field is solved for the various coefficients of the expansion of the distribution function, expanded in a Taylor series in velocity space. Assuming a spatial variation of static electron number density as the mechanism of harmonic generation, explicit expressions for the inner field and the second harmonic current density are derived. The r.f. electric field is assumed to be spatially uniform. The geometry of the plasma considered is that of a rectangular waveguide, but with the parallel plates of one of the two pairs of the metal plate boundaries of the plasma much more closely spaced than those of the other pair. Cyclotron resonance is studied in a situation where the frequency of electron-neutral particle collisions v is much less than the frequency of the r.f. field ω/2π. The resonance effect is obtained, and is found to be more pronounced at the cyclotron frequency ω = ωc than at 2ω = ωc. For v≫ω/2π, the result is not sensitive to the value of the stationary magnetic field, and the resonance effects are absent. The effect of collisions on the process of harmonic generation is also studied.
Pitch angle and energy diffusion coefficients from resonant interactions with ion–cyclotron and whistler waves
Authors: Lyons Lawrence R.
Published: March 2009

General relations for quasi-linear diffusion coefficients in pitch angle and energy are applied to resonant particle interactions with ion–cyclotron and whistler waves. Expressions for the diffusion coefficients, valid for any distribution of wave energy with frequency and wave normal angle, are derived and normalized to be independent of the ambient magnetic field intensity and the electron density. The results illustrate how resonant particle diffusion rates vary with pitch angle and energy, and how the diffusion rates depend upon the distribution of wave energy.
The effects of trapped and untrapped particles on an electrostatic wave packet
Authors: Espedal Magne S.
Published: March 2009

We present a procedure to solve the Vlasov–Poisson equations for electrostatic wave packets. We obtain a Schrödinger type of wave equation, taking the wave– particle interaction into account. We use this equation to study the propagation of one finite-amplitude wave packet. We find a change in amplitude caused by interaction between the packet and particles propagating near to the group velocity. Also, we find a modulation of the plasma in the front of the packet, caused by trapping effects.
Dispersion relation for electron waves propagating in an isotropic plasma containing Maxwellian and suprathermal electrons
Authors: Sanmartin Juan R.
Published: March 2009

The paper discusses the dispersion relation for longitudinal electron waves propagating in a collisionless, homogeneous isotropic plasma, which contains both Maxwellian and suprathermal electrons. It is found that the dispersion curve, known to have two separate branches for zero suprathermal energy spread, depends sensitively on this quantity. As the energy half-width of the suprathermal population increases, the branches approach each other until they touch at a connexion point, for a small critical value of that half-width. The topology of the dispersion curves is different for half-widths above and below critical; and this can affect the use of wave-propagation measurements as a diagnostic technique for the determination of the electron distribution function. Both the distance between the branches and spatial damping near the connexion frequency depend on the half-width, if below critical, and can be used to determine it. The theory is applied to experimental data.
Shock reflexion and shock-wave interaction in field-aligned flows
Authors: Natter Manfred
Published: March 2009

This paper considers the steady two-dimensional problem of regular reflexion and symmetric intersection of oblique magnetogasdynamic shock waves. It is assumed that the fluid medium is a non-viscous, non-heat-conducting, ideal gas of infinite electrical conductivity, and that the applied magnetic field is parallel to the velocity of the approaching stream. In view of the complexity of the shock relations, a graphical method is presented for determining the orientation and strength of the reflected shock wave in terms of the Laval number M*1(flow speed divided by critical sound speed), the Alfvén number A1(flow speed divided by Alfvén speed), and the shock angle ϑ1ahead of the incident shock. Moreover, the possible ranges of M*1, A1, and ϑ1, for which regular reflexion may occur, are calculated and illustrated graphically for the case of a monatomic gas.
Landau damping of surface waves at a plasma— vacuum interface
Authors: Clemmow P. C. , Elgin J. N.
Published: March 2009

