bluuebunny/crossref_metadata_2025 huggingface dataset:
Instability of intensely propagating circularly polarized electromagnetic pulses in a two-component plasma
Authors: Kates Ronald E. , Kaup D. J.
Published: March 2009

For relativistic amplitudes (‘intense propagation’), modulations of electromagnetic (EM) waves in a cold plasma are strongly coupled to longitudinal modes via the ponderomotive force, even if the unmodulated wave is purely transverse. The effect of longitudinal motions is comparable to that of relativistic nonlinearities. Hence a correct and proper expansion procedure requires solution of all the field equations up the appropriate order, including the longitudinal equations. (The plasma is assumed to be fully ionized and cold, with no net charge. The positive component may consist of either positrons or singularly charged ions. Quasi-neutrality is not imposed, but deviations are shown to be small for slow modulations.) We begin by deriving envelope equations (i.e. a reduced set of partial differential equations) governing modulations of intensely propagating, circularly polarized, plane EM plasma waves. (Here the envelope equations are not merely accurate to the appropriate order, but in fact exact.) We then analyse their modulational instabilities. Since the envelope equations are exact, they include the weakly relativistic case (transverse velocities ≪ c) as a limit. We first verify that, in this limit, the envelope equations yield the nonlinear Schrödinger equation (NLS) complete with the correct coefficients and thus the correct modulational instability conditions. Next, although the NLS does not hold for the general case of fully relativistic systems (transverse velocities comparable to c), we still succeed in deriving the modulational instability properties of intensely propagating EM waves in the fully relativistic case directly from the envelope equations, again, reproducing the weakly relativistic case as a test of the perturbation method used. Finally, we apply the results in special cases. For example, in the ultrarelativistic limit (transverse velocities close to c) of either an electron—positron or ion—electron plasma, waves with frequencies below twice the relativistic plasma frequency ωp, where , are unstable. The time scale for growth is comparable to the time for a wave packet to move past a fixed point. (This time scale is much shorter than in the weakly relativistic case, where the time scale for instability is that of the spreading of the wave packet due to linear dispersion.) Our results have important consequences for observations of pulsar micropulses, possible technological applications, and general implications for applications of Whitham theory.
Parametric instabilities of circularly polarized large-amplitude dispersive Alfvén waves: excitation of parallel-propagating electromagnetic daughter waves
Authors: Viñas Adolfo F. , Goldstein Melvyn L.
Published: March 2009

We investigate the parametric decay and modulational instabilities of a large-amplitude circularly polarized dispersive Alfvén wave. Our treatment is more general than that of previous derivations based on the two-fluid equations in that we allow for propagation of the unstable daughter waves at arbitrary angles to the background magnetic field, although our main concern in this paper is the exploration of new aspects of propagation parallel to the DC magnetic field. In addition to the well-known coupling of pump waves to electrostatic daughter waves, we find a new parametric channel where the pump wave couples directly to electromagnetic daughter waves. Excitation of the electromagnetic instability occurs only for modulation (k/k0 ≤ 1) and not for decay (k/k0 < 1). In contrast with the modulational instability excited by the electrostatic coupling, the electromagnetic modulational instability exists for both left-hand (K > 0) and right-hand (K < 0) polarization. For large k/k0, the electromagnetic channel dominates, while at lower values the electrostatic channel has a larger growth rate for modest values of dispersion, pump-wave amplitude and plasma β. Unlike the electrostatic modulational instability, the growth rate of the electromagnetic instability increases monotonically with increasing pump wave amplitude. This analysis confirms that, for decay, the dominant process is coupling to electrostatic daughter waves, at least for parallel propagation. For modulation, the coupling to electromagnetic daughter waves usually dominates, suggesting that the parametric modulational instability is really an electromagnetic phenomenon.
Bistability of a forced hydromagnetic cavity
Authors: Nocera Luigi , Priest Eric R.
Published: March 2009

We study the nonlinear stability of a one-dimensional hydromagnetic cavity into which Alfvén waves are fed by harmonic shear motions of its boundaries and where they interact with slow magnetosonic waves. We use characteristic conditions for the outgoing and ingoing Alfven waves at the boundaries where the magnetosonic oscillations are required to vanish. Forcing of Alfven waves takes place at a frequency close to the eigenfrequency of the lowest-order mode of the cavity. We let the frequency detuning δω vary as a free parameter together with the amplitude of the forcing, the plasma β and the compressive Reynolds number Re0. Given these last three parameters and varying δω, we calculate the amplitude of the nonlinear equilibrium state of the cavity as the stationary solution of a simple forced, dissipative dynamical system that governs the evolution of the cavity over a slow time scale and to which we are led by multiple-scale and Galerkin analyses of the one-dimensional MHD equations. This amplitude is a multi-valued function of δω (bistability), and we discuss the possibility of nonlinear stabilization of the Alfven wave by locking it in one of the bistable states. This amplitude undergoes saddle-node bifurcations: we calculate the two values of δω at which this occurs and the lowest value of the Reynolds number (27/2) for this to happen. We show that the magnetic energy density released during a bistable transition scales as (Re0)2; it has a maximum at β = 1 - (⅔)½ and it may amount to a substantial part of the energy originally stored in the unperturbed cavity. The magnetic power density released scales as (Re0)3 and has a maximum at β = 1 ± (⅓)½5. We conclude that the cavity is a good site for plasma heating such as that of the solar corona.
A generalization of the Taylor constraint to the advection of axisymmetric poloidal magnetic fields
Authors: Watterson Peter A.
Published: March 2009

