bluuebunny/crossref_metadata_2025 huggingface dataset:
Nonlinear electromagnetic waves in an inhomogeneous plasma
Authors: Cicconi Gabriele
Published: March 2009

A stationary theoretical model giving an asymptotic description of the propagation of nonlinear electromagnetic waves in an inhomogeneous plasma is presented. The plasma, considered within the hydrodynamic approximation and assumed to be cold, collisionless, unmagnetized and electroneutral, is described in terms of a nonlinear dielectric function giving the effect of the Miller ponderomotive force. In an infinitely extended slab geometry, a variable transverse density gradient, assumed to be parabolic, is considered in the case when a monochromatic electromagnetic wave is incident upon the slab at an arbitrary angle. The transverse structure of the wave electric field is determined along with the perturbed plasma density profile. The nonlinear wave equation with slowly varying coefficients derived using this model is solved in first and second approximations using an asymptotic multiple-space-scale method due to Bogolyoubov and Mitropolskii. The critical conditions for resonant electrostatic absorption and mode conversion are derived and discussed within these approximations, and some reference numerical calculations are performed.
Parallel solitary Alfvén waves in warm multi-species beam-plasma systems. Part 1
Authors: Verheest Frank , Buti B.
Published: March 2009

A self-consistent reductive perturbation analysis for parallel-propagating magnetohydrodynamic waves in warm multi-species plasmas, in which different constituents can have differing equilibrium drifts, leads to a derivative nonlinear Schrödinger equation for the wave magnetic field. Soliton solutions are discussed, including applications to plasmas with two ion species. Such solitons are larger (in amplitude) and wider than in the non-streaming and/or cold-plasma case, other parameters being equal.
Effects on electrostatic fields excited by radio-frequency waves in a bounded plasma due to the ponderomotive force
Authors: Gutiérrez-Tapia C. R.
Published: March 2009

A one-dimensional model explaining the mechanism of excitation of electrostatic fields by linearly polarized radio-frequency waves in a plasma layer is presented. It is shown that the ponderomotive and driving forces influence this process strongly; however, these forces act at different times when a wave front passes through the plasma. We consider a semi-infinite plasma, and a plasma layer with and without current. It is observed that near to the plasma boundaries, where the electric field is large, there arise amplitude field oscillations, which are slowly exponentially damped in space. It is shown that the physical processes arising near the boundary x = L are similar to those at the boundary x = 0. It is seen that the current in the plasma block excitation at the boundary x = L.
Resonant structures within incompressible ideal MHD
Authors: Zorzan C. , Cally P. S.
Published: March 2009

The resonant characteristics of an incompressible ideal MHD fluid are highly structured. To help expose this structure, an equivalent electrical analogue of the MHD system is developed. The model, in the form of a transmission line, makes it possible to identify a number of new and important concepts, one of which is the effective impedance. This in turn enables entire regions of MHD fluid to be replaced with equivalent impedances. When fully exploited, the model also provides a more consistent interpretation of the spectrum of ideal MHD. The discrete Alfvén modes are found to be highly degenerate, while the transition to a discontinuous profile is accompanied by a redistribution of an uncountably infinite number of ‘poles’ from the continuous spectrum and onto the Alfvén modes. In addition, the electrical analogue shows that within a continuously structured fluid the characteristic behaviour is not necessarily dominated by the ‘surface mode’ alone. This view is also supported by the results of a numerical simulation of the linear MHD equations. Depending on the initial conditions, the collective behaviour can have any frequency within the range spanned by the transition zone. The energy itself is monitored using a new pair of energy and flux expressions derived from a variational (Lagrangian) description of the MHD system. Again the electrical model is used to provide a physical interpretation of the individual terms within these expressions. In particular, it allows a partition of the total energy into separate kinetic- and potential-energy terms.
Kinetic theory for MHD-wave coupling coefficients
Authors: Elvsén Ralf
Published: March 2009

The coupling coefficients for resonant three-wave interaction of magnetosonic and Alfvén waves, derived by means of kinetic theory, are presented. The calculations allow for anisotropic background temperatures. The results are compared with previous ones from fluid theory.
Phase-space description of plasma waves. Part 2. Nonlinear theory
Authors: Rönnmark K. , Biro T.
Published: March 2009

A representation of the physical fields as functions on (k, ω, r, t) phase space can be based on Gaussian windows and Fourier transforms. Within this representation, we obtain a very general formula for the second-order nonlinear current J(k, ω, r, t) in terms of the vector potential A(k, ω, r, t). This formula is a convenient starting point for studies of coherent as well as turbulent nonlinear processes. We derive kinetic equations for weakly inhomogeneous and turbulent plasmas, including the effects of inhomogeneous turbulence, wave convection and refraction.
Oblique and skew ionizing shock waves with non-unique structure
Authors: Leonard B. P.
Published: March 2009

