bluuebunny/crossref_metadata_2025 huggingface dataset:
The guiding centre approximation in lowest order
Authors: Baños Alfredo
Published: March 2009

We present here a simple and direct derivation of the equations governing the motion of a charged particle in space- and time-dependent fields in the guiding centre approximation in lowest order. The method of attack is based initially on the expansion scheme of Bogolyubov & Zubarev (1955) combined with Northrop's averaging process over one gyration period. Thus, we first resolve the instantaneous velocity of the particle into three components, r = ê1u + UE + Tw, where u is the parallel component, UE is the familiar E × B drift, and Tw is the instantaneous perpendicular component as measured in a frame moving with the UE drift. Substituting this expression into the particle's (non-relativistic) vector equation of motion, resolving it into parallel and perpendicular components, and applying Northrop's averaging process, we obtain the averaged equations of motion, in lowest order, for the components u and w. From the latter equation we prove immediately that the magnetic moment of the particle is an adiabatic invariant to lowest order. Next, we resolve the instantaneous velocity of the guiding centre into two components, R = r — p, where p is a rapidly rotating vector directed from the guiding centre to the instantaneous position of the particle. Upon applying Northrop's averaging process we obtain at once the averaged velocity of the guiding centre including the complete set of first-order drifts. From this equation we readily deduce the energy gain equation to lowest order. It is then shown that the simple averaging prescription applied here is mathematically rigorous and yields correctly all lowest order results in an expansion in reciprocal powers of the cyclotron frequency.
Model Fokker—Planck Equations: Part 2. The equation for a multicomponent plasma
Authors: Dougherty J. P. , Watson S. R.
Published: March 2009

A model kinetic equation for a plasma containing many species is set up. It is an approximation to the correct kinetic equation but is considerably simpler in form. The collision operator has the property that particles, momentum and energy are conserved, and it gives to good approximation the correct rates of transfer of momentum and energy between all pairs of species. It is also shown that the equation leads to an H-theorem.
Guided propagation of Alfvén waves in the magnetosphere
Authors: Fejer J. A. , Lee Kaifong
Published: March 2009

The guided propagation of Alfvén waves in a cold plasma is discussed from several points of view. First the field of a line source is calculated at infinity. This calculation leads to a divergence in the radiated power in two directions forming very small angles with the magnetic field.

The divergence is removed if the line source is replaced by a strip source of finite width. It is shown that propagation from a strip source only a few kilo-metres wide is strongly guided by the magnetic field, with almost no spreading, along a field line extending up to, say, 4 earth radii for wave periods of about 100 sec.
Higher order approximations in the theory of longitudinal plasma oscillations
Authors: Einaudi F. , Axford W. I.
Published: March 2009

The non-linear behaviour of one-dimensional electrostatic oscillations in a homogeneous, unbounded, collisionless and fully ionized plasma is considered for the case in which a single wave of small, but finite amplitude is excited initially. The Vlasov–Poisson equations are solved using the method of strained co-ordinates in which the independent variable t, the electric field and the distribution function are expanded in the form of asymptotic series, the terms of which are founded by an iterative procedure. An ordering parameter e is introduced, which is proportional to the initial amplitude of the electric field given by linear theory. Differential equations are derived which can be solved sequentially to obtain uniformly valid solutions to all orders in ε. Solutions are given to second order and applied to the case in which the background distribution function is Maxwellian. It is found that the changes in the real and imaginary part of the frequency are small in comparison to the values obtained in the linear theory; that the free-streaming terms decay exponentially in time with a damping rate proportional to ε2, in contrast with the linear theory where they are Un- damped; and that the analysis allows us to calculate the changes in the background distribution function for large time, resulting from particle-wave interactions.
Skin-depth effect of a cylindrical shock-produced plasma
Authors: Aro T.O. , Walsh D.
Published: March 2009

The microwave reflexion from and transmission around the shock-produced argon plasma whose electron density is greater than 102 times the critical electron density for the 9 Gc/s wave have been found to be similar to those of a metal rod. But the skin depth of the wave in the plasma plus the thickness of the shock boundary layer is found to affect significantly the amount of microwave power transmitted round the cylindrical surface of the plasma.
The origin of the plasma in an electromagnetic shock tube
Authors: Fearn D. G.
Published: March 2009

A pair of electrodes was placed in an electromagnetic shock tube to measure the electric field induced by the flow of an argon plasma through a transverse magnetic field. This investigation suggested that the plasma consisted of two regions, the first of which was non-luminous. Flow velocities, deduced from the variation of induced voltage with electrode separation, were compared with luminous front velocities measured photoelectrically. The first plasma region moved more slowly than the second, and its velocity and duration were consistent with shock-heating. The second region, which was dominant in most, experiments, flowed at the luminous front velocity, and had probably been ejected from the driver discharge. It is proposed that the flow velocity in the second region exceeded that in the first owing to an extensive leakage of gas through the boundary layer at the contact surface.
Stability of an anisotropic relativistic plasma in a magnetic field
Authors: Skilling J.
Published: March 2009

