bluuebunny/crossref_metadata_2025 huggingface dataset:
Ionizing detonation waves in transverse electromagnetic fields
Authors: Gordon A. R. , Helliwell J. B.
Published: March 2009

A simple model of an ionizing detonation wave is studied in which the electrical conductivity jumps from zero to infinity across the wave at which a net release of exothermal energy occurs and which propagates with magnetoacoustic speed relative to the products of combustion. The upstream electric and magnetic fields are mutually orthogonal and transverse to the direction of propagation. The ratios of downstream flow parameters to those upstream and the detonation speed are presented for a range of values of the upstream electromagnetic field. It is surmised that, for a specified upstream magnetic field, physically realistic detonation waves exist only for a limited range of values of the electric field strength of invariant sign.
The evolution of wave correlations in uniformly turbulent, weakly non-linear systems
Authors: Davidson Ronald C.
Published: March 2009

A formalism is developed describing the time evolution of wave correlations in a uniformly turbulent ensemble of weakly non-linear systems. The statistics are built into the formalism a priori. With closure (of the hierarchy of equations for wave correlations) appropriate to the inclusion of resonant three-wave interactions, a (non-linear) kinetic equation for the two-wave correlations is derived and various properties of this equation are discussed. The effects of both bilinear and trilinear non-linearities are considered. Modifications of the formalism in situations where there is a weak (linear) instability γк, (γк/ωк ≪ 1) are also considered.
Asymptotic state of the two-stream instability
Authors: Armstrong Thomas , Montgomery David
Published: March 2009

Previously reported numerical investigations of the non-linear Vlasov equation are extended to an intensive study of the two-stream instability. Strongly unstable initial conditions for the one-dimensional electron plasma are followed in time until the state of the plasma has become essentially time independent. Both the electric field and the distribution function appear to be characteristic of aninhomogeneous equilibrium, as previously conjectured (Armstrong 1966).
On the A.C. electrical conductivity of a Lorentz gas
Authors: Fu J. H. M. , Ong R. S. B.
Published: March 2009

Often one is interested in the electrical conductivity of a plasma for frequencies of the applied electric field comparable to or greater than the effective collision frequency. For the purpose of obtaining an order of magnitude estimate of the conductivity a Lorentz gas model with a Fokker–Planck collision term is used. For this simple model a formula for the a.c. electrical conductivity for two limiting cases is derived in closed form. The first term of the expression for the conductivity in the case where w/k is very large agrees with that obtained by Bernstein & Trehan (1960) for the spatially homogeneous case, while the effect of the spatial gradients is indicated in the higher order terms. In the case where w and k are both equal to zero the expression for the d.c. electrical conductivity of Spitzer (1962) is recovered.
Transport coefficients of partially ionized helium
Authors: Devoto R. S. , Li C. P.
Published: March 2009

Transport coefficients are given in tabular form for partially ionized helium in chemical equilibrium at several pressures and for temperatures up to 35000 °K. Simplified theoretical expressions, derived with the Chapman—Enskog—Burnett method, were used for the computations. The convergence of the approximations to the electrical conductivity was also studied. It was found that the first approximation was within 17% of the true value at low ionization in contrast to recent results for argon where it could not be determined if even the fourth approximation had converged to the true value.
On gyroresonance
Authors: Laird M. J.
Published: March 2009

The motion of a charged particle in the field of a plane circularly polarized wave propagating along a uniform magnetic field B0 is investigated. For the wave magnetic field small compared with B0, the equations of motion simplify to those of the pendulum, and a simple picture of what happens for particles near gyro- resonance results. Expressions are found for the amplitude and period of the pitch angle oscillations. Departures from uniformity and possible applications to the magnetosphere are briefly discussed.
Propagation of nonlinear waves in a plasma in a magnetic field
Authors: Freidberg Jeffrey P.
Published: March 2009

The propagation of nonlinear electromagnetic waves in a plasma is investigated by seeking travelling wave solutions to the macroscopic plasma equations. The model considered is that of a warm, anisotropic electron plasma in a magnetic field, in which the waves are allowed to propagate at any angle with respect to the magnetic field. A nonlinear dispersion relation is obtained which is valid for frequencies sufficiently close to the resonant frequencies. Travelling wave solutions are found for all amplitudes for which the local density remains positive. Also in sufficiently anisotropic plasmas the nature (i.e. propagating or cut-off) of one of the resonant waves can depend upon the amplitude.
The structure and propagation of ionizing wave fronts
Authors: Turcotte D. L. , Ong R. S. B.
Published: March 2009

A non-linear wave propagation mechanism is found for ionization fronts. The fronts propagate due to ionizing collisions between electrons and neutrals. A parameter is obtained which specifies the amount of electrical interaction. For small electrical interaction, charge separation may occur and the front can propagate at any speed greater than a critical value. For large electrical interaction, the number densities of ions and electrons are nearly equal and a lower bound on the propagation speed is also found.
Boundary-layer structure in a shock-generated plasma flow: Part 1. Analysis for equilibrium ionization
Authors: Knöös Stellan
Published: March 2009

