bluuebunny/crossref_metadata_2025 huggingface dataset:
A note on the semi-Lagrangian formulation of the Vlasov equation
Authors: Lewak G. J.
Published: March 2009

In a previous paper [Lewak (1969), see also Pflrsch (1966) for related treatment], it was shown that the Vlasov equation in the Semi-Lagrangian (S.L.) formulation, may be written in a form resembling the fluid equations.

plus Maxwell's equations with the source terms given by

where n is the determinant of the tensor Tij = ∂gi/∂ζj, and N is the constant mean number density of electrons. The averaging notation < > here is defined by

where f(σ) is the electron distribution function to be specified. The equations assume for simplicity a uniform fixed ion background, although this is not a necessary restriction and equations (1) and (2) need only an obvious modification to account for ions. The force fields in (1) are related to the electric field E and magnetic field B in the plasma by
.
Hydromagnetic structure of a current sheet
Authors: Cassen Patrick
Published: March 2009

We investigate the structure of the hydromagnetic boundary layer formed by the mixing of two streams of fluid containing oppositely directed magnetic fields. The flow and magnetic field are aligned at infinity. The fluid is considered to be compressible, viscous, and electrically and thermally conducting. Solutions are presented for the density, velocity, and magnetic field variations through the boundary layer.
Continuum theory of spherical electrostatic probes (frozen chemistry)
Authors: Bush William B. , Fendell Francis E.
Published: March 2009

Continuum theory is adopted to describe the steady, spherically symmetric flow of an unbounded expanse of quiescent, slightly ionized fluid about a perfectly catalytic conductor. The negative charge carrier is taken to be an electron, the potential bias of the probe φP is taken to be negative, and recombination and ionization effects are taken to be negligible. Matched asymptotic expansions are used to study the limit of small Debye number ∈, where ∈ is the ratio of Debye length to conductor radius. The current collected at the probe is found for three ranges of applied potential: small bias, including φp = O(1); moderate bias in which φP = O(log(1/∈)); and large bias in which φP = O(log(1/∈);). The current collected does not saturate (become independent of φP) for the range of c studied here; however, for φP, the current collected remains of order unity while the potential bias varies over several orders of magnitude. The previous asymptotic treatments of this problem, principally due to Su & Lam and to Cohen, are critically reviewed and compared with the results developed here.
Problems of determination of high temperature thermodynamic properties of rare gases with application to mixtures
Authors: Capitelli M. , Molinari E.
Published: March 2009

Thermodynamic properties and compositions of gases in thermal equilibrium at high temperature can in principle be derived quite accurately once the partition functions of the relevant species have been calculated.
Suppression of runaway of electrons in a Lorentz plasma.: I. Harmonically time varying electric field
Authors: Abraham-Shrauner Barbara
Published: March 2009

The suppression of runaway electrons in a Lorentz plasma is demonstrated for a two-component, fully ionized plasma in the presence of a high frequency, weak, uniform electric field. The time for runaway to occur for electric field frequencies high compared to the collision frequency is longer than the runaway time for low electric field frequencies or zero frequency, by the ratio of the frequency of the electric field to the collision frequency squared. Both the resolvant method developed by Prigogine and co-workers and the double perturbation scheme of the Poincaré—Lighthill method are employed to derive the diffusion equation for the modified one-particle distribution function in the collision-dominated region of velocity space.
The decomposition of a decelerationg ionizing shock
Authors: Sloan D. M.
Published: March 2009

The equations governing the collapse of a cylindrical, ionizing shock in an applied axial magnetic field are solved numerically using a method involving characteristics. Initially the collapsing shock accelerates, but subsequently the increasing magnetic forces at the shock produce a retardation and this cools the gas behind the shock. The numerical solution describes the behaviour of the shock until the gas behind ceases to conduct. The decomposition of the ionizing shock is examined.
Kinetic theory of three-wave interaction in a magnetied plasma
Authors: Stenflo L.
Published: March 2009

This paper considers the non-linear resonant interaction between three waves, which propagate in the direction of a constant magnetic field in a homogeneous plasma. A coupled-mode theory, which makes it possible to derive the coupling coefficients within a kinetic description, is developed.
The sheath criterion for a growing sheath
Authors: Andrews J. O.
Published: March 2009

When a sheath grows into a plasma at a slower speed than the local ion speed of sound, an ion rarefaction wave propagates into the plasma ahead of the sheath. It is shown that, in the frame of reference of the sheath edge, the speed of ions arriving at the sheath edge cannot exceed (kTe/M)½.
The two-stream instability and its classification into absolute and convective for hot plasmas
Authors: Infeld E. , Skorupski A.
Published: March 2009

This paper deals with the problem of classification of the two-stream instability for hot plasmas. The method is based on the criterion of Fainberg, Kurilko & Shapiro (1961). The basis of the analysis is the ‘resonance’ distribution, but a modified resonance distribution, leading to better results, is also investigated. The stability limit, classification into absolute and convective instabilities, as well as asymptotic growth rates are given for some chosen values of stream densities and temperatures, and arbitrary stream velocities. A method for finding the maximum temporal growth rates is also outlined.
Long wavelength ion-acoustic waves in a magneto-plasma in a gravitational field
Authors: Liu C. H.
Published: March 2009