The exact surface-wave dispersion relation is expressed in terms of elementary functions for a plasma characterized by a ‘resonance’ velocity distribution function. An approximate form of the relation is derived for the case when the thermal velocity spread is much less than c. The pure surface wave obtained by dropping the term responsible for Landau damping is compared with that predicted on the basis of a fluid model of the plasma. The effect of Landau damping is then investigated, both by analytic approximations and by computation. Two branches of the solution to the dispersion relation are found; and it is shown that the surface wave suffers increasingly severe damping as the frequency grows beyond 1/ √ 2 times the plasma frequency. It is argued that qualitatively similar damping would be present were the plasma to have a Maxwellian equilibrium distribution function.
Lagrangian approach to non-linear wave interactions in a warm plasma
Authors: Galloway J. J. , Kim H.
Published: March 2009

In this paper, the coupled-mode equations and coupling coefficients for three-wave interaction are derived by a Lagrangian approach for a general medium. A derivation of the Low Lagrangian for a warm plasma is then given, which avoids certain problems associated with the original analysis. An application of the Lagrangian method is made to interaction between collinearly-propagating electrostatic waves, and a coupling coefficient is derived which agrees with a previous result obtained by direct expansion of the non-linear equations. The paper serves primarily to present and demonstrate a conceptually useful and efficient theoretical approach to non-linear wave interactions.
Ideally conducting magnetostatic equilibria and associated time dependent, resistive flows
Authors: Stevenson John C.
Published: March 2009

Several types of two-dimensional solutions for the equations of magnetohydrodynamics are described. For all these solutions the magnetic field contains at least one hyperbolic neutral point. Two new magnetostatic equilibria are introduced for the ideally conducting case. The magnetic field associated with one of these is used to construct an exact time-dependent solution of the MilD equations where the fluid is necessarily at rest. In the case where the field lines are hyperbolae, it is demonstrated that retention of the energy equation (ordinarily decoupled for incompressible flows) implies that the flow beginning at rest, remains at trest
Electrostatic oscillations in cold inhomogeneous plasma Part 2. Integral equation approach
Authors: Sedláček Z.
Published: March 2009

Small amplitude electrostatic oscillations in a cold plasma with continuously varying density have been investigated. The problem is the same as that treated by Barston (1964), and in part 1 of this paper, but, instead of starting from a differential equation, we base our treatment on an integro-differential equation for the transverse component of the electric field. This equation is very similar to the Vlasov equation, and we show this to be the cause of the striking similarities between the two theories pointed out in part 1. The normal-mode analysis utilizes the similarity of the integral equation for the eigenfunctions to the equation of anisotropic neutron transport. The continuum eigenfunctions are found in the form of a generalized van Kampen eigenmode, and their calculation is reduced to solving a non-singular integral equation. Equivalence of the eigenfimctions found in this way and of those found by solving the equivalent differential equation is proved, and the question of orthogonality and normalization is discussed.
Closed inner region solution including viscosity for resistive tearing in cylindrical geometry
Authors: Hosking R. J.
Published: March 2009

A closed solution for the increment in the logarithmic derivative &dgr;(Q) over the inner (‘resistivity’) region for resistive tearing theory in cylindrical geometry including ‘parallel’ viscosity is compared with an earlier numerical solution. The singular point Qcrit about which δ(Q) exhibits branch-point behaviour in the presence of compressibility is identified; modification of the viscous theory, to include (for example) finite Larmor radius effects, is suggested. In the incompressible limit, a familiar (inviscid) stability criterion is recovered, in the presence of ‘parallel’ viscosity.
Kinetic energy corrections for the free electrons in a high-frequency, fully-ionized plasma
Authors: Lupu Gheorghe
Published: March 2009

It is found that, for a fully-ionized, homogeneous plasma in a high-frequency electric field, the fundamental term 1 in the kinetic-energy correction is defined by the intensity and frequency of the electric field and by the collision frequency v1. We obtain the Debye–Hükel energy correction in 2, too, as did Theimer & Wright, but this term is much smaller than 1, and its coefficient is no longer a constant.
On the stability of nonlinear magneto-sonic waves in a collisionless plasma
Authors: Infeld E. , Rowlands G.
Published: March 2009