The range of ▿ ∧ (u ∧ B) is determined for an axisymmetric poloidal incompressible B and incompressible u, by solving ▿ ∧ (u ∧ B) = ▿ ∧ v for u, assumed to be confined to within a surface of revolution. Two constraints on V are shown to be necessary for the existence of solutions, viz that the integral of rç/|B| must vanish on each flux surface, and that the integral of v1 around any dosed field line must vanish. The construction of the general solution proves that the constraints are sufficient conditions, providing also that the second derivative, with respect to the poloidal flux function, of the volume contained by flux surfaces does not vanish. The general solution is stated for the homogeneous case, v = 0. For the particular case of poloidal v1 an integral property of the solution u is established.
Kinetic theory of cross-modulation in a weakly ionized plasma
Authors: Garrett A. J. M.
Published: March 2009

Cross-modulation in plasma is an electromagnetic wave interaction in which the modulation of one ‘disturbing’ wave is imposed nonlinearly on the transport properties of the medium, and thence onto a second, ‘wanted’ wave propagating linearly through it. This analysis is restricted to weakly ionized plasma with allowance for ambient magnetic field, as in the lower ionosphere. A kinetic description is used, based on the Boltzmann equation for the electrons, with electron-molecule collisions described by Boltzmann's collision integral. Because of the small mass ratio this simplifies to a differential form. The perturbation of the electron velocity distribution functionf(v, t) due to the disturbing wave is calculated up to terms quadratic in wave amplitude, which are the lowest order to show the effect. The part of the term quadratic in wave amplitude at zero times the fundamental frequency, and isotropic in velocity space, which represents the perturbation in electron energy distributions, is selectively enhanced by an inverse factor of mass ratio, since the excess energy imparted by the wave to the electrons is transferred collisionally to the molecules at a rate inversely proportional to mass ratio. Modulation of the wave induces modulation of the electron energy distribution. A more general expansion scheme, in velocity-space spherical harmonics, is also presented. To calculate the dispersion relation for the second, ‘wanted’ wave, the linear part of the disturbing wave analysis is adapted, and the amplitude of the wanted wave is given in the WKB approximation as a phase integral of the refractive index along the ray path; this contains moments of the electron energy distribution and is modulated. The predictions of older semi-empirical theories, that the effect is enhanced when the fundamental frequency of the disturbing wave is close to the electron gyrofrequency, and that the second harmonic of the modulation is also imposed on the wanted wave, are confirmed. The wanted wave is predominantly amplitude-modulated, and only amplitude modulation of the disturbing wave is picked up; phase modulation is not transferred. There is no cross-modulation if the collision frequency is independent of collision speed, when contributions from all parts of velocity space cancel.
The equations of reduced magnetohydrodynamics
Authors: Zank G. P. , Matthaeus W. H.
Published: March 2009

The equations of high- and low-beta reduced magnetohydrodynamics (RMHD) are considered anew in order to elucidate the relationship between compressible MHD and RMHD and also to distinguish RMHD from recently developed models of nearly incompressible MHD. Our results, summarized in two theorems, provide the conditions under which RMHD represents a valid reduction of compressible MHD. The equations for low-beta RMHD and high-beta RMHD are shown to be identical. Furthermore, as a direct consequence of our analysis, the conditions under which both two-dimensional incompressible MHD (in terms of the spatial co-ordinates as well as the fluid variables) and 2½ dimensional incompressible MHD (i.e. only two-dimensional in the spatial co-ordinates) represent a valid reduction of three-dimensional compressible MHD are also formulated. It is found that the elimination of all high-frequency and long-wavelength modes from the magneto-fluid reduces the fully compressible MHD equations to either two-dimensional incompressible MHD in the plasma beta (β) limit β ≪ 1, or 2½-dimensional incompressible MHD for β ≈ 1. Our approach clarifies several inconsistencies to be found in previous investigations in that the reduction is exact. Our results and analysis are expected to be of interest for plasma fusion and space and solar physics.
Effect of warm beam electrons on electrostatic-shock solutions
Authors: Dey M. , Das U. N. , Goswami K. S. , Bujarbarua S.
Published: March 2009

We use a one-dimensional quasi-neutral fluid model to study the formation of an electrostatic shock associated with the lower-hybrid mode propagating almost perpendicularly to the magnetic field that exists in the auroral zone of the magnetosphere containing cold downward-streaming electrons, cold upward-streaming ions and beam electrons. We examine the effects of finite electron-beam temperature by describing the beam electrons with fluid equations. We then show how exact time-stationary shock solutions may be found when quasi-neutrality is considered.
Sheath potential distribution in a plasma including negative ions
Authors: Yamada H. , Yoshida Z.
Published: March 2009

