bluuebunny/crossref_metadata_2025 huggingface dataset:
The effect of magnetic shear on the crossfield current-driven ion-acoustic instability
Authors: Bharuthram R. , Hellberg M. A.
Published: March 2009

The behaviour of the crossfield current-driven ion-acoustic instability in the presence of a sheared magnetic field and a density gradient is investigated theoretically in the limit in which growth due to inverse Landau damping is small. The shear damping rate is found and the critical shear length shown to vary as (mi/me)⅓ and as ((VD–CS)/CS)–⅔.
Investigations of plasma-wall interaction by H alpha resonant scattering in the tokamak UNITOR
Authors: Reinhold G. , Hackmann J. , Uhlenbusch J.
Published: March 2009

The Hα resonant scattering diagnostics applied to the tokamak UNITOR is described. The measurements yield the density distribution of excited hydrogen atoms as a result of plasma-wall interaction processes and background plasma parameters. Special regard has been given to the influence of recycling processes.
Magneto-acoustic oscillations as a plasma diagnostic technique for a current-carrying plasma column
Authors: Brennan M. H. , McCarthy A. L. , Sawley M. L.
Published: March 2009

Magneto-acoustic oscillations were excited in a non-uniform, current-carrying plasma column. Measurements of the oscillating axial magnetic flux at a number of excitation frequencies were used to determine the equilibrium plasma properties. In agreement with previous theoretical studies, the radial profile of the plasma density is shown to be accurately determined, while it is not possible to obtain detailed information on the radial profile of the equilibrium magnetic field.
Nonlinear stability of doublets against axisymmetric resistive MHD modes
Authors: Jensen Torkil H. , McClain Fred W.
Published: March 2009

Linear stability of doublets against axisymmetric modes in the approximation of resistive MHD was studied earlier; two modes were identified as those most likely to be unstable, namely the ‘up-down’ mode, which tends to move the plasma up or down and the ‘droplet-ellipse’ mode which tends to deform the doublet into either a droplet or an ellipse. In the treatment described in this paper, quadratic terms in the perturbation are retained. For an equilibrium which is symmetric about the midplane it is easy to see that the quadratic terms vanish for the ‘up-down’ mode. For the ‘droplet-ellipse’ mode this is not the case. This mode allows two different deformations according to linear theory; the effect of the quadratic terms is found always to be stabilizing for one of these deformations, and destabilizing for the other. Thus, owing to the effects of such nonlinear terms, one may expect in experiments to observe unstable developments in a preferred direction, namely that of destabilization, and one expects to observe a faster deterioration of an equilibrium than that predicted from linear theory. These tendencies have been observed in doublet experiments. In this paper the formalism for including quadratic terms in the perturbation is discussed and results from numerical examples are given.
Lower-hybrid instability in current-carrying plasmas
Authors: Willett Joseph E. , Mehdian Hassan
Published: March 2009

The stability of lower-hybrid waves in a collisional, fully ionized plasma carrying a field-aligned current is investigated. From the two-fluid equations in the cold-plasma approximation, a generalized dispersion relation and formulae for the real frequency ωI and growth rate ωR are derived. The results of a numerical study are presented showing the dependence of ωR and ωI on the angle between the direction of propagation and the magnetic field, the ratio of the electron drift velocity to the parallel phase velocity, and other plasma parameters. Lower-hybrid instability with electron drift velocity small compared with the parallel phase velocity is predicted.
Nonlinear interaction of spherical waves in a homogeneous isotropic plasma
Authors: Cerisier J. C.
Published: March 2009

The nonlinear interaction of two HF electromagnetic spherical waves is studied in a homogeneous isotropic plasma. Due to space variations in the k vectors of the mother waves, the interaction is localized. The structure and the amplitude of the generated Langmuir wave are calculated and a possible experiment is discussed.
The simulation of plasma double-layer structures in two dimensions
Authors: Borovsky Joseph E. , Joyce Glenn
Published: March 2009

Electrostatic plasma double layers are numerically simulated by means of a magnetized 2½-dimensional particle-in-cell method, periodic in one direction and bounded by reservoirs of Maxwellian plasma in the other. The investigation of planar double layers indicates that these one-dimensional potential structures are susceptible to periodic disruption by plasma instabilities. A slight increase in the double-layer thickness with an increase in its obliqueness to the magnetic field is observed. It is noted that weak magnetization results in the double-layer electric-field alignment of particles accelerated by these potential structures and that strong magnetization results in their magnetic-field alignment. Electron-beam-excited electrostatic electron cyclotron waves and ion-beam-driven electrostatic turbulence are present in the plasmas adjacent to the double layers. The numerical simulations of spatially periodic two-dimensional double layers also exhibit cyclical instability. A morphological invariance in two-dimensional double layers with respect to the degree of magnetization implies that the potential structures scale with Debye lengths rather than with gyroradii. Ion-beam-driven electrostatic turbulence and electron-beam-driven plasma waves are again detected. A simplified one-dimensional model of oblique plasma double layers, using water-bag velocity distribution functions, is presented in an appendix.
Drift dissipative instabilities of electron-acoustic and lower-hybrid waves
Authors: Mohan M. , Yu M. Y.
Published: March 2009

