bluuebunny/crossref_metadata_2025 huggingface dataset:
Anomalous high-frequency conductivity of a turbulent plasma
Authors: Bertotti B. , De Barbieri O.
Published: March 2009

In this work we evaluate the anomalous high-frequency conductivity arising from particle—wave interactions in a multi-species turbulent plasma with no external magnetic field. The calculation is made by using the full three-dimensional model of the quasi-linear theory of plasma turbulence for a wide range of frequencies embracing the electron plasma frequency. It is found that the conductivity tensor is anisotropic and slowly time dependent; this reflects the slow time dependence and the anisotropic character of the distribution functions of the velocities of the particles. It is also found that there is a very narrow range of frequencies (just above the electron plasma frequency) for which the components of the conductivity tensor are negative. The particular case of the two- stream instability is examined in detail. The anisotropic character of the components of the conductivity tensor and their dependence on the frequency of the external field is studied. Finally some possible means for an experimental check of our calculations are suggested.
A model kinetic equation for an electron plasma
Authors: Baum Howard R.
Published: March 2009

A kinetic model equation for an electron plasma is proposed. The principal new feature of the equation is an attempt to incorporate collision terms which model both short-range two-body scattering and many-body small-angle scattering. The equation is then used to study the time relaxation of a spatially uniform plasma. A simplified form of the model is finally used to analyse sound propagation in the plasma. Dispersion equations are derived and studied in several limiting cases. Landau damping in the small wave-number limit is shown to be less important than collisional damping for most plasmas.
Interaction of a relativistic electron beam with an inhomogeneous plasma
Authors: Dorman G.
Published: March 2009

The investigation of the high-frequency interaction of a relativistic electron beam and a plasma is extended to include arbitrary variation of the plasma density. Analysing the coupled linearized Vlasov—Maxwell equations by means of a low-temperature expansion of the orbit integrals, a general equation for the electric field accurate to first order in the plasma temperature, beam temperature, and betatron frequency is obtained. This equation is applied to the investigations of transverse and longitudinal modes. A new transverse mode with |ω − kV0| ∼ ωβ is found to be collisionally unstable. The electrostatic instability is found to be slowed down by both low plasma temperature and low beam temperature, but the betatron oscillations increase the growth rate. A new longitidinal mode with |ω − kV0| ∼ ωβ, is found to be unstable for nonzero beam temperatures. The lowest order correction to the electrostatic growth rate due to a small plasma nonuniformity is obtained. The sign of this correction is found to depend critically on the shape of the inhomogeneity.
An experimental study of transverse ionizing MHD shock waves
Authors: Stebbins Charlles F. , Vlases George C.
Published: March 2009

The jump conditions across a transverse ionizing MHD shock wave, where the magnetic field is in the plane of the shock, are examined. The conservation laws, in conjunction with Maxwell's laws and the equation of state, yield three jump equations in four unknowns. To uniquely describe jumps across an ionizing wave requires an additional descriptive relationship. The theory of Kulikovskii & Lyubimov and, later, Chu, in which the internal structure of the shock itself supplies the missing relationship, is examined. In particular, Kulikovskii & Lyubimov show, for appropriate ratios of thermal to magnetic diffusivities, that for low-speed waves the magnetic field compression across the shock is unity and the jump equations reduce to the ordinary Rankine—Hugoniot relations. For high-speed shock waves, the magnetic field compression, B2/B1, equals the gas compression across the wave, p2/p1, and the jump equations become the magnetohydrodynamic shock jump relations. Furthermore, intermediate speed shocks induce magnetic field compressions between 1 and p2/p1. An experiment was performed in an inverse pinch where E behind the shock, the shock and piston velocities, and the magnetic field compression across the shock, were measured over a wide range of initial conditions and shock velocities in hydrogen. The jump relations were written with B2/B1 as a parameter and programmed into a digital computer. The program was written for real, equilibrium hydrogen. The program provided easy access to a unique solution of the jump equations for any B2/B1. The experiment tends to confirm the Kulikovskii—Lyubimov—Chu theory. Ordinary shock waves were observed at low speeds and near-MilD shocks were observed at high speeds. Further, the relation

was verified for the plasma behind the shock for low-speed shock waves, and was verified to within experimental accuracy for the intermediate class of shock waves.
More uniform perturbation theory of the Vlasov equation
Authors: Lewak G. J.
Published: March 2009

The Vlasov—Poisson equations are reformulated by applying an arbitrary transformation to the velocity variable in such a way that perturbation theory of the transformed equations does not exhibit the customary secularity in time (or space) in second or higher order. The lowest order approximation of the new formulation is discussed and compared with conventional results. The source of the non-uniformity appears to be the divergence of Particle trajectories as calculated by perturbation methods, from the exact ones after long times. The transformation which allows one to follow the particle trajectories is a transformation to a frame of reference moving with a plasma test particle in the self-consistent field.
Motion of a charged particle in superposed Heliotron and biconical cusp fields
Authors: Srivastava M. P. , Bhat P. K.
Published: March 2009

