bluuebunny/crossref_metadata_2025 huggingface dataset:
A numerical investigation of magnetic reconnection
Authors: Anderson Craig , Jamitzky Ferdinand
Published: March 2009

A time-dependent two-dimensional MHD simulation program is used to investigate the magnetic reconnection process with a spatially uniform diffusivity. Various initial conditions are considered and are allowed to evolve until a final steady state is produced. The boundary conditions are carefully handled in order that they be as strict as possible. In the first series of simulations the initial condition is taken to be an analytical solution of the ideal MHD equations given by Biskamp. Dirichlet (fixed) boundary conditions are used, with a small amount of flexibility allowed on the boundary for the stream function in order to prevent any unphysical currents forming. The final steady- state contains a current sheet whose width and length are found to vary as and respectively, and the reconnection rate is found to be independent of the value of Rm, indicative of fast reconnection. Additionally, as Rm, is increased, a region of reversed current and a high-speed jet of plasma are observed to develop along the MHD shock separating the inflow and outflow regions. The second series of simulations uses a slightly different initial condition that allows a faster outflow of plasma from the simulation region. The current sheet width of the final steady state is again found to vary as , and the reconnection rate is again independent of Rm. However, no reversed currents or plasma jetting along the shock are observed, indicating that the plasma jets of previous simulations are due to restrictive outflow conditions, which force the high-speed plasma emerging from the end of the current sheet to divert along the MHD shock. Lastly, the analytical model of Petschek is utilized to provide an initial condition. For this case, however, it is not possible to keep the boundary conditions as strict as before, since both the stream and flux functions have to be allowed to vary slightly in order to deal with the discontinuities of the Petschek model. Although steady-state solutions can be obtained, they are found, owing to the laxness of the boundary conditions, not to exhibit the well-defined structure or small current sheets of the previous results.
Generalized Case—van Kampen modes in a multidimensional non-uniform plasma with application to gyroresonance heating
Authors: Tracy E. R. , Brizard A. J. , Kaufman A. N.
Published: March 2009

The generalization of the Case—van Kampen analysis to a multidimensional non-uniform plasma is presented. Application of this analysis is made to minority-ion gyrolesonant heating in an axisymmetric tokamak. In previous work the Case—van Kampen analysis, in conjunction with the Bateman—Kruskal algorithm, was used in a one-dimensional slab model to compute the collective wave spin-off (to the minority-ion Bernstein wave) and the gyroballistic continuum for minority gyroresonant absorption. The generalization to many gyroresonant dimensions and non-trivial geometries requires several important new developments: In tokamak geometry particles can be trapped, an effect that is absent in the slab model. Also, the ray propagation dynamics for both the flee gyroballistic waves and the collective minority-ion Bernstein wave is far more complicated than in the slab model. In particular, a resonance zone is identified wherein the gyroballistic waves interact strongly and cannot be treated as free. We use the Weyl calculus to construct a local form of the self-consistent gyroballistic equation within the resonance zone. This reduced equation is simplified via a metaplectic transformation (a generalization of the Fourier tiansformation). After this simplification, the equation is shown to be of Case—van Kampen type with weak non-uniformities; hence there are no true Case—van Kampen eigenfunctions. Using the Bateman—Kruskal approach, a local Case—van Kampen basis can be constructed and the initial-value problem solved. The self-consistent interactions of the gyroballistic continuum lead to a collective wave, the minority-ion Bernstein wave. The Bernstein wave is extracted by the spectral deformation approach of Crawford and Hislop. The relevance of this work to the theory of collective phenomena in nonlinear oscillator ensembles is briefly discussed.
Electron transport in the stochastic fields of the reversed-field pinch
Authors: Kim Myung-Hee , Punjabi Alkesh
Published: March 2009

We employ the Monte Carlo method for the calculation of anomalous transport developed by Punjabi and Boozer to calculate the particle diffusion coefficient for electrons in the stochastic magnetic fields of the reversed-field pinch (RFP). in the Monte Carlo calculations represented here, the transport mechanism is the loss of magnetic surfaces due to resistive perturbations. The equilibrium magnetic fields are represented by the Bessel function model for the RFP. The diffusion coefficient D is calculated as a function of a, the amplitude of the perturbation. We see three regimes as the amplitude of the tearing modes is increased: the Rechester—Rosenbluth regime where D scales as a2 the anomalous regime where D scales more rapidly than a2 and the Mynick—Krornmes regime where D scales more slowly than a2. Inclusion of the effects of loop voltage on the particle drift orbits in the RFP does not affect the intervals in the amplitude a where these regimes operate.
Ion-acoustic solitary waves in a weakly relativistic warm plasma at the critical phase velocity
Authors: El-Labany S. K. , Nafie H. O. , El-Sheikh A.
Published: March 2009

