bluuebunny/crossref_metadata_2025 huggingface dataset:
On the kinetic theory of stable and weakly unstable plasma. Part 2
Authors: Rogister A. , Oberman C.
Published: March 2009

In plasma, where collective motions are made possible by the long range of the Coulomb interaction, there is properly no general kinetic equation for the one-particle distribution function alone. In part 1, we gave the foundations of an enlarged kinetic theory of plasma where the time evolution of the electric field fluctuations Ik is considered simultaneously with the time evolution of the one-particle distribution F. Here we improve these equations in a systematic fashion to include all processes which are relevant in stable and weakly unstable plasma. More precisely, the equation for the waves now includes, besides Landau damping and Cerenkov emission, the effect of collisional damping and nonlinear Landau damping, as well as emission via particle-particle scattering (bremsstrahlung), wave-particle and wave-wave scattering. The particle kinetic equation is also improved accordingly so that we obtain a kinetic description which is uniformly valid for all plasma réegimes, if one excludes strong turbulence (for which there is at present no completely satisfactory statistical theory).
Measurement of the electrical properties of a flowing plasma, including a critical comparison of probe experiment and theory
Authors: Billington E. W.
Published: March 2009

The primary quantities characterizing the electricaJ carriers of a flowing plasma in a low density wind tunnel have been determined from measurements using electrostatic probes immersed in the plasma. With the exception of the ion temperature, the plasma parameters have been obtained from the current—voltage characteristics of two types of single electrode probe. The probes consist of a cylinder, the major axis of which is aligned parallel to the flow of the plasma, and a disk, the exposed surface of which is normal to the direction of flow. Experiments with a double electrode probe consisting of a disk-shaped collector electrode which is screened from direct exposure to the plasma by a fine wire mesh, grid electrode, made it possible to obtain current—voltage characteristics with the ion and electron components separated from one another. From the current—voltage characteristic corresponding to collection of ions, using the screen grid probe, values of the ion temperature and drift velocity have been obtained. The measurements have been made at various points along the centre line of flow, for one particular value of the flow rate using argon as the test gas. For a given position of the probes, one value of the ion temperature has been evaluated, together with two independent values of each of the other primary quantities characterizing the electrical carriers of a flowing plasma. Each pair of values agree satisfactorily amongst themselves, good agreement being generally obtained between probe theory and experiment.
Transverse instabilities in a collisionless plasma
Authors: Smith A.
Published: March 2009

Transverse instabilities in an electron gas with a neutralizing background, in the absence of a permanent magnetic field are discussed, mostly when the equilibrium velocity distribution is slightly spheroidal, i.e. of the form

with α ˜ γ and with the functional form of f0 not given explicitly. It is found that two types of unstable waves exist; one grows at a rate proportional to ε½‖ cos θ‖3 whenever ε > 0, the other at a rate proportional to(ε cos2θ)½ whenever ε cos 2θ > 0, where ε = (γ2/α2) — 1, and θ is the angle the wave vector makes with the axis of symmetry of the velocity spheroid. It is shown that within the approximation we are working the complex phase velocity is pure imaginary, i.e. the unstable waves are standing waves. The effect of a small permanent magnetic field is considered. The phase velocity becomes complex, at least for propagation parallel to the magnetic field and the instability rate decreases by a factor where H0 is the permanent magnetic field and 〈H2〉½ the r.m.s. maximum field that grows before non-linear effects take over. The maximum instability rate is compared with the collision rate and is found to be higher in low density, high temperature plasmas such as the solar wind. An application to collisionless shock theory is suggested.
A guiding centre Vlasov equation and its application to Alfvén waves
Authors: Fejer Jules A. , Kan Joseph R.
Published: March 2009

Guiding centre approximations are used to derive the dielectric tensor of a collisionless plasma. This approximate dielectric tensor is used to obtain the dispersion relation of Alfvén waves in a warm plasma. In a ‘low/ β’ equilibrium plasma Alfvén waves are shown to suffer considerable Landau damping if the propagation vector is almost perpendicular to the magnetic field. In a non- equilibrium plasma Alfvén waves can be generated by ‘negative Landau damping’ even if β is low. For sufficiently high β the well-known ‘garden hose’ instability can occur and is then probably dominant. The importance of these two instabilities in the magnetosphere and in the solar wind is discussed.
Theoretical models for resonance oscifiations of inhomogeneous plasmast
Authors: Dorman G.
Published: March 2009

The resonance oscifiations of low temperature, bounded, non-magnetized in-homogeneous plasmas are studied using different methods of solving the linearized Vlasov—Maxwell equations. A low-temperature expansion method of solving the orbit-integral solution of the Vlasov equation is compared to fluid descriptions of the plasma using the truncated moment equations. Numerical results for a one-dimensional plasma slab show qualitative agreement but some quantitative discrepancies.
The effect of weak collisions on ion-acoustic wave instabilities in a current-carrying plasma
Authors: Ong R. S. B. , Yu M. Y.
Published: March 2009