Within the range in which both electric field parameters are free, ionizing shock waves have a unique structure for each pair of chosen parameter values. In a relatively small shock speed range, however, conditions may exist for which at least one intermediate equilibrium region is imbedded within the overall transition. Non-unique structures consisting of different transitions between the same upstream and downstream equilibrium states may then occur. Steady trans-Alfvénic magnetohydrodynamic transitions (which are unacceptable in the pre-ionized case) may occur as part of an ionizing shock structure, because neigh bouring steady solutions always exist. This is due to the existence of skew ionizing shocks which are able to absorb rotational disturbances.
Plasma losses through an adiabatic cusp
Authors: Kaye A. S.
Published: March 2009

Previous calculations of β = 1 cusp losses are extended to the case where there exists a third ‘adiabatic’ invariant of the particle motion, related to the magnetic moment, and additional to the particle energy and angular momentum. Simple analytic results are obtained for the particle and energy loss rate from a Maxwellian plasma in both plane and axisymmetric geometry, electric fields being assumed zero everywhere. The results are valid for a plasma radius large relative to the ion gyro-radius, in which case the adiabaticity in the sense used reduces the loss rate by a factor ⅔λ⅔ to give an overall scaling as λ–⅔ with external mirror ratio λ. The absolute value is about a factor two less than the previously accepted result (for λ = 1 only) for an axisymmetric cusp. cusp. The enhanced scaling with A arises from the absence of a certain class of particles in the sheath, which must be everywhere adiabatic; its applicability to a simple theta pinch is queried, however. The end loss rate of angular momentum is also obtained, and is non-zero at a point cusp. This is shown to lead to rapid rotational instability in a collisionless theta pinch.
Mass motion and heating in a magnetic neutral point system
Authors: Baum P. J. , Bratenahl A.
Published: March 2009

We present optical spectroscopic and magnetic probe observations of a laboratory discharge device, in which magnetic field line reconnexion occurs at an x−type neutral point. Time-resolved spectral-line profiles of the ionized argon line A II λ4348 are presented. These allow the determination of Doppler shifts and broadenings near the neutral point. Plasma heating occurs at the neutral point and downstream from it. Plasma is ejected from the downstream sides of the neutral point region at the local Alfvén speed at all times. This is equal to about one-tenth the upstream Alfvén speed at the one time it is known. The downstream magnetic Mach number or ‘local reconnexion rate’ is found to be nearly independent of the plasma conductivity and time. The rate of transfer of magnetic flux from the upstream to downstream regions is strongly dependent on conductivity and time.
Transport properties of the three-dimensional guiding-centre plasma
Authors: Vahala George
Published: March 2009

Equilibrium and non-equilibrium properties of the three-dimensional guiding-centre plasma (in which the particles move with the guiding-centre drift across constant magnetic field lines, and according to Newton's laws along the field lines) are investigated. In equilibrium, the transverse spatial diffusion and conductivity coefficients are calculated, and are shown to be related via a generalized Einstein relation. The diffusion coefficient consists of a Bohm-like 1/B contribution which tends to zero as the plasma volume tends to infinity, as well as a classical 1/B2 contribution, which is independent of the size of the system. The Gibbs ensemble is constructed, and it is seen that thermal equilibrium results for the pair correlation, fluctuation spectra etc. are exactly the same as for the three-dimensional unmagnetized plasma. In the non-equilibrium case the appropriate Liouville equation and BBGKY hierarchy are considered. It is shown that to first order there is no tendency for the system (assumed spatially uniform) to relax towards thermal equilibrium.
A theoretical investigation of banded chorus
Authors: Nunn David
Published: March 2009

This paper is a computational study of nonlinear resonant particle trajectories in wave fields consisting of an array of narrow-band waves of closely spaced frequencies and wavenumbers. It looks at two analogous systems, cyclotron resonance with a whistler wavefield and Landau resonance with an electrostatic wave field. It is found that the wave array is able to trap particles in much the same way as a single mode. Inhomogeneity plays a vital role by causing the energy of trapped particles to change.

The nonlinear resonant particle current is such as to preserve the modal structure of the wave field, and it does not change the frequency of an individual mode. Power distribution amongst the modes is far from even. Most of the energy goes into the mode at one end of the array, depending on the direction of the inhomogeneity. Also, nonlinear resonant particle excitation of a broad band
signal was found to cause spectral structuring to develop automatically.

The theory was applied to one of Coroniti's FTRS analyses of banded chorus elements. The observed spectral behaviour closely accorded with the computational results. The numbers involved fitted the theory very well, and strongly suggested that nonlinear cyclotron resonant particle excitation is the mechanism for banded chorus.
Spatial evolution of finite-amplitude plasma waves in collisionless plasmas
Authors: Tsai Shih-Tung
Published: March 2009

A numerical simulation concerning the spatial evolution of electron plasma waves and electron distributions in collisionless plasmas is performed. Only those particles in and around the resonant region are followed numerically, while the bulk plasma is treated analytically. Our results are in good agreement with existing theoretical results as well as experimental observations. The method introduced here is valid for waves with arbitrary amplitude. It does not depend on either a large-amplitude asymptotic expansion or a small-amplitude perturbation scheme.
‘Inner’ region solution for the resistive tearing instability including ‘parallel’ viscosity and compressibility
Authors: Marinoff G. M.
Published: March 2009