Ion-acoustic solitary waves in a weakly relativistic warm plasma at the critical phase velocity are investigated using reductive perturbation theory. The basic set of fluid equations describing the system is reduced to a renormalized warmion modified Korteweg—de Vries (mKdV) equation for the first-order perturbed potential and a renormalized linear inhomogeneous equation for the second-order perturbed potential. The stationary solution of the coupled equations is obtained. The cold-plasma limit is considered in order to rule comparisons with work of Pakira et al.
Effect of electroacoustic waves on radiation properties of microstrip matched coaxial termination
Authors: Salem A. M. , Bhatnagar D. , Gandhi J. M.
Published: March 2009

Expressions for the field intensities in a warm ionized plasma for two type of modes (electromagnetic and electroacoustic) pertaining to a microstrip matched coaxial termination are obtained using linearized hydrodynamic theory coupled with a vector function technique. The radiation power and directivity for the respective modes are evaluated for different ratios of plasma to source frequencies. It is observed that electromagnetic fields are similar to other microstrip antenna structures, but more directive in a particular direction. The electroacoustic mode exhibits a complete absence of multilobed structure, which was found for other antenna structures. The efficiency of this structure in a plasma is poor.
Refind theory of tearing growth rates. Part 2. Plasma models with stability threshold
Authors: Barbulla W. , Rebhan E.
Published: March 2009

Following a previous investigation in which the growth rates of tearing modes at weak instability were determined for a frequently used plasma model with convected resistivity, two further models are considered that appear to be more appropriate for realistic situations. In both of them viscosity is included. One has a self-consistently determined equilibrium resistivity that is kept constant during time evolution. In the other Spitzer resistivity is assumed, which, through its temperature dependence, evolves according to the energy law including thermal conductivity. All calculations are carried out for specific equilibria in a sheet pinch. A salient feature of the two models is the emergence of a stability threshold, which was not present in the previous model. Surprisingly, the results obtained for the two new models are almost the same, thus favouring the much simpler model with constant resistivity.
Debye length in a kappa-distribution plasma
Authors: Bryant D. A.
Published: March 2009

The Debye length, the characteristic shielding distance in a plasma, is, when the electrons and ions have Maxwellian velocity distributions, determined by the ratio of the temperatures of these components, to the electron (or ion) number density. Plasmas encountered in space, however, commonly exhibit non-Maxwellian velocity distributions, where the evaluation of an appropriate ‘temperature’ from an observed velocity distribution is no longer a recognized procedure. This paper evaluates the shielding distance for a plasma having a modified power-law, or kappa, family of distribuitons characteristic of some space plasmas.
Nonlinear interaction of electrostatic ion-cyclotron and drift waves in plasmas
Authors: Pokhotelov O. A. , Stenflo L. , Shukla P. K.
Published: March 2009

Model equations describing the nonlinear coupling between electrostatic ion-cyclotron and drift waves are derived, taking into account the action of the low-frequency ponderomotive force associated with the ion-cyclotron waves. It is found that this interaction is governed by a pair of equations, which can be used for studying the modulational instability of a constant amplitude ion-cyclotron wave as well as the dynamics of nonlinearly coupled ion-cyclotron and drift waves.
Momentum-space diffusion due to resonant wave–wave scattering of electromagnetic and electrostatic waves in a relativistic magnetized plasma
Authors: Sugaya R.
Published: March 2009

The momentum-space diffusion equation and the kinetic wave equation for resonant wave–wave scattering of electromagnetic and electrostatic waves in a relativistic magnetized plasma are derived from the relativistic Vlasov–Maxwell equations by perturbation theory. The p-dependent diffusion coefficient and the nonlinear wave—wave coupling coefficient are given in terms of third-order tensors which are amenable to analysis. The transport equations describing energy and momentum transfer between waves and particles are obtained by momentum-space integration of the momentum-space diffusion equation, and are expressed in terms of the nonlinear wave—wave coupling coefficient in the kinetic wave equation. The conservation laws for the total energy and momentum densities of waves and particles are verified from the kinetic wave equation and the transport equations. These equations are very useful for the theoretical analysis of transport phenomena or the acceleration and generation of high-energy or relativistic particles caused by quasi-linear and resonant wave—wave scattering processes.
Effect of simultaneous presence of collisions and ion temperature on modulational instability of ion acoustic waves
Authors: Durrani Ijaz-Ur-Rahman
Published: March 2009