We have studied the behaviour of a charged particle in an axially symmetric magnetic field having a neutral point, so as to find a possibility of confining a charged particle in a thermonuclear device. In order to study the motion we have reduced a three-dimensional motion to a two-dimensional one by introducing a fictitious potential. Following Schmidt we have classified the motion, as an ‘off-axis motion’ and ‘encircling motion’ depending on the behaviour of this potential. We see that the particle performs a hybrid type of motion in the negative z-axis, i.e. at some instant it is in ‘off-axis motion’ while at another instant it is in ‘encircling motion’. We have also solved the equation of motion numerically and the graphs of the particle trajectory verify our analysis. We find that in most of the cases the particle is contained. The magnetic moment is found to be moderately adiabatic.
A new method of determining the transport coefficients for high pressure arcs from experimental data
Authors: Kapp L. B. , Richards P. H.
Published: March 2009

The problem is to determine the electrical and thermal conductivities of high pressure are plasmas from measurements of the current—voltage characteristics of the are and a single radial temperature profile. A new numerical method is described together with the corresponding computer program. The latter is applied to some recent measurements on wall-stabilized nitrogen ares, covering the temperature range 4500—11,000 °K, for which radiation can be neglected, and the results are compared with those of other workers.
On the structure of the boundary layer separating a neutral anisotropic plasma from a magnetic field
Authors: Cohen Leonard G. , Cohen Ira M.
Published: March 2009

The structure of the boundary layer separating a collisionless plasma from a one-dimensional magnetic field has been studied for anisotropic particle velocity distribution functions of the form

,

where F± is a weighting function, H± is the Hamiltonian, a± is a parameter, pz is generalized momenta, m± is particle mass, and δ is the Dirac delta function. Charge neutrality was preserved throughout the boundary layer and self- consistent solutions were obtained for particles having two or three degrees of freedom and moving against either a plane or circular boundary. The results were compared with those for the structure of a boundary layer consistent with a cold streaming plasma having a particle velocity distribution of the form

.
A sensitive microwave interferometer for plasma diagnostics
Authors: Wallington J. R. , Beynon J. D. E.
Published: March 2009

More accurate methods of measuring microwave attenuation and phase are constantly being sought, particularly for such applications as plasma diagnostics. The microwave bridge technique described here was developed for the study of a quiescent plasma having an electron density of 1015 to 1018 m−3 corresponding to a plasma frequency of 3 × 108 to 1010 Hz, and an electron collision frequency of 1010 to 1011 s−1. The plasma had a broad dimension of 0·3 m. For such a plasma a probing frequency of 10 GHz was considered to be the most suitable; at this frequency the attenuation α and phase shift δβ expected were 0·1 < α< 50 dB and 1° < δβ < 1000° respectively.
Stochastic solution of the Boltzmann equation for thermal electrons in an attractive Coulombic potential
Authors: Bell M. J. , Kostin M. D.
Published: March 2009

A stochastic method has been employed to investigate the distribution function of free electrons in gases in the field of a positive ion. Stochastic results have been obtained for several pressures and for both large (Langevin) and small ions, and the results have been compared with the solutions of the diffusion approximation and Pitaevskii's Fokker—Planck approximation to the Boltzmann equation.
On the asymptotic stability of monotonic electrostatic collisionless shock waves
Authors: Biskamp D.
Published: March 2009

Recently the question of existence and stability of laminar one-dimensional coffisionless shock waves has received some new attention (Montgomery & Joyce 1969). These electrostatic shock waves are usually thought of as being generated by ion acoustic waves (pulses) in a plasma with Te ≫ Ti Apart from the well- known class of shock solution with oscillatory structure (Moiseev & Sagdeev 1963) there exist, at least within the framework of Vlasov theory, monotonic transitions from one asymptotic state to another (Montgomery & Joyce 1969). For these shock-wave like solutions it is easy to see that the electrons cannot be in thermal equilibrium (have a Maxwellian distribution) in the downstream state, if they are so in the upstream state. Hence it appears to be natural to investigate first the stability of the homogeneous downstream state (which tells us if the transition is possible at all) by investigating the properties of the class of permitted distribution functions for the electrons, before attacking the much more involved problem of the possible instabilities arising from the inhomogeneitythe transition region of the shock.
Dispersion in inhomogeneous plasma streams
Authors: Burt P. B.
Published: March 2009

The instabilities in a two stream plasma in which the density across the stream is variable are studied from the point of view of a scattering problem. Approximate dispersion relations are developed, one of which is identical with the infinite, homogeneous case. A second relation is obtained which depends upon the scale of density variation.
On the modification of the Bernstein modes by electron—electron collisions
Authors: Watson S. R. , Harding R. D.
Published: March 2009

The dispersion relation for the. Bernstein modes is derived, in the presence of a Fokker—Planck type collision term. Numerical solutions are obtained, and the results give an approximate formula for the collisional damping. The possibility of observing this damping experimentally is discussed.
On the influence of a radial electric field on the stability of a magnetically confined plasma
Authors: Nocentini A.
Published: March 2009