It is shown that drift dissipative instabilities can occur in the frequency regime Ωi ≪ ω ≪ Ωe. These instabilities are associated with the electron-acoustic and lower-hybrid waves.
Nonlinear interaction of waves in sharply bounded plasmas
Authors: Lindgren T.
Published: March 2009

We consider the nonlinear interaction of three high-frequency waves and lowfrequency density perturbations in a sharply bounded plasma. The coupled equations are presented in a general and convenient form. To demonstrate the usefulness of our method we derive explicit expressions for the threshold of a number of possible instabilities in semi-infinite and cylindrical plasmas.
Notes on the stability problem for inhomogeneous equilibria
Authors: Symon K. R.
Published: March 2009

Several conclusions regarding the stability of inhomogeneous Vlasov equilibria are drawn from earlier work. A technique is presented for generating first-order formulae for the change δω in the frequency of any normal mode, when a parameter λ characterizing the equilibrium is changed slightly. Several applications are given, including a first-order calculation of the growth rate or damping of an electromagnetic mode due to the presence of plasma. A condition is derived for the existence of a normal mode with real frequency. When there are ignorable co-ordinates, the normal modes can be written in the form of waves propagating in the ignorable directions. The character of the modes depends on certain symmetries in the dynamic spectral matrix. Special cases arise when the orbits can be approximated in certain ways.
The thermal self-focusing of a wave beam in an underdense plasma. Part 1. The wave spectrum
Authors: Giles M. J.
Published: March 2009

The present series of papers is concerned with the problem of the thermal selffocusing of an electromagnetic wave in an underdense plasma which is examined within the context of ionospheric modification by high-power radio waves. We formulate this problem as a coherent four-wave interaction between a pump wave, Stokes side-band waves and a thermally driven density perturbation. Our treatment assumes that the heating of the electrons in the interference pattern of the pump and side-band waves is in equilibrium with longitudinal heat conduction and energy transfer to the ions and, in addition, that the density perturbation is subject to decay on account of longitudinal ambipolar diffusion, ambient plasma drift motion, recombination and the stabilizing influence of perturbations to the electrical conductivity.
Oscillations and analysis of stability for pinch systems
Authors: Meierovich B. E.
Published: March 2009

Small oscillations of a dense, equilibrium plasma in a strong current channel aro considered in the approximation of two-fluid hydrodynamics of ideal charged liquids. It is shown that chute-type radial oscillations are the ones most likely to affect the system's stability. The instability induced by spontaneous excitation of these oscillations results in a spallation of the diffuse equilibrium state into separate densely compressed current channels. The present investigation of the oscillations near the stability threshold enables one to formulate the stability criterion for the pinch system. It is shown that Bennett-type equilibrium distributions rapidly become unstable with a rise in the current, while the equilibrium distributions for the plasma compressed up to the electron degeneration, are stable, by a considerable margin. The theoretical conclusions on the pinch decay into separate current channels are in agreement with the available experimental data.
The thermal self-focusing of a wave beam in an underdense plasma. Part 3. Linear convection
Authors: Giles M. J.
Published: March 2009

In the third part of this paper devoted to the problem of the thermal self-focusing of an electromagnetic wave in an underdense plasma, we extend the lineary theory of part 1 to include the effect of ambient drift motion perpendicular to the plane of the axis of the beam and the magnetic field. We show that the amplitude of the density perturbation satisfies a third-order hyperbolic equation, when this effect is included, and we apply Riemann's method to obtain its solution in integral form. This solution shows that a state of stationary self-focusing is established within the beam after a time equal to the transit time for a perturbation to drift across it. The form of the axial growth in the stationary state is derived from an asymptotic evaluation of the integral representation for large axial distances. It is found that the axial growth increases across the beam starting from zero at the edge through which plasma enters the beam and reaching its maximum attainable value at or before the opposite edge, depending on the magnitude of the drift velocity. The maximum growth decreases as the drift velocity increases and only occurs at the rates deduced in parts 1 and 2 when the beam width is several times larger than the scale length which describes the decay of a density perturbation within the beam due to the combined effect of drift longitudinal ambipolar diffusion, recombination and the stabilizing influence of perturbations to the electrical conductivity. The factor by which the amplitude of a convected density perturbation is reduced relative to the value it would have in the absence of drift motion is evaluated and the results are applied to the case of ionospheric modification by a transmission from the proposed solar power satellite systems.
The thermal self-focusing of a wave beam in an underdense plasma. Part 5. Cubic nonlinear effects
Authors: Giles M. J.
Published: March 2009

