bluuebunny/crossref_metadata_2025 huggingface dataset:
On the instability of a spatially confined electron beam in a magnetized plasma
Authors: Strangeway R. J.
Published: March 2009

The instability of a field-aligned electron beam of finite width streaming through a uniform magnetized plasma is investigated. An earlier paper presented an analysis of the normal modes for electromagnetic waves in a ‘top hat’ beam– plasma system. The present paper extends the analysis to higher frequencies and different system parameters. Besides discussing the nature of the normal modes, the wave field variation within the beam region is studied. In doing this it is found that an electrostatic approximation is useful in describing the general form of the dispersion relation, specifically showing how the beam width controls the range of allowed solutions. The electrostatic approximation is shown to be good for most of the range of frequencies considered. When the electron gyrofrequency is greater than the electron plasma frequency, the theory predicts that the cold plasma upper-hybrid resonance band (Z mode) is stable to negative Landau damping. A criterion for applying this result to beam-plasma systems other than the ones investigated here is developed, and it is found that the effect should be more readily observable in laboratory experiments than in space plasmas.
Low-frequency electrostatic instability due to anti-loss-cone electrons
Authors: Bhatia K. G. , Lakhina G. S.
Published: March 2009

The energetic anti-loss-cone electrons can drive a low-frequency electrostatic instability, propagating transverse to the ambient magnetic field, in the presence of a cold plasma. The typical real frequency and growth rates associated with this instabifity are respectively, of the order of (ωp being the proton cyclotron frequency). The instability has a transverse wavelength ⋍10ρe (ρe being the Larmor radius of energetic electrons). For the parameters pertinent to auroral plasma at 1RE, the quasi-linear analysis shows that the instability can give rise to an oscillating electric field Esat ⋍0.5−25 mV/ m and an increase of 100–103 K in the temperature of cold electrons. The instability may be relevant to recent observations of low-frequency turbulence on the auroral field lines.
Low-frequency linear response of a cylindrical tokamak with arbitrary cross-section to ‘helical’ perturbations
Authors: Jensen Torkil H. , Chu Ming S.
Published: March 2009

Current driven, ‘helical’ (non-axisymmetric) modes of a tokamak with arbitrary cross-section are considered in the straight (cylindrical) geometry approximation. The plasma is considered surrounded by a resistive wall. The plasma may be unstable on a fast time-scale, namely the MHD or tearing mode time-scale, on a slow time-scale given by the wall properties or it may be stable. The formalism given in this paper allows determination of stability by relatively simple numerical means. In the case of instability on the slow time-scale, the formalism allows determination of growth rates and mode structures. Since the formalism is an eigenvalue formalism with orthogonal eigenfunctions, it is well suited for calculation of the effects on a stable plasma of slow error fields caused by externally driven error currents flowing predominantly in the direction of the ignorable co-ordinate.
Nonlinear evolution of the sheet pinch
Authors: Matthaeus W. H. , Montgomery David
Published: March 2009

An incompressible, dissipative numerical code of the spectral type is used to follow the nonlinear evolution of a magnetohydrodynamic sheet pinch in two spatial dimensions. The evolution involves considerable turbulent activity in the electric current field, with the excited spatial scales ranging from the size of the containing volume down to the dissipation lengths of the magnetic and velocity fields. Strong current filamentation near magnetic X-points is observed, as is lsquo;jetting’, or expulsion of magnetofluid from the vicinity of the X-point parallel to the current sheet.
Plasmadynamics near a self-similar turbulent state
Authors: Balescu R.
Published: March 2009

The transport properties of a turbulent plasma are investigated in the vicinity of a self-similar turbulent state (SSTS). This state plays the same role of reference as the local equilibrium for a collisional plasma. The stability of the SSTS against velocity gradients is proved. Under certain well-defined conditions a plasma- dynamical regime is established, in which the initial conditions are forgotten and the macroscopic plasmadynamical quantities obey closed differential equations. The anomalous viscosity arising in this regime is investigated in detail. This quantity is time-dependent (a feature impressed by the self-similar character of the reference state). A number of additional typically turbulent terms appear in the equation of motion: they arise from interference between flow and collisions or magnetic field.
Ponderomotive pressure effects in laser driven high-temperature plasma flows
Authors: Bobin J. L.
Published: March 2009

Gasdynamical equations taking radiation energy density and ponderomotive pressure into account are investigated. Conditions for these quantities to be important are stated: low absorption, reflexion at cut-off. The density ratio in a discontinuity is studied as a function of ponderomotive pressure, absorbed intensity and Mach number in the initial state. Chapman–Jouguet conditions are defined. Compressive (R type) flows and rarefaction (D type) appear. The structure of the latter is discussed including plasma effects.
The electrostatic instability of rippled, magnetically focused, non-neutral, cylindrical beams of charged particles
Authors: Cuperman S. , Petran F.
Published: March 2009