A magnetically confiuied, slightly non-uniform and non-neutral plasma column is considered. The existence is shown, in plane, infinite geometry, of a mode whose characteristic properties agree with those of an unstable wave detected in a recent experiment.
Non-linear transverse waves in a Vlasov plasma
Authors: Gary S. Peter
Published: March 2009

Non-linear transverse waves in a classical non-relativistic collisionless, Maxwellian electron gas with external magnetic field B0are considered. There is assumed a small, sinusoidal variation in the initial electric and magnetic fields, corresponding to excitation of a discrete wave-number mode. The non-linear Vlasov equation is solved to second order in the long time limit via the Montgomery—Gorman perturbation expansion, and the time-independent, spatially homogeneous part of the second-order distribution function is used to modify the linear dispersion relation. For frequencies near the electron cyclotron frequency a non-linear damping decrement results such that, for many values of the parameters, the damping is less than the linear rate. Thus at sufficiently long times, the rate of damping of transverse electron cyclotron waves should decrease, a result similar to that for non-linear damping of longitudinal electron plasma waves.
On the Rayleigh—Taylor instability in hydromagnetics with finite electrical resistivity and Hall current
Authors: Singh Surindar , Tandon J. N.
Published: March 2009

The effect of Hall current and finite electrical resistivity has been studied on the Rayleigh—Taylor instability of superposed incompressible fluids in the presence of a uniform horizontal magnetic field. It is found that Hall current has a negligible stabilizing influence in the high resistivity limit whereas it has a destabilizing influence in the low resistivity limit.
On the structure of collisionless waves
Authors: Fedele James B.
Published: March 2009

Small amplitude waves and collisionless shock waves are investigated within the framework of the first-order Chew—Goldberger—Low equations. For linearized oscillations, two modes are present for propagation along an applied magnetic field. One is an acoustic type which contains no finite Larmor radius effects. The other which contains the ‘fire hose’ instability in its lowest order terms, does possess finite Larmor radius corrections. These corrections, however, do not produce instabilities or dissipation. There are no finite Larmor radius corrections to the single mode present for propagation normal to the applied magnetic field. Normal shock structure is investigated, but it is shown that jump solutions do not exist. An analytic solitary pulse solution is found and is compared with the Adlam—Allen pulse solution.
Relaxation of a temperature anisotropy in a collisionless plasma
Authors: Montes C. , Coste J. , Diener G.
Published: March 2009

We study the quasifinear relaxation of an aperiodic instability, namely the instability caused by the temperature anisotropy of a collisionless electron plasma in the absence of an external magnetic field. We give a detailed description of the relaxation process and we examine the validity of the quasilinear theory (existence of separate time scales, quasilinearity of the particles' orbits).
Kinetic theory of a spatially inhomogeneous plasma with time independent average properties
Authors: Cairns R. A.
Published: March 2009

Kinetic equations are obtained which describe the variation in one spatial direction of a plasma whose average properties are independent of time and do not vary in the perpendicular direction.

These equations consist of a coupled set giving the variation of the electric field fluctuation spectrum and the particle distribution functions. They take into account particle discreteness effects and describe the plasma both when it is stable and weakly unstable. It is suggested that they may be used to describe an infinite plane shock wave in a plasma.
Application of the collective approach to the thermodynamics of an electron gas
Authors: Caroff Lawrence J. , Liboff Richard L.
Published: March 2009

The collective approach of Pines & Bohm has been applied to the problem of the thermodynamics of the N-particle electron gas including transverse radiation. Partitioning of the internal energy and certain of the other thermodynamic quantities is discussed generally. The system is seen to divide itself into three approximately independent subsystems: (1) an infinite set of free harmonic oscillators, corresponding to the transverse field, with an energy spectrum given by ωT(κ), where ωT(κ), is given by the dispersion relation for transverse electromagnetic waves in a plasma; (2) a set of 8 free harmonic oscillators corresponding to the longitudinal (plasma) oscillations, with an energy spectrum ωT(κ), given by the dispersion relation for plasma oscillations; and (3) a set of (N — 2s/3) quasi-particles of mass approximately equal to the electron mass, interacting via a short-range potential which is essentially screened Coulomb. Analytical expressions for the energy, pressure, and constant-volume specific heat of the transverse oscillators are given, together with approximate expressions applicable to the high-density—low-temperature and low-density—high-temperature limits. Detailed numerical calculations of the internal energy and pressure of the longitudinal modes are presented. In addition, the contributions to the energy and pressure from the particle portion are evaluated in the low-density—high-temperature limit as functions of the cut-off wave vector κc; κc is the maximum k-vector of the longitudinal oscillators.
Dissipation discontinuities in hydromagnetic shock waves
Authors: Coroniti F. V.
Published: March 2009