The collisionless relativistic Boltzmann equation is used to investigate the stability of a large-scale two-component plasma containing numerically small anisotropic relativistic populations. Although most permitted waves are stable, Alfvén type waves are found to be unstable whenever the anisotropy exceeds O(v A/c). Growth times are estimated as days for supernova remnants and millennia for cosmic ray protons.
Slipping stream instability in anisotropic plasma with magnetic shear
Authors: Rao S. S. , Kalra G. L. , Talwar S. P.
Published: March 2009

Starting with the Chew, Goldberger & Low equations, an analysis is made of instability arising due to a tangential velocity discontinuity in a dilute plasma. The velocities on either side are parallel but oppositely directed. Two cases are considered: (i) the magnetic field is uniform and everywhere transverse to the motion, and (ii) the magnetic field vectors on either side are orthogonal, being parallel to the motion on one side and perpendicular on the other. The conditions for instability are obtained and it is found that the effect of magnetic field is destabilizing in both cases. The effect of orthogonality of magnetic fields on the conventional fire-hose instability for a uniform, static plasma is also discussed as special case.
Time-dependent motions of the cavity formed when a uniform corpuscular flux is incident on the magnetic field of n line currents
Authors: Burghes D. N. , Hewson-Browne R. C.
Published: March 2009

Time-dependent motions of the cavity formed when a uniform corpuscular flux is incident on the magnetic field of n line currents are considered. The general problem is formulated and solved in the case of an initially flat-faced cloud of flux approaching and passing the magnetic field of n line currents. The special case of a line dipole is analysed in some detail.
Non-linear scattering of electromagnetic waves near the ion cyclotron frequency in an inhomogeneous plasma
Authors: Teichmann J.
Published: March 2009

The non-linear induced scattering by plasma particles of right-hand and left- hand polarized electromagnetic waves propagating along the magnetic field, is studied. The non-linear Landau damping for frequencies near the ion cyclotron frequency in a weak turbulent inhomogeneous plasma is determined.
Evolutionary conditions for shock waves in collisionless plasma and stability of the associated flow
Authors: Morioka Shigeki , Spreiter John R.
Published: March 2009

The evolutionary condition for transverse and normal shock waves, and the fire- hose and mirror instability conditions for the associated flow, in a collisionless, anisotropic plasma having a strong magnetic field are determined using the theoretical representation of Chew, Goldberger & Low (1956) for such a medium. The results are expressed in terms of the Mach number, Alfvén Mach number, and the ratio of the temperatures parallel and perpendicular to the magnetic field in the flow approaching the shock wave, and applied to ascertain in what range of these parameters various types of instabilities may occur. The effect of the heat flux, which does not vanish generally in a collisionless plasma, on the shock stability is discussed.
Electron interactions and quantum plasma physics
Authors: Rauscher Elizabeth A.
Published: March 2009

The ‘quantum electrodynamics’ of the scattering of radiation from a fully ionized, interacting plasma is to be considered.

The plasma particle interaction must properly be treated quantum mechanically when the electron plasma wave phonon energies are comparable to or greater than the mean random electron energies and/or when the phonon momenta are of the order of magnitude or greater than the average electron momenta in the plasma.

In these two circumstances or either one of them, the plasma particle inter action must be treated in a quantum mechanical manner. The ‘solid-state’ plasma recently discussed by D.E.McCumber is an example of a quantum plasma.

Whether a classical or a quantum plasma is considered, the collective properties, as well as the single-particle properties, need to be considered. The collective properties of the plasma become important when it interacts with a radiation field in the case where the electron plasma frequency, ωp, is of the same order of magnitude, or exceeds, the operating radiation frequency ω, i.e. ωp≥ω.

A criterion to distinguish the properties of a plasma as to whether it is classical or quantum mechanical in nature can be defined in terms of three fundamental lengths of the electron gas. These definitions hold for a one-component plasma. They are: the classical length βe2, the Debye screening length and the thermal de Broglie wavelength defined as 1/kT. From these three quantities, we can define two dimensionless parameters. They are the classical parameter and the quantum parameter δ=λ/λD which is a measure of the quantum effects. For a quantum plasma δ>1 and in the classical limit (h = 0),δ=0, Λ<1.

When we take into account the collective behaviour characterized by the plasma oscillations, screening effects are an automatic aspect of the electron plasma gas.

It is hoped that the present review article will provide the background material for general understanding of the field and easy access to the current literature. It is also hoped that the present discussion will establish greater interest in this subject.

As an example of a calculation of plasma properties, a calculation of the generalized dielectric constant for both a low-density plasma in the classical limit and a high-density plasma in the quantum mechanical limit is performed and compared in a suitable manner.
Stability of laminar magnetofluid flow along a parallel magnetic field
Authors: Kent A.
Published: March 2009

A perfect magnetofluid model is used, without viscosity or resistivity. The simpler velocity and magnetic profiles are classified into stable and unstable groups. The analysis takes account of exponential and non-exponential time dependence, and of rigid and free boundaries.