The structures of some laminar boundary layers in high-density, shock heated, 1 eV argon plasma flows have been investigated theoretically. The analysis is based upon a three-fluid continuum formulation. Boundary-layer equations have been solved numerically on a digital computer by a finite difference technique for the case of thermochemical equilibrium and no radiation and applied electromagnetic fields. The induced electric field has been considered and shown to be important. It strongly couples the diffusive motions of the electron and ion fluids, thus forming ambipolar motion except in a sheath region adjacent to the wall. Argon transport properties, calculated from simple kinetic theory, have been used in the analysis. Important parameters, such as the Prandtl number and the density-viscosity product have been found to vary one or two orders of magnitude in the argon plasma boundary layer, a finding in sharp contrast with results for classical, non-ionized boundary layers. Solutions have been developed for the simple Rayleigh's boundary layer (forming over an infinite flat plate with an impulsively started motion in its own plane) and for the shock-tube side-wall boundary layer (forming behind a plane, ionizing shock wave moving over an infinite, plane wall). Even in terms of appropriate similarity parameters, solutions (for e.g. velocity and temperature profiles) exhibit strong dependence upon free- stream conditions. Assumptions of chemical and temperature equilibria have been checked from the equilibrium solution. Results indicate equilibrium ionization would not be present in typical argon boundary layers, e.g. at temperatures below 9000 °K, at a pressure of 1 atm. Similarly, due to ineffective energy transfer rates between the electron and the heavy-particle fluids and the difference in electron and ion–atom thermal conductivities, the electron temperature would deviate from the heavy-particle temperature in the same temperature region. The electron temperature has been calculated in a linearized model and found to be larger than the ion–atom temperature.
Boundary-layer structure in a shock-generated plasma flow: Part 2. Experiments using a new quantitative schlieren technique
Authors: Knöös Stellan
Published: March 2009

The shock-tube side-wall boundary layer in a 1 eV, high-density argon plasma was studied experimentally using anew, simple, quantitative schlieren technique. The angular refraction of light which enters the shock-tube test section parallel to a side wall and passes through typically 1 mm thick boundary layers was determined in two separate wavelengths. This was done by measuring the displacements of two shadows formed by two thin wires placed in the point source light, which is reflected non-centrally by a concave spherical mirror. The experiments were of exploratory nature only, but clearly demonstrated the feasibility of the new technique in analysing plasma-boundary-layer flows. Measured electron density profiles in the high-temperature region of the sidewall boundary layers agreed within experimental errors with those calculated from the equilibrium-boundary-layer theory.
Measurement of the radio frequency admittance of a plane grid capacitor in a plasma
Authors: Freeston I. L.
Published: March 2009

The admittance of a plane grid capacitor immersed in an ion beam plasma has been measured, and the results are in general agreement with the kinetic theory of the admittance (Buckley 1968). With a steady bias potential applied to the grids, the results showed a deviation from the theoretical behaviour that is attributable to plasma depletion by the grids. The effect of varying the background pressure showed that electron-neutral collisions had a negligible effect on the measured admittance. A significant change in the admittance was found for a measuring voltage applied to the grids of the order of the electron temperature.
Structure of generalized ion Bernstein modes from the full electromagnetic dispersion relation
Authors: Fredricks R. W.
Published: March 2009

The structure of modes for which k┴B0 and ω≪Ω_ (ion waves) has been studied qualitatively in the two limits κR+ ≪ 1 and κR+ ≫ 1, where R+ = (κT+/MΩ+)½ is the mean thermal Larmor radius, without the usual electrostatic approximation. Asymptotic forms of the dielectric tensor elements εij are developed in these two limits. The modes having appreciable k × E can be called ‘generalized’ Bernstein modes. The approximation which yields the familar electrostatic Bernstein modes is εxx = 0. This approximation is shown to be valid only for large κR+ and low β. However, for small and moderate values of κR+ the generalized Bernstein modes partake of a ‘mixed’ electromagnetic- electrostatic character. In particular, for κR+ ≲ 0(1) (but ω/κ < c) the electrostatic Bernstein modes are incorrect approximations. The warm plasma electromagnetic theory is discussed with reference to cold plasma theory for a low β plasma, and it is shown that: (1) the lower hybrid frequency is only an approximate resonance in the warm plasma; (2) electromagnetic cut-offs occur at all harmonics of the gyrofrequency as k → 0; (3) electrostatic resonances occur at all harmonics of the gyrofrequency as k→∞; (4) propagation can occur in warm plasmas at frequencies above the lower hybrid.
A computer simulation of the plasma resonance probe
Authors: Hellberg M. A.
Published: March 2009

A numerical experiment is described in which a one-dimensional plasma model is used to simulate the resonance probe. The trajectories of a large number of plane electron sheets are followed in a self-consistent calculation which takes account of a spatially dependent but smeared-out ion background, and externally applied static and r.f. potentials. No differentiation between sheath and plasma regions is introduced, nor is there any linearization.