Within the hydromagnetic approximation, the effects of resistive, viscous, and thermal conduction dissipation on the structure of shock waves is studied. A Perturbation analysis about the upstream and downstream stationary points is developed, which, when coupled with the shock evolutionary conditions, determines the conditions for the formation of discontinuities in the shock structure. The Viscous subshock for fast shock waves and the hydromagnetic analogue of the gas dynamic isothermal discontinuity for fast and slow shocks are analyzed. Very oblique fast shocks require both resistive and viscous dissipation for a steady shock structure. Strong slow shocks propagationg nearly along the magnetic field fail to steepen if only resistive dissipation is included. The rotational discontinuity does not possess a stable shock structure for any of the dissipation processes considered.
The effects of finite Larmor radius on the perturbation flow mixing of a collisionless plasma
Authors: Morioka Shigeki , Spreiter John R.
Published: March 2009

The Chew—Goldberger—Low theory of a collisionless plasma, modified to include the effect of finite Larmor radius of the ion and the electron, is applied to a linearized problem of two-dimensional steady flow. The zeroth-order terms in the Larmor radius expansions of the velocity distribution functions of the ion and the electron are assumed to be anisotropic Maxwellian. The spatial development of a given velocity profile is investigated for flows with either crossed or aligned magnetic fields, and for various values of Mach number, Alfvén Mach number, and anisotropic pressure ratios in the main flow.
The character of equilibrium of an inviscid, infinitely conducting fluid of variable density in the presence of a horizontal magnetic field with Hall-current
Authors: Ariel P. D.
Published: March 2009

The character of equilibrium of an inviscid, incompressible, infinitely conducting fluid of variable density in the presence of a horizontal magnetic field has been investigated taking into account the effects of Hall-currents. The solution is shown to be characterized by a variational principle. Making use of the existence of variational principle the solution is developed in the case of continuously stratified fluid of exponentially varying density confined between two horizontal planes at finite distance, from which the necessary and sufficient conditions of stability are obtained. The Hall-currents are found to destabilize the wave-number range which is stable otherwise.
A new derivation of quasilinear theory
Authors: Klozenberg J. P. , Bernstein Ira B.
Published: March 2009

A new derivation of quasilinear theory for plasma oscillations is given, subject to the neglect of wave-wave interactions. The theory, which applies equally to damping and growing waves, requires that the individual wave resonances be narrow and the electric field spectrum sufficiently broad.
The effect of velocity space diffusion on the universal instability in a plasma
Authors: Ong R. S. B. , Yu M. Y.
Published: March 2009

The influence of collisions on the universal instability in a fully ionized in- homogeneous plasma is investigated by means of a simplified Fokker-Planck kinetic equation. For the Fokker-Planck model yields results qualitatively similar to the Bhatnagar-Gross-Krook model, but the two models give different collisional effects in the case where b ≥ 1. Further it is shown that collisions in general enhance the temperature gradient instability in a plasma when b ≪ 1 and reduce it when b ≥ 1.
Lagrangian methods in plasma dynamics. I. General theory of the method of the averaged Lagrangian
Authors: Dougherty J. P.
Published: March 2009

Whitham's averaged Lagrangian method is used to yield a relativistically covariant formalism for wave packets in a weakly inhomogeneous (and time dependent) medium. Provided the physics of the medium can be based on a Lagrangian density, a procedure of expansion and averaging is available which gives separate Lagrangians for the dynamics of the background and of the waves. The Euler—Lagrange equations then give immediately the equations of motion for the background, including non-linear reaction of the waves, and the dispersion relation, equations for ray tracing, conservation of wave action and non-linear coupling coefficients, for the waves. Many of these results can be interpreted in an illuminating way by considering the corresponding expansion of the canonical four-dimensional stress tensor.
Theory of a test particle in an inhomogeneous stationary plasma
Authors: Cairns R. A.
Published: March 2009

The motion of a test particle in a plasma whose average properties vary along one direction in space, but are independent of time, is considered. A method is given which enables this problem to be treated similarly to existing theories for a homogeneous plasma.
A boundary problem in a plasma
Authors: Karunarathne V. B.
Published: March 2009

An isotropic Vlasov plasma occupies an infinite space, the upper half of which (y> 0) is a dielectric. A transverse disturbance is incident normally on the face of the dielectric. The waves that are excited in each half of the space are obtained. It is shown that this result can be extended to cover the refiexion problem of any normally incident disturbance in a plasma defined by a dispersion relationDi(w, k). A few examples are considered; in particular transverse waves in a plasma streaming normal to the boundary where Čerenkov instability can occur.
Higher order approximations in the theory of longitudinal plasma oscillations. II
Authors: Einaudi F. , Axford W. I.
Published: March 2009