A variety of stability criteria are established, and related to similar results in non-conducting fluid mechanics. A constant magnetic field is shown to stabilize some velocity profiles but destabilize others.
Landau damping of long wavelength ion acoustic waves in a collision-free plasma with a gravity field
Authors: Parkinson D. , Schindler K.
Published: March 2009

Ion acoustic waves propagating in a collision-free gravity-supported one-dimeiisional plasma are studied, including conditions where the wavelength is of the order of the scale height of the equilibrium plasma. It turns out that the fluid dynamic steepening tendency of waves propagating in the direction of decreasing density is overcome by Landau damping up to wavelengths of the order of the scale height or even larger, depending on the ratio of the electron and the ion temperatures.
A variational approach to the dynamic stability of high-density plasmas in magnetic containment devices
Authors: Wells Daniel R. , Norwood Joseph
Published: March 2009

Variational methods are used to determine the structure of dynamically stable plasmoids. The total energy of the plasmoid is varied subject to a set of constraint integrals on the flow. It is demonstrated that the resulting flow structure results in a plasmoid of the type observed experimentally when the angular momentum of the plasmoid is not conserved. This is the collinear vortex structure. New experimental results are presented which demonstrate that the structures observed in mirror trapping experiments may be of the type predicted by the variational calculation.

It is demonstrated that the collinear plasmoid structures can propagate in a surrounding conducting gas as members of a class of non-linear transverse waves that trap and transport fluid mass. They may also exist as standing waves in a surrounding medium which supports currents and acts as a force-bearing shell. The interaction of the non-linear transverse waves (plasmoids) with each other and with the magnetic mirror field produces a reversed-field closed configuration. Experimental results are presented which illustrate these effects and show details of the structures.

It is also demonstrated that a modification of these solutions that assumes conservation of angular momentum of the plasmoid describes another type of plasma structure which is centred on the magnetic field lines and moves at right angles to the field. This is the field-aligned plasma structure.
A 337 μm CW maser interferometer for plasma diagnostics
Authors: Chamberlain John , Gebbie H. A. , George A. , Beynon J. D. E.
Published: March 2009

Using a 337 μm gas maser (Gebbie, Stone & Findlay 1965; Gebbie, Stone, Slough, Chamberlain & Sheraton 1966) it is possible to obtain precise measurements of the submillimetre absorption and phase shift occurring in specimens of each of the phases of matter and results have already been reported for the soild, liquid and gaseous states (Chamberlain & Gebbie 1965; Gebbie, Stone, Findlay & Pyatt 1965; Chamberlain, Werner, Gebbie & Slough 1967;, Chamberlain, Findlay & Gebbie 1965).
Magnetohydrodynamic shock waves in non-aligned flow
Authors: Morioka Shigeki , Spreiter John R.
Published: March 2009

The steady shock dicontinuity in the flow of a perfectly conducting gas with anarbitrarily oriented magnetic field is considered by taking as the parameters the Mach number, the Alfvén Mach number, the magentic field direction, and the shock angle. The shock solutions satisfying the conservation laws as well as the entrophy and evolutionary conditions are given by the roots of a simple cubic equation and the associated formulas. Several special cases are discussed analytically and numerically. The possible types of magnetohydrodynamic shock waves are shown on the speed-deflexion phase plane, and the possible shock configurations in the physical space are discussed on the basis of them.
On the kinetic equation for resonant three-wave coupling
Authors: Davidson Ronald C. , Kaufman Allan N.
Published: March 2009

The kinetic equation for resonant three-wave coupling is solved exactly in the one-dimensional case assuming that only a single triplet of modes in interacting. No assumptions are made as to the froms of the interaction kernel or of the oscillation frequencies as functions of wave-number. Both positive- and negative- energy waves are allowed to be present simultaenously. In explosively unstable situations the time, t∞, for divergent behaviour to occur is calculated in terms of the interaction keral and intial conditions. In situations where the system is non-linearly stable, the density of quasi-particles is found to tend time-asymptotically to a steady state which depends in detail on the initial preparation of the system.

For the case of two or three dimensions, the asymptotic state is obtained when the system is stable, the k-space is finite, and only one triplet of modes interact. If these modes all have the same sign of energy, the Rayleigh—Jeans distribution is valid; but if one of the modes has the oppsoite sign of energy, an additional conservation law leads to a modification of the Rayleigh-Jeans distribution.
Diocotron instability in presence of a cold plasma
Authors: Nocentini Aldo
Published: March 2009

The influence of the presence of a low density, cold plasma on the stability against electrostatic perturbations of a cylindrical layer of charged particles moving in a uniform magnetic field is considered. It is shown that the influence of the plasma is important when the thickness of the layer is small, and the effect is stabilizing or destabilizing whether the dielectric constant of the plasma is smaller or larger than 1. In particular it is shown that the plasma can cause an unstable precession of the layer.
A quantitative quasi-linear analysis of waves in an anisotropic plasma
Authors: Smith A.
Published: March 2009