The effect of weak collisions on ion-acoustic wave instabifities in a plasma with large ratios of electron to ion temperatures is investigated. The critical current for instability is shown to be signfficantly reduced by collisions. At the critical current the instability first occurs at non-zero values of kλe. As kλe increases the collisional effects become less and less significant.
On the structure of collisionless magneto—plasma shock waves at super—critical Alfvén—Mach numbers
Authors: Woods L. C.
Published: March 2009

Ions reflected from the sharp potential rise in a magneto-plasma, perpendicular shock wave result hi a broad, small-amplitude ‘foot’ in the magnetic field proffle. A theory is given for the structure of this foot, which shows its shape to be a rather flat parabolic curve commencing at about half a Larmor radius in front of the shock front proper. The theory also predicts the amplitude of the foot just in front of the sharp rise as a function of Alfvén—Mach number. Close agreement with experiment is found.
Drift waves in a slightly non-neutral plasma
Authors: Nocentini A.
Published: March 2009

The influence of the lack of neutrality on the drift instabilities (collisionless and collisional) of a non-uniform, isothermal plasma is considered. It is shown that the local dispersion relation depends on the derivatives of the electric field present in the equilibrium of the nonneutral plasma. In particular the influence of the first two derivatives is discussed.
Stability of non-linear plasma waves
Authors: Rpwlands G.
Published: March 2009

The stability of a stationary non-linear wave set up by two counter-streaming cold beams of electrons immersed in a background of stationary ions is examined without recourse to an expansion in terms of the amplitude of this wave. It is found that this wave is unstable to small perturbations and hence one would not expect such waves to exist in practice.
Hot plasma theory of whistler mode wave packet propagation along a non-uniform magnetic field
Authors: Houghton M. J.
Published: March 2009

We discuss the propagation of wave packets of the form

in an infinite uniform plasma, where G(z, t) is a slowly varying function of space z and time t. One can very simply derive the equation of change of G(z, t) for the stable or unstable case. The terms in the equation are of physical interest and clearly define the limitations of linear theory. We then investigate the problem of whistler mode wave propagation in a collisionless Vlasov plasma in a given non-uniform magnetic field. We choose the electric field to be of a W.K.B. form and the particle distribution to be isotropic. We can express the perturbation in the particle distribution in terms of an integration along the zero-order par tide orbits (an integration overtime). These orbits can be found correct to a term linear in a smallness parameter ε (when ε equals zero we arrive back at a uniform magnetic field). The charge and current density due to the perturbation are related through Maxwell's equations to the electric and magnetic field of the wave in the usual self consistent Boltzmann—Vlasov description. We show that the contribution to the current arises from recent events in the history of a given particle because of the finite temperature of the plasma. This result leads to an expansion of slowly varying parameters which in turn gives rise to the equation governing the motion of the wave packet.
Relativistic effects on non-linear waves in a cold collisionless plasma
Authors: Inoue Yoshinori
Published: March 2009

Non-linear periodic waves propagating across a magnetic field are investigated, taking relativistic effects into account. The governing equations of the phenomena are taken to be the relativistic two-fluid plasma equations for a cold plasma together with Maxwell's equations. The analytical solution in the non-relativistic case was obtained by Adlam and Allen and others, a case where the quasi- neutral approximation is a good one and the inertia of the electrons plays an essential role in the dispersion effect of the plasma.

In contrast, the analysis of the relativistic waves shows that the quasi- neutral approximation becomes invalid and that the charge separation plays an essential role in the dispersion effect while the inertia of the electrons plays minor role only. Therefore the phenomena to be investigated have a length scale of the appropriately defined Debye distance (the ion Larmor radius), while in the non-relativistic case the width of the wave is of the order of the geometric mean of the Larmor radii of the electrons and of the ions. In the present case where the electron mass may be neglected, there exists an exact solution which is a good approximation for a real plasma. The solitary wave solution is found as the limiting case of infinite periodicity.
Helicon wave propagation: effect of electron inertia
Authors: Davies B.
Published: March 2009

We investigate the dispersion relation for travelling helicon waves in a uniform non-resistive plasma. We show that the effect of electron inertia for a cylindrical plasma bounded by conducting walls is qualitatively different from the plane wave case, leading to significant differences in the dispersion relation at all frequencies in the range 0 < ω < Ωe.
Landau damping of resonance oscillations in inhomogeneous plasmas
Authors: Dorman G.
Published: March 2009

A self-consistent solution of the Vlasov—Poisson equations is obtained for a low-temperature, bounded, Maxwellian plasma of arbitrary non-uniform density. An eigenvalue equation for the central frequencies and electric fields of the resonance oscillations is obtained, which agrees with the equation obtained by a low-temperature expansion of the orbital-integral solution. The Landau damping rate is given in a general, explicit form in terms of the central frequencies and fields of the resonances.
Magnetic-field re-connexion in a highly conducting incompressible fluid
Authors: Sonnerup Bengt U. Ö.
Published: March 2009