Ion-acoustic waves propagating in a collision-free, gravity-supported plasma in a static magnetic field are studied with a linearized Vlasov equation. The dispersion relation is derived in the limit of vanishing electron to ion mass ratio and wavelength much larger than the Debye length. From this dispersion relation it is shown that the well-known fluid dynamic steepening tendency of waves propagating in the direction of decreasing density is competing with the effect of Landau damping. Depending on the ratio of electron and ion temperatures, the direction of propagation and the strength of the static magnetic field, waves of wavelengths of the order of the scale height or even greater are shown to be damped. Several special cases are discussed.
Discrete spectra and dampes waves in quasilinear theory
Authors: Vahala George , Montgomery David
Published: March 2009

The consequences of the quasilinear equations are explored. Particular attention is paid to the differences between the one-dimensional and the two- and three-dimensional cases, and to the differences between the cases of discrete and continuous wave-number spectra. The possibilities of and problems associated with including damped waves are treated. The relation between conservation laws and the ‘resonance approximation’, in which the limit of zero growth rate for the unstable waves is taken at finite times, is clarified. Numerical solutions for the one-dimensional case with finite growth rate are presented.
Comment on revised quasilinear equations dealing with wave-number spectra
Authors: Abraham-Shrauner Barbara
Published: March 2009

We wish to point out that the revised quasilinear equations found recently by Klozenberg & Bernstein (1970) for continuous wave-number spectra, which are a simplified version of those derived by us for discrete wave spectra (Abraham-Shrauner 1970), can be derived easily from the conventional quasilinear equations (Drummond & Pines 1962; Vedenov, Veliklov & Sagdeev 1962) by analytic continuation. The analytic continuation is the same type used in discussions of the plasma dispersion relation for the linearized Vlasov equation and of the weakly unstable kinetic equation (Balescu 1963; Rogister & Obermann 1969).
Effect of spatially uniform external periodic magnetic field on wave propagation through a hot electron plasma
Authors: Das K. P.
Published: March 2009

Starting from hydrodynamic equations, a dispersion relation is obtained for wave propagation through a hot electron plasma perpendicular to a spatially uniform external periodic magnetic field, B0 cos ω0t, and several excitation conditions are deduced.
Study of the oscillations stimulated at the upper hybrid resonance by a pulsed dipole antenna in a weakly inhomogeneous plasma
Authors: Graff Philippe
Published: March 2009

The oscillations, excited by a pulsed dipole antenna at the upper hybrid resonance in a weakly inhomogeneous plasma, are investigated by the Wentzel—Kramers—Brillouin (WKB) approximation. In addition to a direct component, the field at a given distance from the transmitter is shown to consist in two obliquely reflected rays when the upper hybrid frequency WT is less than twice the electron gyro-frequency WH. The analytical expressions of the frequencies of the echoes intercepted by a moving receiver are given and the influence of the reception time t, the velocity VS of the receiver and the parameters of the plasma are thus pointed out.

As distinct from previous studies, the static magnetic field B0, the velocity of the receiver, and the gradient of the electron density ∂N/∂X, are here vectors of arbitrary directions. The choice of such a general model makes it possible to interpret most of the experimental data concerning the upper hybrid resonance in the ionosphere.
Magnetic stabilization of transverse plasma instabilitiest
Authors: Buti B. , Lakhina G. S.
Published: March 2009

Waves, propagating transverse to the direction of the streaming of a plasma in the presence of a uniform external magnetic field, are unstable if the streaming exceeds a certain minimum value. The magnetic field reduces the growth rate of this instability, and also increases the value of the minimum streaming velocity, above which the system is unstable. The thermal motions in the plasma, however, tend to stabilize the system if the magnetic field is weak (i.e. , Ω being the electron cyclotron frequency, k the characteristic wave-number, and Vt the thermal velocity); but, in case of strong magnetic field (i.e. ), they increase the growth rate, provided (ωp being the electron plasma frequency).
On some similarity solutions in magnetohydrodynamics
Authors: Sozou C.
Published: March 2009

In this paper we employ similarity considerations to investigate the flow field produced by an electric discharge (mathematically a current source) and a jet of momentum emerging from the same hole of a plane wall bounding a viscous, incompressible conducting fluid, which extends to infinity. We also use similarity solutions in considering the axisymmetric configuration of a problem that has recently received some attention in connexion with field line reconnexion in conducting fluids. We derive the similarity equations for an incompressible, viscous conducting fluid, and discuss the solutions for the case when the fluid is perfectly conducting. When the electrical conductivity of the fluid is finite, we could not construct solutions, satisfying the appropriate boundary conditions.
Thermal and collisional corrections to the ordinary wave
Authors: Arumi F. N. , Oakes M. E.
Published: March 2009

