bluuebunny/crossref_metadata_2025 huggingface dataset:
Electromagnetic ion-cyclotron instability vs. electrostatic ion-cyclotron instability in mixed (warm-cold) magnetospheric-like plasmas
Authors: Cuperman S. , Gomberoff L.
Published: March 2009

This work presents a systematic investigation and comparison of electromagnetic ion-cyclotron (e.m.) and electrostatic ion-cyclotron (e.s.) instabilities in uniform mixed warm and cold plasmas for magnetospheric-like plasma parameters. The following main aspects are included: Analytical: (i) we derive simple approximate expressions for the maximum growth rate, γmax for the quasi-electrostatic instability in the regime ωr » …p, к┴ » к∥ (к∥ ≠ 0) with the protons being described by mixed loss-cone and cold populations and with inclusion of electromagnetic coupling effects due to electrons; (ii) we analyse another regime in which electrostatic instalilities first increase with addition of cold plasma and decrease only after having reached a maximum, namely a regime with ωr » …p, к = к≠; (iii) we summarize the corresponding analytical results for parallel propagating electromagnetic ion-cyclotron unstable waves and discuss their validity range.
Magnetic field-line reconnexion by localized enhancement of resistivity. Part 2. Quasi-steady process
Authors: Tsuda Takao , Ugai Masayuki
Published: March 2009

We have described previously the evolutionary process of magnetic field-line reconnexion by a localized enhancement of resistivity. In this paper, it is demonstrated by numerical experiment that the evolution is eventually checked, with the system attaining a quasi-steady state. On the basis of the quasi-steady configuration, established from an initially antiparallel magnetic field, we can now clarify the MHD properties that are characteristic of the diffusion, field reversal and external regions, respectively, and then the mutual dependence among them. Especially, the physical processes in the diffusion region are noteworthy, since the ultimate cause for the present reconnexion process is the bending of the field lines towards the magnetic neutral point, which results from the locally enhanced resistivity assumed in the diffusion region. The present numerical results generally agree with the analytical results for the steady reconnexion, although some discrepancies exist owing to the differences of the postulated basic situations between them. It is pointed out that changes in flow properties across the boundary of the field reversal region agree well with those required for a slow mode compression wave and that the dominant process in the external region corresponds to a fast mode expansion.
Dynamics of four coupled plasma waves to second order
Authors: Walters Dolores , Lewak George J.
Published: March 2009

General equations are derived for the interaction of four waves to second order (i.e. two triplets with two waves common to both). The solutions are analysed under various initial conditions and it is shown that the weaker triplet (as measured by the coupling constraints) is stabilized by the stronger one against explosive instabilities, whereas the converse does not happen. It is further found that under certain circumstances one of the common waves may act as a ‘catalyst’, remaining fixed in amplitude, while the other waves oscillate or even grow exponentially. This work extends the treatment of Karplyuk, Oraevskii & Pavlenko to include the possibility of negative energy waves.
Improved measurement of the electron temperature of a low density shock-heated argon plasma by means of microwaves
Authors: Schneider C. P.
Published: March 2009

The determination of electron temperature of a low density shock-heated argon plasma (3 Torr ≤p1≤ 10 Torr, 5500 °K ≤ 9500 °K) by means of microwave diagnostics is improved with a test section which permits the simultaneous transmission of two microwave beams at different frequencies, and with two corrections applied to the measured attenuation of transmitted waves. The purpose of these corrections is to obtain the true attenuation due to wave power dissipation into the plasma, which is dependent on the electron temperature and density. The first correction takes into account the diffraction of waves by apertures of the test section and the wave defocusing by the plasma. The second correction considers the effect of wave beam bending due to the electron density gradient in the flow direction of the plasma. Both corrections diminish the measured wave attenuation. Consequently a lower ratio of attenuation to phase shift of transmitted waves is determined, which in turn yields lower values of electron collision frequency and electron temperature. This report describes the electron temperature evaluation technique in detail, and presents results. The electron temperature values obtained have a range of uncertainty of – 20 % and +10% only, with exceptions at the beginning of the test time. In most tests, the electron temperature is equal or lower by approximately 1000 °K in comparison with the heavy particle temperature.
On the stability of self-consistent large amplitude waves in a cold plasma. Part 1. Transverse circularly polarized waves in the absence of a large scale magnetic field
Authors: Lee M. A. , Lerche I.
Published: March 2009

We demonstrate that a self-consistent circularly polarized wave in an otherwise field-free homogeneous cold plasma is unstable to small amplitude perturbations. For either an electron-positron plasma or an electorn-proton plasma the instability rate is at least about the order of the effective plasma frequency when the bulk flow speed is zero. For finite bulk flow speeds of the plasma, we show that the electron-positron plasma is unstable – again with a growth rate of the order of the effective plasma frequency; we also show that the electron-proton plasma is unstable (at least at small wave number, k) with a growth rate proportional to k. The instability rates we calculate are conservative, for other modes not investigated here may be more unstable. The results of these calculations bear directly on our understanding of plasma systems thought to be driven by large amplitude waves.
On the periodicity of ion-acoustic waves in an inhomogeneous plasma
Authors: Gunzburger M. D.
Published: March 2009