The typical resonant rectification curves, with resonance below ωp, are obtained. A comparison is made between the plasma behaviour at resonance and in frequency ranges above and below the resonance. For example, the phase of current collection w.r.t. probe potential is studied. Fourier analysis of potential and density variations is used to obtain further information on phase relationships. Orbit diagrams of electrons forming the current under resonant conditions are presented, and a model for the mechanism of resonant rectification in terms of electrons at the sheath edge put forward.
Alfvén waves in relativistic plasmas
Authors: Hoh F. C.
Published: March 2009

Expressions for Alfvén waves, their Landau damping, and magnetosonic waves are derived in a homogeneous relativistic Vlasov plasma. Relativistic effects reduce the speed of both waves.
Rayleigh—Taylor problem for a Hall plasma
Authors: Hosking R. J.
Published: March 2009

Recent calculations for hydromagnetic analogues of the classical Rayleigh– Taylor problem with Hall effect are compared. It is shown that an early calculation is the limiting situation of the work of Taiwar & Kaira, which confirms that the Hall effect introduces new instabilities.
Transport coefficients of partially ionized hydrogen
Authors: Devoto R. S.
Published: March 2009

Transport coefficients have been computed for partially ionized hydrogen at pressures of 0·01, 0·1, 1 and 10 atm and temperatures up to 50,000 °K. Theoretical expressions containing accurate collision integrals for charged particles were employed for the calculations. The electrical and thermal conductivities are compared with recent measurements in the wall-stabilized electric arc. Generally satisfactory agreement is noted for the electrical conductivity to 19,000 °K, but the computed thermal conductivity is considerably lower than that measured.
Shock-like solutions of the electrostatic Vlasov equation
Authors: Montgomery David , Joyce Glenn
Published: March 2009

It is shown how to construct shock-like time independent solutions of the electrostatic Vlasov and Poisson Equations in one dimension. The positive ions are assumed to be at zero temperature. The electrostatic potential is assumed to increase monotonically through the shock from zero to a constant value. The most important feature of the solution is a population of trapped electrons in the shocked plasma. In contrast to time-independent solutions based upon fluid equations, there is no upper limit on the amplitude of the shock.
Longitudinal oscifiations of a plasma having a Fermi distribution of electrons
Authors: Gibbons M.
Published: March 2009

In this paper, the electrostatic oscillations of a plasma having a Fermi distribution of energies are discussed. The electrons, assumed to be tightly bound to the magnetic lines of force, are acted upon by a linear restoring force which causes the electrons to oscillate with a fixed angular frequency ω0. The dependence of the frequencies of oscillation of the plasma on electron density is calculated in the two limiting cases ωp0/ω0 ≪ and ωp0/ω0 ≫ 1.
Small amplitude waves in high β plasmas
Authors: Formisano V. , Kennel C. F.
Published: March 2009

We present a brief survey of the phase velocities and polarizations of linear waves in an infinite, uniform, high β plasma using the two-fluid approximation. Questions of wave-particle damping are deferred. Several features of high β plasma waves differ from the familiar low β case.
Transformation of waves and electron heating in a radially inhomogeneous plasma
Authors: Kopecký V. , Preinhaelter J. , Václavík J.
Published: March 2009

The propagation and the linear transformation of high-frequency electrostatic waves in a hot magnetoactive plasma with a radially decreasing density is investigated. It is shown that in the region of the hybrid resonance cold plasma waves with a long wavelength are transformed into the Bernstein modes with a short wavelength. By this shortening of the wavelength the absorption of the waves increases, particularly for the frequencies near the electron cyclotron harmonics. It might be the cause of the electron heating in plasma—beam experiments.
Non-linear coupling of waves in a magnetized plasma with particle drift motions
Authors: wilhelmsson H.
Published: March 2009

We study non-linear interaction between three monochromatic waves which propagate parallel to the direction of a magnetic field in a plasma. The approach to the problem is hydromagnetic, including temperature effects, and the method of solution is that of coupled mode theory. In particular drift motions of the particles along the magnetic field are considered taking into account relativistic effects. The interaction of two transverse waves and one longitudinal wave is treated as well as that of three longitudinal waves. Besides, the case of two longitudinal waves and one perpendicular wave has been studied in some detail assuming the latter to have a long wavelength.

The present paper represents a generalization of the problem of three-wave interaction in a plasma to situations more complex than have been treated before. The most essential limitation consists in the assumptions made for the directions of propagation of the waves.
Statistical mechanics of a weakly turbulent stable plasma
Authors: Asseo E. , Berthomieu G. , Heyvaerts J. , Mangeney A.
Published: March 2009

The statistical mechanics of the weakly turbulent plasma is treated in an original manner by introducing the waves by means of the van Kampen modes. A system of coupled equations is derived which relates the correlations between waves and waves, waves and particles, particles and particles. The quasilinear theory is obtained at the first order, and the coupling wave equation at second order, under suitable assumptions.
Small amplitude transverse wave propagation in a weakly Langmuir turbulent plasma
Authors: Bel N. , Heynaerts J.
Published: March 2009