Until now, a theoretical derivation to obtain an expression for the logarithmic derivative Δ(Q) of the ‘inner’ or resistivity region has not been attempted for the resistive tearing instability where ‘parallel’ viscosity has been included, although similar derivations have been done using ‘perpendicular’ viscosity type terms. Such a derivation is presented in this paper, along with a numerical procedure for evaluating Δ(Q). Numerical results have been obtained for a hard-core pinch configuration. The resultant graphs show branch-point behaviour that suggests inter alia stabilization due to ‘parallel’ viscosity at high temperature.
Lagrangian methods in plasma dynamics. Part 2. Construction of Lagrangians for plasmas
Authors: Dougherty J. P.
Published: March 2009

Most of this paper is concerned with the construction of suitable Lagrangian functions for the dynamics of a cold plasma, in such a way as to retain the relativistically covariant formalism. In one method, this is achieved by the introduction of a set of three variables which label the world lines of the particles. A second method results in a Clebsch type of representation. Sturrock's relativistic Lagrangian and Low's hot plasma Lagrangian are also briefly discussed in the context of the present work. The behaviour of the canonical stress tensor is considered. The applicability of many of the general results of part 1 is ensured by establishing the existence of the Lagrangian function.
Kinetic equations for plasmas subjected to a strong time-dependent external field. Part 1. General theory
Authors: Balescu R. , Misguich J. H.
Published: March 2009

It is shown that the concept of subdynamics introduced by Prigogine, George & Henin, and extended by Balescu & Wallenborn, can be generalized nontrivially to systems submitted to time-dependent external fields. The distribution vector of the system is split into two components by means of a time- dependent projection operator. Each of these obeys an independent equation of evolution. The description of the evolution of one of these components (the superkinetic component) can be reduced to a kinetic equation for a one-particle distribution function. It is shown that, when the external field vanishes for all timest≤t0, and if the system has reached a (field-free) equilibrium (or a ‘kinetic state’) at timet0, then fort≥t0the kinetic equation derived here provides an exact and complete description of the evolution. A general expression for the nonlinear response of the system to the external field is derived.
Thermal relaxation of a two-dimensional plasma in a d.c. magnetic field. Part 1. Theory
Authors: Hsu Jang-Yu , Montgomery David , Joyce Glenn
Published: March 2009

A theory is presented for the rate of thermal relaxation of a two-dimensional plasma in a strong uniform d.c. magnetic field. The Vahala—Montgomery kinetic description is completed by providing a cut-off time for the time of interaction of two particles which contribute to the collision term. The kinetic equation preclicts that thermal relaxation occurs as a function of the dimensionless time (ωpt) (ωp/Ω) (n0λ2D)−½, where ωp, is the plasma frequency, Ω is the gyrofrequency, and n0 λ2D is the number of particles per Debye square. By contrast, in the absence of an external magnetic field, a two-dimensional plasma relaxes as a function of (ωpt) (n0λ2D)−1.
The magnetoplasma dispersion function: some mathematical properties
Authors: Schmitt J. P. M.
Published: March 2009

The magnetoplasma dispersion function is defined as

It is found in all the dispersion relations for wave propagation perpendicular to the magnetic field in hot plasmas. We review the properties of fω(z), and present several new expansions, which may be of interest in the study of properties of waves in plasmas, or may suggest computational methods for calculating fω(z).
Magnetohydrodynamic waves in a non-uniform current-carrying plasma column
Authors: Vaclavik J. , Weise E.
Published: March 2009

An effect of an axial current on the propagation of low-frequency axisymmetric magnetohydroclynamic waves in a radially non-uniform plasma column was investigated theoretically and experimentally. It was found that the axial current and the density gradient cause a coupling between the torsional and compressional waves.
An experimental investigation of slow-mode shock waves
Authors: Craig A. D.
Published: March 2009

This paper presents an idealized, one-dimensional theoretical model of a novel method of launching a slow-mode hydromagnetic shock wave. The reduction of the transverse magnetic field component, at the boundary of a semi-infinite plasma containing a uniform oblique magnetic field, results in the propagation of a fast-mode expansion wave followed by a slow-mode shock. An experiment designed to test this launching method is described. An initial hydrogen plasma containing axial and azimuthal magnetic field components is set up in a large annular apparatus. The azimuthal field is then reversed at one end of the device, by a fast-rising radial discharge. Diagnosis of the resulting flow, with small magnetic and electric probes, shows the propagation of the fast expansion wave and the slow shock; but there also follows a third wave, having the properties of a ‚piston’. When the theory is extended to include a moving boundary (i.e. ‚piston’), good quantitative agreement is obtained with the experimental results. The annular geometry of the experiment leads to centrifugal effects not considered in the one-dimensional theory; but these are not sufficient to disrupt seriously the main flow pattern. Detailed measurements of the shock indicate a dispersive structure.
An analytical study of the oblique echo model for the topside plasma resonance
Authors: Parkes E. J.
Published: March 2009