We extend previous work by Buti to include the effect of ion temperature and investigate how the instability range is modified in the simultaneous presence of collisions and ion temperature. A salient feature of the calculations is that waves that were stable in the collisionless case for certain values of the wavenumber k now become unstable.
Electron holes and their role in the dynamics of current-carrying weakly collisional plasmas. Part 2. Mobile ions
Authors: Korn J. , Schamel H.
Published: March 2009

New dissipative structural equilibria of the Vlasov-Fokker-Planck-Poisson system in a current-carrying plasma with mobile ions are presented. The dynamical evolution towards these final equilibrium states is explored. First consequences for the parallel transport are derived and it is shown that the anomalous resistivity depends on non-symmetric distortions of the electron distribution function in the thermal range which are affected by collisions and ion mobility. The fundamental role of electron holes as the underlying collisionless structure is emphasized.
On the most probable states of two-dimensional plasmas
Authors: Seyler C. E.
Published: March 2009

The Charney-Hasegawa-Mima equation and two-dimensional magnetohydrodynamics (MHD) have ideal Lagrangian invariants that are used as the basis for most probable state analysis. An information-theoretic entropy defined in terms of the Lagrangian invariants leads to predictions for relationships between the field quantities. These relationships are tested through numerical solution of the equations through the turbulent relaxation of random initial conditions to coherent states. It is found that the predictions for the most probable state for the Charney—Hasegawa—Mima equation are essentially correct, whereas for two-dimensional MHD they are not. Questions and issues are raised pertaining to why a most probable state analysis based upon Lagrangian invariants seems to work in the case of the Charney—Hasegawa—Mima equation but not for two-dimensional MHIJ. A qualitatively correct entropy is proposed for two-dimensional MHD based upon field variables that are not local invariants.
The method of the averaged Hamiltonian and the two-stream explosive instability
Authors: Sedláček Z.
Published: March 2009

Second-order perturbation calculation shows that an explosive instability of three resonantly interacting coherent electrostatic waves can be limited, and converted into a multiple-periodic process by nonlinear terms of the same order as those that destabilize the waves in the first-order approximation. No higher- order nonlinearities are necessary. The method used is purely classical, and consists in transforming the Hamiltonian of the waves into angle-action variables, and canonical averaging of the Hamiltonian over the proper angles. The number of degrees of freedom is thus reduced to one, which permits one to analyse the wave interaction in the phase plane without using the usual equations for the complex wave amplitudes.
Collisional destruction of the Bernstein modes in the high-frequency regime
Authors: Allan W. , Sanderson J. J.
Published: March 2009

The paper investigates the effect, on the Bernstein-mode dispersion relation, of a small collision frequency v, such that , for the high-frequency regime. It is shown that the ion-acoustic mode dominates the Bernstein modes in this regime for homogeneous plasmas; and it is suggested that this also holds for inhomogeneous plasmas.
Effect of wave—particle interaction on recurrence of a nonlinear ion wave
Authors: Watanabe S.
Published: March 2009

The recurrence of ion waves has been examined experimentally in the region where the nonlinearity is so weak that recurrence length is determined oniy by dispersion. We observe that the recurrence length is longer than the theoretical prediction derived from the Korteweg–de Vries equation of hot ions, and that the recurrence is imperfect. The result is qualitatively explained by wave–particle interaction.
The Green' function forwaves in a homogeneous anisotropic absorbing plasma
Authors: Bennett J. A.
Published: March 2009

The Green's function (or matrix) for a source of sinusoidal time dependence in an infinite homogeneous absorbing magneto-ionic plasma is written as a Fourier integral over wavenumber space. It is shown that this Fourier integral solution exists, and is unique as a generalized function. By extending the Fourier integral to complex wavenumbers, it is shown that the far-field expression for the Green's function may be written as an integral over sections of the dispersion surface, which in this case is a complex sub-manifold of the space of three complex variables. Use of the saddle-point method in two dimensions allows a further simplification of the far-field result. The matrix coefficients in the resulting expression are shown to represent a decomposition into modes. Corresponding results are also obtained for sources with spatial dependence, described by either functions of compact support or rapidly decreasing functions.
A ray expansion with matrix coefficients for sourcesin absorbing anisotropic media
Authors: Bennett J. A.
Published: March 2009