The high frequency conductivity tensor of an isotropic plasma is derived taking into account particle correlations at the lowest consistent order in the parameter ωp/ω these correlations describe a weakly Langmuir turbulent plasma. Two special cases are investigated in which the two-particle correlation function is related to the turbulent electrostatic field spectrum. Particular distribution functions and spectra are considered and approximate dispersion relations are derived in both cases in ‘the cold plasma limit’. The importance of the corrective term is discussed in terms of three dimensionless parameters measuring the strength of the turbulence, the shape of the spectrum, and the frequency. The effect could be important for frequencies not too far from the plasma frequency.
The two stream instability in the ‘resonance’ model
Authors: Infeld E. , Skorupski A.
Published: March 2009

In this note the problem of stability of two hot collisionless streams of charged particles is considered. The masses, charges, densities, and temperatures are arbitrary and the distribution functions are modelled by one ‘resonance’ function for each stream. The problem of stability is resolved by Nyquist diagrams, and, for the case of equal plasma frequencies, also by solving the dispersion relation in ω. A comparison with two Maxwellians on the one hand, and a two step function model on the other, is given. Step functions appear to be too crude for this problem.
Normal modes of oscillation in a higher-order Chew—Goldberger—Low plasma
Authors: Sisson A. E. , Yu C. P.
Published: March 2009

The low frequency, linear oscifiation of an unbounded, homogeneous, low density plasma in the presence of a strong, uniform magnetic field is examined using a set of three-dimensional hydromagnetic equations derived from the higher-order Chew—Goldberger—Low theory recently obtained by Frieman, Davidson & Langdon (1966). It is found from the higher-order corrections to the dispersion relation that the waves are generally dispersed and the mirror and firehose instabilities are stabilized.
A temperature-anisotropy instability for electromagnetic waves propagating across a static magnetic field
Authors: Landau R. W. , Cuperman S.
Published: March 2009

The instability of electromagnetic waves propagating across a static magnetic field in the presence of a thermal anisotropy (T∥ > T⊥) is investigated. The marginal stabifity criterion as well as the rate of growth of the instability are derived. When compared with the fire hose instability (of electromagnetic waves propagating along the static magnetic field) it is found that higher electron pressures are required for this new instability to be set up; however, the maximal rate of growth is much larger than in the fire hose case.

The interplanetary plasma is stable to this thermal anisotropy instability; high β plasma devices may be unstable.

The T⊥ = 0 case treated by Hamasaki is recovered.
Solution of the Boltzmann equation for electrons in external electric fields
Authors: Stenflo L.
Published: March 2009

A plasma in a time-dependent external electric field is considered. Collisions are described by means of Fokker—Planck and BGK models. Longitudinal and transverse wave propagation is treated by means of exact analytical solutions of the linearized Boltzmann equation. The results generalize previous calculations on dispersion relations and density fluctuation spectra.
On the re-connexion of magnetic field lines in conducting fluids
Authors: Yeh Tyan , Axford W. Ian
Published: March 2009

The reconnexion of magnetic field lines is described for a special case of steady, incompressible hydromagnetic flow in two dimensions. A similarity solution is obtained which corresponds to the flow of a perfectly conducting, inviscid fluid such that magnetic field lines are carried from two sides toward, then on the other two sides away from, the centre of an X-configuration. The effects of viscosity are important in shocks which form in the vicinity of the X-lines of the configuration. The effects of finite electrical conductivity must be taken into account near the centre of the configuration which, in the symmetrical case discussed, is an X-type neutral point. From an approximate solution valid in this region it is found that the fluid must flow from the larger to the smaller wedges of the X-configuration. Hence, the reconnexion process is such that oppositely directed magnetic field lines move towards the neutral point in the larger wedges, become reconnected at the neutral point, and move away in the smaller wedges. Since the solution in the vicinity of the neutral point appears to be no more than a response to the external flow, which is in turn controlled by conditions far from the neutral point and is essentially unaffected by viscosity and finite electrical conductivity, it is tentatively concluded that the rate of re-connexion of magnetic field lines does not depend on these quantities, and that, in general, re-connexion can be expected to take place rapidly if circumstances are favourable.
Cyclotron harmonic wave propagation and instabilities: I. Perpendicular propagation
Authors: Tataronis J. A. , Crawford F. W.
Published: March 2009

Parts I and II of this paper present a comprehensive picture of longitudinal wave propagation in a warm homogeneous magnetoplasma. Part I discusses computed dispersion characteristics for propagation perpendicular to the static magnetic field. For a ring electron velocity distribution it is found that mode coupling and absolute instability can occur. Similar effects are predicted for a spherical shell distribution. The Maxwellian distribution gives rise to stable propagation of undamped waves, and attenuating standing waves. A mixture of ring and Maxwellian distributions can give absolute instability with stronger growth and lower instability thresholds than for the ring distribution alone. Propagation oblique to the static magnetic field will be dealt with in Part II.
Anisotropic plasma pressure and the dielectric tensor
Authors: Johnston Tudor Wyatt
Published: March 2009