The stability of rippled non-neutral beams of charged particles produced under conditions in which centrifugal, space charge and magnetic forces are not balanced, is investigated. The beams are considered to be cold and assumed to partly fill a conducting pipe in the presence of an axial uniform magnetic field. The calculations hold for small ripple amplitudes and long-wavelength electrostatic perturbations (or, alternatively, thin beams). The rippled equilibrium beams considered in this work are found to support unstable, azimuthally symmetric, surface electrostatic modes. The growth rates are proportional to the relative ripple amplitude and to the effective beam plasma frequency.
Low-frequency heating and induced particle transport in an inhomogeneous plasma with Ohmic current
Authors: Faulconer D. W.
Published: March 2009

Particle and energy conservation relations appropriate to drift and MHD ordering are derived and simplified in the MHD case by exploiting an invariant of guiding-centre motion existing when E. B = 0. An MHD perturbation calculation is made of the local average density and energy rates of change induced by a wave of general transverse-electric type in an inhomogeneous plasma. The resulting expressions, which incorporate the effect of equilibrium electric field on zeroth-order trajectories, are of striking simplicity. In the drift-ordered limit their divergence from other drift results is discussed; particle pump-out in the given heating fields is seen to be much smaller than found previously.
Low frequency response of a resistive plasma to axially independent or axisymmetric perturbations
Authors: Jensen Torkil H. , Thompson W. B.
Published: March 2009

A formalism is described which permits calculation of the low frequency response of a resistive plasma with non-circular cross-section in magnetohydrodynamic equilibrium to an externally imposed current field in the direction of the ignorable co-ordinate. This formalism is limited to slow variations on the resistive penetration or ‘skin’ time-scale and eliminates rapid motions at the hydrodynamic rate. It is useful for calculating the effectiveness of low frequency Ohmic heating and for the study of feedback stabilization. It also determines stability criteria and gives estimates of growth rates. The presence of a hyperbolic axis in the Doublet configuration makes the incorporation of a finite resistivity in the treatment important.
Excitation of lower hybrid waves by electron beams in finite geometry plasmas. Part 1. Body waves
Authors: Shoucri Magdi M. , Gagné Réal R. J.
Published: March 2009

The quasi-static lower hybrid eigenmodes of a plasma column in a cylindrical waveguide are determined, and their linear excitation by a small density electron beam is discussed for the cases of a hot electron beam as well as for a cold electron beam. It is shown that under certain conditions, finite geometry effects introduce important quantitative and qualitative differences with respect to the results obtained in an infinite geometry.
The coherent wave–particle resonance perturbed by turbulence
Authors: Brinca Armando L.
Published: March 2009

Stochastic fields perturb the evolution of coherent wave–particle resonances. Knowledge of the probabifity distribution obeyed by the trapping parameter places upper limits on the time interval where the noiseless description of the resonance is acceptable. Alternatively, given the interaction time, estimates of the relative intensity of the coherent mode and turbulent fields required for a typical resonance effect to occur are obtained.
Nonlinear decay of a propagating lower-hybrid wave in a plasma
Authors: Shukla P. K. , Mamedow M. A.
Published: March 2009

This paper studies the nonlinear coupling between a large amplitude propagating lower-hybrid wave and two electromagnetic waves in a plasma. Using a two-fluid model and Vlasov and Maxwell's equations, we derive a dispersion relation governing this three-wave interaction process. It is shown that a finite wavenumber lower-hybrid pump can decay into a whistler and a kinetic Alfvén wave. Calculations of the threshold condition suggest that this decay process may occur both in the laboratory and in the ionosphere.
Elementary derivation of the kinetic equation for the two-dimensional guiding centre plasma
Authors: Mond Michael , Knorr Georg
Published: March 2009

A kinetic equation for a two-dimensional inviscid hydrodynamic fluid is derived in two ways. First, the equations of motion for the modes of the fluid are interpreted as stochastic equations resembling the Langevin equation. To lowest order a Fokker–Planck equation can be derived which is the kinetic equation for one mode. Secondly, a suitable iteration scheme is applied to the Hopf equation which results in the same kinetic equation. A parameter describing the time scale is arbitrary and cannot be determined by the applied methods alone. It is shown that the kinetic equation satisfies the conservation requirements and relaxes to an equilibrium which is a rigorous solution of the Hopf equation.
Thermal flux reduction by electromagnetic instabilities
Authors: Okada Toshio , Yabe Takashi , Niu Keishiro
Published: March 2009

From a dispersion relation, linear growth rates of electromagnetic instabilities are obtained in an electron plasma whose velocity distribution function has a high-energy tail. Theory is developed to derive the reduction in the thermal flux caused by these electromagnetic instabilities. Nonlinear theory leads to the saturation level of instabilities. Numerical simulations are carried out using a particle-in-cell method. The reduction in thermal conduction predicted by the theory is found to be in good agreement with computer simulations.
Effects of trapped alpha particles on internal kink modes in tokamaks
Authors: Helander P. , Lisak M.
Published: March 2009

The theory of linear interaction between internal kink modes and fusionproduced high-energy alpha particles in a toroidal plasma is extended by including finite-banana-width corrections to the alpha dynamics. An important implication of the theory for the stability properties of kink modes is that the finite-banana-width effects increase the value of the poloidal alpha beta required to attain the stable domain of operation as well as that required to excite the high-frequency fishbone instability. Furthermore, these effects lead to a reduction in the instability growth rate in both the low- and high-frequency unstable regimes.
Relativistic quantum kinetic theory of stimulated bremsstrahlung of an axial vacuum mode by an electron beam travelling in a uniform magnetic field
Authors: Kim S. H.
Published: March 2009