Sheath potential distributions in electrostatic plasmas including negative ions have been studied using the Bohm equation. Since the mean velocity of the negative ions is not necessarily negligible compared with their thermal velocity, the contribution from non-thermal negative ions has been considered. The Sagdeev potential has been introduced to consider structural instabilities of the Bohm system. Wavy solutions related to ion-acoustic solitons bifurcate from the monotone asymptotic Bohm sheath solutions. The solvability conditions have also been discussed for characteristic parameter such as the concentration of negative ions and the Mach numbers of positive and negative ions.
Stimulated emission from a laser-wiggled electron beam travelling in an electrostatic wave
Authors: Kim S. H.
Published: March 2009

An axial emission process by a relativistic electron beam travelling in a laser beam and an electrostatic wave propagating in the direction antiparallel to the electron-beam direction (‘electric wiggler’), which is different from free-electron two-quantum Stark (FETQS) emission, is identified, and the laser gain through this process is investigated using relativistic quantum kinetics. The transverse a.c. source current for this axial emission is produced by the laser field acting as a classical electromagnetic wave to wiggle the electron in the transverse direction. From the viewpoint of quantum kinematics, this radiation-wiggled one-quantum induced Stark (RWOQIS) emission is exactly the same as FETQS emission in which the equivalent transverse source current needed for the axial emission is due to the intrinsic electron spin angular momentum. However, these two emissions differ in dynamics, since the former is an one-quantum process while the latter is a two-quantum process. It is found that the laser gain by RWOQIS emission increases with the laser intensity when ¦eA0/mc2¦ ≪ 1 and decreases with the inverse of the square of the laser intensity when ¦eA0/mc2¦ ≫ 1, where A0 is the potential amplitude of the laser wave and mc2 is the electron rest energy. This newly found emission is an inherently stimulated one, and does not have a corresponding spontaneous emission.
Amplification of magnetovortex waves in planar MHD flows
Authors: Rutkevich I. M. , Mond M.
Published: March 2009

The propagation of magnetovortex waves in an inhomogeneous medium with planar flow and perpendicular magnetic field is investigated. The linearized MHD equations are studied with the aid of the WKB approximation. Within the latter, a set of ordinary differential equations along the streamlines of the basic flow is derived. These equations govern the variations of the transverse as well as the parallel magnetovortex waves along its rays. The amplitude equations are solved explicitly for a particular geometry of the basic flow, and the solutions are investigated for subsonic as well as for supersonic basic flows.
Study of lower-hybrid wave propagation in the presence of low-frequency fluctuations
Authors: Fischer B. , Krämer M.
Published: March 2009

Phase-sensitive probe diagnostics as well as two-point-correlation analysis of radio-frequency probe signals are applied to investigate small-amplitude lower-hybrid (LH) waves launched into a linear nonuniform plasma column by a slow-wave antenna. The LH wave propagation in the inhomogeneous plasma is described by a model taking into account the wavenumber spectrum of the antenna. Special attention is focused on the interaction of the LH waves with the low-frequency density fluctuations. The LH frequency and wavenumber spectra observed can be explained by scattering of the LH waves from the (incoherent) low-frequency density fluctuations. Moreover, the enhanced damping, which is found to be much higher than expected from collisional and electron Landau dampings, is correlated with the level of low-frequency fluctuations.
Numerical study of self-interaction of Bernstein waves by nonlinear Landau damping
Authors: Sugawa Masao
Published: March 2009

When Bernstein waves (B waves) are excited in a magnetized plasma, their self-interaction by nonlinear Landau damping (NLD) becomes the dominant mechanism for the electron heating of the bulk plasma. We examine this behaviour numerically. This occurs only for B waves with relatively small k∥ because the damping of the B waves becomes very small. This occurs in the relatively broad B-wave frequency range betweenω/ωc = 1.45 and 1.78. For B waves with large k∥ (k∥R > 0.15), virtual waves are not generated via self-interaction due to NLD because the quasi-linear cyclotron damping of the B waves becomes the dominant mechanism. The numerical results agree well with experimental ones.
Alfvén surface waves along cylindrical annular streaming jets having a very dense fluid mantle pervaded by longitudinal magnetic fields
Authors: Radwan Ahmed E.
Published: March 2009

The characteristics of Alfvén surface waves along a cylindrical annular streaming column with a solid core and surrounded by a tenuous medium, and pervaded by a longitudinal magnetic field are studied analytically and numerically. Both axisymmetric (m = 0) and non-axisymmetric (m ≠ 0) modes are found to be dispersive. The Alfvén-wave velocity decreases with increasing magnetic field. Under an infinitesimal perturbation, the motion of the system is laminar and stable for all values of m for all short and long wavelengths if the unperturbed state is non-streaming. If the system is streaming, there will be unstable domains not only for m = 0 but also for m ≠ = 0 owing to the strong destabilizing influence of the streaming. However, this instability can be suppressed completely if the magnetic field is sufficiently high that the Alfvén-wave velocity is greater than the streaming velocity. The thicker the solid core the greater is its stabilizing influence for m = ±1, and vice versa for m = 0. A longitudinal field imparts a degree of rigidity to the conducting fluid, so it always has a strong stabilizing influence.
Cosmic-ray particle transport in weakly turbulent plasmas. Part 1. Theory
Authors: Schlickeiser Reinhard , Achatz Ulrich
Published: March 2009