A moment approach is used to find the thermal and collisional corrections to the ordinary wave in a plasma. Results are given that include like- and unlike- particle collisions.
Non-linear electrostatic plasma waves
Authors: Schamel Hans
Published: March 2009

A solution of the one-dimensional time-independent Vlasov–Poisson system, including the condition of no net current, is constructed for a large class of electric potential functions φ(x), including periodic and solitary waves, as well as monotonic transitions. Displaced Maxwell distributions for the free particles, and an unshifted Maxwell distribution for the trapped ions, are used. The condition of positiveness of the unknown distribution function for the trapped electrons (which can be split into two parts, one depending solely on the chosen wave, the other on the given distributions) is examined. It is shown, for a non-linear wave

that this condition plays no rôle when the thickness l of the wave considerably exceeds the Debye length λD(l ≫ λD). If, however, l lies in the neighbourhood of λD(l ≳ λD), there exist limits for the free parameters. The smallest thickness lmin results if the Mach number M lies in the range 1 > M > 2 and the electronion—temperature ratio θ = Te/Ti exceeds 10. This confirms the view that the wave is a steepened ion-acoustic wave. lmin decreases with decreasing amplitude ϕmax of the wave and decreasing number of trapped ions, but does not lie below the Debye length as long as the wave is non-linear. In the linear case, the condition of positiveness imposes no restrictions.
Interpretation of dispersion relations for bounded systems
Authors: Rognlien T. D. , Self S. A.
Published: March 2009

A treatment is given of the problem of constructing normal modes for anarbitrarily bounded system from roots of the linear dispersion relationD( ω, k) = 0 for the corresponding infinite or periodically bounded system. For a system described by continuous macroscopic variables, and of general cylindrical form (uniform along an axisz, say), each transverse eigenmode gives rise to a set of axial normal modes constructed from a pair of dominant rootskαz(ω) ofD= 0 satisfying the boundary conditions which are characterized by complex reflexion coefficients for the dominant waves. The implications of the results for the interpretation of experiments on plasma waves and instabilities on finite cylinders are discussed, with particular reference to the effects of end-plate damping and axial current onQ-machines.
Thermodynamics of the relaxation of a temperature anisotropy in a collisionless plasma
Authors: Montes C. , Peyraud J.
Published: March 2009

A new method for dealing with a typical quasi-linear problem is presented. The quasi-linear relaxation of the temperature anisotropy of a collisionless plasma is completely described within the framework of the thermodynamics of irreversible processes. This is obtained by means of generalized Onsager relations applied to the weakly unstable system. Free energy of the system is analyzed in detail, to study the net work involved in the process.
Dynamic shielding effects in partially ionized gases
Authors: Hahn Hong-Sup , Mason E. A. , Miller E. J. , Sandler S. I.
Published: March 2009

The effects of dynamic shielding of charged-particle interactions on the predicted values of hte transport properties of partially ionized argon are considered. It is found that, at low degreesof ionization, dynamic shielding effects are of little importance, because charged-particle encounters are infrequent, so that the perturbed Lorentzian method may be used to obtain a rapidly convergent solution. At higher degrees of ionization, where the Chapman–Enskog solution converges rapidly, dynamic shielding effects can be taken into account using the expressions presented in the appendix to this paper. It is also found that the static shielding model, assuming complete shielding by electrons only, yields results that are quite close to those obtained when dynamic shielding is considered.
An Improved hierarchy for turbulent magnetized plasma Part 2. Application to resonant three-wave interactions
Authors: Linnebur Eldon J. , Kammash Terry
Published: March 2009

The resonant three-wave interactions in an infinite homogeneous magnetized plasma are re-examined using the improved hierarchy presented in part 1. An equation for the wave energy is obtained which, for a spectrum made up entirely of marginally stable waves, is shown to be a second-order Markoffian differential equation, rather than a first-order equation as obtained by others. The conditions under which a first-order equation is derived are examined and discussed. For a spectrum composed of waves with small growth, rates, it is shown that the equation for the plasmon density always has a stationary solution, thus eliminating the occurrence of an ‘explosive instability’ in such systems.
Sideband growth in nonlinear Landau wave-particle interaction
Authors: Brinca A. L.
Published: March 2009

The distortion of the electron velocity distribution caused by a large amplitude Landau wave is determined analytically for the initial-value problem. The resulting stability of electrostatic perturbations impressed on the evolving plasma is studied. Narrow sidebands of the applied frequency experience consecutive growths of large magnitude during the early stages of the nonlinear wave-particle interaction. The significance of the derived results to both wave propagation experiments and triggered VLF emissions in the magnetosphere is discussed.
Scattering of Langmuir waves produced by a beam with finite transverse dimensions
Authors: Berthomieu G.
Published: March 2009

It has been proposed by Smith that type III radio bursts may be produced by streams of protons with radius of the order of 7 km, which is of the same order as the characteristic lengths of the nonlinear processes which are supposed to take place in the dynamics of these bursts. In this paper, we consider a method for studying systems with finite transverse dimensions and apply it to a simple model: the scattering of a beam of plasma waves by acoustic turbulence and by the particles of the plasma.
Current sheath studies in a co-axial plasma focus gun
Authors: Chow S. P. , Lee S. , Tan B. C.
Published: March 2009

