bluuebunny/crossref_metadata_2025 huggingface dataset:
Nonlinear frequency shift of finite-amplitude electrostatic surface waves
Authors: Stenflo L. , Yu M. Y.
Published: March 2009

The problem concerning the appropriate form for the nonlinear frequency shift arising from slow density modulations of electrostatic surface waves in a semi-infinite unmagnetized plasma is reconsidered. The spatial dependence of the wave amplitude normal to the surface is kept general in order to allow for possible nonlinear attenuation behaviour of the surface waves. It is found that if the frequency shift is expressed as a function of the density and its gradient then the result is identical with that of Zhelyazkov (1987b), who assumed a linear exponential attenuation behaviour.
Electrostatic whistler mode conversion at plasma resonance
Authors: Maggs J. E. , Morales G. J.
Published: March 2009

The mode conversion of an electrostatic whistler wave into a Bohm–Gross mode at plasma resonance is analysed for a magnetized plasma with a longitudinal density gradient (i.e. ∇n0 X B = 0). It is found that a whistler incident upon plasma resonance from inside the plasma converts, without producing a reflected wave, into a short-wavelength Bohm-Gross mode that carries energy down the density gradient away from resonance. The detailed structure of the electric field near the resonance is found analytically. It is shown that the production of the Bohm-Gross wave by mode conversion can be described by a model of plasma resonance driven by a k = 0 electric field (i.e. the capacitor plate model). The relation between the driver amplitude and the amplitude of the incident whistler is derived.
Convective plasma transport modelled with propagators
Authors: Hitchon W. N. G.
Published: March 2009

The transport of plasma under the influence of a significant flow velocity in a toroidal stellarator has been modelled using an efficient numerical scheme based on ‘propagators’. The particle density has been calculated in a poloidal cross-section from the fluid particle conservation equation, using a flow velocity and a diffusion coefficient derived from experimentally obtained values. The formation of hollow density profiles during ECH has been examined, by varying the flow velocity v(r,θ) of the bulk of the plasma while ensuring that (its component in the minor-radial direction, averaged over poloidal angle θ) is consistent with experiment. A radial flow does not seem to account for the very hollow profiles observed in experiment. Hollownesses of between 1·5 and 5 were obtained for other plausible forms of v(r, θ).
On the power law for the wave spectrum
Authors: Abdel-Gawad H. I.
Published: March 2009

In this paper we determine the asymptotic behaviour of the spectral function for two types of waves generated in a turbulent plasma: plasma waves generated by a kinetic electron beam instability, and lower-hybrid waves. It is shown that the wave spectrum behaves in the lowest-order approximation as K–6 and K║–3 in the respective cases (where k and k║ are the wavenumber and the wavenumber parallel to the magnetic field) and is bounded below by an appropriate value. The distribution function is evaluated self-consistently in each case.
Rossby-type electrostatic electron plasma waves
Authors: McKenzie J. F. , Naidu K.
Published: March 2009

This paper explores the properties of Rossby-type electrostatic electron plasma waves at frequencies very much less than the electron gyrofrequency but very much greater than the ion gyrofrequency. Such waves represent the electron counterpart of ion Rossby waves, which propagate at frequencies very much less than the ion gyrofrequency in a plasma in which the ambient magnetic field possesses a spatial gradient perpendicular to its line of action. This feature simulates the ‘β-effect’ that operates in the classical atmospheric Rossby wave: the wave dynamics associated with both ion and electron Rossby waves are structurally similar to those associated with wave perturbations in a rotating fluid, where the β-effect arises from a spatial gradient in the Coriolis acceleration. It is shown that this plasma β-effect gives rise to a ‘new’ mode of the Rossby type, and in addition considerably modifies the conical wave propagation properties characteristic of the electron cyclotron mode. The highly dispersive and anisotropic nature of these waves is described in terms of the topology of the wavenumber surfaces concomitant with plane-wave solutions of the wave equation for the system as a whole.
An analytical solution to the Boltzmann–Fokker–Planck equation for multi-component non-homogeneous plasmas
Authors: Zoler D. , Cuperman S.
Published: March 2009

The previously obtained analytical solution to the Boltzmann equation for nonhomogeneous plasmas with relative large temperature and density gradients is generalized in the following sense. (i) The relatively simple Bhatnagar, Gross and Krook collision operator is replaced by the Fokker-Planck operator expressed in terms of relaxation rates (slowing down, energy exchange, etc.). (ii) The simple Lorentzian plasma model is replaced by a multi-component plasma model with realistic masses and temperatures.
Dynamics of correlation functions with Elsässer variables for inhomogeneous MHD turbulence
Authors: Marsch E. , Tu C.-Y.
Published: March 2009