The first-order temperature terms for the anisotropic-temperature plasma susceptibility are calculated for each species, using the velocity moment equations and circular polarized co-ordinates. The results agree with the expanded terms for the Vlasov equation solution, for which a usefully simple derivation is given. An electrostatic wave result is given. Drift can be included by a transformation of the results for zero drift.
Electromagnetic radiation from a laser produced plasma expanding into a uniform magnetic field
Authors: Dunn H. Searl , Lubin Moshe J.
Published: March 2009

A laser produced plasma expanding in a uniform magnetic field emits far infrared radiation. The time-dependent radiation history is calculated assuming spherical symmetry and compared with experiment. General features of the radiation history agree well with experimental observation. However, a detailed comparison is difficult because of the oversimplified theoretical model employed.
Longitudinal waves in a perpendicular collisionless plasma shock: II. Vlasov ions
Authors: Gary S. Peter
Published: March 2009

This paper presents an analysis of the linear dispersion relation for electrostatic waves in a Vlasov plasma of unmagnetized, Maxwellian ions and magnetized, Maxwellian electrons. The electrons undergo E × B and ∇B drifts, and the electron β is small. For propagation in the perpendicular direction, maximum growth rates can be substantially larger than those of the zero magnetic field ion acoustic instability. For propagation outside a few degrees from the perpendicular the dispersion characteristics are essentially those of the ion acoustic instability.
An exact treatment of collisional effects on temporal plasma wave echoes: free-particle model
Authors: Furutani Y. , Coste J.
Published: March 2009

In the case of a free-particle plasma with no self-consistent field and with collisions described by the LenardBernstein operator we give an exact solution of the temporal echo problem.
A weak turbulence analysis of the two-stream instability
Authors: Smith D. F. , Fung P. C. W
Published: March 2009

In this investigation, we study the effects of non-linear interaction of plasma waves in the weak turbulence approximation on a stream-plasma system which is subject to the two-stream instability. The momentum distribution of the stream is assumed to be a Gaussian function and the background plasma is assumed to be a Maxwellian with a temperature T. The non-linear wave-particle interaction of induced scattering on the polarization clouds of ions may lead to stabilization of the stream—plasma waves in the resonant cone are scattered into the nonresonant region. The non-linear wave-particle interaction of induced scattering on the polarization clouds of ions may lead to stabilization of the stream; plasma waves in the resonant cone are scattered into the non-resonant region and vice versa, leading to a well-defined average energy density in plasma waves which is much less than the energy density of the stream. Non-linear scattering also causes transformation of plasma waves into electromagnetic radiation near the fundamental of the electron plasma frequency of the background plasma, and combination of two plasma waves leads to electromagnetic radiation near the second harmonic of this frequency. Expressions are given for the latter process for emission and absorption for arbitrary values of the ratio of the wave number of plasma waves to the wave number of the electromagnetic wave. The major features of the whole phenomenon are illustrated with the help of a numerical example, with conditions typical for the solar corona in which case an ion stream would be stabilized, but an electron or neutral stream (with the chosen density) would not.
Parametric excitation in an inhomogeneous plasma
Authors: Chen C. S.
Published: March 2009

An infinite, inhomogeneous electron plasma driven by a spatially uniform oscillating electric field is investigated. The multi-time perturbation method is used to analyze possible parametric excitations of transverse waves and to evaluate their growth rates. It is shown that there exist subharmonic excitations of: (1) a pair of transverse waves in an unmagnetized plasma and (2) a pair of one right and one left circularly polarized wave in a magnetoplasma. Additionally, parametric excitation of two right or two left circularly polarized waves with different frequencies can exist in a magnetoplasma. The subharmonic excitations are impossible whenever the density gradient and the applied electric field are perpendicular. However, parametric excitation is possible with all configurations.
The contribution of electronic excitation to the total specific heats of high temperature gases: a misinterpreted absence
Authors: Capitelli M. , Ficocelli E.
Published: March 2009

It is shown that the reported absence of a contribution of electronic excitation on to the total specific heats of helium and nitrogen (10,000–35,000°K, 10−1−10 atm) should be attributed to the presence of compensation effects among the various terms into which the total specific heat can be separated and that these terms are influenced by the electronic contribution.
The structure of hydromagnetic shock waves
Authors: Bickerton R. J. , Lenamon L. , Murphy R V. W.
Published: March 2009

We discuss the structure of hydomagnetic shock waves of various types. The plasma is treated in the two fluid approximation and coffisional transport coefficients are used. This treatment should be valid in a collisional plasma subject to the usual caveat about the use of transport coefficients in situations where the density, temperature, etc., may change significantly over a mean free path. The approach may also have some validity for collisionless shocks if the dissipation mechanisms involve instabilities of sufficiently fine scale and high frequency that they can be described by effective transport coefficients.
Magnetic surfaces in a quadrupole
Authors: Williamson J. H.
Published: March 2009

Local imperfections in the magnetic field can alter the topology of the magnetic surfaces, thereby allowing plasma to escape. A modest longitudinal magnetic field will maintain the nested surfaces near the plasma boundary, so that the residual topological changes near the separatrix become unimportant.
The hydromagnetic Kelvin—Helmholtz problem in a Hall plasma
Authors: McKenzie J. F.
Published: March 2009