A theoretical model is proposed for the process of re-connexion of frozen-in magnetic-field lines at an X-type null point in the field. The model involves a diffusion region, immediately adjacent to the null point and an outer wave- dominated region. For the latter an exact solution to the magneto-hydrodynamic equations is obtained; for the former an approximate relationship is derived between the field-re-connexion rate, measured by the Alfvén number of the incident flow, and the magnetic Reynolds number, based on the width of the diffusion region. The maximum field-re-connexion rate is determined entirely by conditions near the null point and may under suitable conditions become large. A condition for maximum conversion of magnetic energy is derived.
Quasilinear dynamics of ion cyclotron instability in an anisotropic plasma
Authors: Preinhaelter J. , Václavík J.
Published: March 2009

It is shown that in a dense magnetoactive plasma c/cA ≫ 1 with cold electrons and ions with an anisotropic temperature the ion cyclotron waves propagating along the magnetostatic field are excited with a maximum increment. The dynamics of the quasilinear stage of this instability is investigated. It turns out that, at any moment, the ion distribution function is of the form of a step with the steep front. The speed of the front in the velocity space and the characteristic time of the relaxation process are found. It is ascertained that the distribution function arising in the course of the relaxation is stable with respect to the ion cyclotron waves propagating obliquely to the magnetostatic field.
A note on ion rarefaction waves
Authors: Allen J. E. , Andrews J. G.
Published: March 2009

A theory is given of an ion rarefaction wave in a low pressure plasma under conditions where ionization processes are unimportant.
One-dimensional ion-acoustic modes of bounded plasmas
Authors: Rosa Rui , Allen J. E.
Published: March 2009

One-dimensional ion-acoustic normal modes of bounded plasmas are theoretically investigated in plane, cylindrical and spherical geometries. The characteristic frequencies, damping constants and spatial structure of the oscillatory modes are obtained.
Asymptotic matching of plasma and sheath in an active low pressure discharge
Authors: Franklin R. N. , Ockendon J. R.
Published: March 2009

The method of matched asymptotic expansions is applied to the fluid model of the low-pressure positive column. The expansion of the eigenvalue in the plasma balance equation is obtained to second order in plane and in cylindrical geometry, and uniformly valid expressions for charged particle densities and fluid velocity in two separate regions are indicated.

The free-fall model is also examined and the scales of the transition layer and sheath layer found. Comparison is made with the results of direct numerical integration of the equations involved for both models.
Suppression of runaway of electrons in a Lorentz plasma. II. crossed electric and magnetic fields
Authors: Abraham-Shrauner Barbara
Published: March 2009

Suppression of runaway of electrons in a weak, uniform electric field in a fully ionized Lorentz plasma by crossed magnetic and electric fields is analysed. A uniform, constant magnetic field parallel to a constant or harmonically time varying electric field does not alter runaway from that in the absence of the magnetic field. For crossed, constant fields the passage to runaway or to free motion as described by constant drift motion and spiral motion about the magnetic field is lengthened in time for strong magnetic fields. The new ‘runaway’ time scale is roughly the ratio of the cyclotron frequency to the collision frequency squared for cyclotron frequencies much greater than the collision frequency. All ‘runaway’ time scales may be given approximately by t2E Teff where tE is the characteristic time of the electric field and Teff is the ffective collision time as estimated from the appropriate component of the electrical conductivity.
Relativistic synchrotron plasma echo
Authors: Ott E.
Published: March 2009

A self-consistent Vlasov equation treatment will be given for a type of echo which arises due to the relativistic velocity dependence of the gyrofrequency. We consider a relativistic plasma in a homogeneous magnetic field. If at t = 0 and t = T a spatially homogeneous external r.f. electric field is applied perpendicular to B0, then an echo response is produced at t = 2T. The amplitude of the echo is proportional to the amplitude of the first pulse multiplied by the square of the amplitude of the second pulse.
Precursor ionization effects on magnetohydrodynamic switch-on shock structure
Authors: Hoffert Martin I.
Published: March 2009

The influence of shock-induced precursor ionization on the steady-state structure of switch-on shock waves with non-equilibrium ionization and radiation is examined theoretically. A single-temperature monatomic gas is assumed, together with a Clarke–Ferrari model for photoionization of the upstream gas. It is found that the effect of the precursor depends in general on the ratio of a characteristic precursor length to a characteristic magnetic interaction length. For the slightly ionized case treated in some detail, this ratio is much greater than unity, indicating a precursor-independence for the magnetohydrodynamic shock structure.
The steady-state Vlasov equations for a monotonic electric potential
Authors: Smith A.
Published: March 2009

A large class of solutions to the steady-state Vlasov equations for a two component one-dimensional plasma for which the electric potential ø is monotonic is shown to exist. Some of these solutions are shock-like in the sense that the particle densities are also monotonic. If the particle and energy densities at infinity are not constraints of the problem, it is shown that there are always solutions for an arbitrary monotonic ø, and the solutions themselves contain arbitrary functions.
An exact electrostatic shock solution for a collisionless plasma
Authors: Smith A.
Published: March 2009

An exact solution to the steady-state Vlasov equations and Poisson's equation for a one-dimensional plasma of electrons and protons is obtained by splitting the energy equation into two integral equations for the trapped particle distributions. This solution has the properties that the number densities and electric potential are moiiotonic functions of space and do most of their changing over a distance of the order of the Debye length for electrons. The distributions are everywhere differentiable in phase space and are Maxwellian-like, and in terms of elementary functions. Evidence is given to support stability for restricted shock strengths.
Effect of gyro-viscosity on Rayleigh-Taylor instability of a plasma
Authors: Nayyar N. K. , Trehan S. K.
Published: March 2009