On the basis of the ideal MHD equations expressed in terms of Elsässer variables, a new set of equations has been derived that governs the dynamics of the inhomogeneous background plasma and the superimposed incompressible fluctuations. From these equations the dynamic equation for the two-point and two-time correlation tensor has been obtained, and subsequently the equations of motion for the various spectral densities related to energy, cross-helicity and residual energy or the Alfvén ratio have been established. This set of equations offers a new possibility of discussing and perhaps better understanding the mostly incompressible fluctuations observed in the solar-wind plasma and of analysing their radial evolution into interplanetary space and their spectral development. The scope of the paper is limited to giving mainly formal developments of the equations. A detailed evaluation of the many terms in the light of interplanetary observations is intended for the future, but is not presented in this paper.
Investigation of the localized co-interchange instabilities in a rotamak plasma
Authors: Bertram W. K.
Published: March 2009

If the rotamak is regarded as a spherical field-reversed mirror then, according to conventional ideal MHD analysis, it should be unstable to co-interchange modes localized near the vortex point of the magnetic field. It is shown that to study these instabilities in a typical rotamak plasma, the Hall term in Ohm's law cannot be ignored. The effect of the Hall term on the ideal MHD analysis of co-interchange modes is investigated and a stability criterion is derived.
MHD surface waves in high- and low-beta plasmas. Part 1. Normal-mode solutions
Authors: Musielak Z. E. , Suess S. T.
Published: March 2009

Since the first paper by Barston (1964) on electrostatic oscillations in inhomogeneous cold plasmas, it has been commonly accepted that all finite layers with a continuous profile in pressure, density and magnetic field cannot support normal surface waves but instead the waves always decay through phase mixing (also called resonant absorption). Here we reanalyse the problem by studying a compressible current sheet of a general structure with rotation of the magnetic field included. We find that all inhomogeneous layers considered in the high-β plasma limit do not support normal modes. However, in the limit of a low-β plasma there are some cases when normal-mode solutions are recovered. The latter means that the process of resonant absorption is not common for all inhomogeneous layers.
Hydrodynamic equations for a plasma in the region of the distribution-function plateau
Authors: Konikov Yu. V. , Oraevskii V. N.
Published: March 2009

A hydrodynamic theory is presented for plasma particles whose distribution function is close to a plateau in some phase-space region for a finite one-dimensional phase-spase interval. In the framework of the methods of moments, a series expansion of the particle distribution function in an appropriate system of orthogonal (Legendre) polynomials near the state with a plateau is carried out. Deviations from the plateau are due to the presence of a heat flux. The expansion obtained for the distribution function is used to truncate the chain of hydrodynamic equations and to calculate the additional terms arising from the finiteness of the phase interval. The case of one-dimensional Langmuir turbulence is considered as an example. Expressions are presented for the moments of the quasilinear integral of collisions, which describe the variations of the macroscopic characteristics of resonant particles in the respective hydrodynamic equations. Criteria for applicability of the equations obtained are presented. Approximate invariants of motion are obtained in the extreme cases of narrow and broad plateaux.
Electrostatic-field fluctuations and form factors in multi-component non-equilibrium plasmas
Authors: Belyi V. V. , Paiva-Veretennicoff I.
Published: March 2009

Taking the Langevin approach to the evaluation of kinetic fluctuations with respect to a Maxwellian distribution characterized by different constant temperatures and mean velocities per species, the form factors and electrostatic field fluctuations of a multi-component plasma are derived. It is shown that the generalization of the Callen-Welton theorem for non-equilibrium systems, derived using thermodynamical arguments, has to be revised. Explicit values of the intensities of the electrostatic-field fluctuations are calculated, in the high-and low-frequency regimes. The former do not require any modelling of the collision integral. The latter have been calculated with a model that is more correct and simpler, than the Bhatnagar-Gross-Krook model.
Electromagnetic waves in a plasma waveguide
Authors: Ivanov S. T. , Alexov E. G.
Published: March 2009

A detailed analysis of wave dispersion in a plasma-filled waveguide in a finite external magnetic field is presented. The mutual influence of modes on their dispersion curves is treated. A new phenomenon is demonstrated: the coupling of the waveguide EH and HE modes and the parallel appearance of a backward wave. The values of Ω and ωp (the cyclotron and plasma frequencies) and R (the waveguide radius) at which coupling between arbitrary EH and HE modes becomes possible are found. The dispersion relations and field distributions of two new mode families that arise owing to the presence of the anisotropic plasma are analysed.
On waves in spatially cyclic equilibria
Authors: Diver D. A. , Laing E. W. , Sellar C. C.
Published: March 2009

We rederive the dispersion relation for a plasma containing a spatially cyclic equilibrium magnetic field, and discuss the polarization of the resulting waves.
Energetics of compressible models of fast steady-state magnetic reconnection
Authors: Jardine M. , Priest E. R.
Published: March 2009

An understanding of the energy transfer that takes place during magnetic reconnection is crucial to the study of this fundamental process. It depends on two factors: the type of reconnection regime (which is determined by the boundary conditions) and the degree of compressibility. Here we examine the role of compressibility in the energetics of a family of reconnection models. When the inflow Mach number (or reconnection rate) Me is small the effects of compressibility may be more important than the differences between regimes. We find that for a slow-compression regime with Me = 0·005 compressibility decreases by 39% the efficiency of the shocks in converting magnetic energy and increases by 14% the ratio of thermal to kinetic energy in the outflow jet. This compares with a 13% decrease in the shock efficiency and a 7% decrease in the jet ratio obtained by choosing instead a flux-pile-up regime. As Me is increased, however, the differences between regimes become larger and may be comparable to or greater than the effects of compressibility. Thus when the above Mach number is doubled we find that a change of regime now has 1–6 times the effect on the jet energy ratio as the introduction of compressibility. For those regimes, therefore, which only exist at low inflow Mach numbers, compressibility will always be important. At higher values of Me the type of regime may be the dominant factor governing the energetics.
Kinetic equations for a non-uniform plasma in strong fields and resulting particle transport
Authors: Øien Alf H.
Published: March 2009