The oblique echo model for the resonance near the local plasma frequency fN observed by topside sounders involves the propagation of slow waves away from the sounder, which later return as echoes after reflexion due to an electron density gradient. The model is investigated using the WKB technique introduced by Fejer & Yu. The resulting set of saddle-point equations is solved by a method which can, unlike previous work, be applied to both the ‘strong’ resonance (for whichfN > fH wherefH is the electron gyrofrequency) and to the ‘weak’ (fN < fH) resonance. Throughout the calculations, the validity of the approximations made is checked. It is found that the weak resonance solution is not valid for typical topside parameters. For the strong resonance, the electric field of a small pulsed dipole is calculated. Expressions are found for the frequency of the two echoes that are received by the sounder and the frequency of the beating between them. Although these are only strictly valid for times longer than typical observation times, they yield results that agree well with the corresponding results from ray trajectory computations.
Filament model for a stationary field electron ring accelerator: the generalized Bernstein—Green—Kruskal problem
Authors: Ehrman J. B.
Published: March 2009

The longitudinal behaviour of the electron ion ring in a stationary electron ring accelerator (ERA) is studied by means of a filament model which neglects the radial thickness of the ring. There are two widely different time scales (short or STS of the order of a bounce time in the ring, and long or LTS) that characterize the system. The Vlasov equations for a system which is stationary on the STS can be solved in the ion-pickup region by an approximation in which each species of particle essentially sees only a potential well formed by the other species. This gives a generalization of the classical Bernstein–Greene–Kruskal (BGK) problem, in which both species move in the same potential. The conditions under which this generalized BGK problem is well defined are given, and broad classes of quasi-equilibria (i.e. equilibria on the STS) are obtained. The time dependence on the LTS of some of these quasi-equilibria is then obtained by invoking charge conservation, momentum conservation and the adtained invariance of longitudinal action integrals. The stability of these quasi-equilibria (i.e. their behaviour under time-dependent perturbations on the STS) is deferred to a subsequent paper.
Wave propagation in a moving plasma. Part 2. Wave propagation along, and plasma motion normal to, the magnetic field
Authors: Srivastava D. N.
Published: March 2009

This paper analyses the dispersion relation for a collisionless moving electron plasma, when the direction of motion is normal to the magnetic field and that of the wave propagation along the magnetic field. It is shown that, in strong magnetic fields, the one continuous allowed band of the left-handed wave (of the stationary plasma) splits into two, and the right-handed wave shows a second resonance besides the cyclotron resonance. In weak magnetic fields, the lefthanded wave develops a backward wave band, which shows resonance at its low frequency edge, and the right-handed wave also develops an extra band of propagation. The effect of the motion of the plasma, on waves of frequency much lower than the plasma frequency, is identical to a doppler shift, but, on those of frequency much higher than that, is negligible.
Re-normalized quasi-linear approximation of plasma turbulence: Part 3. Collective binary correlations and turbulent de-trapping.
Authors: Misguich J. H. , Balescu R.
Published: March 2009

Collective binary correlations are deduced from the re-normalized quasi-linear (RQL) equation describing the evolution of the singlet average function. For a constant growth rate, a crude calculation suggests that generalized Dupree damping could seriously reduce the trapping of resonant particles.
Self-modulation and stability of finite-amplitude ordinary and extraordinary waves in a cold magnetoplasma
Authors: Furutani Y.
Published: March 2009

The self-modulation parameter of the ordinary and the extraordinary waves propagating in a cold magnetoplasma is given explicitly, by the familiar reductive perturbation method, in the framework of the hydrodynamic approach. Both quantitative and qualitative order-of-magnitude analysis of this parameter are carried out for the lower-hybrid and the upper-hybrid branches of the extraordinary wave. The usefulness of the stability criterion, which is linear with respect to an envelope of these linear waves, is also discussed.
Coherent ion acceleration at a density gradient
Authors: Hsieh Shiew L. , Bloomberg Howard W. , Gary S. Peter
Published: March 2009

The paper describes a model, in which ions are accelerated against the direction of the electric field at a density gradient. A one-dimensional, inhomogeneous, steady-state is constructed, in which cold electrons stream relative to cold ions. The wavenumber and amplitude of the fluctuating potential are calculated, then used to compute the trajectories of representative ions trapped in the potential troughs. Ion acceleration to energies an order of magnitude greater than the applied potential is demonstrated.
Application of the theory of mixing systems to nonlinear Landau damping
Authors: Krlín L
Published: March 2009

Using a simple model of particles in a discrete spectrum of waves, we investigate the influence of stochastic instability of particle motion on the mechanism of nonlinear Landau damping. We show that, as long as particle trajectories in the spectrum are stochastically unstable (at the beat resonances under consideration), diffusion of particles takes place. We discuss the influence of this effect on the normal nonlinear Landau mechanism, and consider briefly the possibility of consequent heating in beam–plasma experiments.
Validity of the weak-coupling approximation in strong plasma turbulence
Authors: Rolland P.
Published: March 2009