The quasi-linear theory of plasma waves in a collisionless plasma in the absence of external fields is formulated in a similar way to that given by Bernstein & Engelmann (1966) but is applied to the case when unstable essentially transverse electromagnetic waves with phase velocities of the order of the r.m.s. electron velocity are present. It is deduced that the wave energy reaches a maximum and then decays leaving the plasma stable. A quantitative description of the time development of a plasma with a slightly spheroidal velocity distribution is given in terms of a parameter x characterizing the anisotropy and it is found that this quantity decays exponentially as the waves grow and ultimately decays like t−β with , and correspondingly the space-averaged field energy grows to a maximum and then decays like t−β.
Theory of a thick dynamic positive-ion sheath
Authors: Sander K. F.
Published: March 2009

The nature of the dynamic positive ion sheath formed in front of the negatively going anode of a gas discharge valve is considered. Approximations valid for thick sheaths at the high voltages appropriate to mercury valves are discussed, and a transient analysis of an idealized model performed. Expressions relating anode—cathode voltage and current to sheath thickness are derived. Approximate forms of these expressions are obtained, and numerical comparison is presented in one situation.
MHD Rankine—Hugoniot equations applied to earth's bow shock
Authors: Mihalov J. D. , Sonett C. P. , Wolfe J. H.
Published: March 2009

This paper compares computed results with upstream and downstream thermal pressures, and the downstream ion density and vector flow velocity measured by the Ames plasma probe on the Pioneer 6 spacecraft as earth's bow shock was traversed. The upstream ion density and vector flow velocity measured on Pioneer 6 by this experiment are used as independent variables, together with Pioneer 6 magnetic field measurements. MRD Rankine—Hugoniot equations for an isotropic plasma are used for these computations. Reasonable agreement is obtained between the measured and computed downstream ion density, thermal pressure and convective velocity magnitude and orientation, only when a 1γ change is made to a downstream magnetic field value used in the calculation. There is disagreement between several determinations of shock orientation and that deduced from coplanarity of the reported magnetic fields, and the shock orientation provides the co-ordinate system for solving the Rankine—Hugoniot equations. If a shock orientation determined by velocity coplanarity is used in the calculations, all computed quantities agree well with the experimental results. Other results suggest that a disagreement between computed and measured upstream thermal pressures may not be negligible in comparison with experimental uncertainties in upstream velocity and density. If the computations included anisotropic pressure terms and/or other factors such as plasma turbulence, better agreement might be obtained between computed and measured upstream thermal pressures.
Saturation and damping of collisionless plasma wave echoes
Authors: Coste J. , Peyraud J.
Published: March 2009

We point out in this paper that when one increases the intensity of the second applied pulse or the time interval between the two pulses, the amplitude of the first echo saturates and multiple echoes of comparable amplitude appear. Moreover, we predict a damping of the echoes which is due to a phase mixing effect; that is collisionless.
Cyclotron harmonic wave propagation and instabilities: II. Oblique propagation
Authors: Tataronis J. A. , Crawford F. W.
Published: March 2009

Part I of this paper has discussed longitudinal wave propagation, perpendicular to the static magnetic field, in a warm homogeneous magnetoplasma. Part II extends the work to oblique propagation. The ring and Maxwellian transverse velocity distributions, which are absolutely unstable and stable, respectively, for perpendicular propagation, are shown here to be both absolutely unstable for oblique propagation. Their instabilities are radically affected by the introduction of axial velocity spread. A detailed study is made for the cases of a Maxwellian transverse distribution with resonance and resonance-squared axial velocity distributions. It is shown that abolute instabilities occur at high energy anisotropies. These become convectively unstable as teh anistropy is reduced, and are quenched as isotropy is approached. The isotropic Maxwellian is treated in detail, and shows both cyclotron and Landau collisionless damping.
Parametric excitation of a plasma
Authors: Chen C. S. , Lewak G. J.
Published: March 2009

The parametric effect of an applied uniform oscillating electric field on both unmagnetized and magnetized plasmas is investigated. By using a perturbation method of multitime scales, we have shown that parametric excitation of transverse waves propagating obliquely to the applied field in an unmagnetized plasma is possible. The growth rate of the excited waves reaches a maximum for transverse propagation. Ion motion does not change the character of the parametric excitation except by reducing the growth rate. In a magnetized plasma it is shown that excitation of a pair of waves is possible where one is a Langmuir wave, propagating along the magnetic field and the other is a circularly polarized transverse wave propagating in the opposite direction.
Diatomic gas-thermal radiation interaction between parallel plates
Authors: Phillips Warren F. , Arpaci Vedat S. , Larsen Poul S.
Published: March 2009