In the fifth part of this paper devoted to the problem of the thermal self-focusing of an electromagnetic wave in an underdense plasma, we extend the nonlinear theory of part 4 to include the effect of cubic nonlinearities. These terms describe the stabilizing influence of perturbations to the electrical conductivity. We assume that a stationary state of the type described earlier has been established and consider the spatial nonlinear interaction of the pump wave with the Stokes side-band waves and the density perturbation corresponding to the most unstable linear mode. We show that the system of єquations describing their interaction possesses three invariants. These invariants are used to reduce the problem to quadratures and an implicit solution is obtained in terms of incomplete elliptic integrals of the first and third kinds. From this solution we derive explicit expressions for the saturation level and the nonlinear growth length. The results are applied to the problem of ionospheric modification by microwave transmissions from the proposed solar power satellite systems.
Coupling mechanism of boundary sheaths and wave launcher in a collisionless plasma
Authors: Fujita H. , Yagura S.
Published: March 2009

The coupling mechanism of boundary sheaths and a wave launcher immersed in a collisionless plasma is experimentally clarified by the addition of an electron emission from the launcher. The wave amplitude increases rapidly with increasing electron emission. The strong increase in a directly coupled signal is a clear observation of ion-acoustic waves which are simultaneously excited at the sheaths.
Inhomogeneous stationary states of two-dimensional magnetofluids
Authors: Calinon Roland , Merlini Danilo
Published: March 2009

We discuss ensemble inhomogeneous states of general two-dimensional magneto-fluids. A subclass of approximate statistical inhomogeneous states of the model equation is constructed using the principle of maximum entropy. The fields are shown to satisfy generalized nonlinear Poisson equations and some limiting cases are solved analytically. The method is then applied to a pseudo-three-dimensional model of an electromagnetic filamentation instability. The results illustrate the general role of the global constants of the motion on the nature of the statistical profiles for the fields describing the most probable states in magnetofluids.
A retarded time superposition principle and the relativistic collision operator
Authors: Hizanidis K. , Molvig K. , Swartz K.
Published: March 2009

A retarded time superposition principle is formulated and proved for the two particle correlation function in a multi-species relativistic, and fully electro-magnetic, plasma. This principle is used to obtain the relativistic collision operator. Starting from the relativistic Klimontovich equation, the statistical (Liouville) average of the Klimontovich equation yields an expression for the collision operator in terms of the two-time two-point correlation function for two particles, G12(1, t12, t2). It is proved that G12(1, t12, t2) can be written in a retarded time superposition form in terms of the self-correlation W11(1, t12, t2) and the discreteness response function P(1, t12, t2). The equation for the pair correlation function G12(1, t12, t2), excluding triplet or higher-order correlations, is thus replaced by the simpler equation for P(1, t12, t2). This is the test particle problem which relates P(1, t12, t2) to the discreteness source term W11(1, t12, t2). The equations for P(1, t12, t2). and W11(1, t12, t2) are solved for stationary, homogeneous plasmas without external fields. With these solutions, the collision operator is expressed in terms of the relativistic dielectric properties of the plasma.
The effect of thermal anisotropy on the propagation of whistler waves in mixed hot-cold electron plasmas
Authors: Hamabata Hiromitsu
Published: March 2009

The first-order CGL fluid equations for electrons including the first-order heat fluxes are applied to the propagation of whistler waves. The dispersion relation of whistler waves is derived for two types of equilibrium electron distribution functions with cold and hot components. The effect of electron temperature anisotropy and the existence of cold electrons on the field-aligned propagation of whistler waves is analysed. It is shown that the electron temperature anisotropy intensifies the tendency of whistler waves to follow the lines of force of static magnetic field, that the existence of cold electrons in an anisotropic plasma further intensifies this tendency, and that under certain conditions the waves propagate only along the static magnetic field.
Field-line reconnexion in the two-dimensional asymmetric case
Authors: Semenov V. S. , Kubyshkin I. V. , Heyn M. F. , Biernat H. K.
Published: March 2009

A detailed mathematical analysis of plane steady-state reconnexion is given for the case when the plasma parameters and the magnetic fields are not identical on both sides of the current sheet. Asymptotic solutions in the sense that the inflow velocity is much less than the local Alfvén velocity as well as the arrangement of shock waves are obtained. Rotational (Alfvén) waves, slow shock waves, rarefaction waves (expansion fans), and a contact discontinuity may occur. Four different types of solution, corresponding to different shock wave configurations, are possible. They depend on the parameters of the inflow regions in a unique way.
Application of catastrophe theory to a point model for bumpy tori with neoclassical non-resonant electrons
Authors: Punjabi Alkesh , Vahala George
Published: March 2009