The effect of finite ion-Larmor radius is considered on the Rayleigh–Taylor instability of a plasma. The macroscopic equations of motion are used where the finite ion-Larmor radius effects are incorporated in the stress tensor. The finite ion-Larmor radius stabilization of the interchange mode is demonstrated. For disturbances propagating along the magnetic field, it is found that the inclusion of gyro-viscosity has a stabilizing effect; it increases the critical wavenumber (compared to its value in the absence of gyro-viscosity) beyond which all modes are unstable.
Effect of dissipation due to firehose instability on perturbation half-jet flow of a collisionless plasma
Authors: Morioka Shigeki , Spreiter John R.
Published: March 2009

The effects of dissipation due to a week firehose instability on steady planar flow of a collisionless plasma are investigated on the basis of the quasi-linear fluid equations. Dissipation terms remain non-linear even within the perturbation theory, and their effects tend to resemble relaxation effects in an ordinary reacting gas rather than ordinary viscous dissipation. As an example, a steady half-jet flow with aligned magnetic field is considered. It is found that the disturbed field decays within a finite distance for some upstream conditions, but grows without limit for others.
Ion waves, drift waves and instability in a weakly ionized magnetoplasma
Authors: Self S. A.
Published: March 2009

A unified treatment is given of low-frequency wave propagation in a weakly ionized magnetoplasma from the fluid equations in which ion inertia is retained. An analysis is made of the instabilities which arise due to the influence of drift of the electrons relative to the ions for three cases: (a) Parallel drift, E∥B, (b) Hall drift, E∥B, and (c) Diamagnetic drift, ∇n⊥B. In all cases an ion acoustic instability is found while additionally, for (c), there is a drift instability for strong magnetic fields. The instability boundaries in parameter space are delineated. Furthermore, for a transversely bounded plasma, the roots ω(kzreal) andkz(ω real) of the dispersion relations are discussed and related to experimental observables. The results are applied to an interpretation of wave propagation and instability on a cylindrical positive column for which all three types of drift are simultaneously present. The relation of this work to the inertialess theories of the current-convective and crossed-field instabilities is also discussed.
Stability of the screw pinch with Hall current
Authors: Malik S. K.
Published: March 2009

The stability of the screw pinch is investigated taking into account the presence of Hall current in Ohm's law. The dispersion relation is obtained as the exact solution of the characteristic value equations governing the general perturbations. It is found that the Hall current has no effect on the hydromagnetic stability of the screw pinch.
Measurement of microwave reflexion from a longitudinally magnetized plasma-filed co-axial wave-guide
Authors: Oldfield M. L. G. , Franklin R. N.
Published: March 2009

The voltage refiexion coefficient from a vacuum-plasma boundary in a co-axial transmission line with an axial magnetic field B0 applied has been measured. The results agree well with a previously published theory for conditions where the microwave-, plasma-, electron collision-, and electron cyclotron-frequencies are of the same order. A 9 GHz co-axial microwave probe is mounted along the axis of a 44mm diameter, hydrogen driven, dry air filled, shock tube in an axial d.c. magnetic field. Shock ionized air (Ms = 9–14, T 4000 °K, electron density nc = 1017 to 3 x 1019 m−3, initial pressure p0 = 1–10 Torr, electron collision frequency v = 1010 to 1011/S) fills the coaxial line and partially reflects a microwave signal. Initially this probe, and a similar rectangular waveguide probe, were used with B0 = 0 to calibrate the plasma (ne, v) in terms of the shock tube parameters (p0, Ms). Measurement of the saturated-ion current to electrostatic probes inset into a fiat plate in the shock tube flow showed that the sheath-edge ion density is close to the predicted free-stream equilibrium ion density. The apparent ionization potential derived from electrostatic probe results decreased as p0 was reduced from 10 to 1 Torr.
Non-linear wave particle processes in an electrostatic wave packet
Authors: Nunn D.
Published: March 2009

The system studied is that of an electrostatic Gaussian wave packet in a cold uniform plasma being excited by a weak resonant beam. To first order in a parameter associated with the weakness of the beam the resonant particle distribution function and resonant particle charge densities are computed.
Theory and numerical solutions for sheath growth in a low-pressure plasma
Authors: Jack A. G. , Sander K. F. , Varey R. H.
Published: March 2009

The theory of the development of thick sheaths given in an earlier paper (Sander 1969) is applied to planar sheath growth in practical situations. The results are compared with those resulting from a purely numerical method and from certain approximate equations suggested by other workers in the field.
Electrostatic oscillations in cold inhomogeneous plasma I. Differential equation approach
Authors: Sedláček Z.
Published: March 2009