A ray or quasi-optical approximation is developed, using complex rays. The ‘amplitude’ terms are matrices, rather than vectors that represent the wave polarization. Thus, the way the propagation resolves a source into various modes is described. The second term in the amplitude series is shown to include a type of inter-mode coupling. It is shown that initial values needed to integrate along the rays can be chosen so that the leading term of the approximation agrees with the far-field solution for localized sources in a homogeneous medium. By invoking the ‘canonical problem’ method, the result is extended to give an approximation for the Green's matrix in a slowly-varying medium.
Ion heating by the electrostatic ion cyclotron instability: theory and experiment
Authors: Dakin D. R. , Tajima T. , Benford Gregory , Rynn N.
Published: March 2009

The theory of ion heating in a Q-machine Barium plasma by the electrostatic ion cyclotron instability is considered in some detail. Linear and quasi-linear theories are considered. The effect on resistivity of the instability is also considered. The ion temperature was observed, optically, to increase to a value in excess of 25 000°K by a mechanism attributable to a collisionless process. Energy transfer from the drifting electron current to the ions is analyzed explicitly. Detailed comparisons with experiments are presented.
The influence of mean shear on Alfvén-internal wave propagation
Authors: Hartman R. J.
Published: March 2009

This paper uses the general solution of the linearized initial-value problem for an unbounded, exponentially-stratified, perfectly-conducting Couette flow in the presence of a uniform magnetic field to study the development of localized wave-type perturbations to the basic flow. The two-dimensional problem is shown to be stable for all hydrodynamic Richardson numbers JH, positive and negative, and wave packets in this flow are shown to approach, asymptotically, a level in the fluid (the ‘isolation level’) which is a smooth, continuous, function of JH that is well defined for JH < 0 as well as JH > 0. This system exhibits a rich complement of wave phenomena and a variety of mechanisms for the transport of mean flow kinetic and potential energy, via linear wave processes, between widely-separated regions of fluid; this in addition to the usual mechanisms for the absorption of the initial wave energy itself. The appropriate three-dimensional system is discussed, and the role of nonlinearities on the development of localized disturbances is considered.
Dynamics of a triple inverse pinch
Authors: Baum P. J. , Bratenahl A. , Cowan M.
Published: March 2009

Experiments show that plasma may be temporarily confined in a potential well created by three symmetrically spaced inverse pinches. X-type neutral points form at each of the three points of first contact of the inverse pinches and these three neutral points act as flux switches impulsively transferring flux into a central confinement region. The confinement is terminated by a transition to anomalous resistivity at the centre of the device resulting in rapid annihilation of the confining flux by resistive dissipation. The subsequent magnetic field pattern is much more like the vacuum field having only one hyperbolic neutral point.

The plasma configuration can probably be made stable for longer periods of time and should also be of interest for studies of interactions between laser light and a plasma in a state of microturbulence.
Analytical derivation of the H.F. electrostatic potential created by an oscillating point source in a streaming water-bag plasma
Authors: Michel E.
Published: March 2009

The purpose of this paper is to demonstrate the possibility of measuring the drift velocity of a thermal plasma with an H.F. quadrupole probe. The plasma is assumed to be isotropic and collisionless. A hydrodynamic model is used without restrictive assumptions on the magnitude of the drift velocity, which can be made smaller or larger than the thermal velocity. Some curves are presented for velocities parallel or anti-parallel to the emission-reception axis of the probe.
Three dimensional equilibria in the magnetohydrodynamic approximation
Authors: Woolley M. L.
Published: March 2009

By introducing field line potentials for the magnetic induction and current line potentials for the current density, it is shown that the equations which describe a static equilibrium system, in the ideally conducting magnetohydrodynamic approximation, may be derived from two equivalent variational principles. The problem of integration is essentially that of finding a transformation of the potentials which changes one of the associated Lagrangian functions into the other. The assumption that the current density has no component in one direction of a rectangular Cartesian coordinate system leads to a new class of fully three dimensional equilibria having a plane symmetry.
Instability of energetic ion beam injection in tokamaks
Authors: Gaffey John D.
Published: March 2009

There is considerable interest in the use of energetic ion beams to heat magnetically confined plasmas to ignition temperature. An uncertainty in this heating technique is the possible role of instabilities driven by the fast ion beams. For this reason, we have investigated homogeneous plasma modes, including the cross field ion-ion wave and the beam ion-acoustic wave, as well as the ordinary electromagnetic mode, which taps the free energy associated with the beam anisotropy. The growth rates of these modes are calculated and the stability thresholds are compared to parameters for both present injection experiments and the proposed TFTR device.
Stabilization of Rayleigh-Taylor growth by thermal conduction
Authors: Brueckner Keith A. , Jorna Siebe
Published: March 2009

Initial growth rates are calculated for unstable modes of the Taylor type driven by temperature and density gradients in the presence of viscous and thermal diffusion. For a laser-driven plasma it is shown that, even without ablative flow, conduction can sharply reduce unstable growth, and that growth should only occur in the region of low temperature near the ablation front.
Statistical mechanics of transport coefficients
Authors: Vasu G.
Published: March 2009

The problem of transport coefficients in statistical mechanics is reconsidered. A general method is given by which the hydrodynamical equations can straightforwardly obtained starting from the kinetic equation for the one-particle distribution function. From the statistical counterparts of the hydrodynamical equations so derived, the statistical expressions for the transport coefficients are immediately identified.