The existence of periodic ion-acoustic waves propagating through an inhomogeneous moving plasma is studied. For supersonic flow speeds it is shown that periodic excitations result in periodic responses independent of the nature of the media properties and the initial conditions. For subsonic flow speeds, periodic responses exist only under certain restrictions on the media and the initial conditions. However, most cases of physical interest are in the class of problems for which periodic or asymptotically periodic responses exist.
On energy of non-resonantly growing plasma waves
Authors: Hirose A.
Published: March 2009

The energy of hydrodynamically unstable plasma waves is re-examined. The modified Landau–Lifshitz factor Re (∂/∂ω) (ω∈) recently proposed is shown to involve several difficulties when energy and momentum conservation are considered.
Stability of relativistic transverse cold plasma waves Part 1. Circularly polarized waves
Authors: Romeiras F. J.
Published: March 2009

This paper is concerned with the stability against small perturbations of a certain class of nonlinear wave solutions of the equations that describe a cold unmagnetized electron–ion plasma. These nonlinear waves are of fixed profile, superluminous, period.ic and transverse. The small perturbations are assumed to propagate in the same direction as the nonlinear wave. A Lagrangian method is used to derive the perturbation equations. The analysis is carried out in the frame where the nonlinear waves are space independent and then the results Lorentz transformed to the laboratory frame. Part 1 refers to circularly polarized waves. In this case it is possible to integrate the equations and obtain an algebraic dispersion relation in the form of an eighth order polynomial equation in the frequency. The analytical and numerical solution of this equation, for a wide range of variation of the parameters involved, reveals the existence of a very unstable mode. Particular attention is given to very large wave amplitudes for which the plasma behaves like an electron–positron plasma; in this case the growth rate of the unstable mode can be as high as the frequency of the nonlinear wave.
Electron-acoustic solitons in a weakly relativistic plasma
Authors: Mace R. L. , Hellberg M. A. , Bharuthram R. , Baboolal S.
Published: March 2009

Weakly relativistic electron-acoustic solitons are investigated in a two-electron-component plasma whose cool electrons form a relativistic beam. A general Korteweg-de Vries (KdV) equation is derived, in the small-|ø| domain, for a plasma consisting of an arbitrary number of relativistically streaming fluid components and a hot Boltzmann component. This equation is then applied to the specific case of electron-acoustic waves. In addition, the fully nonlinear system of fluid and Poisson equations is integrated to yield electron-acoustic solitons of arbitrary amplitude. It is shown that relativistic beam effects on electron-acoustic solitons significantly increase the soliton amplitude beyond its non-relativistic value. For intermediate- to large-amplitude solitons, a finite cool-electron temperature is found to destroy the balance between nonlinearity and dispersion, yielding soliton break-up. Also, only rarefactive electronacoustic soliton solutions of our equations are found, even though the relativistic beam provides a positive contribution to the nonlinear coefficient of the KdV equation, describing relativistic, nonlinear electron-acoustic waves.
Evolution of small-amplitude intermediate shocks in a dissipative and dispersive system
Authors: Wu C. C. , Kennel C. F.
Published: March 2009

Our study of the relationship between shock structure and evolutionarity is extended to include the effects of dispersion as well as dissipation. We use the derivative nonlinear Schrödinger-Burgers equation (DNLSB), which reduces to the Cohen-Kulsrud-Burgers equation (CKB) when finite ion inertia dispersion can be neglected. As in our previous CKB analysis, the fast shock solution is again unique, and the intermediate shock structure solutions are non-unique. With dispersion, the steady intermediate shock structure solutions continue to be labelled by the integral through the shock of the non-co-planar component of the magnetic field, whose value now depends upon the ratio of the dispersion and dissipation lengths. This integral helps to determine the solution of the Riemann problem. With dispersion, this integral is also non-zero for fast shocks. Thus, even for fast shocks, the solution of the Riemann problem depends upon shock structure.
Expansion of a polarized plasma source into an ambient plasma
Authors: Dobrowolny M. , Melchioni E.
Published: March 2009

Plasma sources are used to control spacecraft potentials and, in general, to improve the electrical contact between a charged body and the space plasma. From this point of view, they have been proposed in connection with conducting tethers in space to increase current capability and to allow the use of such tethers for power generation and/or propulsion. In this paper we address the problem of the interaction of a plasma source with the ambient plasma. The source is supposed to be positively charged with respect to the ambient. A self-consistent fluid model is developed to obtain a description of the interaction in the collisionless case. The interaction, which appears to be mainly characterized by the presence of a double layer, is discussed in terms of the ratio between source density and ambient plasma density and the value of the polarizing potential. The current-voltage characteristics of the system are then determined.
On the continuity equation for electrons in microwave-afterglow plasmas
Authors: Abdel-Gawad H. I.
Published: March 2009

We construct a continuity equation for electrons in microwave-afterglow plasmas. The self-similar solution of the equation is obtained for a plasma with plane, cylindrical or spherical geometry.
Poloidal electric field due to electron-cyclotron resonance heating in tokamaks
Authors: Taguchi M.
Published: March 2009