The point model of Hedrick et al. for the toroidal core plasma in the ELMO Bumpy Torus (with neoclassical non-resonant electrons) is examined in the light of catastrophe theory. Even though the point model equations do not constitute a gradient dynamic system, the equilibrium surfaces are similar to those of the canonical cusp catastrophe. The point model is then extended to incorporate ion cyclotron resonance heating. A detailed parametric study of the equilibria is presented. Further, the nonlinear time evolution of these equilibria is studied, and it is observed that the point model obeys the delay convention (and hence hysteresis) and shows catastrophes at the fold edges of the equilibrium surfaces. Although a detailed analysis of the basin boundaries for the simultaneous point attractors is not made, some simple examples are given which illustrate that the final equilibrium state can be drastically affected, not only by the control parameters (neutral density, ambipolar electrostatic potential, electron and ion cyclotron power densities) but also by the initial conditions of the state vector (plasma density, electron and ion temperatures). Tentative applications are made to experimental results.
Resistive convection in a cylindrical plasma
Authors: Gomberoff L.
Published: March 2009

It is shown that the combined effect of resistivity and thermal conductivity is responsible for the existence of marginal stationary modes in a cylindrical current-carrying plasma, under the influence of a shearless magnetic field. These modes occur in the tokamak approximation and for low wavenumbers. In the nonlinear theory they give rise to large-scale stationary convection.
Dissipation by thermal forces in plasmas
Authors: McClelland D. E. , Burman R. R.
Published: March 2009

This paper deals with non-isothermal plasmas in which each species is described by Grad's thirteen-moment approximation. A theoretical framework, which includes a generalized Ohm's law and an ambipolar diffusion law, is used to treat energy dissipation resulting from ‘Motional’ interactions between the species. The frictional forces consist of a momentum relaxation force together with a ‘thermal force’ that occurs, in the presence of heat flow, partly because of the dependence of the collision frequencies on temperature. Detailed results are obtained for binary plasmas and for partially and fully ionized ternary plasmas. Our formalism is then compared with the technique used by Demetriades & Argyropoulos to study dissipation in thirteen-moment plasmas. The effects of thermal forces are illustrated by considering situations in which the drift contribution to the electronic relative thermal flux vector predominates over the thermal flux vector itself. Then, for binary plasmas and for ternary plasmas that are not too lightly ionized, the thermal forces increase the resistivity by a factor of about 5/2.
Electrostatic and electromagnetic eigenmodes near the electron and ion gyrofrequencies in a cylindrical plasma
Authors: Boswell R. W.
Published: March 2009

We show that under a wide range of conditions easily achievable in the laboratory, the dispersion of the radial eigenmodes of electromagnetic whistler mode waves in a cylindrical magneto-plasma is dominated by the electron inertia and becomes synonymous with the electrostatic Trivelpiece-Gould modes. A similar situation exists close to, but just below, the ion gyrofrequency.
Axially symmetric self-focusing of whistler waves
Authors: Karpman V. I. , Kaufman R. N. , Shagalov A. G.
Published: March 2009

The self-focusing of whistler waves in a low-β plasma is considered. Axially symmetric solutions of the MHD and Schrödinger equations are found that describe stationary and homogeneous wave beams together with the plasma ducts in which they are trapped.

The self-focusing occurs both at ω < ½ωc and ω > ½ωc where ωc is the electron cyclotron frequency. The wave leakage which takes place in some types of duct and pre vents self-focusing from developing is investigated in detail.
Transformation approximation for the plasma dispersion function and application to electrostatic waves
Authors: Sato Masumi
Published: March 2009

Simple algebraic approximations for the plasma dispersion function Z(s) and its derivative are obtained by the Aitken's Δ2 or Shanks transformation. Using the approximate function Z'(s), higher-order dispersion relations for the electron wave and ion-acoustic wave are derived.
Magnetohydrodynamic properties near an X-type magnetic neutral line
Authors: Shivamoggi Bhimsen K.
Published: March 2009

The magnetohydrodynamic properties near a two-dimensional X-type magnetic neutral line in a viscous and resistive plasma in the steady-state are investigated.
Burgers' equation and cosmic ray shocks
Authors: Webb G. M. , McKenzie J. F.
Published: March 2009

The time evolution of weak shocks in the classical theory of shock waves may be described by Burgers' equation, which is a small-amplitude, long-wavelength, but nonlinear wave equation. The present paper derives Burgers' equation for three different hydrodynamical models of cosmic ray shocks. The main development of the paper concerns the hydrodynamical model in which Alfvénic effects are neglected. For this model it is shown that the steady-state solution of Burgers' equation is equivalent to the weak, but smooth, transition solutions of the shock structure equation obtained previously. It is shown that Burgers' equation may be regarded as a wave energy equation, in which the interaction of the wave with the background medium is taken into account. Burgers' equation is also derived for Alfvénic models in which the Alfvén waves that scatter the cosmic rays are generated by the cosmic ray streaming instability, and propagate down the cosmic ray pressure gradient, at the Alfvén velocity relative to the background fluid.
Linear tearing mode stability for low-q cylindrical tokamaks
Authors: Rosenblum Moshe
Published: March 2009

Detailed computational results are presented for the stability of linear tearing modes in low-q cylindrical tokamaks with various radial profiles. The stability properties of a widely used ‘classical’ profile are compared with those of a ‘piecewise’ profile. It is shown that the stability properties of low-q tokamak discharges show a sensitive dependence on small changes in the current density profile near the singular surface. While the ‘classical’ profile is stable for a large range of q0, where q0 is the value of the safety factor on the magnetic axis, a similar ‘piecewise’ profile is unstable for the same set of parameters.
Parametric decay of Langmuir waves in an electron beam-plasma system
Authors: Willett Joseph E. , Aktas Yildirim
Published: March 2009