In this note we comment and extend the results of a previous analysis in which the non-linear behaviour of one-dimensional electrostatic oscillations in a homogeneous, unbounded, collisionless and fully ionized plasma was considered. The evolution of a monochromatic wave of small, but finite amplitude is studied by expanding the dependent variables as well as the independent variable tin the form of asymptotic series; an ordering parameter e proportional to the initial amplitude of the electric field is introduced. The expansion of the independent variable in such a series allows us to eliminate secular terms from the part of the distribution function which does not depend on the free-streaming terms. This, in turn, allows us to determine corrections to the complex frequency a. Results of a previous note on non-linear Landau damping for an initially Maxwellian. distribution function are confirmed, but it is indicated that they apply to values of time up to a value τ1 rather than for all times. One can proceed to larger values of time in the manner of the multiple time-scale method. In particular it is found that the Landau damping is increased with respect to the linear value only initially during the first time scale.
Time asymptotic perturbation theory in weak plasma turbulence II. Vlasov description
Authors: Elsässer Klaus
Published: March 2009

In electrostatic turbulence under appropriate conditions we show that we can have an equation for ϕk (time variation of electrostatic potential amplitude) which is essentially instantaneous in time. The coefficients in this equation are uniquely determined by the Poisson equation of the corresponding order. By applying time asymptotic methods of Bogoljubov and Mitropoiski to the corresponding hierarchy equations we obtain a kinetic equation for the spectrum 〈|ϕk|2〉. The resonant mode coupling terms agree with the usual ones. But the non-linear Landau damping terms, as given, e.g. by Frieman & Rutherford (1964), Kadomtsev (1965), Tsytovich (1968), and Rogister & Oberman (1969) are complemented by additional terms which are, at least formally, non-zero. For simplicity the calculations are only done for the weakly unstable (and weakly damped) modes.
Penetration to second order of an electrostatic field into a warm plasma
Authors: Zawadzki E. M. , Lewak G. J.
Published: March 2009

Using a reformulation of ordinary perturbation theory to first and second order, explicit solutions for the penetration of electrostatic waves into a semi-infinite Vlasov plasma are presented. Two types of electron velocity distribution are used, the uniform step (‘water-bag’ model) and the Maxwellian. The existence of propagating modes below the plasma frequency, behaviour of the second harmonic field and the formation of a narrow sheet of electrons near the bounding wall are displayed. Replacement of boundary fields with equivalent charge and current sources is discussed.
Note on the existence of stationary shockwaves in collisionless plasmas
Authors: Pfirsch D. , Schindler K.
Published: March 2009

We first discuss wave propagation perpendicular to a magnetic field. Variables depend on x only. The medium is collision-free, described by the Vlasov theory. We can prove that there exist two, and only two, unique constants of the motion, that are independent of y, z and t, and that at least one of them depends on x. Thus a necessary condition for the existence of stationary shocks is fulfilled. Examples show that the existence proof also suggests a practical tool for solving problems. The oblique case which is also briefly discussed turns out to be qualitatively different in that, owing to the presence of reflected particles, a uniform upstream state cannot be prescribed a priori.
Geometric optics in an ideal magnetohydrodynamic fluid
Authors: Bernstein Ira B.
Published: March 2009

The propagation of small monochromatic disturbances in a stable ideal magnetohydrodynamic fluid is treated by the method of geometric optics. The medium is trirefringent and requires six systems of rays. The problem of a point radiator is solved in the small wave-length limit where the theory holds.
On the effect of stochastic rf-fields on the stability of plasma
Authors: Krlín L.
Published: March 2009

The effect of stochastic high-frequency fields on the stability of electrostatic plasma oscillations in a magnetostatic field is studied. The stabilizing effect can be provided by diffusion in configuration co-ordinates, as well as in the longitudinal and transverse velocities. The parameters of the stochastic field for effective stabilization are estimated, as well as the influence of the accompanying escape of particles due to the stochastic fields.
Stability of parametrically excited drift waves
Authors: Siambis John G.
Published: March 2009

The propagation and stability of drift waves is examined, by means of a perturbation technique, in geometries where the magnitude of the magnetic field varies periodically along the field lines. Two sets of modes are found which can be driven unstable by resonant particles trapped in the magnetic field non-uniformity. One set of modes consists of standing waves with wavelength twice that of the magnetic field non-uniformity. The other set of modes consists of standing waves composed essentially of the sum of a component which does not vary along the line and a component which is a standing wave with wavelength equal to the wavelength of the magnetic field non-uniformity. The advantage of this method is that it predicts simply and pictorially the real frequency of oscillation for these modes.
Non-linear interaction between three ordinary electromagnetic waves
Authors: Stenflo L.
Published: March 2009

This paper considers the non-linear interaction between three resonant, modified ordinary electromagnetic waves, which propagate perpendicular to a constant magnetic field in a spatially homogeneous electron plasma. The coupling coefficients are calculated and discussed. Finally, a general formula, describing the interaction between three waves propagating at arbitrary angles to the static field, is derived.
Stability of an anisotropic plasma jet
Authors: Raghavachar M. R.
Published: March 2009

The stability of an anisotropic plasma jet has been investigated using equations of Chew, Goldberger & Low (1965) in both plane and cylindrical geometries. The main conclusions are as follows:

(i) For waves of small wavelength, when λ (the ratio of plasma density to the density of surrounding non-conducting medium) is much greater than unity, the plasma jet is stable only if 1/6(1 + σ) <p∥/p⊥ < 1 + 2σ, where p∥ and p⊥ denote the components of pressure parallel and perpendicular to the direction of magnetic field in the steady state, and σ denotes the ratio of magnetic pressure to the perpendicular component of plasma pressure.