The poloidal electric field generated by electron-cyclotron resonance heating is investigated for a tokamak plasma in the collisionless regime. This poloidal electric field is calculated by solving an adjoint equation to the linearized Fokker-Planck equation with a quasi-linear diffusion term. It is found from this calculation that the magnitude and the sign of the poloidal electric field depend strongly on the values of the inverse aspect ratio, the poloidal angle of the absorption point, the parallel velocity of resonant electrons normalized by the thermal velocity, and the strength of the relativistic correction to the resonance condition.
On the relaxation of non-thermal plasmas
Authors: McGowan A. D. , Sanderson J. J.
Published: March 2009

The collisional relaxation of various plasma distributions that are initially far removed from thermal equilibrium is investigated numerically using a Fokker–Planck code. It is shown that self-similar and kappa distributions do not remain self-similar or kappa, and that this is due to the velocity dependence of the effective collision frequency. For the relaxation of an isotropic two temperature plasma it is shown that a constant-temperature three-component distribution function is a plausible model for analytical calculations. Investigation of the relaxation of bi-Maxwellian plasmas resolves some discrepancies that have arisen from earlier studies.
Surface-wave-particle interactions in a cylindrical plasma
Authors: Dengra A. , Ballesteros J.
Published: March 2009

A new theoretical model to study surface wave–particle interaction in a cylindrical plasma has been developed. This model is based on linear resolution of the Vlasov equation, with the specular reflection hypothesis. Expressions for the breakdown time of the linear solution and for the rate of increase of kinetic energy per electron, as a function of the critical parameters, have been obtained.
The temporal helicon-wave echo in a plasma with steepened density profile
Authors: Fedutenko E. A. , Lapshin V. I.
Published: March 2009

The hydrodynamic echo on the surface helicon-type modes radiated to vacuum in a magnetized plasma with steepened density profile is investigated. It is shown that perturbations induced by an initial pulse at the plasma boundary are modulated by a later applied second pulse of different wavelength, to yield a non-vanishing echo signal, which can be radiated to vacuum. The angle of the radiation and the density of the energy flow of this signal are determined.
Ion-acoustic wave instability driven by drifting electrons in a generalized Lorentzian distribution
Authors: Meng Zhaoyue , Thorne Richard M. , Summers Danny
Published: March 2009

A generalized Lorentzian (kappa) particle distribution function is useful for modelling plasma distributions with a high-energy tail that typically occur in space. The modified plasma dispersion function is employed to study the instability of ion-acoustic waves driven by electron drift in a hot isotropic unmagnetized plasma modelled by a kappa distribution. The real and imaginary parts of the wave frequency ω0 + ιγ are obtained as functions of the normalized wavenumber kλD, where λD is the electron Debye length. Marginal stability conditions for instability are obtained for different ion-to-electron temperature ratios. The results for a kappa distribution are compared with the classical results for a Maxwellian. In all cases studied the ion-acoustic waves are strongly damped at short wavelengths, kλD ≫ 1, but they can be destabilized at long wavelengths. The instability for both the kappa and Maxwellian distributions can be quenched by increasing the ion-electron temperature ratio Ti/Te. However, both the marginally unstable electron drift velocities and the growth rates of unstable waves can differ significantly between a generalized Lorentzian and a Maxwellian plasma; these differences are also influenced by the value of Ti/Te.
An inhomogeneous plasma equilibrium: asymptotic self-similar solutions
Authors: Saiz E. , Gutierrez J. , Cerrato Y.
Published: March 2009

A perfectly conducting hot plasma in thermodynamic equilibrium is studied without taking account of the effects of collisions and viscosity. The medium is inhomogeneous, unbounded, axisymmetric and subject to a magnetic field B0 parallel to the axis of symmetry of the cylinder. Plasma equilibrium is investigated using a magnetohydrodynamic model, and the system of equations is closed with an equation of state corresponding to the adiabatic law for an ideal gas. Transformation groups are applied to generate asymptotic selfsimilar solutions for the density, pressure and magnetic field magnitudes on the equilibrium, and thus to obtain the spatial dependence of the invariant solutions since the temporal variable is eliminated. From consideration of the nature of these solutions, necessary conditions for equilibria in finite inhomogeneous media are obtained. Results are given for inhomogeneous media with finite conductivity. The degrees of inhomogeneity for pressure and density and their relations with dimensionless constants, arising from the group parameters, provide information on certain drastic changes in equilibrium temperature profiles.
Experimental verification of the reciprocity theorem for antennas and electron plasma waves
Authors: Nakamura Y. , Itoh T.
Published: March 2009

The reciprocity theorem for monopole antennas, a gridded parallel plate, parallel-plane grids and a plane plate, which radiate and receive an electron plasma wave in an unbounded plasma, is introduced theoretically, based on the electron fluid model. The theorem holds experimentally if the d.c. bias potential of antennas is lower than about the floating potential. The measured reception pattern of an antenna is equal to its radiation pattern. The wave amplitude and the impedance between the antenna and the plasma are measured experimentally.
Relaxation oscillations in weak turbulence. The case of nonlinear wave-particle interaction
Authors: Montes C.
Published: March 2009