From the BBGKY equations for a multi-component plasma a derivation of generalized kinetic equations valid for non-uniform, neutral as well as non-neutral plasmas in strong electric and magnetic fields is made. Explicit effects of particle gyration and non-uniformities on the collisional scale are included in the collision terms. For each particle species the collision terms describing interaction between the same or other particle species consist of two parts. The first part is a generalization of the corresponding classical term, to which it reduces when fields and non-uniformities are negligible on the collisional scales. The second part is non-vanishing when non-uniformities are taken account of on the collisional scale. For the case of a neutral plasma, particle transport transverse to the magnetic field and along the density gradient is found. The result shows an increase of particle transport as compared with the classical formula when the Larmor radii are smaller than the Debye length. The underlying mechanism for this increase is pointed out.
A theory of the relaxation of tokamak discharges
Authors: Brandenburg John E.
Published: March 2009

Tokamak equilibria are considered as extremum magnetic-energy states. Two quadratic invariants ∫Ψd3x, and ∫A.Bd3x are found to yield finite-beta equilibria in toroidal geometry. The theory predicts ‘bell’-shaped current profiles for relaxed discharges at finite beta. A ‘main-sequence’ curve of ql/q0 versus βp is presented for circular discharges with low ql and is found to form a limiting curve for experimental data.
Collisional relaxation of relativistic and degenerate electrons
Authors: Hinata Satoshi , Kishi Hideya
Published: March 2009

We derive a Fokker–Planck equation for relativistic and degenerate electrons interacting with ions. The ions may be degenerate and relativistic. Applications to a supernova plasma and laser–plasma interaction motivate this work.
A numerical study of strongly nonlinear plasma motion in a magnetic octupole field
Authors: Eriksson H. G. , Wahlberg C.
Published: March 2009

The strongly nonlinear axisymmetric motion of a z–pinch in an external magnetic octupole field is investigated numerically. A surface-current ideal-MHD approximation of the pinch is used, which allows a ‘contour-dynamics’ formulation of the problem. It is found that the plasma motion in the strongly nonlinear regime results in a collision between the plasma and one (or several) of the X-points. Thereafter, the X-point splits into two magnetic nulls (Y-points), which remain on the plasma surface and between which current reversal occurs. This phenomenon results in a strong force exerted on the outer parts of the plasma and directed towards the centre of the configuration. The force is able to stop the outward plasma motion under certain parameter conditions, which are found to be similar to those observed in experiments on the straight Extrap configuration.
Parametric excitation of a kinetic Alfvén wave at the ion-cyclotron frequency
Authors: Hasan Zehra , Guha S.
Published: March 2009

The parametric decay of an electrostatic ion-cyclotron wave into a low-frequency mixed-mode (EM-ES) kinetic Alvén wave and an electrostatic ion-cyclotron side-band has been investigated in a homogeneous low-β plasma. A nonlinear dispersion relation describing this parameteric interaction is derived. The partially electrostatic nature of the kinetic Alfvén wave and the component of the low-frequency ponderomotive force along the direction of the external magnetic field lead to the dominant coupling. Possible applications in the ionosphere, in the earth's magnetosphere and in laboratory plasmas are discussed.
Energy budget of stable magnetohydrodynamic waves in a homogeneous heat-conducting collisionless plasma in a strong magnetic field
Authors: de la Torre Alejandro
Published: March 2009

The energy transfer between a homogeneous heat-conducting collisionless plasma in a strong magnetic field and a harmonic external current immersed in it is studied in connection with the generation of stable magnetohydrodynamic waves in slow streams in the solar-wind plasma. The net balance of energy, given by the sum of the individual contributions that result from the interchange between each mode of oscillation and the stream, is established as function of the amplitude, frequency and growing rate of the external current and the plasma parameters.
Transfer equations for spectral densities of inhomogeneous MHD turbulence
Authors: Tu C.-Y. , Marsch E.
Published: March 2009

On the basis of the dynamic equations governing the evolution of magneto-hydrodynamic fluctuations expressed in terms of Elsässer variables and of their correlation functions derived by Marsch and Tu, a new set of equations is presented here describing the evolutions of the energy spectrum e± and of the residual energy spectra eR and es of MHD turbulence in an inhomogeneous magnetofluid. The nonlinearities associated with triple correlations in these equations are analysed in detail and evaluated approximately. The resulting energy-transfer functions across wavenumber space are discussed. For e± they are shown to be approximately energy-conserving if the gradients of the flow speed and density are weak. New cascading functions are heuristically determined by an appropriate dimensional analysis and plausible physical arguments, following the standard phenomenology of fluid turbulence. However, for eR the triple correlations do not correspond to an ‘energy’ conserving process, but also represent a nonlinear source term for eR. If this source term can be neglected, the spectrum equations are found to be closed. The problem of dealing with the nonlinear source terms remains to be solved in future investigations.
Acceleration of charged particles in quasi-perpendicular magnetohydrodynamic shocks
Authors: McLoud W. S. , Moraal H.
Published: March 2009