Stimulated emission of ordinary plane-polarized electromagnetic waves propagating in the axial direction by a relativistic or non-relativistic electron beam is investigated using a new quantum kinetics based on the Dirac equation. The momentum and energy conservation laws and the time-reversal invariance of the transition probability are used explicitly to calculate the gain without expanding the transition rate as a power series in ħ. It is found that electroncyclotron masing occurs when the longitudinal temperature differs greatly from the transverse temperature for any beam energy. This electron-cyclotron masing is an individual-electron effect, which is not related at all to the phase bunching.
Attenuation of longitudinal electro-acoustic waves in a plasma
Authors: Papa R. J. , Lindstrom P.
Published: March 2009

There are several practical situations in partially ionized plasmas when both collisionless (Landau) damping and electron-neutral collisions contribute to the attenuation of longitudinal waves. The longitudinal-wave dispersion relation is derived from Maxwell's equations and the linearized Boltzmann equation, in which electron-neutral collisions are represented by a Bhatnagar–Gross–Krook model that conserves particles locally. (The dispersion relation predicts that, for a given signal frequency ώ), an infinite number of complex wavenumbers kn can exist. Using Fourier–Laplace transform techniques, an integral representation for the electric field of the longitudinal waves is readily derived. Then, using theorems from complex variable theory, a modal expansion of the electric field can be made in terms of an infinite sum of confluent hypergeometric functions, whose arguments are proportional to the complex wavenumbers kn. It is demonstrated numerically that the spatial integral of the square of the electric field amplitude decreases as the electron-neutral collision frequency increases. Also, the amount of energy contained in the first few (lowest) modes, and the coupling between the modes, is examined as a function of plasma frequency, signal frequency and collision frequency.
A note on the application of Whitham's method to nonlinear waves in dispersive media
Authors: Dysthe K. B.
Published: March 2009

In this paper, a method developed by Whitham for obtaining equations governing the slow variation of finite-amplitude wave trains, is slightly modified. The relevant equations describing wave-wave interaction, and self-action are derived. The stability of a finite-amplitude wave train is treated in two different ways. The possibility of having a ‘solitary modulation’ on a finite-amplitude wave train is pointed out.
Obliquely propagating unstable whistler waves: a computer simulation
Authors: Cuperman S. , Sternnlieb A.
Published: March 2009

Obliquely propagating unstable electron cyclotron electromagnetic (whistler) waves have been studied with the aid of an especially designed computer simulation experiment. The plasma–wave system considered is homogeneous and infinite, and the plasma is taken to be a mixture of warm (bi-maxwellian) and cold populations. With no cold plasma, the rates of growth of the low k modes maximize for the case of parallel propagation (¸ = 0°;) and decrease as ¸ increases; for higher k modes, the opposite occurs. Changing from k space to ω space the above results indicate that off-angle propagation tends to stabilize the low-frequency whistlers but to destabilize the higher-frequency ones. These results are consistent with linear predictions. In all cases, however, the total electromagnetic energy generated in the system decreases with increasing θ. When cold plasma is added to the system, the total generated electromagnetic energy can maximize for a non-zero propagation angle.
Excitation of the plasma and upper hybrid resonances in a warm magnetoplasma by an alternating electric dipole
Authors: Chassériaux J. M.
Published: March 2009

The potential created by an alternating dipole in a warm magnetoplasma is calculated analytically, in the approximation of the full adiabatic theory, for excitation frequencies ω close either to the upper hybrid frequency ωT or to the plasma frequency ωp The potential is finite at these frequencies. For ω ˜ ωp, the equipotential surfaces can be considered roughly as planes perpendicular to the static magnetic field B. For ω ˜ ωT and ω2p ≪3ω2b (where ωb is the electron gyrofrequency), the equipotential surfaces are cylinders of axis B. On the other hand, if ω2p ≪3ω2b, the potential is the sum of a cylindrical wave and of a wave for which the equipotential surfaces are paraboloids of axis B. These results are used to calculate the mutual impedance ζ of a quadrupole probe, and it is shown that the measurement of Zγ atω = ωT provides a new method for determining the electron temperature.
Fast-wave interaction with a relativistic electron beam
Authors: Sarangle P.
Published: March 2009

The excitation of a relativistic electron beam, by means of a fast waveguide structure, is examined. Here the beam is injected into a modified waveguide, and interacts with the modes of the guide in such a way as to transform some of its energy into microwave radiation. This microwave generation device, called the Ubitron, is based upon a fast-wave excitation of a magnetically modulated relativistic electron beam. The beam is modulated by injecting it into a small spatially periodic magnetic field region within the guide. Analysis of this interaction shows that the slow space charge beam mode couples actively to the fast transverse electric guide mode. The result is parametric instability of the coupled modes. Synchronism between the doppler-shifted transverse travelling wave and the undulating electron beam results in a transfer of energy from the beam to the transverse field. The parametrically growing field can be a source of microwave radiation. The period magnetic field, together with the beam density, provide the coupling media between the unstable waves. The growth rate of the instability is shown to depend, in a nonlinear manner, on the product of the beam plasma frequency and the strength of the applied rippled magnetic field. The growth rate is obtained as a function of the system parameters.
Comparison of quasi-linear predictions with a computer simulation of whistler waves in unstable plasmas
Authors: Cuperman S. , Lyons L. R.
Published: March 2009