A model for nonlinear Landau stabilization of a linear instability is treated analytically. The model may apply to any dissipative system described by: (i) a linear dissipation function γ(k), of one degree of freedom k, which presents a limited unstable domain δK and a damped region for lower values of k, and (ii) a transition probability for the nonlinear Landau damping (nonlinear wave–particle interaction) proportional to k – K'. For a sharply pointed γ(k), the model leads to a kinetic regime presenting periodic relaxation oscillations of large and constant amplitude. Starting from weak turbulence, the system organizes itself into a periodic regime, which may be of interest in connexion with research in morphogenesis. For a smoothed γ(k), the relaxation oscillations damp, slowing down towards a turbulent energy level.
Kinetic equations for plasmas subjected to a strong time-dependent extenal field. Part 2. The weak-interaction approximation
Authors: Balescu R. , Misguich J. H.
Published: March 2009

The general theory developed in part 1 is illustrated for a plasma described by the weak-coupling (Landau) approximation. The kinetic equation, valid for arbitrarily strong external fields, is written out explicitly.
Athermal neutrons and ions in a fusion plasma
Authors: Brueckner K. A. , Brysk H. , Janda R. S.
Published: March 2009

For a laser-driven fusion plasma dense enough to absorb the fusion particles, the slowing down of the reaction products and of their cascade of recoils is calculated (treating discrete energy loss in a collision correctly). The occurrence of reactions between the slowing-down particles and ambient ions is also calculated. The products of these reactions are in turn followed, through as many iterations as necessary. Illustrations are given.
Magnetoplasma equilibria with geometry of double-inverse-pinch
Authors: Yeh Tyan
Published: March 2009

Equilibrium solutions, which represent configurations of a magnetoplasma with the geometry of double-inverse-pinch, are presented.
Fluctuation levels connected with reactive marginal instabilities
Authors: Minardi E.
Published: March 2009

The problem is considered of the analytical calculation of the fluctuation level of the collective electric field in the case of a collisionless non-dissipative plasma subject to a reactive marginal instability. The existence of this instability only depends on the negative sign of the real part of the dielectric constant e and is not related to the dispersive or dissipative effects described by the frequency dependence or the imaginary part of c. A typical example is given by the non- resonance two streams instability with a symmetric distribution function. In this situation the methods of the thermodynamics of Vlasov systems can be applied to calculate the fluctuation level connected with the instability, provided the Vlasov system is near enough to the marginally stable state and the effect of mode coupling can be neglected (at least for a certain time). In the linear limit, the unstable equilibrium is associated with a minimum of the entropy. When the instability develops new nonlinear terms appear in the dielectric coefficient c, related to the inhomogeneization of the system associated with the growing collective field. These nonlinear terms counterbalance the negative sign of the linear part of c, leading to a saturation of the instability. A neighbouring inhomogeneous equilibrium with long wavelength is then realized, which corresponds to a maximum of the entropy and is stable (under the assumed approximations). The corresponding electrostatic potential is proportional to u−uc, where u is the velocity corresponding to the maxima of the two-stream distribution and uc is the critical value of u for the onset of the instability. The results of the thermodynamic method for the neighbouring equilibria are compared with those obtained by solving the stationary Vlasov equation with conventional analytical methods or with computer calculations.
Collision integrals of electronically excited states and transport coefficients of thermal plasmas
Authors: Capitelli M. , Lamanna U.
Published: March 2009

Collision integrals of excited hydrogen atoms were calculated in the temperature range 10000–25 000 ˚K. These values were used for calculating the viscosity and έ the contribution of the heavy components λH to the translational thermal conductivity of a LTE hydrogen plasma. The results show a dependence of έ and λH on the calculated transport cross-sections.
Convection-region solutions for the re-connexion of anti-parallel magnetic fields of unequal magnitude in an incompressible plasma
Authors: Cowley S. W. H.
Published: March 2009

We consider the flow of a highly conducting incompressible fluid in the convection region surrounding an X-type neutral line. The Sonnerup solution is generalized to include cases in which the in-flowing anti-parallel magnetic fields are of unequal magnitude, and in which the plasmas of the two in-flow regions have unequal density. It is found that there exists no unique solution for a given set of in-flow plasma parameters, but that the out-flowing plasma may exit within a certain range of angles with respect to the in-flow direction, depending on in-flow parameters.
Re-normalized quasi-linear approximation of plasma turbulence: Part 2. Validity of short-time expansion and Markovian truncation of the propagator
Authors: Misguich J. H. , Balescu R.
Published: March 2009

In part 1 (Misguich & Balescu 1975) the Dupree description of plasma turbulence (i.e. the weak-coupling approximation of Weinstock) was derived and completed in the framework of the re-normalized quasi-linear approximation. The time behaviour of the frequency shift and of the Dupree damping was proved to be modified by time-ordering effects, usually neglected. In part 2 we show that a Markovian truncation must be applied to the basic average propagator Ū, to recover the short-time expansion of Birmingham & Bornatici. Such an expansion is shown to be generally non-convergent. The corresponding short-time results are invalid.
Kelvin-Helmholtz instability of anisotropic plasma in a magnetic field
Authors: Duhau S. , Gratton J.
Published: March 2009