We consider a quasi-linear theory for the acceleration rates and propagation parameters of charged test particles in weakly turbulent electromagnetic plasmas. The similarity between two recent approaches to modelling of therandom electromagnetic field is demonstrated. It is shown that both the concept of dynamical magnetic turbulence and the concept of superposition of individual plasma modes lead to particle Fokker—Planck coefficients in which the sharp delta functions describing the resonant interaction of the particles have to be replaced by Breit—Wigner-type resonance functions, which are controlled by the dynamical turbulence decay time and the wave-damping time respectively. The resulting resonance broadening will significantly change the evaluation of cosmic-ray transport parameters.
Excitation and reflection of ion-acoustic waves by a gridded plate and a metal disk
Authors: Nakamura Y. , Ito T. , Koga K.
Published: March 2009

Reflection coefficients and excitation efficiency of a gridded plate (a bipolar potential structure where the grid is separate but parallel to the juxtaposed plate) and a metallic disk for ion-acoustic waves have been measured experimentally. When the grid is biased negatively with respect to the plasma potential, reflection in phase with the incident wave and excitation of an outgoing wave are observed only when the bias of the plate is positive. When the bias of the gridded plate is positive, reflection occurs when the grid bias is either negative or positive. For the metal disk, reflection and excitation are observed when the bias is positive. The small reflection detected when the bias is negative is found to be due to scattering of the incident wave at the edge of the disk.
Oblique nonlinear Alfvén waves in strongly magnetized beam plasmas. Part 2. Soliton solutions and integrability
Authors: Deconinck Bernard , Meuris Peter , Verheest Frank
Published: March 2009

Oblique propagation of MHD waves in warm multi-species plasmas with anisotropic pressures and different equilibrium drifts is described by a modified vector derivative nonlinear Schrödinger equation, if charge separation in Poisson's equation and the displacement current in Ampère's law are properly taken into account. This modified equation cannot be reduced to the standard derivative nonlinear Schrödinger equation, and hence requires a new approach to solitary-wave solutions, integrability and related problems. The new equation is shown to be integrable by the use of the prolongation method, and by finding a sufficient number of conservation laws, and possesses bright and dark soliton solutions, besides possible periodic solutions.
Coupling of electromagnetic filamentation instability and electrostatic Langmuir parametric instabilities in laser—plasma interactions
Authors: Chian A. C.-L. , Rizzato F. B.
Published: March 2009

The interaction of electromagnetic filamentation instability and electrostatic Langmuir parametric instabilities (parametric decay instability and oscillating two-stream instability) driven by an intense laser in a plasma is examined. Near the critical layer of an underdense plasma, where the incident laser frequency is close to the local plasma frequency, coupling of unstable electromagnetic and electrostatic modes may occur. The transition from purely electromagnetic and purely electrostatic instabilities to hybrid instabilities is analysed using the generalized Zakharov equations.
Reflection and excitation of ion-acoustic waves in a multi-component plasma with negative ions
Authors: Ito T. , Nakamura Y.
Published: March 2009

Reflection and excitation of ion-acoustic waves by a bipolar potential structure consisting of a grid and a metallic plate have been investigated experimentally in a multi-component plasma with negative ions. Reflection is observed owing to the presence of the negative ions, even if both the grid and the plate are biased negatively with respect to the plasma potential so as to collect positive ions. Reflection coefficients and excitation efficiencies are measured as a function of the bias voltage of the electrodes. The reflection coefficient becomes larger for a negative bias of the grid, and is almost constant for a positive bias of the grid as the partial pressure of SF6 gas is increased.
Finite-Larmor-radius flute-mode theory with end loss
Authors: Kotelnikov I. A. , Berk H. L.
Published: March 2009

The theory of flute-mode stability is developed for a two-energy-component plasma partially terminated by a conducting limiter. The formalism is developed as a preliminary study of the effect of end loss in open-ended mirror machines, where large-Larmor-radius effects are important.
Minority-ion distribution function of a plasma under fundamental and second-harmonic ion-cyclotron heating
Authors: Weyssow B.
Published: March 2009

The distribution function of the minority ions during ion-cyclotron heating is calculated from a kinetic equation composed of a Landau collision term and a surface-averaged quasi-linear heating term. The kinetic equation is solved by a moment method in which the minority-ion distribution function is expanded in irreducible tensorial Hermite polynomials. The coefficients of the expansion are shown to be solutions of a system of coupled algebraic equations, and the effective minority-ion temperature is deduced from a compatibility constraint. The latter equation is in general too complicated to be solved analytically. The distribution function obtained here is therefore a semi-analytical result.
Arbitrary-amplitude electron acoustic solitary waves in a plasma
Authors: Chatterjee Prasanta , Roychoudhury Rajkumar
Published: March 2009