The quasi-linear concept of plateau formation along resonant diffusion surfaces is compared with the time evolution of the electron distribution function during a computer simulation experiment of whistler-mode waves in unstable plasmas. It is found that, as the wave intensities grow, plateau formation does indeed occur, with the distribution function becoming constant along diffusion surfaces at the time when wave intensities maximize. Following the formation of the plateaus, both the wave intensities and the slope of the distribution function along diffusion surfaces oscillate in a manner suggesting msh;mode coupling. Tbe slope of the distribution function along diffusion surfaces, which controls the linear wave growth rate, also gives good predictions of the sign of the actual wave growth rate during the experiment.
A theory for scattering by density fluctuations based on three-wave interaction
Authors: Harker K. J. , Crawford F. W.
Published: March 2009

The theory of scattering by charged particle density fluctuations of a plasma is developed for the case of zero magnetic field. The source current is derived on the basis of, first, a three-wave interaction between the incident and scattered electromagnetic waves and one electrostatic plasma wave (either Langmuir or ion-acoustic), and secondly, a synchronous interaction between the same two electromagnetic waves and the discrete components of the charged particle fluctuations. Previous work is generalized by no longer making the assumption that the frequency of the electromagnetic waves is large compared to the plasma frequency. The general result is then applied to incoherent scatter, and to scatter by strongly driven plasma waves. An expansion is carried out for each of these cases to determine the lower order corrections to the usual high-frequency scattering formulae.
Purely growing electromagnetic modes in high-β plasmas
Authors: Lakhina G. S. , Buti B. , Nayar Girija
Published: March 2009

Electromagnetic waves propagating transverse to an external magnetic field in a high-β (β being the ratio of the kinetic pressure to the magnetic pressure) plasma become unstable through purely growing modes when β∥e, (electron β parallel to the magnetic field) exceeds a certain minimum value β∥*. For J ≦ 2 (J being the distribution index), the region of instability consists of a single band of unstable wavenumbers k, whereas for J ≥ 3 more than one unstable wave number band may exist. The growth rates are largest for J = 0, and tend to decrease as J increases. The presence of hot ions increases the instability region by exciting a low-frequency instability. This instability gets excited at considerably lowered values of β‖e, and has growth rates of the order of ion cyclotron frequency. The effect of T‖i/T‖e and T‖e/T⊥e is destabilizing, whereas that of T⊥i/T⊥e is stabilizing.
General relations for resonant particle diffusion in pitch angle and energy
Authors: Lyons Lawrence R.
Published: March 2009

By applying quasi-linear diffusion theory, general expressions are obtained for particle diffusion coefficients in both pitch angle and energy. The results are valid for resonant interactions with any mode of weak plasma turbulence, with wave energy distributed over any range of frequencies and wave normal angles. Simple relations are found between the diffusion coefficients, these relations reflecting the geometry of the diffusion surfaces for resonant particles.
Nonlinear interaction of waves in an active molecular plasma
Authors: Bonnedal M. , Wilhelmsson H.
Published: March 2009

The purpose of the paper is to investigate, by means of kinetic theory, the wave—wave couplings that may occur in a magnetized and partially ionized plasma medium containing neutrals (or ions) with inverted population levels. We study the interaction of three monochromatic waves which propagate parallel to the direction of a magnetic field in the medium. Transverse as well as longitudinal waves are considered. The present paper, which represents a generalization of previous contributions to the subject, offers several new interesting processes of interaction, which may be basic to the description of phenomena occurring in astrophysics. Furthermore, it is of interest in connexion with laboratory plasma and laser experiments.
An analytical study of the oblique echo model for the topside upper hybrid resonance
Authors: Parkes E. J.
Published: March 2009

The oblique echo model for the resonance near the local upper hybrid frequency fT observed by topside sounders involves the propagation of slow waves away from the sounder, which later return as echoes after refiexion due to an electron density gradient. The model is investigated using the WKB technique introduced by Fejer & Yu. The resulting set of saddle-point equations is solved by a method which can, unlike previous work, be applied to both the ‘strong’ resonance (for which fT < 2fH where fH is the electron gyrofrequency) and to the ‘weak’ (fT 2fH) resonance. Throughout the calculations the validity of the approximations made is checked. It is found that the weak resonance solution is not valid for typical topside parameters. A condition is derived for the existence of intercepting ray paths and for the maximum time delay which occurs when they do exist. For the strong resonance the electric field of a small pulsed dipole is calculated. Expressions are found for the frequency of the two echoes which are received by the sounder and the frequency of the beating between them. Although they are only strictly valid for times longer than typical observation times, they yield results that agree well with the corresponding results from ray- trajectory computations.
Diffusion of resonance particles in strong plasma turbulence
Authors: Gupta M. R.
Published: March 2009