Backscattering of Langmuir waves from low-frequency electrostatic waves in a plasma traversed by an electron beam is studied. The analysis is based on the use of beam electron, plasma electron, and ion susceptibilities provided by kinetic theory. For the case of a warm electron beam, formulae are derived for the growth rate and threshold associated with resonant backscattering from an ion-acoustic wave modified by the presence of the beam. For the case of a cold electron beam, formulae are derived from the growth rates associated with resonant back-scattering from a modified ion-acoustic wave and from a higher-frequency beam-plasma mode. A numerical study of the effects of an electron beam on these parametric instabilities is included.
Hydromagnetic equations for collisionless plasmas in strong magnetic fields
Authors: Duhau S.
Published: March 2009

The Chew, Goldberger & Low equations are a one-fluid system for the thermodynamic variables of the ions that are coupled to the electrons only through the electromagnetic variables. The magnitude of these variables in a collisionless plasma is re-examined in the present paper and it is found that, in the limit in which the Larmor radius and the electron-to-ion mass ratio are both zero, the current, in the plane normal to the magnetic field, is entirely transported by the electrons in the reference frame that moves with the bulk velocity. The first-order electric field contributes to the ion equation of motion with a zero-order term that couples the thermodynamic variables of both species. So the energy equation of the electrons must now be included in the equation set; to close this equation, a simple mathematical representation of the measured quasi-stationary velocity distribution function of this species is used. A two-fluid equation system in the limit in which the Larmor radius and the electron-to-ion mass ratio are both zero is then found.
Diffusion coefficient and Kolmogorov entropy of magnetic field lines
Authors: Zimbardo Gaetano , Veltri Pierluigi , Malara Francesco
Published: March 2009

A diffusion equation for magnetic field lines of force in a turbulent magnetic field, which describes both the random walk of a single field line and how two nearby lines separate from each other, has been obtained using standard statistical techniques. Starting from such an equation, a closed set of equations for the moments may be obtained, in general, with suitable assumptions. From such a set of equations the Kolmogorov entropy may be explicitly calculated. The results have been applied to the most interesting examples of magnetic field geometries.
The spectrum of resistive MHD modes in cylindrical plasmas
Authors: Ryu C. M. , Grimm R. C.
Published: March 2009

A numerical study of the normal modes of a compressible resistive MHD fluid in cylindrical geometry is presented. Resistivity resolves the shear Alfvén and slow magnetosonic continua of ideal MHD into discrete spectra and gives rise to heavily damped modes whose frequencies lie on specific lines in the complex plane. Fast magnetosonic waves are less affected but are also damped. Overstable modes arise from the shear Alfvén spectrum. The stabilizing effect of favourable average curvature is shown. Eigenfunctions illustrating the nature of typical normal modes are displayed.
Resonant parts of nonlinear response tensors
Authors: Melrose D. B. , Kuijpers J.
Published: March 2009

It is pointed out that ambiguities arise in taking the resonant parts of nonlinear response tensors. A prescription is proposed and used to evaluate the resonant parts explicitly in terms of a covariant and gauge invariant formalism. Symmetry properties of the resonant parts are identified. The prescription used can be justified by analogy with a calculation based on QED where no ambiguity arises; it is also justified directly by classical arguments. In some standard treatments of nonlinear damping processes a necessary symmetry is not imposed. When this symmetry is imposed, the relations derived here imply that turbulent bremsstrahlung, as defined by Tsytovich et al., does not exist.
The energy density of electromagnetic waves in a cold magnetoplasma
Authors: Storey L. R. O.
Published: March 2009

General expressions are derived for the energy density of electromagnetic waves in a cold collisionless magnetoplasma. Random as well as coherent waves are considered.
Experimental results on trapping a gun plasma in a toroidal magnetic cusp experiment
Authors: Pincosy P. A. , Myers B. R. , Levine M. A. , Feinberg B. , Niland R. A. , Soroka L.
Published: March 2009

A start-up method for producing a plasma in the bi-cusp field configuration of a toroidal magnetic cusp (TORMAC) is described. The method uses the radial injection and trapping of a toroidal gun plasma. Measurements of an injected plasma with a velocity of 17 μsec–1 and 4·5 × 1018 particles is presented. The plasma was observed to be stopped and trapped in an equilibrium position. A well-defined outer boundary remained stationary for 20 μsec. Particle flux distribution emanating from the cusp field lines defined a sheath having a width of 1–1·5 ion gyroradii in the poloidial field. This translates to a narrow outer boundary and a broad inner boundary based on the gradient of the poloidial field at the two radial positions. Measurements of Thomson scattering and interferometry give a Te of 15eV, a 15μsec density decay time, and a 5μsec energy decay time. These results show that this injection and trapping method is successful, and thus a higher gun plasma energy combined with a flux conserving barrier may lead to higher temperatures for testing containment in TORMAC.
Bifurcation of the resistive Alfvén wave spectrum
Authors: Dewar R. L. , Davies B.
Published: March 2009