The energy gain of a non-relativistic charged particle in a quasi-perpendicular shock is studied. This is done by the usual procedure of transforming the shock structure to a perpendicular one. The difference with earlie'r studies is that we are able to derive a new, exact expression for this energy gain in closed form. Two successive approximations of this expression are presented and discussed. Finally, the average energy gain of an isotropie particle distribution in the original shock system is derived.
Gyrokinetic stability theory of z–pinches
Authors: Åkerstedt Hans O.
Published: March 2009

From the Vlasov-fluid model a set of approximate stability equations describing the stability of the pure z–pinch is derived. The equations are valid for equilibria with small gyroradius compared with the pinch radius, but the perturbation wavenumber k may be of the order of the gyroradius ρi, δ = kρi = 0(1) - so-called gyrokinetic ordering. The equations are used to study the stability of the m = 0 and m = 1 internal modes of the z–pinch. In the limit of zero gyroradius δ → 0 we recover previously obtained results. For δ ≠ 0 we find that increasing δ at first gives a rapidly decreasing growth rate, and for δ ≈ l the growth rate compared with perpendicular MHD is γ/γMHD ≈ 0·09. For larger δ however, the growth rate increases to a quite large value. For the m = O mode we find, provided that drift resonances can be neglected, a stability criterion for δ ≥ 1, which is fulfilled both for the Bennett equilibrium and the constant-current-density equilibrium.
Non-axisymmetric magnetohydrodynamic stability of a streaming annular jet containing very dense fluid cylinder and surrounded by a tenuous medium pervaded by a varying azimuthal magnetic field
Authors: Radwan Ahmed E.
Published: March 2009

The magnetohydrodynamic stability of a streaming annular jet containing a very dense fluid cylinder and acted upon by inertial and electromagnetic forces, in the presence of a varying transverse magnetic field pervading a tenuous surrounding medium, is considered. A general dispersion relation is established and studied analytically, and the results are confirmed numerically. The magnetic fields are stabilizing or destabilizing for each of the symmetric (m = 0) and non-axisymmetric (m ≠ 0) modes under some restrictions. The streaming has a strong destabilizing character, and its influence is to enlarge the magnetohydrodynamic instability domains and shrink the stability domains. The thicker the dense fluid core, the greater the number of magneto-hydrodynamically stable states. Increasing the magnetic field intensity shrinks the unstable domains. The (in)stability situation is much worse for m ≠ 0. However, if the axial field intensity is sufficiently high and greater than the transverse field intensity, the destabilizing character of the model, in a few cases, may be suppressed. This occurs if the Alfvén-wave velocities interior and exterior to the annular jet are greater than the unperturbed fluid velocity.
Electron-temperature effects on lower-hybrid-drift vortices
Authors: Bharuthram R. , Tagare S. G.
Published: March 2009

The nonlinear evolution of lower-hybrid-drift waves in an inhomogeneous magnetized plasma with warm electrons and cold ions is considered. The effect of finite electron temperature on a soliton solution of the set of nonlinear equations is examined.
Linearized potential of an ion moving through plasma
Authors: Peter Thomas
Published: March 2009

The solution of the linearized Vlasov–Poisson equations describing a projectile ion moving through a classical isotropic electron plasma is investigated analytically and numerically for a wide range of projectile velocities vp Extending the range of earlier computations considerably, our calculations were performed for velocities up to vp = 15vth, showing the wake field behind the ion for distances 0 ≤ d ≤ 200λD, where vth is the thermal electron velocity and λD the Debye length of the plasma. As a new feature, we demonstrate that the amplitude of the wake field in the region vp/vth ≤ d/λD ≤/23(vp/vth)3 is almost undamped, and only for larger distances from the ion does it take the 1/d behaviour shown in other work. Thus the wake field of a single ion persists for much longer than previously thought. The question of whether this effect could have practical consequences, for example, for ion-beam cooling, is briefly addressed.
Bootstrap-current computations for a stellarator-reactor plasma
Authors: D'Haeseleer W. D. , Hitchon W. N. G. , Beidler C. D. , Shohet J. L.
Published: March 2009

Numerical results for the bootstrap current in a stellarator-reactor plasma are presented. The distribution function f is computed numerically from a kinetic equation that is averaged over the helical ripple. The parallel flows and the current are obtained as v‖ moments of f. The physics issues embedded in the code are discussed concisely, concentrating on the justification as to why the bootstrap current can be estimated from an averaged scheme. Results are presented for typical stellarator-reactor parameters. The numerical code FLOCS predicts that the momentum-restoring terms in the collision operator have no significant impact on the value of the bootstrap current (the difference being about 10%). The results obtained are related to the equilibrium flows, and a physical interpretation based on the kinetic picture is presented. Finally, an estimate for the impact of J‖ on the rotational transform is given.
Electrogravitational instability of an annular fluid jet coaxial with a very dense fluid cylinder under radial varying fields
Authors: Radwan Ahmed E.
Published: March 2009