Linearized hydrodynamic modes have recently been the object of very thorough reserach from the viewpoint of irreversible statistical mechanics; in particular, the Brussels school formalism has been used by Résibois to derive the eigenfrequencies of the hydrodynamical modes, whereby operatorial equations for transport coefficients have been obtained (Résibois 1970; see also the instructive book by Balescu (1975) on this subject).
Explosive instabilities in a cold beam plasma system
Authors: Kerst R. A. , Raether M.
Published: March 2009

Wave-wave coupling is investigated for spatially growing waves in a cold beam-cold plasma system. Numerical solutions of the wave coupling equations are obtained for various combinations of three waves as well as several interacting triplets of waves that are of experimental interest. It is found that most three wave interactions in this system are explosive if they involve the most unstable mode. The results are compared, where applicable, with analytic criteria for the unboundedness of the solutions.
Nonlinear coupling of polarized plasma waves
Authors: Inoue Yoshinori
Published: March 2009

Weak nonlinear coupling between two polarized transverse waves in a weakly relativistic plasma is studied including the effect of dispersion. The frequency of the coupled waves is of the same order of magnitude as the electron plasma frequency. By using the multiple scale method it is shown that the slow modulation of the complex amplitudes is described by simultaneous nonlinear Schrödinger equations. Travelling wave solutions are then obtained for this system of equations by the analytical and the numerical methods. As the result of the wave-wave interaction, two envelope waves are, in general, composed of dispersive shock waves or non-periodic nonlinear wave-trains, while the usual solitary waves or periodic nonlinear wave-trains can exist as a special case. case. The results of analysis can readily be applied to other coupled waves with different polarizations in a nonlinear dispersive medium.
Modification of a turbulent spectrum through the injection of a monochromatic wave Part 2. The dispersion relation
Authors: Brinca Armando L.
Published: March 2009

Analysis of the influence of an injected monochromatic wave on a turbulent spectrum shows that the resulting nonlinear dispersion relation for the stochastic modes displays a real frequency shift and a corrected growth rate when contrasted with the classical quasi-linear dispersion equation.
Non-symmetric two-stream instability
Authors: Cuperman S. , Gomberoff L. , Roth I. , Bernstein W.
Published: March 2009

The recent Plum Brook—NASA experiments on counterstreaming plasma instabilities in which electric field emissions at frequencies [(n + ½) ±α]ωe (n = 1, 2, 3,…, 9, α < 0·5) have been observed, raised the theoretical problem of the non-symmetric two-stream instability. This is the case in which the counterstreaming beams have different velocities in the directions parallel and perpendicular to the static magnetic fields as well as different particle density.

We investigate theoretically this problem. The instability of quasi-electrostatic waves at shifted half odd integer multiples of the cyclotron frequency, due to two non-symmetric counterstreaming electron beams, is considered. The beam velocities parallel and perpendicular to the static magnetic field are represented by different double Dirac delta functions; no parameter limitation is imposed. A systematic investigation of (i) the coupling between plasma modes and cyclotron modes and (ii) the coupling between cyclotron modes (beam 1) and cyclotron modes (beam 2) resulting in shifted half odd integer multiples of the cyclotron frequency is carried out.

The results include approximate but simple analytical expressions for maximum growth rates and for marginal stability as well as exact numerical solutions for the detailed unstable spectra (1 ≤ m ≤ 20) in both ωτ- and kr-space. The relative weakening or suppression of certain modes is also predicted.
A sufficient condition for instability of BGK type waves in both unmagnetized and magnetized plasmas
Authors: Infeld E. , Rowlands G.
Published: March 2009

This paper investigates the general problem of stability of Bernstein—Greene— Kruskal type waves. By investigating perturbations perpendicular to the wave, we obtain a general sufficient condition for instability. This is then extended to the case of magnetized plasmas with a uniform magnetic field in the direction of the BGK wave. New perturbed modes, having no counterpart in linear theory, are also found. Various special cases are considered and previous, more particular results confirmed.
Precursor photo-ionization model for magnetically-driven transverse shock waves
Authors: Leonard B. P.
Published: March 2009