The hydromagnetic analogue of the Kelvin–Helmholtz problem is extended to include the effects of the Hall term. In contrast to other results in the literature it is shown that, in the case of incompressible fluids, the stability of a shear plane is unaffected by the introduction of the Hall term. The special case of a hot, uninagnetized fluid on one side of the interface and a cold, magnetized fluid on the other is studied in some detail. In this case it is shown that the presence of the Hall term can have either a stabilizing or a destabilizing effect, depending upon whether the sound speed in the hot fluid is very much greater than the Alfvén speed in the cold fluid or vice versa.
Linear stability of exponential density profiles
Authors: Croci R. , Saison R.
Published: March 2009

The problem of the linear stability of a plasma with density profiles

in a homogeneous magnetic field B = îzB0 has been solved exactly. The dispersion relation leads to stability criteria less severe than those obtained in the local approximation. As examples, we consider Bernstein waves and the low-frequency drift instability. In the second example the marginal stability curve

is given for different values of the parameters kx, Ri, Ri n′/n, with Ti = Te. Further, the same method is applied to a plasma with equilibrium distribution function in a linear electric potential φ = αx and a homogeneous magnetic field B = îxB0.
Electron cyclotron echoes from plasma
Authors: Bruce R. L.
Published: March 2009

The observed response of a low-density magnetoplasma column to a pair of RF pulses near the cyclotron frequency is a series of pulses known as two-pulse echoes. A similar three-pulse echo train may be obtained by applying a third pulse. This behaviour involves some type of non-linearity, and for a low-density plasma the most promising mechanism appears to be velocity-dependent electron-neutral collisions. This gives velocity-dependent decay to induced currents, and velocity-dependent diffusion. The latter may be important in three-pulse echo formation. In this paper computations from these theories are compared with experimental data with these findings: (1) diffusion is not primarily responsible for three-pulse echoes; (2) the predictions of the collisional current decay theory are in reasonable agreement with the experimental results.
Magnetogasdynamic shock polar for aligned fields
Authors: Lynn Y. M.
Published: March 2009

An equation for magnetogasdynamic shock polar, given in terms of magnetic induction polar variables (i.e. the magnetic induction polar), is obtained. Evolutionary and entropy non-decrease conditions, given in terms of these polar variables, assume a very simple form, and admit immediate geometrical interpretation. It is found that this magnetic induction polar is far more natural and convenient to use than the shock polar given in terms of conventional velocity polar variables.
Propagation of Alfvén waves in ion-sound turbulent plasma
Authors: Rogister André
Published: March 2009

The propagation of low-frequency, large-scale (compared to the ion Larmor frequency Ωi and radius Ri), oblique Alfvén waves in a turbulent plasma is investigated in the framework of kinetic theory. The turbulent field is the statistical average of one-dimensional ion-sound waves of very high frequency and short wavelength (ω ≫ ΩiRe≫ λ). In the absence of resonant particle effects, and to first order in a finite Larmor radius expansion, it is shown that the turbulence can lead either to spatial diffusion (damping) or anti-diffusion (growth), with Bohm scaling, of the low frequency wave. Finite Larmor radius and frequency effects in the propagation of oblique Alfvén waves are simultaneously obtained for arbitrary β plasma; the results can easily be generalized, merely by deforming certain integration contours, to obtain the corresponding Landau decrement.
Whistler instability in plasmas with anisotropic and non-Maxwellian velocity distributions
Authors: Lee Kai Fong
Published: March 2009

The instability of right-handed, circularly polarized electromagnetic waves, propagating along an external magnetic field (whistler mode), is studied for electron plasmas with distribution functions peaked at some non-zero value of the transverse velocity. Based on the linearized Vlasov-Maxwell equations, the criteria for instability are given both for non-resonant instabilities arising from distribution functions with no thermal spread parallel to the magnetic field, and for resonant instabilities arising from distribution functions with Maxwellian dependence in the parallel velocities. It is found that, in general, the higher the average perpendicular energy, the more is the plasma susceptible to the whistler instability. These criteria are then applied to a sharply peaked ring distribution, and to loss-cone distributions of the Dory, Guest & Harris (1965) type.
Quasi-wave trains in a cold collisionless plasma
Authors: Inoue Yoshinori
Published: March 2009

Non-linear hydromagnetic waves in a cold collisionless plasma are investigated by numerical and analytic methods. For this problem, Saffman has already implied that there may exist a non-periodic wave different from the well-known solitary wave (or wave train). His analysis is based on the assumption that the quasi-ergodic theorem can be applied to the present problem. However, the propriety of the assumption has not been discussed.