The electrodynamic instability of a self-gravitating dielectric annular fluid jet possessing a very dense fluid (of negligible inertia) cylinder mantle surrounded by another dielectric self-gravitating medium pervaded by a radial varying electric field is investigated. A general eigenvalue relation valid for all possible symmetric m = 0 and asymmetric m ≠ 0 perturbation modes is derived and discussed. The electrodynamic force has a strong destabilizing influence not only to m = 0 but also to m ≠ 0 disturbance modes. The self-gravitational force is stabilizing to all pure m ≠ 0 modes, while to m = 0 it is stabilizing or destabilizing according to conditions. The destabilizing effects of the internal and exterior varying electric fields shrink the gravitationally stable states and simultaneously increase the unstable ones. The electrogravitodynamic instability character of the model can be minimized if the electrodynamic force effect is extremely small in comparison with that of the self-gravitational force, but the instability will never be suppressed.
Wave interaction and low-frequency magnetic field generation in planar free-electron lasers
Authors: Rizzato F. B.
Published: March 2009

In recent work by the present author the full dispersion relation for multi-dimensional perturbations propagating in saturated free-electron lasers was derived. A number of approximations were used in order to derive a simplified description of the unstable modes. Although this simplified analysis was shown to be appropriate for quasi-transverse modes, it was not possible to describe the generic case of non-transverse ones. In the present paper, via a numerical analysis of this dispersion relation, we argue that a considerable number of modes do indeed not satisfy the quasi-transversality condition. The generation of low-frequency maenetic fields is also analysed.
Analytical study of plasma heating by resonant absorption of the modified external kink mode
Authors: Van Eester D. , Goossens M. , Poedts S.
Published: March 2009

A simplified analytic description is used to understand recent results of large-scale numerical simulations of resonant absorption and to disentangle the basic physics. It is shown that very efficient absorption takes place at frequencies where a discrete external kink and an Alfvén continuum mode merge into a modified external kink mode. The relation between this ‘hybrid’ mode and ‘pure’ continuum or discrete spectrum modes is discussed.
Magnetic-energy release from a zero-net-current layer
Authors: Kim J.-S. , Van Hoven G. , Schnack D. D. , Drake J. F.
Published: March 2009

The storage of magnetic energy in many natural systems is driven by localized convection. Since the initial state can often be described as a potential field, the stress arising from subsequent magnetic twisting is characterized by vanishing net-current flow. Such a layering scheme provides the lowest global energy excess for a given local field twist. In this paper we investigate the nonlinear release of this stored energy by the resistive magnetic-tearing instability. Our aim is to discover whether the evolution of this dynamic reconnection process is modified by the finite width and restoring force of the energizing field reversal. We use a force-free magnetic-field model with the sheared reversing component varying as tanh y sech Ky. We study the unstable nonlinear evolution by a 2·5-dimensional resistive magnetohydrodynamic simulation in a slab geometry. Almost all of the perpendicular (with respect to the ignorable coordinate) stored magnetic energy is released for some cases in this model. Although the magnetic reconnection is due to resistivity, the resulting closed flux surfaces evolve to a lower-energy state, i.e. to a nearly circular one, by mostly ideal MHD. Thus an elongated flux surface drives the plasma flow, and the flow speed is comparable to the Alfvén speed. The excess or stored magnetic energy is thereby released. In general, however, these processes take place only after reconnection occurs, and thus the release of energy is limited by the reconnection rate. The evolution of our new current/field system, which is more realistic as a model of a solar flare, exhibits an energy-release rate similar to that of more conventional field configurations. This rate can be increased, however, by the effects of an assumed anomalous resistivity enhancement.
Self-interaction of Alfvén waves in a cylindrical waveguide filled with an ideally conducting compressible plasma
Authors: Kumar Nagendra , Srivastava Krishna M.
Published: March 2009

The nonlinear behaviour of azimuthally symmetric Alfvén waves propagating along the axis of a cylindrical ideally conducting compressible fluid-filled waveguide is investigated. It is shown that the nonlinear evolution of such waves is governed by the nonlinear Schrödinger equation. Modulational instability for fundamental (m = 1) radial mode is discussed for α2 = 0·1,0·2, 0·3 and different values of k. The amplitude-dependent frequency and wavenumber shifts are calculated and their variations with wavenumber are shown graphically.
Theoretical study of a plasma column sustained by an electromagnetic surface wave in the dipolar mode
Authors: Benova E. , Ghanashev I. , Zhelyazkov I.
Published: March 2009