Small amplitude electrostatic oscillations in a cold plasma with continuously varying density have been investigated. The problem is the same as that treated by Barston (1964) but instead of his normal-mode analysis we employ the Laplace transform approach to solve the corresponding initial-value problem. We construct the Green function of the differential equation of the problem to show that there are branch-point singularities on the real axis of the complex frequency-plane, which correspond to the singularities of the Barston eigenmodes and which, asymptotically, give rise to non-collective oscillations with position-dependent frequency and damping proportional to negative powers of time. In addition we find an infinity of new singularities (simple poles) of the analytic continuation of the Green function into the lower half of the complex frequency-plane whose position is independent of the spatial co-ordinate so that they represent collective, exponentially damped modes of plasma oscillations. Thus, although there may be no discrete spectrum, in a more general sense a dispersion relation does exist but must be interpreted in the same way as in the case of Landau damping of hot plasma oscillations.
The interaction of homogeneous wave turbulence and a magnetohydrodynamic tangential discontinuity
Authors: Tam Christopher K. W.
Published: March 2009

The interaction of homogeneous wave turbulence and a magnetohydrodynamic tangential discontinuity is studied. Attention is focused on the turbulent shear stress produced as a result of such an interaction. A magnetohydrodynamic description is used which is believed to be adequate for plasma problems in interplanetary space. As a model for wave turbulence, it is assumed that the turbulent wave field is made up of the seven modes of magnetohydrodynamic waves. They are the entropy waves, the Alfvn waves (two independent modes), the fast and slow waves (each with two independent modes). It is found that to a first approximation the turbulent shear stress acting on the surface of discontinuity is linearly proportional to the energy density of the fluctuating magnetic field and to the kinetic energy density of the plasma fluctuations. On applying the present theory to the problem of interaction between the turbulent waves in the magnetosheath and the magnetopause, it is found that the turbulent shear stress produced is too weak to produce any large-scale internal magnetospheric convection as was previously contemplated.
Relativistic kinetic theory of the large-amplitude transverse Alfvén wave
Authors: Barnes Aaron , Suffolk Graham C. J.
Published: March 2009

It is shown that the relativistic Vlasov–Maxwell equations admit a solution very much like the transverse Alfvén wave of magnetohydrodynamic theory. This wave propagates as a plane electromagnetic wave of arbitrary amplitude, is noncompressive, is associated with fluctuations in direction (but not magnitude) of magnetic field, is characterized by a non-linear ‘dispersion relation’, and reduces in the limit of small amplitude to the transverse Alfvén mode of linearized plasma wave theory. The dispersion relation yields a criterion for the firehose instability which turns out to be the same as that derived from linearized theory.
The gravitational instability of a rotating magnetoplasma in the guiding centre approximation
Authors: Lunn A. D.
Published: March 2009

Jeans's criterion for instability is found to be changed only for the case of perturbations perpendicular to the magnetic field and rotation parallel to it, when rotation and finite Larmor radius effects tend to stabilize the plasma.
Growth rates of plasma oscillations for symmetrical double-humped velocity distributions
Authors: Nishimura Keiichi
Published: March 2009

Inside any symmetrical double-humped plasma velocity distribution, all growing waves with real wave-number have zero phase velocity. Growth rates of such plasma oscillations are calculated for distributions made up of resonance functions and of Gaussian functions. The results are compared with an earlier calculation made with less realistic distribution functions with no infinite tails.
Non-linear interaction of electrostatic monochromatic waves in a magnetoplasma
Authors: Tataronis J. A. , Teichmann J.
Published: March 2009

The resonant interaction of three monochromatic waves propagating in a uniform magnetoplasma is considered in the electrostatic approximation. It is shown that, for arbitrary directions of propagation, the coupling coefficients are in general complex, and are symmetric with respect to interchanges of the wave vectors.
Electrostatic waves in periodic inhomogeneous plasma
Authors: Bertrand P. , Feix M. R. , Baumann G.
Published: March 2009

In periodic, inhomogeneous plasma, the dispertion relation w(k) can begeneralized to a relation w(k, K), where K is the wave-number of the periodic steady state. Two models are studied: the ‘water-bag’ model and the ‘two-stream’ model. The solution for these models is obtained easily by the introduction of a Lagrangian formulation. Results are presented. It is shown that, in the water-bag case, the appearance of narrow bands of allowed frequencies practically discretizes the lower part of the spectrum. In the two-stream case, while the long wavelengths have a smaller growth rate, an increased instability is found for k/K = ½
Existence conditions for collisionless hydromagnetic shock waves along the magnetic field
Authors: Kato† Yusuke , Tajiri Masayoshi , Taniuti Tosiya
Published: March 2009

This paper is concerned with existence conditions for steady hydromagnetic shock waves propagating in a collisionless plasma along an applied magnetic field. The electrostatic waves are excluded. The conditions are based on the requirement that solutions of the Vlasov-Maxwell equations deviate from a uniform state ahead of a wave. They are given as the conditions on the upstream flow velocity in the wave frame (i.e. in the form of inequalities among the upstream flow velocity and some critical velocities). The conditions crucially depend on the pressure anisotropy, and demonstrate possibilities of exacting collisionless shock waves for high β plasmas.
Plasma models of the topside ionosphere and electrostatic wave propagation
Authors: Fang M. T. C. , Andrews M. K.
Published: March 2009