This paper derives an expression for the velocity space diffusion tensor (time asymptotic) for resonant particles in the weak-coupling limit of strong plasma turbulence theory. The analysis is based on an improved approximation scheme for the determination of the actual particle trajectories, rather than the determination of &ensemble averaged particle orbits’ with the help of the &average Vlasov propagator’. Except for numerical factors of order unity, the results agree with those of Birmingham & Bornatici, both when Tc → 0 (Tc is the correlation width of the fluctuating field as seen by the resonant particles), and when Tc is finite but small. The paper indicates the limits of this method, as well as those of Birmingham & Bornatici.
Nonlinear effects of two modified ordinary monochromatic waves
Authors: Selim A. A.
Published: March 2009

Quantum field theory is used to investigate the nonlinear effects of two modified ordinary monochromatic waves propagating across a uniform magnetic field. Amplitude-dependent wavelength and frequency shifts are derived. Unlike previous work that employs the Krylov–Bogoliubov–Mitropolskii method, the investigation uses the diagrammatic technique of field theory. The calculations show that increase of the above-mentioned physical parameters due to nonlinear interaction and drifting electrons depends upon the ratio of drifting to phase velocity.
Re-normalized quasi-linear approximation of plasma turbulence: Part 1. Modification of the Weinstock weak-coupling limit
Authors: Misguich J. H. , Balescu R.
Published: March 2009

A re-normalized expansion is presented for the solution of the fluctuating Vlasov equation for turbulent plasmas. Its first term can be identified with the Weinstock result in the weak-coupling approximation. The use of time-ordering operators allows one to solve the Weinstock UA evolution operator explicitly. Detailed results are given for the weak-coupling approximation, presented here as a simple re-normalization of the quasi-linear theory. Results of Weinstock and Birmingham & Bornatici, concerning the frequency shift, resonance broadening and Dupree damping appear to be deeply modified by similar corrective terms. These arise from a consistent handling of expressions involving non-commuting operators.
Reflexion and transmission theorems for characteristic waves in stratified anisotropic absorbing media
Authors: Suchy Kurt , Altman Colman
Published: March 2009

The solutions of Maxwell's equations and of their adjoint equations, being essentially different in absorbing media, are written in terms of matrizants. A relation between these is established, utilizing the constancy of the bi-linear concomitant. With this, and with the concept of the conjugate field, introduced in Suchy & Altmann (1975), a theorem, connecting the transfer matrices of the field and the conjugate field, is derived. This, in turn, leads to a corresponding theorem connecting the scattering matrices, which are composed of the refiexion and transmission matrices.
The propagation of a pulse in a dispersive plasma: an exact solution compared with various approximations
Authors: Buckley R.
Published: March 2009

This paper considers an example of the propagation of a finite wave-train in a plasma of relatively simple dispersive properties. In this case, the wave field can be evaluated exactly. The concept of a wave-packet moving at the group speed can therefore be tested rigorously. Various approximations to the field, physically more transparent than the exact solution, are presented and compared with the latter. One of these, relevant in the neighbourhood of the ideal group front, is in fact applicable to a wide range of dispersion laws. The paper demonstrates broadening with time, and eventual disappearance, of the pulse.
Two-stream instability in plasmas for arbitrary propagation
Authors: Aggarwal S. S. , Talwar S. P.
Published: March 2009

The problem of the two-stream instability in warm, collisionless, field-free plasmas is investigated for arbitrary direction of propagation vector, using the moment equations. It is found that the configurations characterized by (i) a beam of electrons with ions immobile, and (ii) all electrons moving through mobile ions, are stable for subsonic interpenetration speeds. For supersonic speeds, however, the configurations are unstable both for electrostatic and electromagnetic perturbations. The former instability is restricted only to a cone of propagation about the streaming direction, while the latter exists for all angles, and has growth rates that are even larger than the electrostatic growth rates in the limit of long-wavelength perturbations.
The use of quasi-normality assumptions in the theory of the two-dimensional guiding-centre plasma
Authors: Cook I.
Published: March 2009

It is argued that the use of quasi-normality or ‘random phase’ approximations in the kinetic theory of the two-dimensional guiding-centre plasma gives rise to unphysical and inconsistent results.
On the interaction of wave beams in plasmas
Authors: Giles M. J.
Published: March 2009

We consider two non-parallel beams, each of width a, that interact in a plasma and excite a wave that travels across their region of intersection. We determine the dependence of the amplitude of the excited wave on a for the limiting cases of large and small values of the ratio of the initial beam intensities.
Quasi-static modes of oscillation of a cold toroidal plasma
Authors: Love John D.
Published: March 2009

The normal modes of oscillation of a cold dielectric plasma ring are analysed in the quasi-electrostatic approximation. An exact dispersion relation is derived, valid for all aspect ratios. Its solutions are shown to be extremely close to those of an infinite cylindrical plasma with cross-section equal to the minor cross-section of the ring, when the cylinder is considered as a wavelength-preserving limit of the toroidal geometry.
The second-harmonic resonance for nonlinear hydromagnetic waves
Authors: Matsumoto Yasuji , Sugimoto Nobumasa , Inoue Yoshinori
Published: March 2009