This paper presents a theoretical model of a plasma column sustained by an electromagnetic surface wave in the dipolar (m =1) mode for two different gas-discharge regimes: free-fall/diffusion and recombination respectively. The dispersion characteristics of the wave and the axial profiles of the plasma density, wave power, wavenumber and wave-field components for a given regime are specified by one numerical parameter σ = ωR/C, where ω is the angular wave frequency, R the plasma radius and c the speed of light, irrespective of the gas nature and pressure. It is established that there exists a ‘critical’ value of this parameter, σcr = 0·3726, below which a plasma is not likely to be sustained. A comparison between the axial structures of plasma columns sustained by electromagnetic waves in the dipolar and azimuthally symmetric modes is made. The model is in agreement with the available experimental results.
Propagation of electromagnetic waves in a density-modulated plasma
Authors: Lontano Maurizio , Lunin Nicolai
Published: March 2009

The properties of electromagnetic wave propagation in a uniformly densitymodulated plasma are studied, starting from a unidimensional scalar wave (Hill) equation for the wave electric field. Introduction of the formalism of the spatial propagator Q(z2, z1), from the point z1 to the point z2 allows reduction of the problem to determination of the propagator relevant to a single plasma layer that constitutes the entire periodic structure. The transmission coefficient of a single layer can be computed for any kind of density profile by means of the Magnus approximation, satisfying energy flux conservation at each order in the relevant expansion. The appearance of ‘forbidden zones’ in parameter space leads to the possibility that the incident electromagnetic wave can be partially or completely reflected if a sufficient number of periods are present. The explicit computation of the transmission coefficient for a series of n successive layers confirms this effect as the result of a ‘resonant’ interaction of the incident wave and the ‘periodicity’ of the medium.
Stochasticity caused by radiation misalignment in magnetized free-electron lasers with trapped particles
Authors: Rizzato F. B.
Published: March 2009

A theoretical and numerical analysis is performed on the conditions under which electron stochastic detrapping due to small misalignments between the laser wave vector and the global symmetry of the system occurs in magnetically guided free-electron lasers. In particular, it is shown that the threshold for stochasticity is only weakly dependent on the transverse momentum of trapped particles, which allows some simple general conclusions to be drawn regarding the maximum values allowed for this misalignment.
A new representation of relativistic wave damping above the electron-cyclotron frequency
Authors: Granata G. , Fidone I.
Published: March 2009

The full relativistic dielectric tensor for a Maxwellian plasma in the electron-cyclotron range of frequencies is investigated. A new representation for arbitrary values of the wave frequency and direction of propagation of the anti-Hermitian part is presented that avoids the standard expansions of the Bessel functions. A compact form of the wave damping for ω ≽ 2ωc is obtained that is useful for the investigation of synchrotron radiation in hot plasmas.
Finite-frequency surface waves on current sheets
Authors: Wessen K. P. , Cramer N. F.
Published: March 2009

The dispersion relation for low-frequency surface waves at a current sheet between two magnetized plasmas is derived using the cold-plasma dielectric tensor with finite ion-cyclotron frequency. The magnetic field direction is allowed to change discontinuously across the sheet, but the plasma density remains constant. The cyclotron frequency causes a splitting of the dispersion relation into a number of mode branches with frequencies both less than and greater than the ion-cyclotron frequency. The existence of these modes depends in particular upon the degree of magnetic field discontinuity and the direction of wave propagation in the sheet relative to the magnetic field directions. Sometimes two modes can exist for the same direction of propagation. The existence of modes undamped by Alfvén resonance absorption is predicted. Analytical solutions are obtained in the low-frequency and magnetic-field-reversal limits. The solutions are obtained numerically in the general case.
Non-ideal stability: variational method for the determination of the outer-region matching data
Authors: Pletzer A. , Dewar R. L.
Published: March 2009

Within the framework of studies of the stability of magneto-plasmas to non-ideal modes, such as resistive modes, the problem of determining the asymptotic matching data arising from the outer (ideal) region is considered. Modes possessing both tearing and interchange (ballooning) parity are considered in finite-pressure plasmas. The matching data, which form a matrix whose elements represent the small solution response to forcing by a big solution, are shown to derive from a variational (energy) principle. The variational principle, as presented, applies to both cylindrical and two-dimensional (toroidal) geometries. Allowing for the presence of multiple rational surfaces, a reciprocity relation between off-diagonal elements of the matching data matrix is obtained. The variational principle is suitable for numerical approximation, and, in particular, for the finite-element method, for which convergence rates are estimated. By packing nodes near the rational surface, maximum convergence, proportional to the inverse square of the number of mesh nodes for tent functions, is achieved.
Drift instability in the presence of a parallel electric field and an inhomogeneous magnetic field: particle aspect analysis
Authors: Tiwari M. S. , Varma P.
Published: March 2009

The theory of particle aspect analysis is extended to a drift wave in the presence of an inhomogeneous magnetic field and an applied electric field parallel to the ambient magnetic field. The effect of a parallel electric field is included in the zeroth-order distribution function through modification of the particle thermal velocity in that direction. The plasma under consideration is assumed to be anisotropic and with low β. The dispersion relation and growth rate are evaluated and discussed for particular plasma parameters. The limitations of the theory are also pointed out.
Scattering of electromagnetic waves by hybrid waves in a two-electron-temperature plasma
Authors: Sharma S. K. , Sudarshan A.
Published: March 2009