Shock waves produced by magnetic compression are called transverse when the magnetic field contains no component in the direction of the shock wave normal. It is experimentally well known that very strong shocks of this type show classical MHD behaviour in terms of both jump conditions and structure. It is also known that relatively slow transverse shocks can be of an ionizing gasdynamic type with no jump in the imbedded transverse field. Since there are fundamental differences in both the structure and the jump relationships of these two types of shock waves, it is of interest to investigate the transition behaviour in the intermediate shock speed regime. A previously widely accepted model due to Kulikovskii & Lyubimov and Chu assumes no precursor ionization and requires significantly large values of the magnetic Prandtl number, Pm, within the shock structure. That model is shown to be physically inappropriate because experimentally observed transition speeds and corresponding post-shock temperatures imply negligibly small shock Pm values. Also in that model, MHD conditions are approached only asymptotically at large shock speeds. The present precursor ionization model assumes effectively zero Pm values throughout transition and into the low-speed MHD regime. As distinct from the previous theory, this model predicts the attainment of full MHD conditions at and above a well-defined finite shock speed. The assumption of a characteristic post-shock temperature model for the ionization mechanism allows unique jump relations to be formulated independently of other transport mechanisms. Results include computed values of various jump ratios and the electric field as functions of shock speed throughout gasdynamic, transition, and MHD regimes. The solutions form a one-parameter family depending on the relative combination of upstream magnetic field and density (e.g. the Alfvén velocity). Shock structure phase plane trajectories are computed at a number of typical shock speeds throughout transition.
Parametric excitation of magnetoacoustic waves by a pump magnetic field in a high-β plasma
Authors: Cramer N. F.
Published: March 2009

The parametric excitation of slow, intermediate (Alfvén) and fast magneto-acoustic waves by a modulated spatially non-uniform magnetic field in a plasma with a finite ratio of gas pressure to magnetic pressure is considered. The waves are excited in pairs, either pairs of the same mode, or a pair of different modes. The growth rates of the instabilities are calculated and compared with the known result for the Alfvén wave in a zero gas pressure plasma. The only waves that are found not to be excited are the slow plus fast wave pair, and the intermediate plus slow or fast wave pair (unless the waves have a component of propagation direction perpendicular to both the background magnetic field and the direction of non-uniformity of the field).
Electromagnetic ion-cyclotron wave growth rates and their variation with velocity distribution function shape
Authors: Shrauner Abraham , Feldman W. C.
Published: March 2009

The sensitivity of electromagnetic ion-cyclotron wave growth rates to the details of the shape of proton velocity distribution functions is explored. For this purpose two different forms of bi-Lorentzian for the proton distribution functions were adopted. The growth rates for the two types of bi-Lorentzians and the biMaxwellians for the beam (hot) protons are compared. Although the growth rates for the three shapes depend on the velocity moments of the different velocity distributions in a similar way, their magnitudes were found to vary considerably.
Alfvén waves in a stochastic magnetic field
Authors: Mittal M. L. , Prahalad Y. S.
Published: March 2009

Parametric amplification of Alfvén waves in a plasma, subjected to a spatially uniform but temporally stochastic magnetic field, is investigated. The analysis is made using Bogoliubov and Mitropoisky's asymptotic method and Stratanovich's method for stochastic differential equations. This enables us to obtain the probability distribution function for the evolution of the wave, under Markovian approximation. Thus, a complete statistical characterization of the wave can be obtained, if needed. It is shown that Alfvén waves with wavelengths larger than the radius of the plasma column are amplified with probability unity, if the power spectral density of the fluctuating field at twice the wave frequency is non-zero.
Generalized elliptic equilibria in the magnetohydrodynamic approximation
Authors: Woolley M. L.
Published: March 2009

A simple class of static equilibria, in the ideally conducting magnetohydrodynamic approximation, is found to include linear systems having surfaces of constant hydrodynamic pressure with a cylindrical topology and elliptic transverse cross-section functionally dependent on an axial co-ordinate. These suggest a possible mode of behaviour for non-axisymmetric toroidal systems and might themselves be realized experimentally as free boundary configurations of a plasma in an applied quadrupole-like magnetic field.
Ion dynamics in a perpendicular collisionless shock
Authors: Sherwell D. , Cairns R. A.
Published: March 2009