Recently Mace et at. studied electron-acoustic solitary waves in a plasma using a pseudopotential approach. To find the finite ion-temperature Sagdeev potential, they used a numerical technique developed by Baboolal, Bharuthram & Hellberg. In this paper we show that the exact pseudopotential can be obtained in this case in an analytical form. The numerical results obtained by Mace et at. are compared with our result, and complete agreement is found. We also discuss the conditions for the existence of solitary-wave solutions, and obtain the soliton solutions in some cases when these conditions are satisfied.
Stability of obliquely propagating plane solitons of the Zakharov–Kuznetsov equation
Authors: Allen M. A. , Rowlands G.
Published: March 2009

By determining to first order the growth rate of a small, long-wavelength, perturbation to a Zakharov–Kuznetsov plane soliton moving at an angle α to the magnetic field, it has been found that such solitons are unstable for α α0( ∼ 38 °). To determine the stability for angles greater than α0, one needs the growth rate to higher order. The conventional approach generates a second-order growth rate that is singular at α = α0. We rigorously obtain an expression that is bounded at this point, by developing a method in which exponentially secular terms that arise are regrouped before their subsequent elimination. We then show that these solitons are unstable for all α, although the growth rate is small for α>α and goes to zero as α→½π. The relevant linearized equation is solved numerically, and excellent agreement between analytical and numerical results is obtained.
Modelling and numerical simulation of microwave pulse propagation in an air-breakdown environment
Authors: Kim J. , Kuo S. P. , Kossey Paul
Published: March 2009

The dependences of the propagation characteristics of an intense microwave pulse on the intensity, frequency, width and shape of the pulse in an air- breakdown environment are examined. Numerical simulations lead to a useful empirical relation P3W = α = const, where P and W are the incident power and width of the pulse and α depends on the percentage of the pulse energy transferred from the source point to a given position. The results also show that, using a single unfocused microwave pulse transmitted upwards from the ground, the maximum electron density produced at, for example, 50 km altitude is limited by the tail erosion effect to below 106 cm-3. Repetitive-pulse and focused-beam approaches are then examined. Both approaches can increase the maximum electron density by no more than an order of magnitude. Hence a scheme using two obliquely propagating pulses intersecting at the desired height (e.g. 50 km) is considered. It is shown that the generated electron density at the lowest intersecting position can be enhanced by more than two orders of magnitude.
Wave dispersoin and resonant deposition profiles of electron-cyclotron Gaussian beams in toroidal plasmas
Authors: Cirant S. , Nowak S. , Orefice A.
Published: March 2009

A peculiarity of the quasi-optical propagation of a Gaussian beam of electromagnetic waves is that it requires a treatment taking account, step by step, of all of its rays together. The dispersion relation from which such a ray- tracing may be deduced is in fact characterized not only by the medium where the beam is launched but also by the intrinsic beam structure. The behaviour of three-dimensional Gaussian beams in the electron-cyclotron frequency range is considered, with particular attention paid to their propagation in toroidal plasmas of fusion interest (with ITER-like parameters and various magnetic equilibrium configurations), to the generality of their launching conditions and to their power deposition profiles around resonant layers.
Surface Alfvén waves of negative energy
Authors: Ruderman M. S. , Goossens M.
Published: March 2009

The stability of an MHD tangential discontinuity is studied in an incompressible plasma where viscosity is taken into account at one side of the discontinuity. When the shear velocity is smaller than the threshold value for the onset of the Kelvin-Helmholtz (KH) instability, two surface waves can propagate along the discontinuity. There is a critical value for the shear velocity, which is smaller than the threshold value for the onset of the KH instability. When the shear velocity is smaller than the critical value, the two surface waves propagate in Opposite directions. When the shear velocity is larger than the critical velocity, the two waves propagate in the same direction, and the wave with smaller phase velocity is a negative-energy wave. Viscosity causes this negative-energy wave to be unstable, and the instability increment is proportional to the viscosity coefficient.
Thermal instability in a star—gas system
Authors: Talwar S. P. , Bora M. P.
Published: March 2009

A composite interstellar model consisting of stars and optically thin radiating plasma is considered in order to investigate the thermal instability arising from possible radiation and other heat-loss mechanisms. The stellar dynamics is governed by the Vlasov equation, while the gas is supposed to be a hydromagnetic plasma, described by the MHD equations, with a density- and temperature-dependent heat-loss function. It is shown that while with cold stars the system is in general unstable irrespective of thermal effects of the plasma, with warm stars having a Maxwellian distribution the thermal plasma considerably influences the stability of the composite system. It is also shown that the otherwise stable composite (with warm stars) configuration may become unstable in the presence of a radiating plasma because of coupling between the heat-loss mechanisms and stellar populations.
Symmetries of the triple degenerate DNLS equations for weakly nonlinear dispersive MHD waves
Authors: Webb G. M. , Brio M. , Zank G. P.
Published: March 2009