The effect of rarefaction, optical depth and ratio of conduction to radiation on the heat transfer through stagnant diatomic gas between parallel plates is investigated. A three-fluid formulation (translator–rotator–photon) at low temperature and [translator–(rotator and vibrator)–photon] at high temperature, based on continuous distribution functions, molecule–molecule elastic collisions, molecule–photon inelastic collisions, grey gas, and local equilibrium is solved by the linearized moment procedure for fully accommodating surfaces. Results include the error involved in decoupled total heat flux.
Effect of Hall current and resistivity on the stability of a gas–liquid system
Authors: Kalra G. L. , Kathuria S. N. , Hosking R. J. , Lister G. G.
Published: March 2009

The stability of a non-conducting, compressible fluid (gas) flowing across the surface of incompressible conducting fluid (liquid) is discussed. Finite resistivity and Hall current are included in the hydromagnetic equations, together with surface tension. Both subsonic and supersonic flows are treated and some new instabilities are found, together with modifications to real and oscillatory modes obtained in earlier treatments.
Stability of relativistic anisotropic plasmas to perpendicular magnetosonic waves
Authors: Landau R. W. , Cuperman S.
Published: March 2009

The stability of relativistic anisotropic plasmas to the magnetosonic (or righthand compressional Alfvén) wave, near the ion cyclotron frequency, propagating perpendicular to the magnetic field, is investigated. For this case, and for wavelengths larger than the ion Larmor radius and large ion plasma frequency () the dispersion relation is obtained in a simple form and solved. It is shown that for T‖ ╪ T⊥ (even T‖ ≥ T⊥) no instability occurs. This conclusion applies also to the case of the anisotropic interplanetary medium.

We note a peculiarity of the dispersion relation. Zero-order and first-order terms cancel so that the relation is of second order in our expansion parameter. The non-relativistic numerical results of Fredricks and Kennel are recovered.
Dynamic stability of closed plasma configurations
Authors: Wells Daniel R.
Published: March 2009

The global stability of closed plasma configurations is related to the dynamical principle of least constraint and the spacetime and gauge symmetries of the flow fields. This leads to an entirely new concept of MHD stability which is more basic than stability predictions which rely on a linearized perturbation analysis. The predictions of the theory are compared to recent experimental results obtained in studies of the stability of plasma confinement geometries. The theory predicts the violent ‘instabilities’ of these systems which are currently attributed to other mechanisms. Several pertinent details of the theory which are widely misinterpreted are discussed and clarified.
A class of solutions of quasilinear equations
Authors: Ivanov A. A. , Teichmann J.
Published: March 2009

A method for obtaining a class of generalized solutions of the system of quasilinear equations has been developed for the case where the wave vector k and the velocity v of the particles are oriented in a general direction with respect to the magnetostatic field. The method is demonstrated on the case of the quasilinear relaxation of an ion beam penetrating a cold magnetoplasma.
Longitudinal waves in a perpendicular collisionless plasma shock: I. Cold ions
Authors: Gary S. Peter , Sanderson J. J.
Published: March 2009

This paper considers electrostatic waves in a Vlasov plasma of unmagnetized ions and magnetized, Maxwellian electrons. The linear dispersion relation is derived for waves in a perpendicular shock such that the most important sources of instability are the E × B and ∇B electron drifts. For the case of cold ions, propagation perpendicular to the applied magnetic field, and the E × B drift alone, a numerical analysis of frequency vs. wave-number is presented. The effects of the ∇B drift are also considered, and it is shown that the maximum growth rate can be larger than the maximum growth rate for the zero magnetic field ion acoustic instabifity under comparable conditions.
Resistive loading by a finite plasma cylinder
Authors: Hasti D. E. , Oakes M. E. , Schlüter H.
Published: March 2009

The loading resistance of a coil-plasma system operated near the lower hybrid resonance in hydrogen and argon has been measured. The results are consistent with the predictions of a theoretical model that includes finite plasma effects.
Radiation from a charged particle in a magnetoplasma
Authors: Trulsen J. , fejer J. A.
Published: March 2009

Two expressions for the power radiated by a charged particle in a homogeneous magnetoplasma are derived, using a method similar to that of Kolomenskii, Eidman and Liemohn. The first expression is identical with that of Eidman. The reason for the correctness of Eidman's result for dispersive media, in spite of his complete neglect of dispersion in the derivation, is explained. Liemohn, by taking dispersion into account at only one stage of the derivation, obtains a result which disagrees with the present one, often by many orders of magnitude, as illustrated by computations.