Some properties of perpendicular collisionless shocks are investigated, using a model in which the ion orbits in the shock are assumed to be determined by the average electric and magnetic fields in the shock. These fields are modelled, with the jump in magnetic field across the shock being determined by the conservation relations, and the potential jump determined self-consistently within the model, using the fact that the mean ion velocity downstream of the shock is determined by the conservation relations. Extensive numerical calculations of ion orbits show that effective ion heating can occur in the absence of any dissipative process, with the energy residing in non-Maxwellian velocity distributions in the downstream regions. Results on this and on a number of other features of shock waves, agree well with experiments.
Nonlinear, superluminous, periodic waves in a plasma with magnetic field
Authors: Clemmow P. C.
Published: March 2009

The exact theory of plane waves of fixed profile travelling with constant velocity cZ/n (0 ≤ n ≤ 1) through a uniform, cold, electron-ion plasma in a magneto-static field is examined in terms of the governing equations referred to the frame of reference in which there is no space dependence. Canonical periodic solutions are defined as those with zero average rate of flow of electrons (and a fortiori of ions) in the laboratory frame. It is shown that the equations lead to a second- order, nonlinear, ordinary vector differential equation for the reduced velocity u of the electrons. A scalar first integral is obtained, from which it is deduced that the path in u-space of any solution lies within a bounded domain. It is shown that, for propagation across the magnetic field, a polarization is possible in which the particle velocities and the electric field are orthogonal to the magnetic field. The simpler model of an electron Plasma is considered. Explicit canonical periodic solutions, with the stated polarization, are obtained for propagation across the magnetic field in the case n = 0 and the case n ≃ 1. These support the conjecture that, for any fixed value of n in [0, 1], there are two ‘modes’ of arbitrary amplitude which reduce to the familiar monochromatic waves of linear magneto-ionic theory in the small amplitude limit.
Magnetic field-line reconnexion by localized enhancement of resistivity: Part 1. Evolution in a compressible MHD fluid
Authors: Ugai Masayuki , Tsuda Takao
Published: March 2009

The temporal dynamics of field-line reconnexion is studied by numerical experiment in a compressible conducting fluid. It is shown that because of localized enhancement of resistivity the reconnexion takes place in an initially antiparallel magnetic field and that an X-type field configuration develops, occupying an extended region. There is also a remarkable release of magnetic energy into kinetic and thermal energies. The global flow pattern can spontaneously be set up through the field-line reconnexion under no specially imposed boundary conditions.
Beat frequency heating of a magnetized plasma by circularly polarized microwaves
Authors: Willett J. E. , Ellialtioglu R.
Published: March 2009

The mixing of two parallel or antiparallel beams of circularly polarized microwaves propagating in the extraordinary mode along a uniform, static magnetic field is examined. Resonant excitation of longitudinal electron plasma waves at the beat frequency is found to enhance the microwave absorption. An analysis is based on Maxwell's equations and the continuity and momentum equations for the electron gas with both collision and temperature effects included. Formulae for the average power absorption density and the absorption efficiency are derived. The results of a numerical study of the coupling constant and the efficiency are presented.
Shocks in an anisotropic plasma
Authors: Hudson P. D.
Published: March 2009

The basic conservation equations for a perfectly conducting anisotropic plasma are used to derive curves relating physical quantities in uniform regions on either side of a shock. These curves are independent of the shock mechanism and for any specific mechanism only small segments of the curves would be allowable. Comparison is made with shocks in isotropic magnetohydrodynamics.
The phase velocity, ray velocity, and group velocity surfaces for a magneto-ionic medium
Authors: Walker A. D. M.
Published: March 2009

The phase velocity surface for waves propagating in a uniform cold plasma is sometimes misinterpreted as having the shape of a wave-front. A summary is presented of the correct interpretations of the phase velocity, ray velocity, and group velocity surfaces. A full set of computer generated plots of such surfaces are presented. These are intended as an aid to visualization of wave propagation in such a medium.
Quasi-linear relaxation of runaway electrons in a HF heated tokamak plasma
Authors: Klíma R. , Parail V. V.
Published: March 2009

The theory of quasi-linear diffusion of runaway electrons in the field of electromagnetic waves (HF field) excited by external sources is given. The frequency of the waves is somewhat less than the electron cyclotron frequency. The time-averaged distribution function of resonant electrons is derived. The presence of the toroidal electric field changes the process of quasi-linear relaxation considerably. It also leads to a continuous absorption of energy and momentum from the HF field. On the other hand, the HF field increases the number of high-energy electrons. As a consequence, beam instabilities can arise. A comparison with experimental results is given.
Variational method for electromagnetic waves in a magneto-plasma
Authors: Berk H. L. , Dominguez R. R.
Published: March 2009