A co-axial plasma focus device is operated in deuterium gas at ambient pressures from 0·2 to 0·7 mm Hg and condenser bank voltages from 10 to 22 kV. Magnetic probing reveals an axisymmetric parabolic current sheath which propagates down the co-axial tube (steady propagation region) and collapses off the end of the co-axial gun forming a dense plasma focus. The state of the plasma just before the focusing action is very much dependent on the velocity in the steady propagation region. This velocity is experimentally studied and compared with a snow- plough theory. The collapsing phase of the current sheath is studied using high speed framing photography and current and voltage measurements. The results indicate a focus of length 1·5 cm and radius less than 1·7 mm.
On the stability of nonlinear cold plasma waves
Authors: Infeld Eryk
Published: March 2009

The exact form of a nonlinear, stationary wave, travelling against a background of cold plasma, is investigated for stability. The result is that it is marginally stable, and therefore can exist in practice. This is found without expanding in the wave amplitude. Another problem, that of a nonlinear wave at rest against a background of two counter-streaming cold electron beams, is also commented on.
Short-life mode of electrostatic electroncyclotron harmonic waves
Authors: Oya Hiroshi
Published: March 2009

Dispersion curves of electrostatic electron cyclotron harmonic waves with a phase exp {i(k. r – ωt)}, where ω and k are the angular frequency and wave vector, respectively, are calculated numerically for a case of real ω and complex k that is pertinent for a case of pulsed short dipole excitation of plasma waves. Oblique propagation with respect to the ambient magnetic field direction is considered. There are positive κi and negative κi modes, where k is the imaginary part of the wave number κ = ∣κ∣ in the solutions. The energy propagates in opposite directions in the two modes, and the waves are always subjected to thermal damping. The positive κi mode usually indicates a large κi value (i.e. a large attentuation rate); and it is here called the ‘short-life’ mode.
Total reflection of a plane wave by a semi-infinite random medium
Authors: Sulem P. L. , Frisch U.
Published: March 2009

An exact result in the theory of wave propagation in random media is presented. Using the ergodic theory of dynamical systems, it is shown that a semi-infinite, one-dimensional random medium is totally reflecting. A direct numerical study shows that the mean reflection coefficient converges exponentially to one.
Electron density and temperature measurements in the lower ionosphere as deduced from the warm plasma theory of the h.f. quadrupole probe
Authors: Chasseriaux J. M. , R. Debrie  , C. Renard
Published: March 2009

The frequency response of the h.f. quadrupole probe is calculated to be used as a diagnostic tool for measurements of electron density and temperature. In §2 the magnetic field is assumed to be zero, and ion motions are neglected. For a Maxwellian plasma, the so-called ‘Landau wave approximation’ is compared with various more sophisticated treatments, such as numerical integration or super-Cauchy and multiple water-bag models. The range of validity of this approximation is shown to be large, and the results can be applied to the most interesting parts of the experimental observations. All results previously established are recovered with greater speed. Having studied various disturbances (collisions, inhomogeneity and relative motion of the probe with respect to the plasma), it is deduced that the best way to determine the electron temperature is to use the anti-resonances due to beating between the Landau wave and the cold plasma field. In § 3 we describe the quadrupole probe, launched in December 1971 as part of the CISASPE rocket experiment. To deduce the electron density and temperature from these measurements, it is necessary to consider the influence of a static magnetic field, such as the earth's magnetic field. The general case could be treated by numerical integration, though with great difficulty, but it is shown that in most ionospheric conditions, in the vicinity of the upper hybrid frequency ωT the above treatment is again possible, the plasma frequency simply being replaced by ωT, and the thermal velocity slightly modified. These assumptions are used to deduce the electron density and temperature profiles.
Energy absorption in cold inhomogeneous plasmas: the Herlofson paradox
Authors: Crawford F. W. , Harker K. J.
Published: March 2009

The Herlofson paradox is exemplified by a capacitor containing cold, collisionless, inhomogeneous plasma as the dielectric: its response to a sinusoidal driving signal can exhibit continuous energy absorption, even though the system is lossless. The underlying mechanism has been explained generally by Barston in terms of the transient response of the system. In this paper, we confirm Barston 's conclusions by examining in detail several analytically tractable cases of delta-function and sinusoidal excitation, and consider the effects of collisions and non-zero electron temperature in determining the steady state fields and dissipation. Energy absorption without dissipation in plasmas is analogous to that occurring after application of a signal to a network of lossless resonant circuits. This analogy is pursued, and extended to cover Landau damping in a warm homogeneous plasma, in which the resonating elements are the electron streams making up the velocity distribution. Some of the practical consequences of resonant absorption are discussed, together with a number of paradoxical plasma phenomena which can also be elucidated by considering a superposition of normal modes rather than a single Fourier component.
Effect of the plasma inhomogeneity on the nonlinear damping of monochromatic waves
Authors: Asseo E. , Laval G. , Pellat R. , Welti R. , Roux A.
Published: March 2009

We study the resonant interaction of particles with a monochromatic wave in an inhomogeneous plasma. The effects of the inhomogeneity are represented by a variable phase velocity of the wave. This introduces, in the wave frame, an inertial force due to the non-Galilean transformation of co-ordinates. Asymptotic expressions are obtained for the spatial damping coefficient of the wave in two physically different cases.