Lie symmetries, conservation laws, and Lagrangian and Hamiltonian formulations of the triple degenerate, derivative nonlinear Schrödinger (TDNLS) equations for weakly nonlinear dispersive, magnetohydrodynamic (MHD) waves are derived. The equations describe how Alfvén waves propagating parallel to the background magnetic field B interact with the magneto-acoustic modes near the triple umbilic point where the fast, slow and Alfvén mode phase speeds coincide. The Lie point symmetries are used to derive classical similarity solutions of the equations. In particular, the similarity solutions corresponding to time translation, space translation and rotational invariance symmetries are reduced to quadrature. The dispersionless TDNLS system is of hydrodynamic type, and has three families of characteristics analogous to the slow, intermediate and fast modes of MilD. The Riemann invariants corresponding to each of these families are obtained in closed analytic form. Examples of solitary wave and periodic travelling wave solutions are investigated by plotting the contours of the Hamiltonian H(v, w) in the (v, w) phase plane, where the canonical variables v and w correspond to the normalized transverse magnetic field perturbations. An analysis of the prolongation Lie algebra is carried out in order to investigate the integrability of the equations.
Effects of charge dispersion in dusty plasmas
Authors: Aslaksen T. K.
Published: March 2009

We investigate the charge-dispersive effects on a sheath of monosized dust particles in equilibrium. This is done through describing the dust particles by using equations in (x, v) space (kinetic space) that include terms originating from the charge distribution of the dust particles. The charge-dispersive terms are assumed to be completely determined by the local charging processes. We find that the effects due to these terms are opposed by the ordinary gradient terms in the current equation in kinetic space, and they are therefore smaller than first expected. We also identify kinetic effects that are not included in the usual expression for the dust charge in hydrodynamic space.
A new Hamiltonian formulation for fluids and plasmas. Part 2. MHD models
Authors: Larsson Jonas
Published: March 2009

The new Hamiltonian formulation of the perfect fluid equations presented in part 1 of this series of papers is generalized to a class of IVIHD models, including for example ideal MHD and the Chew–Goldberger–Low equations. The mathematical structure is to a great extent unchanged by this generalization, and most results about the small-amplitude expansion of the perfect fluid equations remain obviously valid. For example, we now have a rigorous proof of the Manley-Rowe relations in resonant three-wave interaction, valid for this class of MHD models and for quite general inhomogeneous but stationary background states, including equilibrium flows.
Relativistic transverse modulational instability of two electron cyclotron waves
Authors: Yang Kwang-Sup
Published: March 2009

The transverse modulational instabilities of two finite-amplitude electron-cyclotron waves due to the ponderomotive force and relativistic mass variation of electrons are considered using the coupled nonlinear Schrödinger equation model. The waves are modulationally unstable, with maximum growth rate larger than that of a single wave. The stable waves can be unstable by the effect of coupling. The instability is caused only by the mass variation of electrons, and the contribution of the ponderomotive force is negligibly small. The instability of copropagating waves has a convective nature and that due to the counterpropagating waves has an absolute nature, no matter how large the pump intensities are. The threshold of modulational instability is also considered for finite-length plasmas.
Magnetogravitational instability of compressible streaming superposed fluids
Authors: Radwan Ahmed E.
Published: March 2009

The magnetogravitational instability of compressible streaming superposed fluids pervaded by different transverse magnetic fields is investigated. A perturbed sinusoidal wave is assumed to propagate along the direction of the streaming velocities. The stability criterion has been derived in a general form, and some limiting cases are recovered from it. The influences of different forces and factors are identified. The system under consideration is unstable not only for states with long wavelengths but also for those with short wavelengths.
TM mode radiation guiding in an REB-induced plasma duct
Authors: Parashar Jetendra , Lalita
Published: March 2009

An intense relativistic electron beam propagating through a plasma creates a low-density plasma duct capable of guiding a free-electron laser mode. The beam dynamics plays an important role in the propagation of TM modes. For (where and are the beam and plasma densities respectively, and a and b are the x and y dimensions of the duct) and beam energy of about 2 MeV, the threshold current turns out to be about 20 kA. For marginal radiation guiding, the size of the plasma duct decreases with beam voltage. Application of a strong DC magnetic field shows that an even narrower duct can guide high-frequency radiation.
Kinetic Alfvén solitons in a low-β plasma under the influence of electron drift motion
Authors: Kalita B. C. , Devi N.
Published: March 2009

Fully nonlinear kinetic Alfvén solitary waves are investigated, taking account of the drifting effect of electrons in the direction of the external magnetic field in a low-β plasma (where β = 8πn0T/c2B02 is the ratio of the kinetic pressure to the magnetic pressure). Both compressive and rarefactive Alfvén solitons are found to exist in different ranges of kz (direction of wave propagation), depending on the values of M (the Mach number) and ve (the drift velocity, occurring implicitly in an effective parameter A). The existence domain of kinetic Alfvén solitons is found to be concentrated in the upper regime of β (≪ 1) and lower regime ofM ( < 1), but the values of M in the case of rarefactive solitons are observed to be higher than those of compressive solitons. The range of existence of kinetic Alfvén solitons is substantially narrowed when the initial drift velocity v′e of the electrons is taken into account.
Quantum plasmadynamics: role of the electron self-energy and the vertex correction
Authors: Melrose D. B. , Hardy S. J.
Published: March 2009