(ii) When λ ≫ 1, the plasma jet is unstable if the parallel component of pressure exceeds the sum of the perpendicular component of pressure and twice the magnetic pressure of the plasma.

(iii) For long waves, we find that there exists an infinite number of growing and decaying waves. Expressions for the growth rates have been obtained.
Adiabatic transverse waves in a conducting gas
Authors: Roberts B. , Sozou C.
Published: March 2009

This paper is an investigation of the effect of a magnetic field on transverse waves in a perfectly conducting gas which is rotating like a Rankine vortex about the axis of a cylinder. The magnetic field is assumed to be in the axial direction. There are three waves: two waves are rotating in the same direction as the gas, one faster and the other slower than the core speed of the gas, and one wave rotates in the opposite direction.
Identities between reflexion and transmission coefficients and electric field components for certain anisotropic modes of oblique propagation
Authors: Heading J.
Published: March 2009

A wide-ranging investigation is rendered possible by a judicious combination of products of electric field components and electric polarization components for two distinct modes of propagation of electromagnetic waves in an anisotropic, ionized, stratified medium. The differential equations, governing oblique propagation in these two distinct modes in such a medium, are combined to yield various integral identities when integrated throughout the medium. These lead to a large number of relations between the reflexion and transmission coefficients (for incidence from below and from above) and the fields throughout the medium, each containing as a factor just one of the components of the external magnetic field pervading the medium.
Kinetic theory of a two-dimensional magnetized plasma
Authors: Vahala George , Montgomery David
Published: March 2009

Several features of the equilibrium and non-equilibrium statistical mechanics of a two-dimensional plasma in a uniform d.c. magnetic field are investigated. The calculations have been motivated by the recent derivation of Bohm's diffusion coefficient given by Taylor & McNamara for this system. The charges interact only through electrostatic (logarithmic) potentials. The problem is considered both with and without the guidiiig-centre approximation. With the guiding centre approximation, an appropriate Liouville equation and BBGKV hierarchy predict no approach to thermal equilibrium for the spatially uniform case. For the spatially non-uniform situation, a guiding-centre ‘Vlasov’ equation is discussed, and is solved in special cases. The most interesting features of thermal equilibrium theory (with and without the guiding-centre approximation) are (i) a collapse of the system above a critical value of the plasma parameter, and (ii) a divergence in the electric field fluctuation spectrum (minus the selfenergy terms) for small plasma parameter and very large systems. For the nonequilibrium, non-guiding-centre case, a Boltzmann equation and a Fokker—Planck equation are derived in the appropriate limits. The latter is more tractable than the former, and can be shown to obey conservation laws and an H-theorem, but contains a divergent integral, which must be cut off on physical grounds. Several unsolved problems are posed.
Electron heating in a perpendicular collisionless shock
Authors: Cairns R. A.
Published: March 2009

A model is proposed to explain the observed electron heating in perpendicular collisionless shock waves. This relies on trapping of the electrons by the turbulent electric field to modify their orbits in such a way that they gain energy from the steady potential jump across the shock. With simple assumptions about the nature of this trapping, reasonable agreement with the experimentally observed heating is obtained. In addition, the model provides qualitative agreement with a number of other experimental observations.
The propagation of plasma waves near multiples of the electron gyrofrequency
Authors: Andrews M. K. , Fang M. T. C.
Published: March 2009

The dispersion relation for electrostatic plasma waves propagating at frequencies near the electron cyclotron harmonics has been evaluated, and used to determine the refractive index curves for varying values of the angle θ between the k vector and the ambient magnetic field B0 in a warm magnetoplasma. It is shown that, under certain circumstances (which are defined), the (@, θ) curves have the characteristic ‘nose’ shapes that are necessary to provide a reflexion in the ambient plasma. Thus, the oblique echo reflexion mechanism (McAfee 1968, 1969a, b), which accounts for the appearance of the resonance signals or ‘spikes’ at the plasma and upper hybrid frequencies fN and fT on topside ionograms, may also be applied to the plasma waves propagating at frequencies near the electron gyro-harmonics. The relatively high damping that occurs for θ # 90° severely restricts the ranges of θ and wave-number k over which the reflexion mechanism applies. The restriction is such that the damping is severe for all values of θ when k is large, and for all values of θ outside a cone of ∽ 2° centred on θ = 90° when k is small.
Non-linear waves in a non-uniform plasma
Authors: Gribben R. J.
Published: March 2009

The work of Butler & Gribben (1968) on a general formulation ofthe problem of non-linear waves in non-uniform plasmas is extended. The particular case treated in Butler & Gribben, § 6, is discussed again (the distribution functions fs and electrostatic potential depend only on one space co-ordinate, that in the direction of propagation of the wave, the wave is slowly varying only with respect to this co-ordinate and time, the magnetic field vanishes and relativistic effects are negligible). Conditions necessary to avoid secular terms in the solutions of the Vlasov and Poisson equations are rederived, but without resorting to assumed series expansions in e, the perturbation parameter describing the non-uniformity, for the dependent variables, and using a different notation which simplifies and retains the symmetry of the equations. The corresponding general boundary condition, to be satisfied by fs innergy space at the boundary of the trapped particle region, is also derived.