The Kelvin-Helmholtz problem is analyzed by a set of general hydromagnetic equations, which includes ideal magnetohydrodynamic and Chew-Goldberger-Low models as particular cases. A formalism is given that facilitates comparison between results from different models. A sheared flow is one in which the velocity has no component in the y direction, and such that the x and z components of the velocity depend on the y co-ordinate. A sheared field is defined similarly. The differential equations for linear modes of oscillation of a sheared flow in a sheared magnetic field is obtained; and the energy of these modes is studied. As a particular case of oscillations of a sheared flow, the properties of the modes excited by arbitrary modulation of a tangential discontinuity are studied. The relationship between radiation of waves from such a discontinuity and instability of the system is brought out by considering the system energy. Domains of absolute stability are given; and the different hydromagnetic models are compared by examining the predicted domains. It is found that anisotropy plays an important role in the conditions of stability.
Ion beam ordinary electromagnetic mode instability
Authors: Gaffey John D.
Published: March 2009

The instability of the ordinary mode propagating perpendicular to the magnetic field is discussed for two ion beams counter-streaming along the magnetic field through a plasma of stationary electrons and ions. The instability criterion gives the necessary and sufficient condition for a purely growing mode. Although the instability threshold is high (u/Voi ≳ (2βoiNoi/Noi)-½ if the streaming velocity is 10% larger than the threshold value), large growth rates of the order of the ion cyclotron frequency result.
Self-consistent Vlasov equilibria for intense hollow relativistic electron beams
Authors: Davidson R. C. , Striffler C. D.
Published: March 2009

This paper discusses the procedure for constructing intense hollow relativistic electron beam equilibria within the framework of the steady-state (∂/∂t = 0) Vlasov–Maxwell equations. It is assumed that the electron beam propagates parallel to a uniform axial guide field Bext0 = B0 êz inside a grounded cylindrical conductor, and that the positive ions provide a partially neutralizing background with density n0i(r) = fn0e(r), where f = const. = fractional neutralization. The equilibrium properties are calculated for the specific choice of electron distribution function , where H, Pθ, and Pz are the energy, canonical angular momentum, and axialcanonical momentum, respectively, for an electron moving in the equilibrium fields, and , and P0 are constants. For this choice of distribution function, the mean axial velocity of the electron beam is equal to , and the beam density profile is hollow with inner and outer radii, R0 and R1, determined self-consistently from nonlinear boundary conditions that involve the equilibrium parameters Po, γb, γ0, etc., and the equilibrium self fields. Closed expressions for Ro and B1 are obtained for the case where the collisionless skin depth c/ωpe is large in comparison with the characteristic radius of the electron beam, and the beam density is sufficiently low that . The two cases, Po>0 and Po<0, are considered.
Energy transfer equation and universal spectrum of ion–acoustic wave turbulence
Authors: Tajima Toshiki , Ichimaru Setsuo , Nakano Tohru
Published: March 2009

The energy transfer equation in wavenumber space of ion–acoustic wave turbulence is obtained through investigation of the effects of turbulent fluctuations on the propagator of a test wave in the plasma. Those turbulent fluctuations whose wavelengths are shorter than that of the test wave give rise to collisional effects, while those with longer wavelengths act to deform continuously the shape of the test wave, thereby producing a diffusive flow of the turbulence energy in k space. Dimensional analysis, coupled with the Kolmogorov hypothesis, is then carried out on the resulting equation; a universal spectrum proportional to in the large k subdivision and to k−4 in the small k subdivision of the inertial domain is thus obtained.
Parametric excitation of Alfvén and acoustic waves
Authors: Hung Nguyen The
Published: March 2009

The nonlinear interaction between two Alfvén waves and a sound wave is studied, using the normal-mode approach. This leads, in a simple way to a set of coupled equations, and consequently to a dispersion relation for the waves under consideration. It is shown that a large-amplitude Alfvén wave can give rise to two distinct types of parametric instabilities, namely the oscillating and the purely growing waves. In each case, the expressions for the threshold pump intensity, the frequency shift and the growth rate of the excited waves are obtained. In particular, the results for a propagating pump under perfect frequency matching conditions are compared with those of Sagdeev & Galeev.
Criteria for three-wave instabilities in a cold collisionless plasma
Authors: Hruška A.
Published: March 2009

A new systematic method of analysis of three-wave interactions is proposed, and applied to a description of interactions of waves (0, 1 and 2) in a homogeneous electron plasma, in which Landau damping is insignificant. Transverse, linearly polarized wave 0, which may represent an external (‘ pump’ ) wave, is assumed to be in resonance with longitudinal and transverse waves 1 and 2 already existing in a weakly-turbulent plasma. The rate (d W/ dt)j, at which energy is transferred from wave j to the others, is calculated, assuming that directions of propagation of resonating waves are restricted by conditions of three-wave resonance only. Conditions of the form (dW/dt)j = 0 constitute threshold criteria for amplification of wave j to occur. There is a brief discussion of processes during which the energy of one of the resonating waves remains constant, although energy is transferred between the other two waves. The relation between energy absorbed by the plasma and energy transferred between waves is evaluated.
Radiation from charged particles in weakly inhomogeneous magnetic fields
Authors: Cook David M.
Published: March 2009