In this paper, we use the hydrodynamic approach to study the stimulated scattering of high-frequency electromagnetic waves by a low-frequency electrostatic perturbation that is either an upper- or lower-hybrid wave in a two-electron-temperature plasma. Considering the four-wave interaction between a strong high-frequency pump and the low-frequency electrostatic perturbation (LHW or UHW), we obtain the dispersion relation for the scattered wave, which is then solved to obtain an explicit expression for the growth rate of the coupled modes. For a typical Q-machine plasma, results show that in both cases the growth rate increases with noh/noc. This is in contrast with the results of Guha & Asthana (1989), who predicted that, for scattering by a UHW perturbation, the growth rate should decrease with increasing noh/noc.
Analytical solutions for the current driven by a rotating magnetic field in a spherical plasma
Authors: Watterson Peter A.
Published: March 2009

The steady currents driven in a spherical plasma by a rotating magnetic field via the Hall effect are studied analytically. The total field is shown to be symmetric across the origin. Integral relationships are obtained between Ohmic dissipation, angular momentum and the oscillating axial current density. The topology of the sum of a Hill's vortex field and a rotating field is documented. Analytical solutions for the driven current are obtained by expansion for the limits corresponding to small rotation frequency, to small number density, to large rotating-field magnitude, to small resistivity, and to small rotating-field magnitude combined with very small resistivity. The latter solution, relevant to the reactor limit, indicates that, with control of the vertical field magnitude, an MHD equilibrium can be generated with total current any fraction of the currentcorresponding to synchronous rotation of the electrons. Oscillating currents sufficient to drive the synchronous current are determined.
Parametric excitation of surface waves in a strongly inhomogeneous plasma
Authors: Brodin G. , Lundberg J.
Published: March 2009

The parametric excitation of surface waves in a warm inhomogeneous plasma is investigated. It is demonstrated that the coupling between the surface wave and plasmons that can be excited in the transition layer must be taken into account. The growth rate and the threshold value for the instability process are calculated. It is also shown that thermal effects are of importance even for very low temperatures, since the plasmons can now propagate out of the resonance region.
Space-dependent quasi-linear theory of lower-hybrid waves
Authors: Canobbio E. , Croci R.
Published: March 2009

The quasi-linear diffusion coefficients for the inherently space-dependent wave amplitudes in lower-hybrid heating and current-drive experiments are derived and compared with the usual space-independent approximation. The distribution function is derived and the dependence on the radio-frequency field amplitude gradient of the ‘plateau’, which is an essential quantity in thetheoretical description of LH experiments, is stressed.
Modelling of a plasma column sustained by a travelling circularly polarized electromagnetic wave (m = 1 mode) in the presence of a constant axial magnetic field
Authors: Benova E. , Staikov P. , Zhelyazkov I.
Published: March 2009

We present a set of equations modelling a low-pressure plasma column sustained by a travelling electromagnetic wave in the dipolar mode in the presence of a constant external magnetic field. It is shown that, from a practical point of view, only the m = 1 mode (the right-hand-polarized wave) can sustain plasma columns in a wide region of gas-discharge conditions: plasma radius R, wave frequency ωo, magnetic field Bo and low pressures, irrespective of the nature of the gas. We have examined two gas-discharge regimes: freefall/diffusion and recombination respectively. For a given gas-discharge regime the axial column structure and wave-field characteristics are specified by two numerical parameters: σ = ωR/c and ω = ωc/ω, where c is the speed of light and ωc the electron-cyclotron frequency. The main result of our study is that the magnetic field-makes it possible to sustain a plasma column for values of σ smaller than σcr = 0.3726, below which, in the absence of a magnetic field, the dipolar wave cannot produce a plasma. Moreover, at a fixed wave power, the magnetic field – in contrast with the case of plasma columns sustained by azimuthally symmetric waves – increases the plasma density and its axial gradient. The limit of an infinite external magnetic field (Ω → ∞) is also considered. A three-dimensional wave structure is obtained, and it indicates that the wave can be a generalized surface mode, a pure surface or a pseudosurface one.
Exact solution of the dispersion equation for electromagnetic waves in sheared relativistic electron beams
Authors: Cuperman S. , Heristchi D.
Published: March 2009

The transcendental dispersion equation for electromagnetic waves propagating in the slow mode in sheared non-neutral relativistic cylindrical electron beams in strong applied magnetic fields is solved exactly. Thus, rather than truncated power series for the modified Bessel functions involved, use is made of modern algorithms able to compute such functions up to 18-digit accuracy. Consequently, new and significantly more important branches of the velocity shear instability are found. When the shear-factor and/or the geometrical parameter a/b (pipe-to-beam radius ratio) are increased, the unstable branches join, and the higher-frequency, larger-wavenumber modes are significantly enhanced. Since analytical solutions of the exact dispersion relation cannot be obtained, it is suggested that in all similar cases the methods proposed and demonstrated here should be used to carry out a rigorous stability analysis.
Nonlinear generation of the fundamental radiation in plasmas: the influence of induced ion-acoustic and Langmuir waves
Authors: Rizzato F. B. , Chian A. C.-L.
Published: March 2009