The weak-coupling approximation takes stochastic perturbations of orbits into account, but neglects a part of mode coupling. This approximation, which is non-trivial, is discussed here. Its domain of validity appears to be T E ≪Tt provided the turbulence is strong enough so that γNL- γL ñ γL. If γL ≪ a stronger condition is required. It is shown that the growth rate γNL can be calculated either from the nonlinear dispersion equation εNL =0, or from the energy equation, provided thepropagator conserves particles. Dupree's propagator U does not do this; but it gives a correct approximation of γNL, provided Δv≫vth.
Effect of ionic temperature on propagation of ion-acoustic solitary waves in a collisionless plasma of warm-ion fluid and non-isothermal electrons
Authors: Tagare S. G.
Published: March 2009

Using a perturbation technique, we derive Modified Korteweg—de Vries (MKdV) equations for a mixture of warm-ion fluid (γ i = 3) and hot and non-isothermal electrons (γ e> 1), (i) when deviations from isothermality are finite, and (ii) when deviations from isothermality are small. We obtain stationary solutions for these equations, and compare them with the corresponding solutions for a mixture of warm-ion fluid (γ i = 3) and hot, isothermal electrons (γ i = 1).
Parametric backscattering and absorptive instabilities in homogeneous unmagnetized plasmas
Authors: Bornatici Marino
Published: March 2009

The paper considers the two scattering instabilities photon decays into photon plus plasmon (t → t' + l) and photon decays into photon plus phonon (t → t' + s) and the two absorptive instabilities photon decays into plasmon plus plasmon (t → l + l' ) and photon decays into plasmon plus phonon (t → l + s). The corresponding growth rates and thresholds are determined for a homogeneous, unmagnetized plasma. The regimes of weak and moderately strong pump fields are examined, together with the possibility of purely-growing instabilities for the decays t → t' + s and t→ l + s.
The collisional drift mode in a partly-ionized plasma
Authors: Hudson Mary K. , Kennel Charles F.
Published: March 2009

The structure of the drift instability is examined in several density regimes. Let λ e be the total electron mean free path, kz the wave-vector component along the magnetic field, and ν ⊥ / ν ∥ the ratio of perpendicular ion diffusion to parallel electron streaming rates. At low densities (kz ν e > 1), the drift mode is isothermal, and should be treated kinetically. In the finite heat conduction regime

the drift instability threshold is reduced at low densities (v⊥/v‖<0·1) and increased at high densities (v⊥/v‖>0·1), as compared with the isothermal threshold. Finally, in the energy transfer limit (kzλe<(m/M)½), the drift instability behaves adiabatically in a fully-ionized plasma, and isothermally in a partly-ionized plasma, for an ion-neutral to Coulomb collision frequency ratio vin/vii>2(m/M)½ at Ti = Tc = Tn.
Derivation and properties of a Balescu–Lenard like equation for stationary plasma turbulence in the weak-coupling approximation
Authors: Pelletier Guy , Pomot Claude
Published: March 2009

In this paper, we derive a kinetic equation and discuss its validity for a stationary turbulent plasma. We use, for this purpose, the Dupree— Weinstock model in the weak-coupling approximation, and take into account ballistic streams. Frictional effects appear, in addition to the velocity diffusion. The diffusion causes a resonance broadening, the friction causes a frequency shift. Our model is a generalization of the dressed test particle model, and leads to a kinetic equation formally similar to Balescu— Lenard' s. A comparison between our model and the Dupree ‘clump’ theory is developed. Physical quantities are conserved, the H theorem is satisfied; but the asymptotic solution is not necessarily a Maxwellian distribution function.
Analysis of electromagnetic instabilities parallel to the magnetic field
Authors: Pilipp W. , Völk H. J.
Published: March 2009

Transverse waves and instabilities propagating along the magnetic field in a homogeneous plasma are discussed analytically and numerically for frequencies of the order of the ion cyclotron frequency and below. The free energy driving the instabilities is assumed to be provided by thermal anisotropies, with the parallel temperature exceeding the perpendicular temperature, a situation appropriate to the solar wind near the earth and to the downstream conditions in collisionless shocks propagating approximately parallel to the magnetic field. It is shown that in the case where the ion β is of order one the long wavelength Firehose instability is not stabilized by finite Larmor radius effects, but that for smaller wavelengths it goes over smoothly into the resonant proton mode, discussed by Kennel & Scarf (1968).
Transonic plasma flow past an obstacle
Authors: Stangeby P. C. , Allen J. E.
Published: March 2009

In many plasmas the ions are cold relative to the electrons but have a directed, subsonic velocity (the sonic velocity is (kTe/M)½). The behaviour of this flow around an obstacle is considered and solutions obtained for cylindrical geometry. The results are of direct interest in the interpretation of probe characteristics, especially when relative density measurements are involved, as the effects of the flow are typically of the same order of magnitude as the relative variations expected. Plasma flow past an obstacle may be of interest in other contexts (e.g. the case of dust particles in a gas discharge).
Energy absorption in the continuous spectrum of ideal MHD
Authors: Tataronis J. A.
Published: March 2009