We investigate second-harmonic resonance for weakly nonlinear hydromagnetic waves travelling in a cold collisionless plasma by the method of multiple scales. We find that the second-harmonic resonance can occur between the magneto-acoustic modes; but it can occur neither between the magneto-acoustic and the Alfvé n modes, nor between the Alfvé n modes. The resonant frequency of the magneto-acoustic modes is characterized by the geometric mean of the ion and electron Larmor frequencies. We obtain steady-state solutions to the dynamical equations governing the second-harmonic resonance. The result of analysis shows that the envelopes of the two resonant waves are composed of two periodic wave- trains, two solitary pulses or a solitary pulse and a phase jump. We also extend the problem to more general dispersive wave systems.
Kinetic description of linear theta-pinch equilibria
Authors: Batchelor D. B. , Davidson R. C.
Published: March 2009

Equilibrium properties of linear theta-pinch plasmas are studied within the framework of the steady-state (∂ / ∂ t = 0) Vlasov– Maxwell equations. The analysis is carried out for an infinitely long plasma column aligned parallel to an externally applied axial magnetic field Bzext ê 2. Equilibrium properties are calculated for the class of rigid-rotor Vlasov equilibria, in which the jth component distribution function f j(H⊥, Pθ, υ 2) depends on perpendicular energy H⊥ and canonical angular momentum Pθ, exclusively through the linear combination H⊥ – ω jPθ, where ω j = const. = angular velocity of mean rotation. General equilibrium relations that pertain to the entire class of rigid-rotor Vlasov equilibria are discussed; and specific examples of sharp- and diffuse-boundary equilibrium configurations are considered. Rigid-rotor density and magnetic field profiles are compared with experimentally observed profiles. A general prescription is given for determining the functional dependence of the equilibrium distribution function on H⊥−ωjPθg in circumstances, where the density profile or magnetic field profile is specified.
The electromagnetic interchange mode in a partly-ionized collisional plasma
Authors: Hudson Mary K. , Kennel Charles F.
Published: March 2009

A collisional electromagnetic dispersion relation is derived from two-fluid theory for the interchange mode coupled to the Alfvé n, acoustic, drift and entropy modes in a partly-ionized plasma. The fundamental electromagnetic nature of the interchange mode is noted: coupling to the intermediate Alfvé n mode is strongly stabilizing for finite k2. Both ion– viscous and ion–neutral stabilization are included; and it is found that collisions destroy the FLR cutoff at short perpendicular wavelengths.
Water-bag stability theory for planar bounded plasmas with counter-streaming injection. Part 1. The neutralized diode
Authors: Hu K. M. , Klevans E. H.
Published: March 2009

The stability of a bounded, homogeneous, neutralized plasma with counter- streaming electron beams is analysed. A water-bag model is used to describe the electron distribution in velocity space, so that finite beam temperature and a background plasma are included in the theory. For boundary conditions, the absorber– source wall (the diode boundary) and the reflecting wall are considered. For the former, growth-rate calculations indicate that the instability is a combination of charge bunching (counter-streaming) and diode circuit effect. As the diode length increases, the growth rate of all modes in the system approaches the maximum growth rate. For the reflecting wall, as the length increases, the maximum growth rate transfers to higher and higher order modes with shorter wavelength, while the growth rate of the lower-order modes goes to zero.
Resistive instability in a uniformly rotating magnetoplasma
Authors: Lunn A. D.
Published: March 2009

A closed set of guiding centre equations, derived for a rotating plasma in a static magnetic field, is applied to the problem of the stability of a plasma in a sheared field. The rotation is found to have a stabilizing effect in the absence of resistivity.

A pair of coupled, linear differential equations is derived for the rotating plasma in a weakly sheared field. Dispersion relations are obtained by phase integral methods and, in the absence of finite Larmor radius effects and rotation, instability growth rates proportional to η½13 are found which become proportional to when either is included. The inclusion of both finite Larmor radius and rotation gives growing instabilities proportional to η which are stabilized by the rotation when the finite Larmor radius terms predominate.
Finite-Larmor-radius equations for coffisionless plasmas in general magnetic fields
Authors: Bowers E.
Published: March 2009

Expressing the Vlasov equation in a local system of co-ordinates defined by the magnetic field, the distribution function is expanded in terms of a small parameter e (assumed < 1), the ratio of the ion Larmor radius to a characteristic length of change perpendicular to the magnetic field. Since the finite-Larmorradius (FLR) approximation restricts consideration to weakly unstable systems, the equations apply only to magnetic configurations in which the curvature of the lines of force is weak. In allowing for the effects of plasma pressure (β ˜ I) it is found that the FLR corrections to the stress tensor take their simplest form in the centre-of-mass frame, while the case of low β yields equations best expressed in the guiding-centre frame.
The Effect of Impurity ions on the stability of drift Waves
Authors: Ong R. S. B. , Yu M. Y
Published: March 2009

The propagation and stability of ion and electron drift waves in a non-homogeneous plasma containing impurity ions is considered. It is shown that the presence of impurities in the plasma may significantly affect the stability criteria of these low frequency waves. Furthermore, perturbations at frequencies which are multiples of the impurity ion cyclotron frequency may also be unstable when ½K2u R21 > 1.
The multiple water-bag model for forced oscillations in a warm isotropic plasma
Authors: Noyer M. L. , Navet M. , Feix M. R.
Published: March 2009

It is shown that the multiple water-bag model, with both analytic and numerical properties, is fairly well suited to the study of forced oscillations launched by grid systems, for different geometries with possible non-uniform charge distribution, and for any distance within the range 0–100 Debye lengths.