The second expression is derived by several authors by different methods; it is more suitable for computations than the first one. The radiation bands and their limiting frequencies are discussed systematically.
Time asymptotic perturbation theory in weak plasma turbulence I. Macroscopic description
Authors: Elsässer Klaus
Published: March 2009

The time asymptotic method of non-linear mechanics (Bogoljubov & Mitropoiski 1961) is used to solve the hierarchy equations of low-amplitude wave correlations. We start with a formal description of individual dispersive and undamped waves and derive the usual kinetic equation for the energy spectrum and the three-wave correlation in the lowest order (three-wave processes). We show that the equations are automatically closed (‘Quasi-Gaussian’) even in the case where the correlations have the same order of magnitude as the corresponding moments. This approach parallels the multiple-time formalism of Sandri and Frieman, but it represents an alternate systematic and unique method (without ‘extension’ in the sense of Sandri).
Interaction of electrostatic waves in collisionless plasmast
Authors: Lewak G. J.
Published: March 2009

The interaction of three electrostatic waves in a collisionless plasma is treated to fourth order neglecting the wave—particle interaction (damping). Using the principles of energy conservation, and invariance under time reversal, conditions on the coupling constants are derived, enabling the solution to be expressed as a function of only two coupling constants. Phase plane diagrams of the solutions are sketched showing that the only singular points are stable equili bria. It is suggested how the theory may be applied to the explanation of the ‘floating spike’ resonance observable when one-half the hybrid frequency is the difference between the plasma and gyro frequencies (Hagg & Muldrew 1968).
Comment on negative diffusion coefficients in quasi-linear theory
Authors: Montgomery David , Bodner Stephen
Published: March 2009

A recent paper on quasiinear theory by Klozenberg & Bernstein is commented upon. It is argued that improper treatment of the perturbed electron distribution for damped waves has led to a diffusion-type equation with a negative diffusion coefficient.
Reply to the ‘Comment on Negative Diffusion in Coefficients in Quasilinear Theory’ by David Montgomery and Stephen Bodner
Authors: Bernstein Ira B. , Klozenberg J. P.
Published: March 2009

The criticisms of Montgomery & Bodner (preceding paper) seem to stem from a misunderstanding of the claims in the paper of Klozenberg & Bernstein (1970) in part perhaps semantic. The derivation criticized was intended to apply only to those particle velocities v corresponding to the range in phase velocities βк/к for which there is an appreciable wave excitation. The term ‘resonant phase velocity’ was intended to mean those phase velocities in a small interval Δ such that ν − ½Δ < βк/к < ν + ½Δ, which interval in the integral determining the diffusion coefficients leads to the familiar expression involving δ(βк кν). When this contribution is non-vanishing it determines the lowest significant order contribution, in the small parameters of the problem, of ∂ƒ0/∂t, assuming that the wave excitation at the time in question is so large that effects associated with initial conditions are indeed negligible.
Quasi-linear theory in the non-resonant region
Authors: Bodner Stephen E.
Published: March 2009

By solving for the changes 〈Δν〉 and 〈ΔνΔν〉 for a particle, it is shown that there is no diffusion equation for non-resonant particles when the electric field wave is damping. By indirect means it is then shown for this case that the appropriate quasi-linear solution for ƒ1(к, ν, t) is proportional to ∂ƒ0(ν, 0)/∂ν rather than ∂ƒ(ν, t)/∂ν.
On resonances of a plane plasma condenser in crossed electric and magnetic fields
Authors: Nikolov N. A.
Published: March 2009

Resonance frequencies of a plane plasma condenser in crossed electric and magnetic fields are determined, using the two-component magnetic hydrodynamical equations. The perturbed plasma parameters (ion and electron densities and velocities and the electric field in the plasma), due to an external a.c. electric field are found. The calculated resonance is not exact since dissipative processes are neglected.
Non-linear Landau damping of electromagnetic cyclotron waves
Authors: Akinrimisi Jibayo , Sudan R. N.
Published: March 2009

The non-linear scattering of circularly polarized electromagnetic waves is studied. Expressions for matrix elements of interaction are derived and for interacting right-handed circularly polarized waves (whistler waves) the matrix is explicitly calculated for particular velocity distribution functions of electrons. Non-linear damping rates are computed.It is shown that non-linear scattering is not in general a dominant process for whistlers in the magnetosphere.
Effect of ion motion on parametric oscillations of a cold plasma in a magnetic field
Authors: Prasad R.
Published: March 2009

Dispersion relations for first-order oscillations in an infinite homogeneous two- component plasma, in response to an externally applied constant magnetic field and a right-hand circularly polarized external electric field, and with propagation vector parallel to the magnetic field, has been obtained. The external electric field, assumed to be spatially homogeneous, is perpendicular to the applied magnetic field. It has been shown that the left-hand mode is excited and is unstable when its frequency ≃ ν–ωρ, where ν is the frequency of the external electric field and ωρ is the characteristic plasma frequency. When the applied magnetic field is large, both the left- and right-hand modes are excited and may be unstable when their frequencies ≃ Ωic – ωρ where Ωic represent the electron (i = 1) and the ion (i = 2) cyclotron frequencies. The principal criterion for the validity of these results is the condition of spatial homogeneity of the external electric field.
The effects of ion-ion coffision on a ion-acoustic plasma pulse
Authors: Espedal Magne S.
Published: March 2009

The effects of ion-ion collisions, described by a Fokker-Planck operator in the kinetic equation, on an ion-acoustic plasma pulse, are studied. Our investigations show that the coffisions give a broadening of the pulse, and reduce the effect of interaction between the main plasma and the pulse.
Interaction of test particles with a plasma
Authors: Laingal E. W. , Lamont A. , Fielding P. J.
Published: March 2009