A phase integral (WKBJ) theory of damped modes in a resistive cylindrical plasma column is developed. The theory predicts several phenomena observed previously in numerical studies: (i) the complex frequency ω has a point spectrum lying on a locus which is approximately independent of the resistivity, and which intersects the ideal continuum only at its end points (at angles of 45° and 30°); (ii) the qualitative features are independent of current profile and m–number, provided |k.B| is monotonic and strictly positive; and (iii) the two branches of the spectral locus joining the two end points of the ideal continuum correspond to precisely defined ‘internal’ and ‘wall’ modes, and bifurcate from a ‘global’ mode at a certain complex frequency which can be predicted from the topological features of the Stokes diagram in the complex radial position plane. In order to derive consistent connexion formulae for reflexions from the wall, the magnetic axis, and from turning points, we reduce the resistive hydromagnetic equations to a scalar wave equation, uniformly valid over the entire plasma to two orders in an expansion in the square root of the resistivity. Good numerical agreement is found between eigenvalues from the full equations, the reduced equation, and from the WKBJ method.
Longitudinal electron waves for a plasma with a bi-Maxwellian velocity distribution
Authors: Trotignon J. G.
Published: March 2009

An original method for calculating and representing the excitation coefficients of longitudinal electron waves is applied to the case of a hot, collisionless, homogeneous and isotropie plasma with a bi-Maxwellian velocity distribution function. Using a Van Kampen treatment we introduce a ‘wave density’ distribution which is represented graphically. When hot electrons are added to a plasma of cool electrons the Landau mode is distorted and its damping increases with the hot/cold temperature ratio θ. The Landau mode separates into two modes for θ ≥ θ0 where θ0 increases as the hot/cold density ratio α decreases. We show that no wave seems to be able to propagate at frequencies below the plasma frequency. Using an abrupt cut-off in the hot electron distribution function, we recover the results for a Maxwellian plus water-bag distribution.
The ponderomotive force of an electromagnetic wave in a collisional plasma
Authors: Sawley M. L.
Published: March 2009

The nonlinear propagation of a circularly polarized, electromagnetic wave in a collisional, infinite, magnetized plasma is considered. The presence of collisions leads to spatial variation in the amplitude of the wave field which gives rise to a time-independent ponderomotive force. The ponderomotive potential for a left (right) circularly polarized wave attains a maximum at the ion (electron) cyclotron frequency. In the vicinity of the cyclotron frequency it is shown to be always positive. A decrease in both the particle density and the real and imaginary parts of the complex wavenumber is shown to result from the effect of the ponderomotive force.
Solitary surface waves on a magnetized plasma cylinder
Authors: Gradov O. M. , Stenflo L. , Sünder D.
Published: March 2009

We analyse high-frequency electrostatic solitary surface waves that propagate along a plasma cylinder in the presence of a constant axial magnetic field. The width of such a solitary wave, which is found to be inversely proportional to its amplitude, is expressed as a function of the magnitude of the external magnetic field.
Nonlinear propagation and localization of intense electromagnetic waves in relativistic plasmas
Authors: Mofiz U. A. , De Angelis U.
Published: March 2009

An analytical formulation is presented for envelope-type solutions of intense polarized electromagnetic waves propagating in cold unmagnetized plasmas. Induced charge separation is fully taken into account and nonlinearities due to mass variation of both electrons and ions are included. Localized solutions are found for the case of subluminous wave phase velocity. The spectrum of solutions (dependence of wave amplitude on the free parameters in the theory, phase velocity and frequency) is discussed and compared with previous analytical and numerical results.
Some properties of the Fokker-Planck equation
Authors: Lewak G. J. , Soto L. A.
Published: March 2009

The solution of the Fokker-Planck equation for the distribution function of heavy ions in a background of electrons is studied. It is found that quite broad physical conditions on the distribution function (such as the positive requirement and the existence of all velocity moments) are sufficient to eliminate any ambiguity in the time-independent steady-state solutions and to determine a discrete spectrum of the time-dependent Fokker–Planck operator. The more physical case of a Maxwell-Boltzman electron distribution function is treated using the small mass ratio expansion. First-order mass ratio corrections are calculated. A plasma heating application-is suggested.
Turbulent disruptions from the Strauss equations
Authors: Dahlburg Jill P. , Montgomery David , Matthaeus William H.
Published: March 2009