(i) When the inertial force is greater than the force due to the trapping (strong inhomogeneity case) instead of the null asymptotic behaviour that one obtains in the homogeneous case, the spatial nonlinear damping coefficient behaves asymptotically like the linear Landau damping coefficient.

(ii) When the inertial force is lower than the trapping force (weakinhomogeneity case), the spatial nonlinear damping coefficient for short distances is proportional to the ratio of the inertial force to the trapping force. For long distances, this coefficient is proportional to the square of the preceding ratio multiplied by the number of trapping lengths. In both cases, the proportionality coefficient is the linear spatial Landau damping rate.
Kinetic theory of a two-dimensional magnetized plasma. Part 3. Limit of very large magnetic field
Authors: Vahala George
Published: March 2009

The BBGKY hierarchy for a two-dimensional magnetized plasma is considered in the weak-coupling and small plasma parameter limits for very large magnetic fields. The Fokker-Planck and Balescu-Lenard equations satisfy an H-theorem and conservation laws, and exhibit two cut-offs related to the periodicity of the particle orbits and to the distance of closest approach of a thermal particle.
Electrical conductivity from electric arc measurements
Authors: Devoto R. S. , Mukherjee D.
Published: March 2009

A technique involving the use of a trial function containing several adjustable parameters has been developed for the purpose of deducing the electrical conductivity from measurements on the electric arc. It is used to re-analyze experiments in argon, xenon and nitrogen. Some improvement in agreement between theory and experiment is noted.
The relative intensities of nitrogen lines in the semi-coronal regime
Authors: Cilliers W. A. , Hey J. D. , Rash J. P. S.
Published: March 2009

At plasma densities lower than about 1018 cm-3, strictly speaking, the LTE model cannot be used when the electron temperature is calculated from measured spectral line intensity ratios. In this work a number of nitrogen spectral lines were studied at an electron density of about 1016 cm-3, and the results are discussed with reference to the LTE and semi-coronal models. A method is suggested for analyzing line intensity ratio data from plasmas in the semi-coronal regime.
Linearized theory of inhomogeneous multiple ‘water-bag’ plasmas
Authors: Bloomberg H. W. , Berk H. L.
Published: March 2009

The problem of the stability of inhomogeneous, electrostatic, multiple water-bag plasmas is considered. Equations are derived for general stationary water-bag equilibria, as well as for the corresponding perturbations. Particular attention is directed to systems with trapped particles in periodic equilibria, and special boundary conditions for the perturbation equations at the trapped-particle turning points are introduced. A normal-mode analysis is carried out for a configuration involving trapped particles occupying a finite region in the vicinity of the trough of an equilibrium wave (BGK mode). The results confirm the validity of the bunched-beam approximation.
Heterogeneous electron behaviour in a turbulent plasma jet
Authors: Demetriades Anthony , Doughman Ernest L.
Published: March 2009

Uncommonly large electron density fluctuations, accompanied by large skewness and flatness factors, have been observed in the transitional zone of a plasma jet. This paper investigates these further by a digital analysis of Langmuir probe signals from this zone. The electron aggregate is found split into a decaying laminar-fluid remnant and a growing population of turbulent fluid. The uncommon statistics are caused by the double-humped histogram, while those of each population separately are normal. The mean electron density of the aggregate displays no simple chemical decay trend, but that of the laminar population fits known argon recombination schemes.
Instabilities of drift magnetosonic waves due to the magnetic drift resonance
Authors: Ishihara Takemi
Published: March 2009

The drift magnetosonic waves in a finite-pressure plasma are considered. Instabilities arising from the magnetic drift resonance of particles with waves are investigated for two cases: quasi-perpendicular and oblique propagations. It is shown that, in a wide range of both the density and temperature gradients, these waves can be excited even in a high-β (β≥1) plasma.
Characteristics of the fast and slow magnetosonic waves in layered plasmas
Authors: Tamao Tsutomu
Published: March 2009

Propagation characteristics of two magnetosonic waves, the fast and slow modes, in layered plasmas with different β values are studied, where β is the ratio of plasma pressure to magnetic pressure. In the first part we consider the efficiency of wave penetration from one region to another with different β ratios, β1 and β2. In particular, the condition for the total reflexion, amplitude and phase of the reflexion and transmission coefficients at the interface are obtained for both modes. The results indicate that the range of deviation of the ratio β2/β1 from unity is very small for penetration of the slow mode, while the ratio for the fast mode covers a wide range. In the second part, the fast and slow normal modes of magnetosonic waves in layered plasmas are discussed and their phase and group velocities, and the spatial damping rate due to partial leakage of wave energy are compared between two modes. From these, it is concluded that the presence of the slow magnetosonic waves is restricted to within the high-β plasma region. Finally, application of these to the earth's magnetosphere is given qualitatively.
Penetration of high-frequency waves into a weakly inhomogeneous magnetized plasma at oblique incidence and their transformation to Bernstein modes
Authors: Preinhaelter J. , Kopecký V.
Published: March 2009