Freeston (1968) and Freeston & Malik (1971) compared measurements precisely with theoretical values of the electric field near a system of grids and antennas immersed in a plasma. Results provided a valuable diagnostic tool in space research; and radio-frequency probing was used successfully (Beghin & Debrie 1972; Chasseriaux, Debrie & Renard 1972).
On the stability of nonlinear waves coexisting with plasma beams
Authors: Infeld E. , Rowlands G.
Published: March 2009

In this paper we consider the stability of one-dimensional stationary waves set up by two counter-streaming beams of electrons in a background of stationary ions. The perturbations considered are long-wave in a direction perpendicular to the wave. The presence of a uniform magnetic field in the direction of the wave and the effect of a perpendicular pressure are taken into account. In the long-wavelength limit growth rates are diminished by the nonlinear wave. When the amplitude of this wave tends to its maximum value, the growth rates tend to zero. Thus the wave has a stabilizing effect for long-wave perturbations. Three- dimensional effects lead to additional instabilities which are also quenched by the nonlinear wave, but not as fast as the one-dimensional calculation indicates.
On the linear cross-field instability problem
Authors: Dysthe K. B. , Misra K. D.
Published: March 2009

A re-examination of the linear E x B instability problem for infinite stratified media gives results differing from those published. The main point is to warn against the application to inhomogeneous media of the usual instability criterion, as developed for
homogeneous media. The fact that the dispersion relation gives complex values of ω for real k does not always indicate the existence of an instabifity. It could also describe propagation of a constant wave energy through an inhomogeneous medium. It is demonstrated that in certain situations it is possible to choose dependent variables in such a way that these two effects disentangle, allowing for a definite solution of the instability problem.

In this paper the linear stability' problem for an infinite inhomogeneous, partially ionized gas penetrated by crossed electric and magnetic fields, is re-examined. Several authors (e.g. Reid 1968; Whitehead 1967, 1971; Cunnold 1969; Chimonas 1969; Linson & Workman 1970; looper & Walker 1971; Sato 1971; Sato & Tsuda 1972; Kato 1972) have considered the possibility that the so-called cross-field instability exists in the ionosphere. Our reason for treating the problem again is to point out a deficiency in the literature.
Wave propagation in a plasma in the presence of a spatially uniform external periodic magnetic field
Authors: Das K. P.
Published: March 2009

Starting from the kinetic equation and Maxwell's equations, a dispersion relation is obtained for wave propagation through a fully-ionized plasma along a spatially-uniform, external, periodic magnetic field B0 cos ω0t, and several excitation conditions are deduced. The parametri excitation of waves in a plasma by spatially uniform external periodic electric field has been considered by several authors (Aiev & Silim 1965; Montgomery & Alexeff 1966; Jackson 1967; Prasad 1967, 1968; Nishikawa 1968 a, b). The effect of spatially uniform external periodic magnetic field on wave propagation through a hot plasma was considered by Das (1971), who used hydrodynamic equations to study the effect of wave propagation perpendicular to a spatially-uniform, external, periodic magnetic field.
A proposed high-current nanosecond source of energetic ions
Authors: Nation John A.
Published: March 2009

Experiments by Friedman (1972), and theoretical analysis by Sudan & Lovelace (1973), Rostoker (1972), Rostoker & Poukey (1971) and Wheeler (1974), considered ion emissionin a vacuum diode. The ions emitted (e.g. in the Friedman experiment) were generated by laser irradiation of the anode. Using this technique, multiply-ionized species
could be obtained. The ion currentwas limited non-relativistically to the square root of the mass ratio times the electron current, so that energy transfer to the ions was relatively inefficient. Some improvement was obtained at relativistic electron energies.

Sloan & Drummond (1973) proposed a high-current ion accelerator, where the transfer of energy to the ions is achieved by a negative energy cyclotron wave on an intense E beam. Such an accelerator requires an ion source capable of providing several hundred Amperes of protons at energies in the range of a few hundred keV to several MeV. In this article, we propose a suitable ion source for an accelerator.
Statistical acceleration of electrons by lower-hybrid turbulence
Authors: Wu C. S. , Gaffey J. D. , Liberman B.
Published: March 2009

The statistical acceleration of electrons along an ambient magnetic field by large-amplitude lower-hybrid turbulence is discussed. Perturbations driven by a crossfield current and propagating nearly perpendicular to the applied magnetic field are considered. It is assumed that the instability saturates rapidly and that the fluctuating electric field is predominantly electrostatic. This work is not concerned with the detailed saturation mechanism, but rather with what happens to the electrons after the turbulence has saturated. If the turbulence is characterized by a spectrum of small parallel wavenumbers, such that the parallel phase velocity of the waves is greater than the electron thermal velocity, then the turbulence can only accelerate electrons moving with large velocities along the magnetic field. The qusai-linear diffusion equation is solved using a Green's function technique, assuming a power law spectral energy density. The time evolution of an initial Maxwellian distribution is given and the time rate of change of the mean electron energy is calculated for various cases.
Nonlinear interaction of a Gaussian electromagnetic beam with an electrostatic lower-hybrid wave: Brillouin scattering
Authors: Sodha M. S. , Singh Tarsem , Sharma R. P.
Published: March 2009