It is seen from the computer calculations that in general the waves do not have periodicity, as Saffman pointed out. Furthermore, some concrete examples show the behaviour of these ergodic waves more clearly. The width of the waves is of the order of ion Larmor radius. These waves are here called quasi-wave trains. In some special cases, the waves reduce to wave trains (with periodicity). Some of them have a length scale of the geometric mean between the Larmor radii of the electron and of the ion.
Collisional drift waves in the presences of coherent ion acoustic or Langmuir waves
Authors: Dobrowolny M. , Negrini P.
Published: March 2009

The dispersion properties of drift waves in a low β weakly collisional plasma, in the presence of ion acoustic or Langmuir waves parallel to magnetic lines, are investigated. It is shown that the non-linear interaction with an ion acoustic wave mainly leads to a shift of the drift wave spectrum towards lower frequencies (and only under very particular conditions affects the stability of the drift wave). The interaction with a Langmuir wave, on the contrary, yields a contribution to the imaginary part of the frequency. The conditions under which this stabilizes unstable drift modes are derived and discussed.
Higher branches of the dispersion relation for perpendicular magnetosonic waves in relativistic anisotropic plasmas
Authors: Cuperman S. , Metzler N.
Published: March 2009

Dispersion relations are calculated and solved for frequencies near the first two harmonics (Ω/Ω+ = 2, 3) of perpendicular magnetosonic waves in relativistic anisotropic plasmas. In this, wavelengths larger than the ion Larmor radius and large plasma frequency (Ω2p, ≫ Ω2+) are assumed. It is found that, even for Tψ ≫ T the plasma is stable. This result has application to the steady-state, spherically symmetrical, expanding, solar-wind plasma.
Magnetic structure of ionizing shock waves Part 1. Skew shocks
Authors: Leonard B. P.
Published: March 2009

Initially non-conducting gas is ionized by a thin viscous shock wave. Upstream there can be no magnetohydrodynamic interaction because of the zero conductivity, but the conducting downstream region may have a magneticStructure which interacts with the flow variables. A theoretical analysis is made in the zeromagnetic-Prandtl-number (‘non-viscous ’) limit, i.e. ohmic dissipation is the dominant diffusion mechanism. Unlike magnetohydrodynamic shocks in a pre-ionized gas, ionizing shock waves are not necessarily plane-polarized. Thus ‘skew ’ shock structures can exist, in which the upstream and downstream magnetic field vectors and the shock wave normal do not all lie in a single plane. Explicit solutions are given for typical values of the governing parameters, showing how the magnetic field vector rotates about the shock wave normal as its transverse component changes in magnitude through the shock layer. Skew shocks are necessarily sub-Alfvénic downstream. Unlike the pre-ionized case, the range of trans-Alfvénic shock waves is not excluded, since these shocks can absorb Alfvén waves within their structure. With strong magnetic fields it is possible to achieve very high downstream temperatures by Joule heating. Alternatively, in some cases, magnetic energy can be fed into directed kinetic energy, producing an overall expansion shock.
Magnetic structure of ionizing shock waves Part 3. Normal shocks
Authors: Leonard B. P.
Published: March 2009

Normal ionizing shock waves are considered as a subclass of oblique shocks in which the upstream transverse magnetic field component is zero; i.e. the upstream field is normal to the plane of the shock. Non-trivial (switch-on) normal shocks involve a non-zero downstream transverse field component; magnetically trivial normal shocks are simply gas shocks with an imbedded constant normal magnetic field. As with oblique shocks, switch-on normal ionizing shock waves are plane- polarized, provided the conductivity is a scalar. Ohmic structures are discussed for several values of shock Alfv én number, treating the electric field as a free parameter, as usual. For Alfv én numbers extending from zero to two (for the infinite-Mach-number case), there is always a finite range of E field values. Above two, only the gas shock exists, and this requires a unique electric field value. Because the magnetic field magnitude increases through switch-on shocks, there is no mechanism available for converting magnetic energy into thermal energy, as is the case for oblique or skew shocks. Thus, there is no significant downstream heating above the viscous temperature; and, in some cases, slight downstream cooling may even occur. Expansion shocks are not possible in this geometry. Previous studies are reviewed in the light of structural requirements, and some erroneous results are clarified; in particular, it should be noted that MHD switchon solutions for the pre-ionized case are not imbedded in the family of ionizing switch-on solutions.
Diatomic gas—thermal radiation interaction A model equation for the internal fluid
Authors: Phillips Warren F. , Arpaci Vedat S.
Published: March 2009

A model kinetic equation for the internal fluid of diatomic molecules which interacts with thermal radiation is proposed. The cross-collision term developed for the molecule-photon interaction has the property that molecules and the sum of internal and photon energies are conserved. An alternative approach to this term based on the product of two BGKW collision operators yields the same result. It is also shown that the proposed model leads to an H-theorem.
A Lagrangian theory for nonlinear wave packets in a collisionless plasma
Authors: Dewar R. L.
Published: March 2009