Particular attention is devoted to the Vlasov equation, and the derived general result is used to obtain the appropriate necessary condition from this equation, correct to O(ε). This shows that, unlike the leading-order theory, at the next stage an extra length scale appears in the equations, which would be needed if e.g. the theory were to be used to discuss shock waves. It is argued that this result, taken with the mixing process described in Butler & Gribben (which supplies a mechanism for the formation of shocks), appears to place the theory at least on as satisfactory a level as the Navier-Stokes theory for the discussion of shock wave structures.

Another aspect of the analysis is the comparison with the Whitham (1965a) averaging method for treating the propagation of non-linear waves in other fields. Similar features are pointed out, and it seems likely that the averaging method is equivalent to the leading-order theory. It is thought that the present approach might prove to be useful in other wave problems.
Kinetic theory of three-wave interaction in a magnetized plasma
Authors: Stenflo L.
Published: March 2009

The resonant interaction between three waves, propagating perpendicular to a constant magnetic field in a spatially uniform plasma, is considered. Significant terms, which have been neglected in the coupling coefficients of previous work, are included.
Nonlinear interaction of resonant plasma oscillations
Authors: Lewak G. J. , Ogunlana J.
Published: March 2009

Using the water-bag model of an electron plasma the nonlinear interaction of two plasma wave pulses (each of sufficiently narrow wave-number spectrum) is discussed. It is shown that, for the special case of a resonant (zero group velocity) pulse interacting with a non-resonant pulse, the interaction produces an effective slowing down of the group velocity of the non-resonant pulse. An application of this theory to the explanation of the apparent resonances at fractions of the plasma frequency observed in the ionosphere is discussed.
Production of intense ion beams by high-frequency electric fields
Authors: Sindoni† E. , Eubank H. P.
Published: March 2009

We present an experimental investigation of electron cyclotron resonance plasma accelerators as a source of high-intensity, low-energy (keV) ions in which ion current and electron and ion energies are related to r.f. power and gas pressure.
High-β effect on the generalized ion Berstein mode near the lower hybrid frequency
Authors: Nambu† Mitsuhiro
Published: March 2009

The dispersion curves of mixing mode between electrostatic and electromagnetic waves propagating perpendicularly to the ambient magnetic field are computed for frequency range near the lower hybrid frequency in the case of a finite-β plasma with a Maxwellian velocity distribution. The detailed results apply to a hydrogen plasma. The result indicates that the lower hybrid frequency is neither the resonance frequency of the electromagnetic wave nor the cut-off frequency of the electrostatic wave. In a high-β plasma, the plateau of the dispersion curve disappears and the electrostatic approximation (Bernstein mode) is not valid up to the wavelength of the order of proton Larmor radius. The polarization is left-handed, and a trace of the most dominant intensity ratio of wave magnetic field energy to the electric field energy in each branch is given approximately by the cold-plasma dispersion curve.
Boundary conditions in the presence of Hall current of finite ion Larmor radius effects
Authors: Hosking R. J. , Kalra G. L.
Published: March 2009

Boundary conditions appropriate to a model with finite ion mass corrections of ideal hydromagnetic theory are reviewed. It is shown that these boundary conditions have been correctly satisfied in earlier theory for the stability of an interface between two semi-infinite regions. This theory predicts instability due to Hall current.
The Rayleigh—Taylor problem with a vertical magnetic field, including the effects of Hall current and resistivity
Authors: Lister G. G. , Hosking R. J.
Published: March 2009

The influence of resistivity and Hall current on the Rayleigh-Taylor problem involving two superposed fluids of finite density in the presence of gravitational and magnetic fields normal to the fluid interface is examined. Unlike the related problem in which the magnetic field is parallel to the interface, it appears that the dispersion relation does not exhibit singular behaviour in the zero resistivity limit. The ‘potentially stable’ situation is considered throughout. The results are compared with earlier ideal and resistive theories, and an apparent anomaly regarding the existence of normal modes in such systems is resolved.
Ray tracing in an anisotropic absorbing medium
Authors: Suchy† Kurt
Published: March 2009

With the generalized group velocity vg = Re (∂ω/∂k) for media with moderate absorption, derived in a previous paper, the Hamilton equations for group propagation in non-absorbing media are generalized to include moderate absorption. They contain directional derivatives not only in the direction of v but also in the direction of Im (∂ω/∂k). Two iterative computational methods are presented for ray tracing with the generalized Hamilton equations.
Hydromagnetic flow about a curved neutral sheet
Authors: Teske† M. , Lam S. H.
Published: March 2009