Propagation of high-frequency electromagnetic waves in a weakly inhomogeneous magnetized plasma is investigated. We suppose the density gradient to be perpendicular to an external magnetic field, and the waves to be incident obliquely upon the plasma from vacuum. We find that the transmission coefficient of the ordinary wave through the plasma resonance is approximately equal to one in a fairly wide range of angles of incidence γ near the value γ0 = arcsin (Ωc/)(Ωo + Ω) ½. The transmitted ordinary wave is fully transformed into an extraordinary wave at higher densities. Then it propagates back to the region of a smaller density, and is fully transformed into the Bernstein modes in the vicinity of the hybrid resonance. Complications connected with the evanescent layer, which arise when the high-frequency energy is transmitted into the plasma in the form of the extraordinary wave, can thus be removed by using the ordinary wave with the angle of incidence chosen appropriately.
Structural determination of electric field conditions in ionizing shock waves
Authors: Leonard B. P.
Published: March 2009

Ionizing shock waves may involve a non-zero transverse electric field in the non-conducting upstream region. The possibility of this field means that two extra parameters are involved in ionizing shock transitions, in addition to the usual three MHD shock parameters. The present paper investigates the question of existence or absence of structurally determined relationships between the five parameters. The results show that ionizing shock waves can be categorized into three types, depending on the nature of their downstream singular points in a three-dimensional phase space. Thus, if shock Mach number, Alfven number, and upstream magnetic field angle are given, type 2 shooks are characterized by a unique transverse electric field in both magnitude and orientation, type 3 shocks allow one degree of freedom to the electric field but specify a relationship between the magnitude and orientation, and in type 4 shocks both electric field parameters are free to range between certain limits. These structural conditions correspond exactly to previously investigated evolutionarity conditions based on wave perturbations, the interpretation of which has been incomplete due to a lack of knowledge of the possibility of skew shocks. In light of the author's subsequent work on skew shocks and the new general three-dimensional results, a complete map of the behaviour of ionizing shock waves is now possible, and the present article attempts to construct its essential features. Earlier works are reviewed and clarified in reference to this general framework.
Transverse ionizing MHD detonation waves. Part 2. Numerical simulation
Authors: Friedland Allan B. , Frankenthal Shimshon
Published: March 2009

A numerical method for simulating the temporal evolution of an ionizing MHD detonation, is presented, together with flow profiles for various combinations of imposed magnetic field and ionization temperature in the limit of large downstream conductivity. The propagation speeds asymptotically approach the values predicted by the jump relations and the MHD Chapman–Jouguet condition. The downstream flow approaches a self-similar solution. The wave evolution is discussed for situations where the Chapman–Jouguet and jump relations admit either no solution or multiple solutions.
Interaction between three modes in a non-homogeneous plasma
Authors: Maroli C.
Published: March 2009

The interaction between three modes in a non-homogeneous plasma is analyzed in a very simple situation. It is shown that, unlike the homogeneous case, and on account of the regular character of the perturbation procedure used, the problem does not call for a nonlinear algorithm. A strong interaction takes place when both pump and idler modes exist inside the plasma and all modes have wavelengths (much) smaller than the plasma non-homogeneities.
Shock-wave structure in a fully ionized gas
Authors: Lu C. S. , Huang A. B.
Published: March 2009

The structure of a steady plane shock in a fully ionized gas has been investigated using the Boltzmann equation with the Gross–Krook type model as the governing equation and the discrete-ordinate method as a tool. The present results agree well with the results obtained by the continuum approach for weak shocks. For strong shocks the present approach gives results that are considerably different from those yielded by the continuum approach, particularly in the high pressure region. Also, the present method gives smooth and continuous shock profiles for high Mach numbers. On the other hand, the results from the continuum approach contain discontinuities in slope. The ion and electron distribution functions across the shock are found to be singly peaked for all cases considered and the effects of the induced electric field is small.
Wave propagation in a moving plasma: motion and wave propagation normal to the magnetic field
Authors: Srivastava D. N.
Published: March 2009

The dispersion relation for a collisionless moving electron plasma when the directions of motion and wave propagation are normal to the magnetic field is analyzed. It is shown that the ordinary wave remains unaffected, but the extraordinary wave shows a different behaviour, especially at small phase velocities. It has different cut-off frequencies, propagates for all frequencies from zero to infinity, changes the sense of polarization accompanied by anomalous dispersion and does not show any resonance.
On a family of exact nonlinear waves in plasmas
Authors: Goldstein Shyke , Salu Yehuda
Published: March 2009