A Lagrangian, for the slowly varying complex amplitude of an almost monochromatic electrostatic plasma wave in an unmagnetized plasma, is derived. The method is a variant of the averaged Lagrangian technique of Whitham, adapted for use in plasma physics by employing Low's Lagrangian, together with certain elimination procedures to simplify the Lagrangian to usable form. The expansion in powers of the wave amplitude is carried out to quartic terms, and non-adiabatic terms are also retained. Variations with respect to the amplitude lead to a nonlinear Schrödinger equation for the amplitude, while variations of the particle trajectories lead to a modified Vlasov equation, which includes the nonlinear reaction of the wave on the average trajectories. It is assumed that there are no resonant particles. These equations are coupled through the nonlinear frequency shift. It is found that the particle aspect of the plasma has a profound effect on the stability of the system, due to resonance of the wave envelope with particles moving at the group velocity. This effect, nonlinear Landau damping, is always destabilizing, leading to growth of modulations. In terms of the nonlinear Schrodinger equation, the effect changes the equation from a Hartree-Fock equation with a delta-function interaction to one with a non-momentum-conserving, non-local interaction. In the limit of fairly small wavelength, of the modulations, it is shown that the growth rate approaches that expected from plasma kinetic theory.
The velocity of a wave packet in an anisotropic absorbing medium
Authors: Suchy† Kurt
Published: March 2009

The field of a pulsed beam (a ‘wave packet’), travelling through a medium with moderate absorption, is calculated by the saddle-point method. The packet velocity (i.e. the velocity of the spatial amplitude maximum) has the same direction as the velocity Re (∂ω/∂k), a generalization of the group velocity ∂ω/∂k in non-absorbing media. It differs from the absolute value of this velocity by a correction factor depending on the absorption, beam width and pulse duration. This factor is unity for vanishing absorption and infinite beam width. The velocity Im (∂ω/∂k) has no apparent physical meaning.
Diffusion controlled breakdown of gases in a rectangular microwave cavity
Authors: Maldonado C. D. , Ayala I. L.
Published: March 2009

The boundary-value problem for diffusion-controlled breakdown of gases in microwave cavities is converted to a variational principle for the square of the reciprocal of the ‘effective’ diffusion length. For a rectangular cavity excited in the TEαγ0 mode, the resultant variational principle was minimized by an iterativevariational procedure. This was done using the high-frequency ionization coefficient of Herlin & Brown. However, any other functional dependence on the r.m.s. value of the electric field could have been used for this purpose. The resultant hierarchy of approximations to the variational principle obtained by this iterative-variational procedure for a cavity of square transverse crosssection is applied to the TE110 and TE220 modes of excitation. Adequate convergence is obtained with the first six approximations. Resultant plots of the ratio of the ‘effective’ to the characteristic diffusion length as a function of the Herlin & Brown parameter β, for various ratios of longitudinal to effective transverse cavity dimensions, imply that diffusion loss is greater for the TE220 mode of excitation. Also, from this theoretical investigation it is felt that the first ten approximations to the variational principle should provide adequate convergence for most situations encountered in practice with regard to β, as well as cavity dimensions.
Plasma heating and acceleration due to Landau damping of hydromagnetic waves
Authors: Barnes Aaron , Hung R. J.
Published: March 2009

We analyze energy and momentum exchange associated with Landau damping of hydromagnetic waves, from a macroscopic viewpoint, and compare the conclusions with those of the resonant quasiinear theory. It is found that the heating of protons and electrons is correctly given by the resonant theory, but that the momentum exchange is not correctly described by the resonant theory.
Measurement of ion-rich sheath thickness by ion acoustic wave
Authors: Watanabe S. , Ishihara O. , Tanaca H.
Published: March 2009

Measurements of sheath thickness in a low-pressure plasma are reported. The sheath is ion-rich and contains both ions and electrons; the sheath edge is taken as a boundary for ion acoustic waves. The thickness of the sheath is estimated from a frequency shift of the wave. Despite the actually continuous transition from plasma to sheath, a clear-cut sheath edge is observed. It should be emphasized that even a very small increase in thickness, such as 0·1mm, can be measured by this frequency-analysis method. The experimentally obtained sheath boundary is in agreement with the Tonks–Langmuir value as modified by Self.
Experimental study of force-free, collinear plasma structures
Authors: Nolting E. E. , Jindra P. E. , Wells D. R.
Published: March 2009

Detailed measurements of the trapped magnetic fields and currents in plasma structures generated by conical theta-pinches are reported. Studies of these structures interacting with a magnetic barrier, and with each other in a collision at the centre of a magnetic mirror, are reported. The magnetic well formed by the collision has been studied by simultaneous use of several diagnostic techniques. The measurements are in agreement with a force-free, collinear magnetic field configuration (Wells 1972). Arguments relating superposability and collinearity of flow fields to these observations are given.
Comments on the reconnexion rate of magnetic fields
Authors: Parker E. N.
Published: March 2009

The reconnexion rate of magnetic fields is crucial in understanding the fields found in turbulent flows in the solar photosphere and in the galaxy, and in flare phenomena. This paper examines the behaviour of magnetic fields in the neighbourhood of an X-type neutral point. The treatment is kinematical, specifying the velocity field v and constructing solutions to the hydromagnetic equation for B. The calculations demonstrate that the reconnexion rate is controlled by the diffusion in the near neighbourhood of the neutral point, and is not arbitrarily large, as has been suggested by similarity solutions of the complete field and fluid equations for vanishing diffusion