The relationship between energy absorption and the continuous frequency spectrum of the linearized equations of ideal MHD is investigated. We limit ourselves to incompressible fluid perturbations for which the continuum stems from resonant surfaces where the oscillation frequency equals the local frequency of an Alfvén wave. Details of this absorption process are illustrated by obtaining the response of the diffuse sheet pinch to an external current source. Expressions are derived that give the rate at which energy is transferred to the plasma, and show the spatial distribution of the absorbed energy. The results indicate that the absorption is enhanced if the plasma profile has regions of large spatial gradients. This enhanced absorption is a consequence of the presence of surface waves.
Space-charge limits in unneutralized relativistic electron beams
Authors: Read M. E. , Nation J. A.
Published: March 2009

Limiting currents in annular unneutralized relativistic electron beams are calculated and compared with experiment. The limiting factor for short beams is found to be the space-charge depression of the potential due to the unneutralized beam; in longer beams self-magnetic and electric fields impose a power limit. Typical beam impedances are found to be of the order of 15 Ω with a 350 keV beam. The role of shear in the axial velocity of the beam is discussed.
The Maxwellian plus water-bag model: application to the propagation of longitudinal electron waves in a plasma with Maxwellian and mono-energetic supra-thermal electrons
Authors: Treguier J. P. , Henry D.
Published: March 2009

This paper is a theoretical and experimental study of the propagation of longitudinal electron waves in a collisionless, homogeneuos, isotropic plasma, composed of Maxwellian and supra-thermal electrons. Assuming the supra-thermal electrons are mono-energetic, the velocity distribution function is chosen as a Maxwellian plus water-bag distribution; then, using the method of residues (inverse Fourier–Laplace transform), the behaviour of the electric field is found to be in good agreement with experimental results obtained for a plasma of Maxwellian and quasi-mono-energetic electrons. The plasma parameters can be deduced from the theoretical dispersion curves matching the experimental points; they are found to agree well with those measured by electrostatic probes. Experimental values of damping and excitation coefficients are also compared with the theoretical. The results suggest that a longitudinal electron wave propagation experiment may be used as a powerful diagnostic tool to examine non-Maxwellian plasmas.
Hydrodynamic theory of surface-wave fluctuations in inhomogeneous plasma
Authors: Aliev Yu. M. , Vuković S. , Gradov O. M. , Kyrie A. Yu.
Published: March 2009

This paper investigates the fluctuation spectrum of the surface waves in a semi-infinite plasma, and in a plasma cylinder, with an inhomogeneous boundary layer. It is shown that the correlations of the surface waves are dependent on temperature and density distributions in the boundary layer. The correlation function is determined by temperature values in the points of transition layer, where the longitudinal dielectric permeability becomes equal to zero. Dependence of the obtained correlation function on co-ordinates, in the electrostatic limit, is characterized by the complex correlation length, which is fully determined by the inhomogenity of the plasma density near the boundary.
The Maxwell field, its adjoint field and the ‘conjugate’field in anisotropic absorbing media
Authors: Suchy Kurt , Altman Colman
Published: March 2009

In absorbing media, where Maxwell's equations are not seif-adjoint, the adjoint field is introduced via the differential operator adjoint to the Maxwell operator. The concomitant vector can be made equal to the time averaged Poynting vector at a boundary with a non-absorbing medium. In general, the adjoint field represents an electromagnetic
field in a medium other than the absorbing medium under consideration. To draw conclusions about the latter, a [conjugate field] in this medium is defined, using a conjugating transformation of the Maxwell operator and field. Relations between the conjugate and adjoint fields are established, allowing one to gather physical information about the first absorbing medium from the adjoint field.
Thermodynamics of the magnetic equilibria of a semi-collisionless plasma
Authors: Minardi Ettore
Published: March 2009

A statistical model of the collisionless or semi-collisionless equilibria of a magnetically confined plasma is presented which allows the calculation of the entropy and of the thermodynamic potentials as functionals of the collective equilibrium quantities. The entropy principle enables the identification of the magnetic equilibria which are preferentially chosen by the plasma. Stability criteria are derived by declaring unstable an equilibrium which admits in its neighbourhood an accessible equilibrium with higher entropy. The requirement of thermodynamic stability imposes considerable restrictions on the magnetic configuration, on the pressure distribution and on the velocity distribution function. New conditions for magnetic stability are derived and known results reinterpreted. The theory points towards the force-free configurations, in the case of a current carrying plasma subject to certain physical constraints, or towards the minimum-B configurations, in the general case of arbitrary ², as the most stable states from the thermodynamic point of view. The formalism is applied to identify the most promising lines to be pursued experimentally in order to achieve magnetic stability in a thermonuclear device.
Nonlinear excitation of magneto-acoustic oscillations by means of an oscillating axial current
Authors: Jones I. R. , Sawley M. L.
Published: March 2009

In this paper a theoretical description is given of the nonlinear excitation of magneto-acoustic oscillations of a magnetized plasma column by means of an oscillating axial current. These oscillations occur at the second harmonic of the axial current. A suitable choice of plasma parameters and excitation frequency leads to the usual resonant behaviour of the oscillations.
Kinetic analysis of electromagnetic wave backscattering in a magnetized plasma
Authors: Willett Joseph E. , Bilikmen Sinan
Published: March 2009