We describe a family of exact nonlinear solutions of Vlasov's equations; the linear counterpart being circularly waves. An exact solution for a sub-group of initial conditions is given. The plasmas treated are multi-species, infinite and homogeneous, embedded in a uniform magnetic field.
The anomalous skin effect in cylindrical plasmas
Authors: Blevin H. A. , Greene J. M. , Jolly D. L. , Storer R. G.
Published: March 2009

A theoretical analysis of the anomalous skin effect in cylindrical plasma is carried out for a model where the radial electron-density distribution is of Gaussian form. It is shown that there are major qualitative differences between the results for cylindrical and those for plane geometry. Calculations of the electromagnetic field distribution over the plasma cross-section show that the present theory is in satisfactory agreement with experiment.
On the analytic solution of the helical equilibrium equation in the MHD approximation
Authors: Woolley M. L.
Published: March 2009

The second-order elliptic partial differential equation, which describes a class of static ideally conducting magnetohydrodynamic equilibria with helical symmetry, is solved analytically. When the equilibrium is contained within an infinitely long conducting cylinder, the appropriate Dirichiet boundary-value problem may be solved in general in terms of hypergeometric functions. For a countably infinite set of particular cases, these functions are polynomials in the radial co-ordinate; and a solution may be obtained in a closed form. Necessary conditions are given for the existence of the equilibrium, which is described by the simplest of these functions. It is found that the Dirichlet boundary-value problem is not well-posed for these equiilbria; and additional information (equivalent to locating a stationary value of the hydrodynamic pressure) must be provided, in order that the solution be unique.
Nonlinear interaction of wave packets
Authors: Mendonça J. T.
Published: March 2009

We study the frequency shift suffered by a wave packet propagating in a homogeneous and stationary plasma, when subjected to the influence of a second wave packet which nonlinearly changes the dielectric properties of the plasma. The opposite cases of an adiabatic frequency shift and a relativistic Doppler shift are discussed in detail. The contribution of the inverse Faraday effect to the adiabatic situation is also taken into account. The results might be relevant in the search for new generators in the sub-millimetre ranges and for the understanding of spectral transfers of energy in a plasma.
Nonlinear Kelvin–Helmholtz instability in hydromagnetics
Authors: Nagano H.
Published: March 2009

Nonlinear Kelvin–Helmholtz instability for an incompressible plasma under the influence of gravity is investigated theoretically, using the method of multiple time-scales. The effect of nonlinearity is to reduce the growth rate for the linear instability and to narrow the unstable wavenumber domain. There are two cases, in one of which the effect is strong and in the other slight. The difference between these cases is studied.
Lower hybrid oscillating two-stream instability in a plasma with magnetic shear
Authors: Wersinger J. M. , Kritz A. H. , Troyon F.
Published: March 2009

Magnetic shear is found to have a strong effect on the propagation characteristics of the lower hybrid parametric daughter waves but no significant effect on the pump wave. The analysis of the OTS instability shows that the convective damping introduced by magnetic shear acts on a distance L⋍ H(me/mi)½, where H is the magnetic shear scale length. There are two regimes for the convective damping, depending on the wavelength of the parametric daughter waves. For small wavelengths the growth rates are linear functions of (kL)-1. For large wavelengths the growth rates are exponentially decreasing functions of (kL)-1.
Self-similar resistive decay of a current sheet in a compressible plasma
Authors: Kirkland Keith B. , Sonnerup Bengt U. ö.
Published: March 2009

Self-similar solutions of the magnetogasynamic equations are derived which describe the resistive decay of a plane current sheet in a compressible plasma. Such current sheets are thought to provide the magnetic energy storage in solar flares. They also occur at the boundaries between regions containing different magnetic-field directions in interplanetary space, and at the interface between the solar wing and the earth' magnetic field. It is shown that the resistive decay of a current sheet in a compressible plasma must involve plasma motion. The convective effects associated with this motion are incorporated in the analysis; the inertia effects are not. The electrical and thermal conductivities are taken to be constant, but the analysis may easily be generalized to include realistic temperature and magnetic field dependences of these quantities. Radiative and viscous terms are not included. The ordinary differential equations resulting from the similarity hypothesis are solved numerically, yielding curves of the plasma density, temperature, and velocity, as well as of the magnetic and induced electric fields, as functions of the similarity variable. The non-dimensional groups of importance are: y, the ratio of specific heats at constant pressure and constant volume; Kx, the ratio of thermal to resistive diffusivity; β∞, the ratio of plasma pressure to magnetic pressure at large distances from the current sheet. The first of these ratios is kept constant and equal to 5/3, corresponding to a monoatomic gas. The behaviour of the solution when the other two ratios are varied is investigated. The plasma velocity at large distances from the current sheet does not vanish in these solutions. It is always directed toward the sheet. However, when the diffusivity ratio K∞ is small, plasma flow away from the centre of the sheet also occurs in two narrow regions, one on each side of the centre. As a result of the reversals in the flow direction, the density then displays a relative minimum at the centre of the sheet with two outward travelling maxima adjacent to it. The plasma temperature at the centre of the sheet becomes very large for small K∞ and β∞ The expansion of the sheet becomes explosive and inertia effects can no longer be neglected. The physical meaning of these results is discussed and directions for further research are outlined.
Magneto-viscous resistive tearing of cylindrical flux surfaces
Authors: Hosking R. J.
Published: March 2009