The effect of a test particle, moving through a two-dimensional Maxwellian plasma, has been studied both analytically and by computer simulation. For a stationary test particle, Debye shielding occurs. When the velocity of the test particle approaches the electron thermal velocity, there is a concentration of electrons several Debye lengths downstream, an effect which is essentially a heavily damped plasma oscillation. The analytic results agree closely with the computer simulation. As the velocity of the test particle increases, it is shown analytically that the damping diminishes, and eventually a fully developed plasma oscillation is established in the wake of the particle.
Coherent ion plasma oscifiations in a d.c. corona discharge in rarefied air
Authors: Lilienfeld Pedro
Published: March 2009

Stable, phase coherent ion plasma oscillations are found superimposed on the d.c. potential and current of positive coaxial corona discharges in air at pressures of the order of 1/100 of one atmosphere. The frequency of these oscillations, typically several hundred kHz, is a function of air density, and varies with the concentration of gaseous trace contaminants.
Effects of electron—electron Coulomb interactions in low-voltage neon discharges
Authors: Shaw David T.
Published: March 2009

The electron-energy distribution in a neon discharge is determined from the Boltzmann equation. Inelastic collisions with neutral atoms, as well as electron—electron Coulomb interactions, are included in the calculation. It is shown that, as predicted by Crescentini & Maroli (1968), the distribution is very close to the Druyvesteyn function when the electron density is very low (ne > 107 cm-3). The same conclusion, however, is not correct as the electron density increases to a higher value (ne > 1011 cm-3). In this case, the electron—electron Coulomb interactions play an important role in restoring the distribution toward a Maxwell jan function.
A singular perturbation analysis of theoretical models for warm inhomogeneous plasmas
Authors: Miura Robert M. , Barston Eugene M.
Published: March 2009

Owing to the complexity of the Vlasov–Maxwell equations for inhomogeneous plasmas, it is of general interest to investigate simpler approximate models. We compare three specific models, proposed in the literature in connexion with the high frequency oscillations of such plasmas, by means of a singular perturbation expansion in powers of E = (λD/L)⅔, where λD and L are appropriate electron Debye and equilibrium scale lengths, respectively. Explicit formulas are obtained for the eigenfrequencies (to second order) and for the electric field eigenfunctions (to leading order), and the computation of these quantities for various equilibrium parameters becomes very simple indeed. We find that, whereas the electric field eigenfunctions differ in zero order for the three models, the eigenfrequencies are identical through first order.
Wave-particle interactions in electrostatic waves in an inhomogeneous medium
Authors: Nunn D.
Published: March 2009

The system studied is that of a narrow-band electrostatic wave packet in a collision-free plasma. Inhomogeneous effects are represented by a wave-number, which varies linearly with distance. The system is excited by a weak resonant beam, and, to first order in a smallness parameter associated with the weakness of the beam, the resonant-particle distribution function and charge densities are calculated. It is found that second-order resonant particles become stably trapped in the wave, and, after a few trapping periods, make a dominant contribution to the resonant particle charge density. The growth rate due to the resonant beam was found to increase linearly with trapping time, and typically a pulse which traps particles forntrapping periods exhibits a growth rate ˜ntimes the linear Landau value. Furthermore, a reactive component of charge density was found that was able to cause a steady change in wave frequency and wave-number. These features of large growth rates and changing frequency should appear in parallel problems involving other wave types. An obvious application is that of VLF emissions in the whistler mode.
Cyclotron radiation in hot magnetoplasmas
Authors: Trulsen Jan
Published: March 2009

The effects of thermal motions on the cyclotron radiation from test particles gyrating in a homogeneous magnetoplasma are studied. These effects take care of all singularities that exist in the theory of cyclotron radiation in cold magneto- plasma, e.g. the divergence in energy loss for small particle energies. Around the hybrid frequencies thermal corrections become of dominant importance. At these frequencies cold-plasma theory breaks down. Thermal effects arise in two ways: by modifying the wave modes known from cold plasma theory, and by the introduction of a new longitudinal wave mode, known as the Bernstein mode. All wave modes are damped (in stable plasmas), the damping increasing rapidly with the product (V/v|) (ω - s), where the wave frequency ω is measured in units of the gyro frequency; V is the thermal velocity; v| the parallel component of the particle velocity, and s is an integer.
Non-linear theory of hydromagnetic waves in a high β plasma
Authors: Dobrowolny Marino , Rogister André
Published: March 2009

A non-linear integro-differential equation is derived, governing the space time evolution of non-linear hydromagnetic waves in a finite β collisionless plasma. The theory is done for quasi-perpendicular propagation, for wave frequencies above ion cyclotron frequency, and wavelengths smaller than ion Larmor radius. In the low β limit, the derived equation reduces to a Korteweg de Vries equation.
E-layer precession in a plasma
Authors: Berk H. L. , Sudan R. N.
Published: March 2009