The linear response 4-tensor for a relativistic quantum electron gas may be calculated by reinterpreting the electron propagator in the expression for the vacuum polarization tensor as statistical averages over the electron gas. We apply a similar procedure to two other radiative corrections: the electron self-energy and the vertex correction. When the photon propagator in these expressions is interpreted as a statistical average over a distribution of waves in the medium, these radiative corrections lead to a relativistic quantum expression for the ponderomotive force and to a new class of ‘hybrid’ emission processes.
Unified theory of damping of linear surface Alfvén waves in inhomogeneous incompressible plasmas
Authors: Ruderman M. S. , Goossens M.
Published: March 2009

The viscous damping of surface Alfvén waves in a non-uniform plasma is studied in the context of linear and incompressible MHD. It is shown that damping due to resonant absorption and damping on a true discontinuity are two limiting cases of the continuous variation of the damping rate with respect to the dimensionless number Rg = Δλ2Re, where Δ is the relative variation of the local Alfvén velocity, λ is the ratio of the thickness of the inhomogeneous layer to the wavelength, and Re is the viscous Reynolds number. The analysis is restricted to waves with wavelengths that are long in comparison with the extent of the non-uniform layer (λ ≪ 1), and to Reynolds numbers that are sufficiently large that the waves are only slightly damped during one wave period. The dispersion relation is obtained and first investigated analytically for the limiting cases of very small (Rg ≪ 1) and very large (Rg ≫ 1) values of Rg, For very small values of Rg, the damping rate agrees with that found for a true discontinuity, while for very large values of Rg, it agrees with the damping rate due to resonant absorption. The dispersion relation is subsequently studied numerically over a wide range of values of Rg, revealing a continuous but nonmonotonic variation of the damping rate with respect to Rg.
Non-inductive current drive via helicity injection by Alfvén waves in low-aspect-ratio tokamaks
Authors: Cuperman S. , Bruma C. , Komoshvili K.
Published: March 2009

A theoretical investigation of radio-frequency (RF) current drive via helicity injection in low aspect ratio tokamaks is carried out. A current-carrying cylindrical plasma surrounded by a helical sheet-current antenna and situated inside a perfectly conducting shell is considered. Toroidal features of low-aspect-ratio tokamaks are simulated by incorporating the following effects: (i) arbitrarily small aspect ratio, Ro/a ≡1/∈; (ii) strongly sheared equilibrium magnetic field; and (iii) relatively large poloidal component of the equilibrium magnetic field. This study concentrates on the Alfvén continuum, i.e. the case in which the wave frequency satisfies the condition , where is an eigenfrequency of the shear Alfven wave (SAW). Thus, using low-β magneto- hydrodynamics, the wave equation with correct boundary (matching) conditions is solved, the RF field components are found, and subsequently current drive, power deposition and efficiency are computed. The results of our investigation clearly demonstrate the possibility of generation of RF-driven currents via helicity injection by Alfvén waves in low-aspect-ratio tokamaks, in the SAW mode. A special algorithm is developed that enables one to select the antenna parameters providing optimal current drive efficiency.
Resistive tearing-mode instability in a magnetic-field-reversing current sheet with coplanar viscous stagnation-point flow
Authors: Ip Justin T. C. , Sonnerup Bengt U. Ö.
Published: March 2009

The tearing-mode instability of a magnetic-field-reversing current sheet in the presence of coplanar incompressible stagnation-point flow is examined. The unperturbed equilibrium state is an exact solution of the steady-state, dissipative, incompressible magnetohydrodynamic equations; thus the analysis is valid even for small viscous and resistive Lundquist numbers Sν and Sη. The instability problem has no known analytical solution; for this reason, it is studied numerically by use of a finite-element method. Simulation results indicate stability for sufficiently small values of Sν or Sη and instability for large values. The boundary separating stable and unstable regions in the (Sν, Sη) plane is located. In the unstable regime, the simulation results show formation and subsequent convection of magnetic islands along the current sheet at about 80% of the unperturbed outflow flow speed, on average. Stretching and pinching of convecting magnetic islands are also observed. The results show the occurrence of multiple X-line reconnection at the centre of the current sheet (x = 0). Small-scale structures of vorticity and current density near the X-point reconnection sites are found to be qualitatively consistent with results obtained by Matthaeus. Normalized global linear growth rates are found to obey the approximate power law, within the ranges 20 ≦ Sν ≦ 70 and 200 ≦ Sη 1000. At least for Sν ≦ 1000, the number of magnetic islands is found to be nearly independent of Sν indicating the existence of a narrow band of dominant wavelengths in this range. The stretching of magnetic islands, which is present in this coplanar flow and field configuration, but not in the perpendicular flow and field configuration examined by Phan and Sonnerup, causes a substantial decrease in linear growth rate relative to that obtained by those authors. The stability curves obtained are qualitatively similar in both analyses, but the stable region is much larger for coplanar flow and field. Unlike most simulations of the tearing mode, no symmetry conditions are imposed on the perturbations; nevertheless, they develop in a symmetric manner.
Electron holes and their role in the dynamics of current-carrying weakly collisional plasmas. Part 1. Immobile ions
Authors: Korn J. , Schamel H.
Published: March 2009