The circumstances under which certain plasma dispersion equations may be used in electrostatic ray tracing problems connected with studies of ionospheric topside plasma resonances are investigated. Three plasma ‘models’ of increasing complexity are compared with each other. The models are based on the assumption of: (i) an adiabatic process with a scalar pressure, (ii) a fully adiabatic process (Buneman 1961), and (iii) an electrostatic kinetic description. It is found that near fN, and within 10° of the static magnetic field, all three models may be used with good accuracy, and collisionless damping is very small. Near fT, and for propagation nearly across the field, only the second model (ii) gives tolerably accurate results as judged by the kinetic equation. For frequencies within 10 kc s-1 of fT such as are encountered in ray tracing, collisionless damping may be neglected within a cone of ∽ 10° about the perpendicular to the field for fT < 2fH, and within ∽ 20° whenfT ≫ 2fH Model (iii) may be used to examine the dispersion equation near the electron gyroharmonics: this topic is discussed in Andrews & Fang (1971).
Generalized theory of the stabifity of shock waves in magnetogasdynamics
Authors: Woods L. C.
Published: March 2009

Stability of MGD shock waves can be investigated either by disturbing the shock discontinuity by incident waves and then considering whether the response of the shock is unique and determinate or not, or by studying the behaviour of the dissipative shock structure with variations in the magnitudes of the dissipations. Both approaches yield the same results, which appears at first sight to be a coincidence. In this paper we show, from a single treatment that includes each as special cases, why the two methods yield the same conclusions.

Also, by including the Hall term on Ohm's law, we are able to resolve the uncertainty about the stability of switch-on and switch-off shocks that occurs in the usual MHD treatment of the problem. Finally, it is shown that the Hall term also introduces the possibility of electric field layers in the unsteady shock and thereby reduces the number of shock boundary conditions. This throws some doubt on the value of the wave-interaction theory for shocks in real plasmas.
Some strong effects due to weak coupling in an assembly of oscillators
Authors: Peyraud J. , Peyraud N.
Published: March 2009

The mathematical treatment of the influence of a weak coupling on an
assembly of damped oscillators with different eigenfrequencies permits us to exhibit a peculiar property of the solution: namely, the existence of a high frequency solitary, weakly damped mode. We propose to apply these results to the ionic oscillations of a bounded plasma.
Cut-off criteria of electronic partition functions and transport properties of thermal plasmas
Authors: Capitelli M.
Published: March 2009

It is shown that the effect of the cut-off criteria of the electronic partition functions on transport properties varies with the particular coefficient considered. For example, the cut-off has little effect on translational thermal conductivity, but a large effect on viscosity and reactive thermal conductivity.
Ordinary-mode electromagnetic instability for counter-streaming plasmas with anisotropic temperatures
Authors: Gaffey J. D. , Thompson W. B. , Liu C. S.
Published: March 2009

The instability of the ordinary electromagnetic mode propagating perpendicular to an external magnetic field is studied for two counter-streaming plasmas with anisotropic temperatures. A necessary and sufficient condition for this instability is derived and the growth rate is calculated. Although instability can occur in a plasma with low β‖e, provided the streaming velocity is comparable to the parallel electron thermal velocity, β‖e of the order of unity and large electron temperature anisotropy (T‖e≫ T⊥e) are required for large growth rates. These large growth rates are typically of the order of the electron cyclotron frequency. Comparison with the electrostatic two-stream instability is made.
Interaction processes in a weakly turbulent Vlasov plasma
Authors: Olbers Dirk J.
Published: March 2009

In this paper we consider the interaction between waves and particles in a weakly turbulent, collision-free plasma for the case of pure Coulomb interaction and zero magnetic field. Starting with the Vlasov equation we suggest a solution by means of a perturbation expansion and a diagram technique, which classifies the various interaction processes and leads to the derivation of kinetic equations.
On the flute instability in a Q-machine
Authors: D'Ambrogio Enos , Nocentini Aldo
Published: March 2009

The influence of the cathodes of a double-ended Q-machine on a flute instability of the Rayleigh–Taylor type is investigated for a low β plasma column. It is shown that flute modes are strongly affected by the end plate conditions and by the machine length. The occurrence of ion-rich sheaths is a necessary condition for the validity of the dispersion relation of the unbounded case. The range of values of the column length for the existence of a given flute mode is determined.
On the derivation of the quasilinear equations
Authors: Fukai Junichiro , Harris Edward G.
Published: March 2009

A derivation of the quasilinear equations is given, which is sufficiently general to include damped waves. The cause of some difficulties in previous derivations, momentum and energy conservation, and the origin of irreversibility are discussed.
Longitudinal waves in a perpendicular collisionless plasma shock Part 4. Gradient B
Authors: Gary S. Peter
Published: March 2009

This paper considers electrostatic waves in a Vlasov plasma of unmagnetized ions and magnetized electrons undergoing E x B and gradient B drifts. The linear dispersion relation is solved numerically for Te & Ti. The results show that, as in the Te <Ti case, increasing electron β decreases the maximum growth rates.
Equilibrium configurations of Vlasov plasmas carrying a current component along an external magnetic field
Authors: Kan J. R.
Published: March 2009