Demehenko & Hussein (1973) discussed some properties of nonlinear magneto-sonic waves in a collisionless plasma. The relevant equation describing the space dependence x of the magnetic field may be written in the form
d2y/dx2+f(y) = 0, (1)
where f(y) is a nonlinear function of y only.
Formation and recurrence of ion wave solitons
Authors: Watanabe S.
Published: March 2009

The interaction between an ion wave and its second harmonic is discussed theoretically, on the basis of coupled-mode equations derived from the Korteweg–de Vries equation. Using an exact solution of the coupled-mode equations, we give a numerical analysis of the properties of the solutions; and we show that superposition of two waves can describe the formation of two solitons, the interaction between them, and the recurrence of an initial state. Our theory can explain completely recent experimental results on ion wave solitons excited by a continuous sine wave.

The propagation of a nonlinear wave in a dispersive medium has been extensively studied in the last decade. In a plasma, a finite-amplitude ion wave can form solitons in the course of its evolution, if wave damping is neglected.
Ion-acoustic wave induced convective cells
Authors: Shukla P. K. , Yu M. Y.
Published: March 2009

It is shown that a finite-amplitude ion-acoustic wave in a uniform magneto- plasma can enhance two-dimensional plasma vortices. The latter results from a modulational instability. The growth rates are obtained analytically.
The interaction of a moving neutral gas with a stationary magnetized plasma
Authors: McKenzie J. F. , Varma R. K.
Published: March 2009

In this paper it is shown that a stationary plasma can be accelerated by a moving neutral gas only if the velocity of the neutral gas exceeds Alfvén's critical velocity. An expression for the terminal velocity of the interaction is given which shows that, in the limit of high incoming neutral gas speeds, the composite plasma is accelerated up to one quarter of the gas speed. We also discuss terminal velocities associated with the inverse problem, namely the deceleration of a magnetized plasma as a result of its motion through, and interaction with, a stationary neutral gas.
Wave excitation by inhomogeneous suprathermal electron beams
Authors: Freund H. P. , Dillenburg D. , Wu C. S.
Published: March 2009

Wave excitation by an inhomogeneous suprathermal electron beam in a homogeneous magnetized plasma is investigated. Not only is the beam density non-uniform, but the beaming electrons also have a sheared bulk velocity. The general dispersion equation including both electrostatic and electromagnetic effects is derived. Particular attention is paid to the whistler mode. It is found that the density-gradient and velocity-shear effects are important for waves with frequencies close to the lower-hybrid resonance frequency.
Propagation of hydromagnetic waves in a relativistic plasma
Authors: Granik A.
Published: March 2009

The hydrodynamic approach to a relativistic gas is studied on the basis of methods used by Chew, Goldberger & Low and by Scargle. As the result of this study, the explicit form of the energy–momentum tensor is obtained by straight-forward application of Lorentz transformation. The term corresponding to non-zero momentum density in the plasma frame of reference is included in the energy–momentum tensor. For the limiting case of small bulk velocities compared with the speed of light in vacua, the energy flux as described by non- relativistic theory is immediately recovered. For the special case of scalar pressure, the energy–momentum tensor considered by Taub and by Harris follows directly from our expression. In a small-perturbation approximation, it is possible to close the system of MHD equations. As a result the solution describing all possible wave modes is derived. This solution coincides with the solution obtained by means of the kinetic theory.
Comments on the paper ‘Self-similar state of a weakly turbulent plasma’
Authors: Vekstein G. E. , Ryutov D. D. , Sagdeev R. Z.
Published: March 2009

In a recent paper, Balescu (1980) criticizes the self-similar solution in the problem of anomalous plasma resistivity (Vekstein, Ryutov & Sagdeev 1970) and comes to the conclusion that this solution is not correct. The aim of this comment is to show why Balescu's arguments are erroneous.

We consider here the simplest case of the one-dimensional collisionless plasma in the presence of an external electric field.