Solutions of the Vlasov-Fokker-Planck-Poisson system in a current-carrying plasma are analysed theoretically and numerically in the collisionless and weakly collisional approximations. The class of electron holes is extended, and new solitary electron hole and hump equilibria are found. Numerical solutions of the full time-dependent self-consistent problem are presented that show the non-existence of structural dissipative equilibria as long as ions are treated as an immobile background.
Almost-invariant surfaces for magnetic field-line flows
Authors: Hudson S. R. , Dewar R. L.
Published: March 2009

Two approaches to defining almost-invariant surfaces for magnetic fields with imperfect magnetic surfaces are compared. Both methods are based on treating magnetic field-line flow as a 1½-dimensional Hamiltonian (or Lagrangian) dynamical system. In thequadratic-flux minimizing surfaceapproach, the integral of the square of the action gradient over the toroidal and poloidal angles is minimized, while in theghost surfaceapproach a gradient flow between a minimax and an action-minimizing orbit is used. In both cases the almost-invariant surface is constructed as a family of periodic pseudo-orbits, and consequently it has a rational rotational transform. The construction of quadratic-flux minimizing surfaces is simple, and easily implemented using a new magnetic field-line tracing method. The construction of ghost surfaces requires the representation of a pseudo field line as an (in principle) infinite-dimensional vector and also is inherently slow for systems near integrability. As a test problem the magnetic field-line Hamiltonian is constructed analytically for a topologically toroidal, non-integrable ABC-flow model, and both types of almost-invariant surface are constructed numerically.
Absolute equilibrium entropy
Authors: Shebalin John V.
Published: March 2009

The entropy associated with absolute equilibrium ensemble theories of ideal, homogeneous, fluid and magnetofluid turbulence is discussed, and the three-dimensional fluid case is examined in detail. A σ function is defined, whose minimum value with respect to global parameters is the entropy. A comparison is made between the use of global functions σ and phase functions H (associated with the development of various H theorems of ideal turbulence). It is shown that the two approaches are complementary, though conceptually different: H theorems show that an isolated system tends to equilibrium, while σ functions allow the demonstration that entropy never decreases when two previously isolated systems are combined. This provides a more complete picture of entropy in the statistical mechanics of ideal fluids.
The simple map for a single-null divertor tokamak
Authors: Punjabi Alkes , Verma Arun , Boozer Allen
Published: March 2009

We present the simple map for a single-null divertor tokamak. The simple map is an area-preserving map based on the idea that magnetic field lines are a single-degree- of-freedom time-dependent Hamiltonian system, and that the basic features of such systems near the X-point are generic. We obtain the properties of this map and the resulting footprints of field lines on the divertor plate. These include the width of the stochastic layer, the edge safety factor, the area of the footprint and the amount of magnetic flux diverted. We give the safety factor profile, the average and median values of strike angles, lengths and the Liapunov exponents. We describe how the effects of magnetic perturbations can be included in the simple map. We show how the map can be applied to the problem of the determination of heat flux on the divertor plate in tokamaks.
Inverse cascades of angular momentum
Authors: Li Shuojun , Montgomery David , Jones Wesley B.
Published: March 2009

Most theoretical and computational studies of turbulence in Navier—Stokes fluids and/or guiding-centre plasmas have been carried out in the presence of spatially periodic boundary conditions. In view of the frequently reproduced result that two-dimensional and/or MHD decaying turbulence leads to structures comparable in length scale to a box dimension, it is natural to ask if periodic boundary conditions are an adequate representation of any physical situation. Here, we study, computationally, the decay of two-dimensional turbulence in a Navier—Stokes fluid or guiding-centre plasma in the presence of circular no-slip rigid walls. The method is wholly spectral, and relies on a Galerkin approximation by a set of functions that obey two boundary conditions at the wall radius (analogues of the Chandrasekhar— Reid functions). It is possible to explore Reynolds numbers up to the order of 1250, based on an RMS velocity and a box radius. It is found that decaying turbulence is altered significantly by the no-slip boundaries. First, strong boundary layers serve as sources of vorticity and enstrophy and enhance the early-time energy decay rate, for a given Reynolds number, well above the periodic boundary condition values. More importantly, angular momentum turns out to be an even more slowly decaying ideal invariant than energy, and to a considerable extent governs the dynamics of the decay. Angular momentum must be taken into account, for example, in order to achieve quantitative agreeement with the predicition of maximum entropy, or ‘most probable’, states. These are predicitions of conditions that are established after several eddy turnover times but before the energy has decayed away. Angular momentum will cascade to lower azimuthal mode numbers, even if absent there initially, and the angular momentum modal spectrum is eventually dominated by the lowest mode available. When no initial angular momentum is present, no behaviour that suggests the likelihood of inverse cascades is observed.