An analysis is presented which describes the stimulated backscattering of an electromagnetic wave with frequency large compared with the electron cyclotron frequency and the electrostacic scatterer wave frequency. The electron and ion susceptibilities provided by kinetic theory are employed in convenient approximations valid at moderate temperatures. Formulae are derived which permit calculation of the growth rate and threshold in bounded and unbounded plasmas. A numerical study of the effects of a static magnetic field on the stimulated backscattering of a carbon dioxide laser beam in a hydrogen plasma is included.
Nonlinear excitation of vortices at the upper-hybrid layer
Authors: Rahman H. U. , Yu M. Y. , Shukla P. K.
Published: March 2009

It is shown that convective cells can be excited by large-amplitude propagating upper-hybrid waves in a plasma. Using the two-fluid model, we obtain a coupled set of differential equations. A nonlinear dispersion relation for the modulational instability is then derived. This relation is investigated for two parameter regimes and expressions for the growth rates are obtained analytically. The limiting case of a dipole pump field is also considered. The relevance of our work in laser-produced, as well as magnetically confined, plasmas is discussed.
Effects of collisional and viscous dissipations on the ion-acoustic–Langmuir interactions
Authors: Mohan M. , Buti B.
Published: March 2009

A pair of modified Zakharov equations coupling the high-frequency Langmuir oscillations to the low-frequency ion-acoustic perturbations in a turbulent, collisional plasma with a neutral background is derived. The time evolution of the coupled ion-acoustic–Langmuir solitons show that the electron–ion and electron–neutral collisions damp the Langmuir oscillations and let the ion density perturbations radiate away. On the other hand, the ion–neutral collisions damp the ion density perturbations letting the Langmuir oscillations flow out. In the case of ion viscosity, however, both the ion density perturbations and the Langmuir oscillations radiate away one after the other. In these processes, electron–ion and electron–neutral collisions seem to dominate over the other two.
Dynamics of charge density fluctuations in two-component hydrogen plasma
Authors: Yoshida F.
Published: March 2009

A systematic study is made of the dynamical properties of the charge density fluctuations in strongly coupled two-component plasmas. The time-correlation function of the partial density fluctuations is described with the use of the memory function formalism. A second-order memory function is approximately expressed in terms of its self-part by taking into account the total momentum conservation law. After assuming a Gaussian time-dependence for the self-part, the excitation spectrum of the charge density fluctuation is calculated for the semi-classical hydrogen plasma, and is in fairly good agreement with the molecular dynamics calculation due to Hansen & McDonald. It is found that the collisional effects play an important role in the strongly coupled system.
Turbulent ‘polarization’ terms and the Balescu–Lenard operator
Authors: Krommes John A. , Kotschenreuther Michael T.
Published: March 2009

Certain unfamiliar terms in renormalized plasma turbulence theory are interpreted in terms of the familiar physics of the Balescu–Lenard collision operator. Specifically, it is argued that the so-called polarization parts of the operator which renormalizes the particle propagator are related to fluctuations of the Fokker–Planck coefficient which describes polarization drag, and to fluctuations of the effective dielectric function of the medium.
Rayleigh–Taylor instability of a plasma in a magnetic field: nonlinear theory
Authors: Shivamoggi Bhimsen K.
Published: March 2009

Kaira & Kathuria used the method of multiple scales to develop nonlinear analysis of Rayleigh–Taylor instability of a plasma in a magnetic field. Their calculations remain valid only for wavenumbers k away from the linear cut-off value kc, and break down for wavenumbers near kc. The purpose of this paper is to treat the latter case. The solution uses the method of strained parameters. The results show the instability persists even at k = kc, despite the cut-off predicted by the linear theory.
Further analysis of nonlinear, periodic, highly superluminous waves in a magnetized plasma
Authors: Clemmow P. C.
Published: March 2009

A perturbation method is applied to the pair of second-order, coupled, nonlinear differential equations that describe the propagation, through a cold electron plasma, of plane waves of fixed profile, with direction of propagation and electric vector perpendicular to the ambient magnetic field. The equations are expressed in terms of polar variables π, φ, and solutions are sought as power series in the small parameter n, where c/n is the wave speed. When n = 0 periodic solutions are represented in the (π,φ) plane by circles π = constant, and when n is small it is found that there are corresponding periodic solutions represented to order n2 by ellipses. It is noted that further investigation is required to relate these finite-amplitude solutions to the conventional solutions of linear theory, and to determine their behaviour in the vicinity of certain resonances that arise in the perturbation treatment.
Reply to the Comments by G. E. Vekstein, D. D. Ryutov and R. Z. Sagdeev
Authors: Balescu R.
Published: March 2009

I cannot agree with the reasoning of Vekstein, Ryutov & Sagdeev (1982) (VRS), the more so as I see no basic contradiction between their results and mine.