In the present paper we have studied the nonlinear interaction of an electrostatic lower-hybrid wave with a high-power Gaussian EM beam, propagating perpendicular to the static magnetic field in the ordinary mode in a collisionless hot magnetoplasma. On account of the Gaussian intensity distribution of the EM beam in a plane transverse to the direction of propagation, a d.c. component of the ponderomotive force becomes finite and leads to the modification of the background electron/ion density. Thus the electrostatic lower-hybrid wave gets coupled with the pump EM wave. This coupling can lead to the focusing of the lower-hybrid wave and if appropriate conditions are satisfied leads to Brillouin scattering.
The bumpy Z-pinch
Authors: Jensen Torkil H. , Chu Ming Sheng
Published: March 2009

The ‘bumpy Z-pinch’ is a magnetic configuration with potential usefulness for fusion reactors. A conceptually simple version of the configuration is axisymmetric. It contains regions of closed and open field lines. In the region of closed field lines, the field line topology is much like that of a tokamak; these regions link the region of open field lines around the axis of symmetry. Assuming that the plasma spontaneously maintains an equilibrium as described by J. B. Taylor, it is possible to maintain indefinitely the regions of closed field lines by driving an axial current through the plasma in the region of open field lines. The ratio between the total axial driven current and the total poloidal current in each of the tokamak-like regions can, in principle, be made arbitrarily small, which means that the load impedance can be arbitrarily large. In addition, the configuration has the inherent virtue similar to that of the spheromak that the tokamaklike part of the plasma does not link any material coils.
Stability of Vlasov equilibria. Part 1. General theory
Authors: Symon K. R. , Seyler C. E. , Lewis H. R.
Published: March 2009

We present a general formulation for treating the linear stability of inhomogeneous plasmas for which at least one species is described by the Vlasov equation. Use of Poisson bracket notation and expansion of the perturbation distribution function in terms of eigenfunctions of the unperturbed Liouville operator leads to a concise representation of the stability problem in terms of a symmetric dispersion functional. A dispersion matrix is derived which characterizes the solutions of the linearized initial-value problem. The dispersion matrix is then expressed in terms of a dynamic spectral matrix which characterizes the properties of the unperturbed orbits, in so far as they are relevant to the linear stability of the system.
Electromagnetic waves in a relativistic plasma stream: fusion instability
Authors: Mohanty J. N. , Misra P.
Published: March 2009

We derive the dispersion formulae for electromagnetic waves including relativistic kinematics and a corresponding Maxwellian equilibrium distribution function without any approximations and having anisotropy in the streaming velocity. For non-relativistic temperatures, waves propagate when the streaming velocity is much smaller than the thermal velocity of the species, with varying thermal modes.
Tranverse intermediate waves in a relativistic plasma with a finite conductivity
Authors: Granik A.
Published: March 2009

The propagation of intermediate waves in a turbulent relativistic plasma, characterized by an effective electrical conductivity σeff due to microinstabilities, is studied. The process is governed by a set of diffusion-type equations. An initial magnetic perturbation of a Gaussian wave form subsequently decays owing to dissipation. For the almost-Newtonian gas and the ultra-relativistic gas, relativistic effects tend to change the polarization of the initial magnetic impulse from a linearly polarized wave to a circularly polarized wave.
Near-magnetosonic envelope upper-hybrid waves
Authors: Rao N. N.
Published: March 2009

A systematic analysis of envelope upper-hybrid wave propagation near the magnetosonic speed has been presented. Using the full set of fluid equations for the low-frequency dynamics, we obtain various model nonlinear equations describing the magnetosonic response to the envelope waves. In particular, we derive driven KdV as well as driven Boussinesq equations that are valid for near-magnetosonic propagation. These equations are coupled to the usual Schrödinger-like equation for the envelope wave. Exact stationary solutions of the coupled equations are explicitly obtained. It is shown that a, new class of upper-hybrid solitons with antisymmetric wave envelope exist for nearmagnetosonic propagation. Integral invariants for the driven KdV case have been obtained and evaluated for localized solutions. A set of stationary governing equations is derived that takes account of the full nonlinearity in the low-frequency response as well as departures from the frozen-in-field approximation. A detailed comparison of the various model equations as well as their validity has been made.
Short-wave low-frequency equilibrium spectra in a current-carrying plasma
Authors: Vakoulenko Maxim O.
Published: March 2009

Short-wave (wavelengths smaller than the ion gyroradius) low-frequency (frequencies not exceeding the ion gyrofrequency) electromagnetic equilibrium spectra are found in a current-carrying plasma. Owing to cross-field correlations, the mean values of the integrals of motion increase, whereas their cascade rates are inhibited.