The spectral distribution of radiation emitted by a charged particle moving nonrelativistically in a prescribed electromagnetic field, consisting of a strong uniform magnetic induction on which is superimposed a weak inhomogeneity, is determined. The calculation is confined to trajectories characterized by small Larmor radii, and to the azimuthal average of the full angular distribution of the radiation, the azimuthal angle being measured in a co-ordinate system for which the uniform component of the field defines the polar axis. If the particle gyrates for a time long compared to the gyro-period, the spectrum separates into several independent lines. Quantitative expressions for the distribution of energy within each line are presented, and then evaluated for selected inhomogeneities. Qualitatively, it is found that inhomogeneities (i) may distort the distribution of energy within the spectral line at the gyro-frequency by broadening, displacing, destroying the symmetry of, and/or splitting that line, and (ii) may also generate spectral lines at aipproximate harmonics of the gyro-frequency. These harmonics are second order in the inhomogeneity, are of successively higher order in the Larmor radius, involve successively higher-order spatial derivatives of the inhomogeneities, may occur at frequencies whose ratios are not precisely ratios of integers, and may be split into two or more closely spaced components.
Coffision integral between particles of disparate mass
Authors: Surdo C. Lo
Published: March 2009

Two alternative approaches to expanding the binary collision integral for particles of very different mass in powers of their small mass ratio m/M are examined in detail. One of them in particular is found to be suitable for a subsequent expansion of the above quantity in series of spherical harmonics. This reduces to a simple algebra the labour of determining the angular-moment form of the Boltzmann equation for Lorentzian mixtures.
On the equations for non-linear wave solutions of the Vlasov and Poisson equations
Authors: Gribben R. J.
Published: March 2009

Butler & Gribben (1968) showed how to generalize non-linear, uniform, wave type solutions of the Vlasov–Poisson system of equations to allow for slow variations in the properties of the plasma. Here one equation of the derived set (that obtained by ensuring that the appropriate solutions of the Poisson equation are non-secular) is rearranged (i) so as to bring out the physical importance of those particles, trapped and untrapped, travelling near the wave speed, and (ii) so as to yield a form particularly suited to the case when the electric field is small.
Electrostatic shielding of a test charge in a non-neutral plasma
Authors: Davidson R. C.
Published: March 2009

The electrostatic shielding of a test electron embedded in a magnetically confined pure electron gas column is investigated. For rigid-rotor equilibria with nearly uniform density in the column interior, it is shown that the shielding length is the local electron Debye length for the case that the test electron is at rest relative to the mean motion of the column.
Kinetic equations for plasmas subjected to a strong time-dependent external field: Part 4. Dynamics of stochastic correlations
Authors: Balescu R. , Misguich J. H.
Published: March 2009

In close analogy with part 1, the dynamics of stochastic correlations is used to reformulate the preceding treatment of turbulent equations. The result is an exact and closed equation for an average function, involving only asymptotic stochastic correlations, and no initial fluctuation. This stochastic kinetic equation is valid for all initial conditions, and the corresponding function is a significant particular projection on an independent subspace R(t).
Confluence of three shock waves for transverse shocks and shocks in an aligned MHD field
Authors: Bestman A. R.
Published: March 2009

The paper studies the confluence of three shock waves meeting at a point, in an ideally conducting perfect gas, for transverse shocks and shocks in an aligned MHD field. The method used involves the hodograph mapping technique. A presentation of the shock polars in the total pressureP*, flow deflexion δ(δ,P*/P*0) plane is thus given. The algebraic complexity of the problem prohibits discussion of an alternative mathematical approach.
A new and extended concept for reflexion and transmission coefficients for waves propagating in isotropic and anisotropic plasma
Authors: Heading J.
Published: March 2009

It is common practice to define reflexion and transmission coefficients for waves propagating through isotropic and anisotropic inhomogeneous plasma in terms of coefficients of waves existing within homogeneous regions of the plasma below and above the inhomogeneity. This concept is shown to be very restricted, and corresponding coefficients are defined for solutions existing within the inhomogeneous regions of the plasma. The extended concept is shown to satisfy conditions usually associated with the more common definitions, notably energy conservation and reciprocity. The theory is developed using integral equations and matrix theory, and special precautions are taken so that the results extend from the inhomogeneous plasma into free-space domains.
Nonlinear waves in a hot plasma by Lorentz transformation
Authors: Clemmow P. C.
Published: March 2009

Wave propagation in a hot, collisionless electron plasma (without ambient magnetic field) is analyzed by coisidering the frame of reference in which the field has no space dependence. It is shown that the governing equations are of the same form as those for a cold plasma, and are likely to have corresponding exact (nonlinear, relativistic) solutions. In particular, it is shown that there exists a solution representing a purely transverse, circularly polarized, monochromatic wave. Three approximate forms of the dispersion relation of this wave are obtained explicitly, the first being valid when the temperature correction is small, the second applying to weak waves, and the third to strong waves. Purely longitudinal waves are also discussed.
Variational calculations for resonance oscillationsof inhomogeneous plasmas
Authors: Peng Y-K.M. , Crawford F. W.
Published: March 2009