A class of equilibrium configurations of Vlasov plasmas carrying a current component along an external magnetic field is presented. The present slab model contains the diamagnetic current jy, and the field-aligned current jz for arbitrary βc (= particle pressure/magnetic pressure of the applied constant field). For fixed βc and field-aligned current, our model admits a family of equilibrium solutions in which the diamagnetic currents range from zero to a maximum value. The amount of diamagnetic current flowing in a machine depends on the width of the machine, the field-aligned current and other plasma parameters. The Helmholtz free energy of the system is calculated under the constraints that the total number of particles and the field-aligned current are conserved. The least unstable equilibrium configuration in a machine is obtained by minimizing the free energy under the stated constraints among all equilibria whose plasma widths do not exceed the width of the machine.
A boundary problem in a plasma (oblique incidence)
Authors: Karunarathne V. B.
Published: March 2009

An isotropic plasma occupies an infinite space, the upper half of which (y 0) is a dielectric. A transverse disturbance is incident obliquely on the face of the dielectric. The waves produced in each half of the space are obtained. Possible extensions are discussed. ome particular examples are considered.
Reformulation of quasi-linear theory
Authors: Kaufman Allan N.
Published: March 2009

A new formulation of quasi-linear theory is presented, which allows for only resonant diffusion, caused by both growing and damped waves. Nonresonant terms do not appear in the diffusion equation, but contribute to wave momentum and energy, and ensure conservation of total momentum and energy.
X-ray fine structure of dense plasma in a co-axial accelerator
Authors: Bostick W. H. , V. Nardi  , Prior W.
Published: March 2009

The intensity of X-ray sources in a focused deuterium plasma produced by a coaxial accelerator has been analysed as a function of position, X-ray energy and time of emission. The X-ray source in the axial region can be resolved (by micro- densitometer readings on X-ray pinhole camera films) as a sequence of small sources (linear dimension ∼ 0.1–0.3 mm) of hard radiation ≳ 2 ke V inside a more diffused source (cylindrical region of 1–4mm diameter) of softer X-rays. In each discharge the point sources are distributed for the most part in the general axial region of the discharge and two or more sources with different radial positions can be frequently observed for one specific value of the axial co-ordinate. Images of localized X-ray sources are also observed in the off-axis halo region. Multiple repinching of the axial plasma column or emission from metal-vapour clouds (by anode bombardment) can be ruled out in this experiment (hollow central electrode, or anode, radius 3·4 cm). The source multiplicity can be related to a complex (filamentary) structure of the plasma.
Comparison of wave propagation in the stationary and moving plasma: motion and wave propagation along the magnetic field
Authors: Srivastava D. N.
Published: March 2009

The three important aspects of wave propagation in a stationary and a moving plasma (namely frequency, polarization and dispersion) are compared, taking the phase refractive index of the wave as the independent variable. Wave propagation and the motion of the plasma are taken to be along the magnetic field. The plasma is assumed to consist of one species only, and the effect of collisions is neglected. Wave propagation in a moving plasma has been shown to possess several important features, such as the absence of cyclotron resonance, reversal of the sense of polarization when the phase velocity becomes equal to the plasma velocity, and the existence of backward waves for very small and very large phase velocities.
The thickness of perpendicular collisionless shocks in a hot plasma
Authors: Cairns R. A.
Published: March 2009

By linearizing about the upstream state, the characteristic length for the growth of magnetic field in a laminar wave front, propagating perpendicular to an external magnetic field, is found as a function of βi, the ratio of ion pressure to magnetic pressure. For values of βi, between 10–2 and 1 the thickness is found to scale as . This scaling is in good agreement with the observed scaling of turbulent shocks, suggesting that for such shocks the shock thickness is closely related to that of the corresponding laminar pulse.
Instability of a large-amplitude plasma wave due to inverted trapped particle population
Authors: Liu C. S.
Published: March 2009

The large-amplitude plasma wave with a trapped-particle distribution monotonically increasing in energy is found to be unstable if the trapped-particle plasma frequency ωt = (4πnte2/m)½ is greater than the bounce frequency ωb = (eΕ0κ0/m)½.
Propagation of electronic longitudinal modes in a non-Maxwellian plasma
Authors: Henry D. , Trguier J. P.
Published: March 2009

The experimental modifications of the classical Landau mode (modification of the first pole, and occurrence of a new propagating mode below the plasma frequency) are due to a peculiar distribution function. This distribution function is approximated by a simple model (i.e. a Maxwellian function plus a water-bag function). A numerical calculation with this model gives new dispersion curves, which agree with experiment.
Effects of collisions and gyroviscosity on gravitational instability in a two-component plasma
Authors: Herrnegger F.
Published: March 2009

The dispersion relation for gravitational instability has been given within the framework of a two-fluid theory. It has been shown that the Jeans criterion is changed by finite Larmor radius and by collisions for waves propagating perpendicular to the magnetic field. The critical wavenumber for instability decreases with increasing Alfvén velocity and with increasing gyroviscosity. Instability does not set in with overstabiity.
Plasma fluid equations in the high collision-frequency limit
Authors: Greene John M.
Published: March 2009