The basic equations of the quasi-linear theory are the kinetic equations determining the time evolution of the distribution functions of the electrons and ions, ∂tfe,i and of the spectral densities ∂tψσ(κ) (plus the definition of the diffusion coefficient and the dispersion relations). It is agreed that these equations must be satisfied in any event. The marginal stability is an added approximation (as VRS, of course, admit), and can only be accepted if it is compatible with the basic equations.
Oblique whistler-mode propagation in a hot anisotropic plasma
Authors: Sazhin S. S. , Sazhina E. M.
Published: March 2009

An approximate dispersion relation is obtained for quasi-longitudinal whistler mode propagation in the hot anisotropic plasma. The influence of plasma temperature and anisotropy on whistler energy focusing along the magnetic field and whistler trapping in the magnetospheric ducts are considered for the case when the whistler wave normal angle is not equal to zero.
Parametric drive of vortex and magnetostatic modes in a strongly non-isothermal plasma
Authors: Rahman H. U. , Shukla P. K. , Murtaza G.
Published: March 2009

In this paper, we have discussed the possibility of excitation of zero-frequency modes by a finite-amplitude electron-sound wave in a highly non-isothermal (Ti ≫ Te) magnetoplasma. According to our investigation, the modulational instabilities of the electron-acoustic waves may produce enhanced twodimensional vortices (convection cells) and magnetic field fluctuation. Both of them can, in turn, modify transport properties of a hot magnetoplasma.

Our results could be applicable to plasmas in the earth's magnetotail (Frank, Ackerson & Lepping 1976) or thetapinches, both of which have Ti≫Te. However, for thetapinch application, one should actually modify our results to include plasma non-uniformities. In such a situation, instead of electron-acoustic waves, one encounters ion drift waves (e.g. Shukla, Yu & Varma 1981) whose modulational instabilities can readily be studied following the procedure discussed here.

Owing to the lack of experimental data, we cannot at present verify predictions of our theory for plasmas either in space or in a laboratory. However, a typical example shows that the growth rates of both the convection cells and the magnetostatic modes are quite substantial. Hence, the phenomena discussed here may indeed appear in nature.

We are grateful to Ming Yu for many useful discussions. The work of one of us(P. K. S.) was performed under the auspices of the Sonderforschungsbereich Plasmaphysik Bochum/J ülich. One of us (H.U.R.) thanks the Deutsche Akademische Austauschdienst for the award of a fellowship.
Side-scattering of an ordinary electromagnetic wave by electron-acoustic oscillations
Authors: Sharma R. P. , Yu M. Y.
Published: March 2009

The scattering of an ordinary electromagnetic wave into a circularly polarized wave by electron-acoustic oscillations is considered.

In this paper, we consider a parametric instability involving electron-acoustic waves which does not have a counterpart in a hot electron plasma, namely the scattering of an ordinary electromagnetic wave into a circularly polarized wave by electron-acoustic waves.
Excitation of whistlers and quasi-static modes by an annular electron beam in a plasma cylinder
Authors: Talukdar I. , Jain V. K.
Published: March 2009

A non-local theory of whistler and quasi-static mode excitation by an annular electron beam in a plasma cylinder is presented. Čerenkov and slow-cyclotron interaction are considered in the weak-beam approximation. The growth rate is found to be quite sensitive to the beam radius except in the case of slow-cyclotron interaction of quasi-static modes. The growth rate varies significantly with beam velocity in the case of Čerenkov interaction of quasi-static modes, but in other cases it is rather insensitive to the beam velocity.
Thermodynamic properties and waves in a dipole plasma
Authors: Mulugeta Solomon , Malnev V. N.
Published: March 2009

A low-temperature plasma containing polar molecules with constant electric dipole moment as the neutral component is considered. The thermodynamic functions and the dispersion properties of such a plasma are investigated.
Low-frequency flute modes in a magnetic quadrupole
Authors: Willett Joseph E. , Wu Hsi-Shu
Published: March 2009

An eigenvalue equation is derived for electrostatic waves with frequencies below the ion bounce frequency in a plasma confined by a magnetic quadrupole. This integral equation for the electrostatic potential is developed to second order in the curvature and contains the effects of electron and ion temperature gradients. A dispersion equation for flute modes is derived from it. The present theory applied to the private flux region of the UMIST quadrupole predicts that low-frequency flute modes will propagate in the electron and ion diamagnetic drift directions.
Renormalization-group theory for Alfvén-wave turbulence
Authors: Zhou Ye , Vahala George
Published: March 2009

є-Expansion renormalization-group theory is applied to a model Alfvén-wave turbulence equation. In particular, the effect of small ‘unresolvable’ subgrid scales on the large scales is computed. It is found that the removal of the subgrid scales leads to a renormalized response function v. The Lorenzian wavenumber spectrum of Chen & Mahajan can be recovered for finite є, but the nonlinear coupling constant still remains small, fully justifying the neglect of higher-order nonlinearities introduced by the renormalization-group procedure.
The filamentary structure in the accelerating plasma sheath of a plasma focus: a simplified three-dimentional analysis
Authors: Di Vita Andrea
Published: March 2009

The role of filamentary current distributions in the evolution of plasma-focus discharges is discussed. The force-free structures affect the energy balance during the acceleration of the plasma sheath. As a consequence, saturation of the neutron yield for high values of the energy stored in the capacitor bank occurs.