In this paper, the electrostatic resonance properties of an inhomogeneous plasma column are treated by the Rayleigh–Ritz method. In contrast to Parker, Nickel &
Gould (1964), who carried out an exact computation, we use a description of the RF equation of motion and pressure term that allows us to express the system of equations in Euler–Lagrange form. The Rayleigh–Ritz procedure is then applied to the corresponding Lagrangian, to obtain approximate resonance frequences and eigenfunctions. An appropriate set of trial co-ordinate functions is defined, which leads to frequency and eigenfunction estimates in excellent agreement with the work of Parker et al. (1964).
Parametric instabifity of transverse and Langmuir waves in a plasma
Authors: Lee Kai Fong
Published: March 2009

The parametric excitation of transverse and Langmuir waves by an externally-driven electromagnetic field of frequency (ω0 > 2ωp) in a warm and collisional plasma is studied, using the fluid equations. By an application of the multiple- time-scale perturbation method, the threshold intensity and the growth rate above threshold are obtained. The results are compared with those of Goldman (1969) and Prasad (1968), both of whom worked with a kinetic model.

The theory of parametric instabilities in plasmas has been the subject of numerous investigations in recent years. Broadly speaking, the instabilities can be grouped into two categories: those for which the excited waves are purely electrostatic (see e.g. DuBois & Goldman 1965, 1967; Silin 1965; Lee & Su 1966; Jackson 1967; Nishikawa 1968; Kaw & Dawson 1969; Tzoar 1969; Sanmartin 1970; McBride 1970; Perkins & Flick 1971; Fejer & Leer 1972a, b; Bezzerides & Weinstock 1972; DuBois & Goldman 1972), and those for which one of the excited waves is electromagnetic (see e.g. Goldman & Dubois 1965; Montgomery & Alexeff 1966; Chen & Lewak 1970; Bodner & Eddleman 1972; Fejer & Leer 1972b; Lee & Kaw 1972; Forslund et al. 1972).
Thermalization of a beam by beam-plasma interaction
Authors: Van Wakeren J. H. A. , Hopman H. J.
Published: March 2009

We present measurements proving the successive excitation of two distinct instabilities by electron beam–plasma interaction along a plasma column. The first, appearing near the gun, grows in space, until the beam is trapped in the wave electric field, and decays. In this process the time-averaged distribution function changes, from a δ-type distribution function, into a plateau. This new beam–plasma distribution is also unstable; and another instability grows until the beam is again trapped. Numerical calculations show that the second instability can be explained, assuming that the beam distribution thermalizes when propagating from the first instability to the second.
A model laser-compression experiment
Authors: Crow J. E. , Spalding I. J. , Wesson J. A.
Published: March 2009

The compression of plasmas by laser beams to produce a significant thermonuclear energy requires very sophisticated experimental techniques and equipment, costing millions of dollars. We review here comparatively simple techniques which should permit a time-resolved demonstration of an isentropic density compression, using low-powered lasers of a type commonly encountered in university research laboratories, and diagnostic equipment of modest cost. Althoughthermonuclear burn cannot be investigatedwith such simple apparatus, many aspects of flux-limited thermal transport, light absorption, and end-effects (i.e. intensity assymmetries) could be conveniently and quantitatively investigated.
Relativistic effects on strong Langmuir turbulence
Authors: Freund H. P. , Liu C. S. , Kulsrud R. M.
Published: March 2009

The relativistic effects on strong Langmuir turbulence which arise from both relativistic plasma temperatures and high-amplitude oscillations (i.e. the oscillatory electron velocity in the wave approaches the speed of light) are considered. When relativistic effects arise primarily from high plasma temperature, a kinetic formalism is employed and a nonlinear Schrüdinger equation is derived from expansion of the Vlasov-Maxwell equations. The analysis is appropriate to either hydrogen or electron-positron plasmas, and the relativistic effect is found to provide a new type of nonlinear phase-amplitude coupling in three dimensions. A fluid treatment is used when the relativistic effects of high wave amplitudes predominate. Here, ion dynamics are ignored and the relativistic electron mass correction results in the same type of three-dimensional phase-amplitude coupling as in the kinetic analysis. A Lagrangian formalism for each limiting case is described which leads to a virial theorem from which thresholds for collapse of arbitrary wave packets can be derived.
Stability of Vlasov equilibria. Part 3. Models
Authors: Seyler Charles E. , Lewis H. Ralph
Published: March 2009