The Strauss equations of reduced resistive magnetohydrodynamics are solved pseudo-spectrally, inside a cylinder of square cross-section. Conducting, free-slip, boundary conditions are imposed at the boundaries normal to the direction of the imposed d.c. magnetic field and net current, and periodic boundary conditions are imposed in the third direction. The emphasis is on the development of disruptions. Initial conditions are not analytical equilibria, and are characterized by wide-band noise perturbations in many Fourier modes. Typical spatial resolution is 32 × 32 × 16. At this resolution, the code takes approximately 0·7 seconds per time step on a CRAY-1 computer. Lundquist numbers are limited by the need to resolve the small-scale turbulence which develops. Disruptions are characterized by (i) a burst of kinetic fluid activity which is roughly equipartitioned with the magnetic fluctuations at the small scales, but which involves overall kinetic energies which are much less than the magnetic energies; (ii) a helical ‘m = l, n = 1’ current filament which develops out of the wide-band turbulent noise and wraps itself around the magnetic axis; and (iii) relatively mild disturbances of the magnetic field lines, at least at these low values of Lundquist number (S ≃ 100). The results are compared with those from similar codes which solve the linearized Strauss equations.
Time evolution for different geometrical configurations of charged particles in a time-varying magnetic field
Authors: Bouquet S. , Cairó L. , Feix M. R.
Published: March 2009

Through rescaling and obtaining invariant equations, we study the expansion of charged particles immersed in a time-varying magnetic field B(t) = B0(1+Ωt)–β. We develop the theory for a configuration of point particles confined in a plane with an initial cylindrical symmetric configuration. It is found that the system expands according to (1+Ωt)2β/3 for β ≤ 1 and it is conjectured that in a properly rescaled space and time, it reaches asymptotically an inhomogeneous (in space) Brillouin flow with rigid rotation at half the cyclotron frequency (ω = ½ωc). Particular attention is given to the ‘pivot’ case β = 1. It is shown then that the radius of the rescaled configuration is now dependent on the ratio Ω/ωc, and grows indefinitely with time for Ω/> 3.2–3/2;. Numerical experiments are presented which confirm these theoretical predictions and conjectures. Finally, the properties of this system are compared with those of single-particle and ‘rod’ electrostatic models.
Particle aspect analysis of drift wave in the presence of inhomogeneous magnetic field
Authors: Tiwari M. S. , Pandey R. P. , Misra K. D.
Published: March 2009

The theory of particle aspect analysis is extended to the drift wave in the presence of an inhomogeneous magnetic field. The dispersion relation and growth rate of the wave are evaluated and discussed when the magnetic field gradient is directed opposite to the density gradient. The plasma under consideration is assumed to be anisotropic and the effects of temperature anisotropy on the dispersion characteristics and growth rate of the wave are also studied. The dispersion relation and the growth rate are evaluated for the space plasma parameters.
Alfvdén wave heating of a cylindrical plasma using axisymmetric waves. Part 1. MHD theory
Authors: Donnelly I. J. , Clancy B. E. , Cramer N. F.
Published: March 2009

MHD theory with the Hall term has been used to analyse the Alfvén resonance heating of cylindrical plasmas using axisymmetric waves excited by an antenna. An analytic expression for the antenna impedance has been derived for a simple plasma model and this is used to help interpret the computational results for small, medium and large plasmas. Compressional wave eigenmodes give large antenna resistances; however, the energy is deposited near the plasma surface. At a frequency just above each eigenfrequency, the Alfvén resonance damping is zero. Below the first eigenfrequency, the energy can be deposited near the plasma centre; however, the antenna resistance is fairly low except for medium size plasmas with a nearly constant central density. Ion cyclotron wave resonances are briefly discussed. Some general concepts relevant to the penetration of wave energy into large plasmas are presented.
Firehose and mirror instabilities in a collisionless heat conducting plasma
Authors: Kalra G. L. , Singh Bhupinder , Kathuria S. N.
Published: March 2009

A closed set of CGL equations, modified to include heat flux correction, is used to study the firehose and mirror instabilities in a rarefied plasma. A significant feature which has been noticed is that some of the terms contributed by the higher-order moments are of the same order as the terms in the unmodified CGL equations. We study the effect on the firehose and mirror instabilities of those terms which persist in the limit of vanishing heat flux vector. It is found that these terms lead to a new criterion for mirror instability. The criterion for hose instability, however, remains unaffected.
Ripple transport at low collision frequency
Authors: Hitchon W. N. G. , Beidler C. D. , Mynick H. E. , Shohet J. L.
Published: March 2009

A new stellarator ripple-transport mechanism is predicted at the low collision frequencies characteristic of ions in a reactor plasma. A heuristic argument is used to derive an approximate diffusion coefficient whose magnitude, scaling and range of applicability agree well with the results of Monte Carlo calculations. The proposed diffusion coefficient is independent of collision frequency within its range of validity, which encompasses the parameters of most ions in a reactor. Its magnitude is smaller than previous estimates for the diffusion coefficient in this range, but larger than the diffusion coefficients in all other low-collision-frequency regimes. An explanation of the form of the diffusion coefficient is given in terms of analytic theory of ripple transport.
Modified Korteweg—de Vries ion-acoustic solitons in a plasma
Authors: Nakamura Y. , Tsukabayashi I.
Published: March 2009