The present paper examines the magnetic boundary layer along a curved interface between two opposing fluid streams carrying oppositely directed magnetic fields. This problem is known classically as the neutral sheet or X neutral-point problem. A formal two-dimensional theory is constructed that depends solely on the mechanism of magnetic diffusion and thus eliminates the need for any added MHD waves. This theory shows clearly the detailed structure of the neutral sheet boundary layer and, more importantly, the parametric dependence of the solution on free-stream parameters such as the magnetic Reynolds number and the Alfvén number. It is shown that a thin, powerful jet of high thermal and kinetic energy exists within the boundary layer. Sample numerical solutions are presented, and the various mathematical difficulties associated with this class of problems are discussed.
On the nonlinear damping of a plasma mode
Authors: Nandan R. , Pocobelli G.
Published: March 2009

We present a theory of the nonlinear damping of a plasma mode based on a solution of the Vlasov–Poisson system. The formulation is exempt from the objectionable separation of the particles into ‘resonant’ and ‘nonresonant’, and is valid for ion as well as for electron modes. The effect of the damping of the mode on particle motion is taken in account. In particular, we evaluate numerically the damping of an ion mode for a temperature ratio Te/Ti = 16. We also obtain a number of small new shifts in the damping of a plasma mode in general, including contributions from the second derivative of the stationary distribution function.
Ordinary-mode electromagnetic instabifity for counter-streaming ions with anisotropic temperatures
Authors: Gaffey J. D. , Thompson W. B. , Liu C. S
Published: March 2009

The instability of the ordinary electromagnetic mode propagating perpendicular to an external magnetic field is investigated for two ion beams with anisotropic temperatures, counter-streaming along the magnetic field. A necessary and sufficient condition for instability is derived. The growth rate is calculated, and found to be typically several times the ion cyclotron frequency Ωi, although in extreme cases γmax may be as large as (Mi/me)½Ωi.
Nonlinear interaction between ordinary electromagnetic modes
Authors: Krishan S. , Rankin D. , Selim A. A.
Published: March 2009

Resonant interaction between three ordinary modes, modified by electrons streaming parallel or antiparallel to the static magnetic field of a homogeneous plasma, is investigated. The modes propagate perpendicular to the magnetic field. If the unperturbed current density is zero, the scattering matrix for three-wave resonant interaction depends only on the cube of the electron drift velocity. If two electron beams of equal density are counter-streaming, the scattering matrix vanishes completely. If the unperturbed current density is non-zero, the matrix depends on the linear and cubic terms in the electron drift velocity. In the present investigation, the Hamiltonian approach, which is microscopic in nature, has been used, and therefore the results are valid for arbitrary ratios of Larmor radius to wavelength.
Thermodynamic bounds on the magnetic fluctuation energy in unstable anisotropic plasmas
Authors: Davidson R. C. , Tsai S. T.
Published: March 2009

Thermodynamic bounds on the magnetic fluctuation energy in unstable anisotropic plasmas are obtained. The spatial variation in equilibrium and perturbed quantities is assumed to be exclusively in the z direction, which coincides with the direction of a uniform external magnetic field B0êz. In addition, the positive ions are assumed to form a fixed (mi→ ∞) background providing overall charge neutrality, and only the electron dynamics are included in the analysis. For this configuration it has recently been shown that the non-linear Vlasov–Maxwell equations support two independent energy constants for arbitrary-amplitude electromagnetic disturbances propagating parallel to B0 êz. In this paper, Fowler's method for calculating thermodynamic bounds on the field energy in unstable plasmas is generalized to incorporate two energy constraints (in addition to entropy and number conservation). An upper bound on the magnetic fluctuation energy is obtained for arbitrary initial distribution function fe0 = fe(z, v, 0), and the results are applied to unstable (i) bi-Maxwellian and (ii) loss-cone distributions. Depending on the parameter regime, it is found that the bounds obtained by enforcing two energy constraints can be an order-of-magnitude lower than the bounds obtained by enforcing a single (total) energy constraint. The theoretical bounds are compa red with the maximum change in field energy measured in computer simulation experiments for the case where fe0 is bi-Maxwellian. For sufficiently large initial anisotropy, it is found that the bound obtained with two energy constraints is less than 1·5 times the measured change in field energy.
Wave propagation in a partilly-ionized chemically-reacting plasma
Authors: Fang Ta-Ming , Baum† Howard R.
Published: March 2009

Multi-fluid equations derived in a previous paper are used to study small- amplitude wave motion in a partially ionized chemically-reacting plasma. The plasma is assumed to be infinite and without external fields. The dispersion equations are derived and solved both numerically and analytically for several limiting cases. The effects of chemical reactions have been explicitly obtained. It is found that at the long-wavelength limit, the ionization and recombination terms play the dominant role for the damping of certain longitudinal waves even for a nearly frozen plasma.