A weak E layer in a non-uniform magnetic field will tend to precess as a rigid body in response to the radial focusing of external magnetic fields and fields due to wall currents. We study the interaction of this precessional mode with a background plasma, and we explicitly include dissipation mechanisms in the plasma, walls and external resistors. When the plasma background is treated in the MHD approximation, we find that the mode changes character from a precessional mode at low density to a compressional Alfvén wave at high density. For a very weak E layer, instability is found, even without dissipation, when a sufficiently high background plasma density is present. However, for moderate E-layer strengths, the modes are found to be stable, even with dissipation.
A Fokker—Planck treatment of non-linearly interacting waves
Authors: Cook I.
Published: March 2009

The statistical properties of non-linearly interacting waves are considered from a physically motivated viewpoint. A Fokker-Planck wave transport equation is derived. In certain circumstances an H theorem can be proved.
Stability of anisotropic plasmas to almost-perpendicular magnetosonic waves
Authors: Landau† R. W. , Cuperman S.
Published: March 2009

The stability of anisotropic plasmas to the magnetosonic (or right-hand compressional Alfvén) wave, near the ion cyclotron frequency, propagating almost perpendicular to the magnetic field, is investigated. For this case, and for wavelengths larger than the ion Larmor radius and for large ion plasma frequency (w2p+ ≫ Ωp+) the dispersion relation is obtained in a simple form. It is shown that for T # T' (even T ≫ T) no instabifity occurs. The resonant ters are also included, and it is shown that there is no resonant instabifity, only damping.
Mass and heat transfer in a diatomic gas
Authors: Haas J. C. , Arapaci V. S. , Springer G. S.
Published: March 2009

The transfer of mass and heat through a diatomic gas bounded by two plane parallel surfaces is investigated by a kinetic model which includes translational, rotational and vibrational degrees of freedom. A full range moment method is employed in the solution. Numerical solutions obtained for small temperature and pressure differences show the effect of inelastic collisions on the mass and heat fluxes. Approximate analytical expressions are derived for the mass and heat transfer rates, which are valid over the entire density range and yield the correct free-molecule and continuum limits. The results agree well with existing heat transfer and density measurements.
Longitudinal waves in a perpendicular collisionless plasma shock: Part 3. Te ˜ Ti
Authors: Gary S. Peter
Published: March 2009

This paper considers electrostatic waves in a Vlasov plasma of unmagnetized ions and magnetized electrons undergoing an E x B drift. The linear dispersion relation is solved numerically for Te ΰTi. For a fixed ratio of drift velocity to electron thermal velocity, the growth rates of the E x B electron drift instability are smaller, and the waves are stabilized at much smaller values of k. B than in the Te ≫ Ti case.
Electron pitch-angle diffusion driven by oblique whistler-mode turbulence
Authors: Lyons L. R. , Thorne R. M. , Kennel C. F.
Published: March 2009

A general description of cyclotron harmonic resonant pitch-angle scattering is presented. Quasi-linear diffusion coefficients are prescribed in terms of the wave normal distribution of plasma wave energy. Numerical computations are performed for the specific case of relativistic electrons interacting with a band of low frequency whistler-mode turbulence. A parametric treatment of the wave energy distribution permits normalized diffusion coefficients to be presented graphically solely as a function of the electron pitch-angle.

The diffusion coefficients generally decrease with increasing cyclotron harmonic number. Higher harmonic diffusion is insignificant at very small electron pitch-angles, but becomes increasingly important as the pitch-angle increases. One thus expected the rate of pitch-angle scattering to decrease with increasing electron energy, since the resonant value of the latter varies proportionately with harmonic number. This indicates that, in mirror-type magnet field geometrics, such as the Earth's radiation belts, the diffusion losses of high energy electrons are likely to be appreciably slower than those at low energy. Integration of the diffusion rates along a complete bounce orbit will be required to clarify this point, however, since the high-energy particles will be subject to more rapid first harmonic diffusion near their mirror points.
Magneto-acoustic resonance in a non-uniform current carrying plasma column
Authors: Vaclavik J.
Published: March 2009

The forced radial magneto-acoustic oscillations in a plasma column with nonuniform mass density and temperature are investigated. It turns out that the oscillations have a resonant character similar to that of the magneto-acoustic oscillations in a uniform plasma column. The properties of the axial and azimuthal components of the oscillating magnetic field are discussed in detail.
Method of Characteristics for supersonic flow of a guiding centre plasma
Authors: Whang Y. C.
Published: March 2009

A study of the compressive magneto-acoustic waves in a guiding centre plasma shows that the wave-front that emerges from a point disturbance after a finite time is a simple oblate spheroid with the axis of revolution parallel to the field lines. Thus, in a steady three-dimensional supersonic flow of guiding centre plasma a simple analytic expression can be obtained to represent the characteristic surfaces. From a proper linear combination of the governing macroscopic equations, the characteristic equation is obtained. It represents the propagation of disturbances on the characteristic surface. The characteristic theory can be used to study the interaction of the solar wind with the moon and possibly with other planetary bodies.