Propagation of nonlinear ion-acoustic waves in a multi-component plasma with negative ions is investigated experimentally. At a critical concentration of negative ions, both compressive and rarefactive solitons are observed. The velocities and widths of the solitons are measured and compared with the soliton solutions of the modified Korteweg–de Vries equation and of the pseudopotential method. The modified Korteweg–de Vries equation is solved numerically to investigate overtaking collisions of a positive and a negative soliton. Fluid equations together with Poisson's equation are numerically integrated to simulate their head-on collisions.
Dispersion relation for Bernstein waves using a new transformation for the modified Bessel function
Authors: Sato Masumi
Published: March 2009

Aitken's or Shanks' transformation of the exponent-modified Bessel function produces better approximations. Dispersion relations for the hybrid and Bernstein waves using these provide better thermal and parallel wavenumber corrections. They also predict more closely the evolution and mode-conversion of these waves.
Lower-hybrid instabilities driven by an ion velocity ring
Authors: Akimoto K. , Papadopoulos K. , Winske D.
Published: March 2009

The lower-hybrid instabilities in high-beta (ratio of plasma to magnetic pressure) plasmas driven by ring-ion distributions in velocity space are investigated. A dispersion equation including electromagnetic effects is derived. In the low-beta limit, analytic expressions are obtained which illuminate the physical nature of the instabilities. The complete dispersion equation is solved numerically as a function of ring speed and plasma beta for several types of ring distribution. Electromagnetic effects are important for relatively energetic rings even in the low-beta regime, suppressing growth rates and shifting the angle of propagation to more oblique angles. Stabilization by thermal effects is also discussed. Application of these results to the Earth's bow shock, AMPTE, comets and solar flares is suggested.
Resonant particle instabilities in a uniform magnetic field
Authors: Kennel C. F. , Wong H. V.
Published: March 2009

We present here a simple expression for the resonant particle growth rate of arbitrary plasma waves propagating at an arbitrary angle to a uniform magnetic field in a spatially homogeneous plasma. We then are able to see that cyclotron harmonic wave-particle resonances contribute to instability when the resonant particle pitch angle distributions are anisotropic, while the phase velocity resonances of the Landau form are unstable to beam type phenomena. A sufficient condition for resonant particle stability is that particle distributions be isotropic and monotonically decreasing with increasing energy everywhere.
Ambipolar diffusion and drift of added carriers in a semiconductor in the presence of a magnetic field
Authors: Maldonado C. D.
Published: March 2009

The theory of Allis and Rose based on the hypotheses of congruence and proportionality is used to formulate the problem of ambipolar diffusion and drift of a plasma of added carriers in a semiconductor in the presence of a magnetic field. These hypotheses together with the linearized equations for the particle flow densities of the electrons and holes permit an expression for the particle flow density of the added carriers to be derived. In its final form this expression is composed of a drift and diffusion term in which the ambipolar group mobility and diffusion coefficient appear as tensorial quantities. These antisymmetric tensors will reduce to the scalar quantities of van Roosbroeck (1953) when the magnetic field is set equal to zero and to the proper tensorial quantities for the added minority carriers in strong extrinsic n or p type semiconductors. Finally, as an illustrative example, the ambipolar continuity equation for the particle density of added carriers is solved as an initial-value problem in an unbounded domain in order to analyze the space and time behaviour of a pulse of added carriers whose initial distribution is a Dirac delta function.
Thermal conductances in a collisionless gas between coaxial cylinders and concentric spheres
Authors: Wu Yau
Published: March 2009

The thermal conductances in a collisionless gas between coaxial cylinders and concentric spheres have been obtained for arbitrary thermal accommodation coefficients. This exact theory is based on the general theory of thermal conduction of collisionless gas developed recently by Wu which has been established according to his revised theory of thermal transpiration. The classical theory of thermal conductance between coaxial cylinders by Knudsen and Von Smoluchowski is only accurate to the first power of the temperature difference in which the velocity distribution in the system is assumed to be nearly Maxwellian. However, in the present paper, it is unnecessary to make this usual assumption and the exact theory has been established according to the revised theory of thermal transpiration.
Wave propagation in non-uniform plasmas near the second electron cyclotron harmonic
Authors: Baldwin D. E.
Published: March 2009

Equations are derived which may be used to describe the propagation of electromagnetic waves in non-uniform magnetized plasma when the wave frequency is near the second electron cyclotron harmonic. The method used is to expand the linearized Vlasov equation in powers of the electron Larmor radius divided by a typical scale length. The general equations are then specialized to the problem of the coupling of transverse waves to the longitudinal modes (Bernstein modes) which exist when all quantities vary only in a plane perpendicular to a straight magnetic field. The form of these equations for two simple models of the equilibrium plasma is given. Comments are made about the equations for the higher harmonics, and the question of boundary conditions is discussed. Finally, the general equations are examined in the limit Ω→0 in order to provide equations suitable for the description of high frequency waves in non-magnetized plasmas.