The stability of cylindrical flux surfaces in the presence of finite resistivity and parallel ion viscosity is reconsidered, and in particular the increment in the logarithmic derivative Δ(Q) over the inner dissipative region. Correction of the viscosity coefficient removes the branch-point behaviour at large growth rates reported earlier. Numerical results for real Q in the high-beta hard-core pinch are supported by mathematical analysis to show that parallel ion viscosity renders Δ(Q) positive definite provided D < 0, with a positive minimum increasing with temperature. This stabilization is associated with coupling of the parallel plasma motion in the presence of magnetic field curvature. The viscous compressible value of Δ(Q) is somewhat less than its inviscid compressible counterpart at small real Q, so that relative to purely compressible theory parallel ion viscosity can be slightly destabilizing.
Nonlinear coupling of three waves in non-uniform plasma
Authors: Pramanik G. C.
Published: March 2009

This paper considers nonlinear interaction between three monochromatic waves in a hot non-uniform electron plasma. With the aid of coupled mode theory the interaction of three longitudinal waves is studied and a specific case of the interaction of two longitudinal waves and one perpendicular wave is derived for the limiting case of long wavelength. Furthermore, the non-uniformity involves generalization of the theory of the interaction of two transverse waves and one longitudinal wave of a previous contribution.
Critical-level behaviour of ion cyclotron waves
Authors: McKenzie J. F.
Published: March 2009

This paper provides an analysis of the propagation characteristics of ion cyclotron waves in a magnetized plasma whose density varies in a direction perpendicular to the ambient magnetic field. It is shown that the component of the wave energy flux across the density stratification is conserved except at a critical level (which is associated with a resonance singularity in the wave equation) at which the jump in the wave energy flux is balanced by wave absorption by the plasma. The relationship of this behaviour with field line resonance is briefly discussed, as is its possible relevance to ULF waves propagating in the vicinity of the earth's plasmapause.
The theory of ionizing shock waves in a magnetic field. Part 2. Transverse, normal and switch-off shock waves and the piston problem
Authors: Liberman M. A. , Velikovich A. L.
Published: March 2009

Solutions for transverse, normal and switch-off ionizing shock waves have been obtained on the basis of the general theory of ionizing shock waves in a magnetic field presented in part 1. Some details of the shock structure were considered at Pm → 0. In particular, the transition from the gasdynamic to the magnetohydrodynamic regime, while increasing the shock velocity, is traced in detail. The additional relationship, obtained in part 1, determines the value of a transverse electric field ahead of the front for the case of a transverse shock wave and for normal and switch-off shock waves, if the latter are shock waves of type 3. In the case of normal and switch-off shock waves of type 4, basic relationship obtained in part 1 is not a boundary condition, but determines the position of a viscous isomagnetic jump in the shock structure. The transition of ionizing shock waves from the GD to the MHD regime, while increasing the shock velocity, was considered. The width of such a transition on shock velocity scale depends significantly on the intensity of precursor photo-ionization. In particular, this transition occurs slowly at zero precursor photo-ionization: the electric field ahead of the front tends to zero as l/vxo when vxo increases. The problem of formation of ionizing shock waves ahead of a magnetic piston and a conducting piston with a magnetic field directed along the normal to the piston surface has been solved. We indicate the set of flow parameters, for which Chapman-Jouguet's model of ionizing front motion ahead of the piston is inapplicable. A transition from the Chapman-Jouguet regime to the MHD one is considered.
Electrostatic instabilities and anomalous transport excited by an energetic ion beam
Authors: da Jornada E. H. , Gaffey J. D. , Caponi M. Zales
Published: March 2009

Electrostatic instabilities excited by an energetic ion beam injected at an arbitrary angle with respect to the magnetic field in a collisionless plasma are discussed. Threshold conditions on the angle of injection and on the beam density are derived for the cross-field ion-ion mode, the modified two-stream mode and the ion-acoustic modes. The time evolution of the momentum and the thermal energy of each plasma component in the presence of the instabilities is calculated from moments of the quasi-linear equation. The background ions are significantly heated by most of the waves, exceptions being the modified two-stream mode and the resonant ion-acoustic mode. A wave with phase velocity close to the slow ion-acoustic wave has been found when the beam has a small density and a velocity greater than the acoustic speed by approximately a factor of five.
The parametric excitation of kinetic Alfvén waves by a magnetic pump
Authors: Cramer N. F. , Donnelly I. J.
Published: March 2009

The parametric decay of a magneto-acoustic pump wave into low-frequency waves modified by finite temperature effects is considered. The excited waves are the kinetic Alfvén wave and the ion-acoustic wave. The former wave plays an important role in linear heating schemes employing the mode conversion of magneto-acoustic waves at the Alfvén resonance. Here we calculate the parametric growth rates and pump thresholds for excitation of these waves. The main result is that finite temperature effects tend to reduce the growth rate of Alfvén waves.