A nonlinear emission mechanism of electromagnetic waves at the fundamental plasma frequency has been examined by Chian & Alves. This mechanism is based on the electromagnetic oscillating two-stream instability driven by two oppositely propagating Langmuir waves. The excitation of the electromagnetic oscillating two-stream instability is due to nonlinear wave–wave coupling involving Langmuir waves, low-frequency density waves and electromagnetic waves. In this paper the Chian & Alves model is improved using the generalized Zakharov equations. Attention is directed toward the influence of induced low-frequency and Langmuir waves on the properties of the electromagnetic oscillating two-stream instability. Presumably, the properties derived in the present context may be relevant to both space and laboratory plasmas.
Modulational instability of an ion wave packet in a cylindrical plasma-filled waveguide
Authors: Ghosh B.
Published: March 2009

The method of multiple scales is used to derive a nonlinear Schrödinger equation describing the nonlinear evolution of an ion wave packet propagating along a cylindrical plasma-filled waveguide. Numerical evaluation of nonlinear and dispersive terms shows that the wave is modulationally unstable if the wavenumber exceeds a certain critical value. On comparing with the case of an unbounded plasma, it is shown that finite geometry causes a significant shift of this critical value towards smaller wavenumbers, where Landau damping is relatively small.
Stability of electron inertia Alfvén solitons
Authors: Frycz P. , Rankin R. , Samson J. C.
Published: March 2009

Das, Kamp and Sluijter have proposed equations describing three-dimensional electron inertia Alfvén waves for which the characteristic length scales in directions parallel and perpendicular to the ambient magnetic field are of the same order. Planar, obliquely propagating soliton solutions of these equations are known to be linearly unstable. Numerical simulations reveal the nonlinear phase of the evolution of these solitons: a transition from flat to cylindrical solitons is observed, followed by breaking-up into three-dimensional localized cavities. The final stage corresponds to wave breaking; no final stable structure is achieved within the model.
Nonlinear self-interaction of plasma electromagnetic pulses propagating obliquely to a very strong ambient magnetic field
Authors: Kates Ronald E. , Kaup D. J.
Published: March 2009

We study nonlinear self-interactions including modulational instability in the case of a plane electromagnetic pulse propagating through a magnetized cold plasma at an arbitrary oblique angle to the external magnetic field. For intended applications to pulsar magnetospheres, the magnetic field is so large that both the electron- and ion-cyclotron frequencies are enormous compared with the plasma frequency or the frequency ω of the wave itself. The plasma is assumed to contain two singly charged species, either electrons and positrons or electrons and ions. (No approximation is made with respect to the mass ratio.) We restrict ourselves to the case eE0/mω ≪ 1 (i.e. the wave amplitude E0 excites the electrons to weakly, but not fully, relativistic velocities). We consider a pulse whose linear polarization is in the plane of the wave vector and the magnetic field. (The orthogonal polarization is purely electromagnetic, and induces no motion along magnetic field lines.) The pulse is assumed to be modulated along the direction of the group velocity vector. We show, using a self-consistent multiple-scales solution, that the envelope obeys the nonlinear Schrödinger equation, and from the coefficients of this equation we derive the conditions for modulational instability. Computation of the nonlinear coefficients requires detailed consideration of ponderomotive, relativistic and harmonic effects, all of which, in the ‘weakly relativistic’ case considered here, enter at the same order in the approximation scheme. Unlike the case of propagation parallel to a strong magnetic field, in oblique propagation we find a wide parameter range for modulational instability and soliton formation on time scales appropriate for pulsar micropulses.
On vertical spinning Alfvén waves in a magnetic flux tube
Authors: Campos L. M. B. C. , Isaeva N. L.
Published: March 2009

We derive the Alfvén-wave equation for an atmosphere in the presence of a non-uniform vertical magnetic field and the Hall effect, allowing for Alfvén speed and ion gyrofrequency that may vary with altitude; the pair of coupled second-order differential equations for the horizontal wave variables, namely magnetic field or velocity perturbations, is reduced to a single complex, second-order differential equation. The latter is applied to spinning Alfvén waves in a magnetic flux tube, in magnetohydrostatic equilibrium, in an isothermal atmosphere. The exact solution is found in terms of hypergeometric functions, from which it is shown that at ‘high altitude’the magnetic field perturbation tends to grow to a non-small fraction of the background magnetic field. By ‘high-altitude’ is meant far above the critical level, which acts as a reflecting layer for left-polarized waves incident from below, i.e. from the ‘low-altitude’ range. We also obtain the exact solution near the critical level, where the left-polarized wave has a logarithmic singularity, and the right-polarized wave is finite. The latter is plotted in this region of wave frequency comparable to ion gyrofrequency, and it is shown that the Hall effect can cause oscillations of wave amplitude and non-monotonic phases with slope of alternating sign. The latter corresponds to ‘tunnelling’, i.e. waves propagating in opposite directions or trapped in adjoining atmospheric layers; this could explain the appearance of inward- and outward-propagating waves, with almost random phases, in the solar wind beyond the earth, for which the Hall effect on Alfvén waves should be significant.