In this third of a series of papers on the stability of Vlasov equilibria, the dispersion functional technique developed in part 1 is applied to the multi-species Vlasov plasma and to the Vlasov-fluid model. An alternative form of the dispersion functional is derived for the Vlasov-fluid model in which magnetohydrodynamic and kinetic aspects of the problem are separated explicitly. A necessary and sufficient condition is derived for stability with the Vlasov-fluid model. Stability of the multi-species Vlasov plasma is discussed and a necessary and sufficient condition for stability near a marginal point is derived. Explicit formulae for quantities occurring in the dispersion functional are given in cylindrical co-ordinates for the Vlasov-fluid model when there is one nonignorable co-ordinate in the equilibrium. The dispersion functional for a multi-species Vlasov plasma is shown to be related to the ponderomotive Hamiltonian.
A study of the mass ratio dependence of the mixed species collision integral for isotropic velocity distribution functions
Authors: Garrett A. J. M.
Published: March 2009

This paper is concerned with the Boltzmann collision integral for the one-particle distribution function of a test species of particle undergoing elastic collisions with particles of a second species which is in thermal equilibrium. This expression is studied as a function of the ratio of the masses of the test and host particles for the case when the test particle distribution function is isotropic in velocity space. The analysis can also be considered as referring to the zeroth-order spherical harmonic in velocity space of a general velocity distribution function. The resulting collision term, due originally to Davydov, is of Fokker–Planck form and effectively describes a diffusion in energy. The method of derivation employed here is more systematic than hitherto, and is used to calculate the first correction to the Davydov term. Differences between classical and quantum cross-sections are considered; the correction to the Davydov term is checked by means of a comparison with the exact solution of the associated eigenvalue problem for the special case of Maxwell interactions treated classically.
Analysis of a generalized nonlinear diffusion equation in fusion plasma physics
Authors: Anderson D. , Lisak M.
Published: March 2009

Using similarity methods, an investigation is made of a generalized nonlinear diffusion equation arising in plasma physics in connexion with several recently proposed models for turbulent plasma energy transport and particle diffusion.

In almost every field of physics, diffusion or transport equations of the form Ψt = Δ. (DΔΨ) play an important role. The theory of linear diffusion equations, where the diffusion constant D is independent of Ψ, has been developed to a high degree of sophistication (e.g. Carsiaw & Jaeger 1959).
Evolution of current sheets following the onset of enhanced resistivity
Authors: Forbes T. G. , Priest E. R. , Hood A. W.
Published: March 2009

An important aspect of pre-flare current sheets in the solar atmosphere is the sudden enhancement of the effective electrical resistivity in the sheet due to the onset of a plasma micro-instability. Numerical and analytical solutions to the isothermal MHD equations are here presented that describe the evolution of a current sheet subsequent to such an enhancement in the resistivity. The solutions show that, if the initial width of the current sheet is less than the acoustic-diffusion length obtained by dividing the resistivity by the sound speed, then isomagnetic shocks are formed. These shocks propagate outward from the the centre of the current sheet and are transformed into fast-mode magneto-acoustic waves when they reach the edges of the current sheet. The fast-mode waves thus formed continue to propagate outward beyond the confines of the current sheet. In contrast to a previous study by Cheng, the present solutions demonstrate that flow speeds several times greater than the local fast-mode wave speed can be produced if the plasma beta parameter and the initial sheet width are sufficiently small. The results may be relevant to the triggering of a solar flare, as in the emerging flux model of flares.
Stability of strong electromagnetic waves in overdense plasmas
Authors: Romeiras F. J.
Published: March 2009

We consider the stability against small perturbations of a class of exact wave solutions of the equations that describe an unmagnetized relativistic cold electron plasma. The main feature of these nonlinear waves is a transverse circularly polarized electric field with periodic amplitude modulation in the longitudinal direction. Floquet's theory of linear differential equations with periodic coefficients is used to solve the perturbation equations and obtain the instability growth rates.
Low-frequency nonlinear resonances and averaged potential in bounded parallel fields plasma
Authors: Nikolov N. A. , Malinov P. N.
Published: March 2009

We investigate nonlinear resonances and the averaged potential in a bounded non-isothermal plasma, placed in a constant magnetic field and a parallel external a.c. electric field. The treatment assumes one component MHD. It is assumed that a standing Alfvén wave exists before the electric field is switched on.
Stationary surface waves in magnetohydrodynamics
Authors: Shivamoggi Bhimsen K.
Published: March 2009

A uniformly-streaming, semi-infinite, incompressible, infinitely-conducting plasma subjected to a gravitational field is confined by a vacuum magnetic field aligned with the stream. The system is disturbed by introducing a source of external steady pressure acting on the interface between the plasma and the magnetic field. The resulting wave motion at the interface is studied by using the Fourier-transform method to determine the solution for the displacement of the interface.
New stationary vortex solutions of the Hasegawa–Mima equation
Authors: Nycander J.
Published: March 2009

Two different families of explicit stationary solutions of the Hasegawa–Mima equation are obtained. In the first case the well-known modon (dipole vortex) is used as the zeroth-order solution, and new solutions that are close to but distinctly different from it are found by perturbation analysis. In the second case the dispersive term of the equation is treated as a small parameter, and a radially symmetric solution (a monopole vortex) is used as the zeroth-order approximation. Both families of solutions are found to be infinite and to contain an arbitrary function. A recent general proof of the existence of infinitely many stationary solutions containing an arbitrary function is examined and found to be invalid.