The nature of the fluid approximation for plasmas in the high collision-frequency limit is examined in an effort to understand some of the limits of validity of the commonly used ideal magnetohydrodynamic equations. The plane wave dispersion relation for a homogeneous medium is evaluated. The dependence of the damping on the various dissipative terms is examined for each type of wave predicted by the dispersion relation. The effects of these terms are then compared, using the standard values for transport quantities with collision frequency larger than gyro-frequency. When the total dissipation is considered as a function of collision frequency, it is found that there is a minimum in the region where the collision and gyro-frequencies are about equal. This is the régime for which ideal magnetohydrodynamics is a good approximation. As collision frequency is increased, dissipation reaches a maximum when the wave is in resonance with the resistive skin depth, and then decreases into a régime where ordinary sound and light waves propagate. Lower collision frequencies, where thermal conduction and equilibration are important, are considered.
Magnetogasdynamic shock polar: exact solution in aligned fields
Authors: Bertram Lee A.
Published: March 2009

The shock conditions for a perfect gas in aligned-fields magnetogasdynamics are solved to give all variables downstream as rational functions of the density ratio. The thermodynamically admissible, evolutionary shock solutions are exhaustively classified into seven shock polar types, including a new type of supersonic, sub -Alfvénic polar. Example polars of each type are presented in the magnetograph (dimensionless magnetic induction vector plane) and in the Taniuti–Resler diagram (M, Aplane) in order to display, respectively, the shock geometry and the state of the gas. A short discussion of the relation of the shock properties to flow over bodies is presented.
Nonlinear propagation of electromagnetic waves in a plasma containing random irregularities
Authors: Liu C. H.
Published: March 2009

The problem of propagation of finite-amplitude electromagnetic waves in a plasma containing random irregularities is studied. Using a recently developed perturbation technique, a general equation for finite amplitude coherent waves is derived. Included in this equation are both the effects of quasi-harmonic nonlinear heating of electrons and random scattering by irregularities. The equation is solved in general by the equivalent linearization procedure. The amplitude of the coherent wave is found to be attenuated by collision and scattering. Both attenuation are affected by the nonlinear heating of the electrons. Curves showing the results for a specific example will be presented.
Magnetoplasma equilibria with planar symmetry
Authors: Yeh Tyan
Published: March 2009

Equilibria of magnetoplasma with planar symmetry are presneted. Among the equilibria illustrated are configurations of plasmas confined inside a cylindrical wall and plasma in a double-inverse-pinch device.
Electromagnetic instabilities in non-uniform anisotropic plasmas
Authors: Butt B. , Lakhina G. S.
Published: March 2009

Electromagnetic waves propagating perpendicular to an external magnetic field in a non-uniform anisotropic plasma can become unstable due to the excitation of either resonant ion instability or resonant electron instability. The former instability can exist in the absence of both the temperture anisotropy and the temperature gradients, whereas for the excitation of resonant electron instability the presence of at least one of them is necessary. An off-resonance drift cyclotron instability can also get excited if the temperature gradients are much stronger than the magnetic field gradients.
Stability of isothermal magnetohydrodynamic shock waves
Authors: Bel Nicole , Laury-Micoulaut Colette
Published: March 2009

The stability of normal isothermal magnetohydrodynamic shock waves is studied with respect to isothermal as well as adiabatic perturbations. The problem is solved by the normal-mode analysis. The isothermal normal MHD shock appears to be stable.
The effect of gradients of density and static magnetic field on the propagation of surface waves and on wave–beam interaction
Authors: Demchenko V. V. , El-Siragy N. M. , Hussein A. M.
Published: March 2009

The propagation of slow surface waves in an inhomogeneous plasma is investigated. Both ‘axial’ and ‘radial’ density gradients n(r) and those of the static magnetic field B0 are taken into account. It is demonstrated that the axial in- homogeneities n(z) and B0(z) result in the dependence of the natural surface- wave frequencies on the ‘axial’ co-ordinate z. The dependence ωSW(z) affects the phase velocity νph = ωswsol;K where K iS the propagation constant. So, in the case of surface-wave excitation by a charged particle beam in an ‘axially’ inhomogeneous plasma, the Cherenkov resonance ωSW= KV0 between the beam and the surface waves breaks, thereby reducing the growth rate of unstable oscillations. This phenomenon might be considered as the stabilization of the beam by the ‘axial’ density gradient. It is also shown that the ‘radial’ gradients n0(r) and B0(r) essentially affect the surface-wave natural frequencies as well. Dispersion equations, expressions for the natural frequencies and growth rates are obtaind, taking into account the gradients of the density and the static magnetic field.
On the perturbation of a plasma and particle collection by a cylinder in a magnetic field
Authors: Lafon J. P.
Published: March 2009

The inhomogeneous sheath that surrounds a probe immersed in a weakly collisional magnetized plasma is investigated from the microscopic point of view, in the case when the probe is cylindrical and parallel to the magnetic field. Arbitrary surface effects of the probe (such as absorption, reflexion and emission of particles) are taken into account. The sheath is described with a model based on the solution of a boundary-value problem for the self-consistent Boltzmann—Maxwell—Poisson equation. The spatial variation of the magnetic field is discussed. Typical results of numerical computations concerning the structure of the sheath and the currents collected by the probe are given and discussed.