A variational method is presented to derive the electromagnetic response for waves of a model plasma with arbitrary β in a magnetic field whose curvature simulated by a gravitational field. The variational method is particularly well suited for deriving the electromagnetic local dispersion relation and differential equations of long-wavelength modes. In particular, the result is applied to finding the critical β needed for stabilization of low-frequency drift waves with density and temperature gradients.
On the filamentation of large amplitude lower-hybrid waves
Authors: Spatschek K. H. , Shukla P. K. , Yu M. Y.
Published: March 2009

We consider the propagation of a large-amplitude lower-hybrid wave. Modulational instabilities arising from its interaction with low-frequency electrostatic perturbations are investigated. The growth lengths of the convective instabilities are obtained and compared with previous results for adiabatic perturbations.
Refraction of hydromagnetic Shocks
Authors: Bestman A. R.
Published: March 2009

In this paper we have studied the refraction of a hydromagnetic shock wave in an aligned field, when it encounters an interface between two streams of gases at different mach and Alfvén numbers. The hodograph mapping technique is employed in all the discussions. Both regular and irregular refractions are considered for the fast and slow shocks, but in the case of the fast shock, the discussions have been restricted to the first type. A brief account of the refraction of transverse shocks is also given. A detailed discussion is not necessary because of the similarity between this problem and that of the type 1 fast shock.
Nonlinear propagation of high-frequency plasma waves in a magnetized plasma
Authors: Shukla P. K.
Published: March 2009

We study nonlinear effects associated with large amplitude electron plasma waves propagating at an arbitrary angle to the external magnetic field. It is shown that the nonlinear coupling of high-frequency plasma waves with static density perturbations leads to a convective instability. The growth length of the latter is obtained. The evolution of the wave electric field is also investigated.
On reconnexion experiments and their interpertation
Authors: Baum P. J. , Bratenahl A.
Published: March 2009

A number of reconnexion concepts and experiments are briefly reviewed in order to re-examine the present interpretation of these experiments. In particular, we offer explanations as to why some experiments appear to develop Petschek modes, tearing modes, or netural current sheets. The explanations require an understanding of the proper role of magnetic Reynolds numbers, the limits of the frozen-in concept, and the importance of natural importance of natural boundary conditions. We find that netural current sheets usually from in experiments with highly symmetrical (and therefore unnatural) boundary conditions. The classical tearing mode develops from perturbations of a neutral current sheet. In less constrained geometries multiple neutral points may appear but the classical tearing mode theory needs modification to explain these cases rigorously. A Petschek mode develops in even less constrained systems although the theoretical description is highly idealized. We offer explanations as to why some experimenters appear to find neutral current sheets in quadrupole fields and examine the usefulness of concepts derived from neutral current sheet theory.
The ray velocity surface and the CMA diagram
Authors: Walker A. D. M.
Published: March 2009

The CMA diagram as a means for classifying electromagnetic waves propagating in cold plasmas is generalized to include boundaries on which the ray surface, rather than the refractive index or wave normal surface, undergoes topological changes. Since the ray surface has the shape of a wavefront for a wave originating from a point source, such boundaries are of importance in understanding wave behaviour. Formulae are presented applying to the case of a cold plasma including the effect of positive ions. Calculations are presented for the special casea hydrogen plasma.
On the relation between phase path, group path and attenuation in a cold absorbing plasma
Authors: Bennett J. A. , Dyson P. L.
Published: March 2009

General expressions have been derived relating the attenuation, A, to the group and phase refractive indices μ′ and μ. This has been done by considering a perturbation about the case in which the collision frequency is zero. It is found that the expressions forμ′ –μ and the imaginary part of the refractive index are closely related in form so that the attenuation can be related to the difference in the group and phase paths, P′–P. Approximations of this form have been obtained in the past but only for situations in which the Q.L. and Q.T. approximations are valid. The expressions derived in this paper are not restricted in this way and numerical calculations show that the ranges of these Q.L. and Q.T. approximations are rather limited. Numerical calculations have enabled new approximations with much greater ranges of validity to be established for these cases.
The nonlinear behaviour of axisymmetric hydromagnetic waves in a partially ionized plasma
Authors: Sawley M. L.
Published: March 2009

Finite amplitude effects in the propagation of axisymmetric hydromagnetic waves in a cylindrical, magnetized plasma are considered. The influence of the Hall term and the presence of neutral atoms on the resulting second-order fields is treated. For the specific case of torsional wave propagation, the combined effect of these two factors is to produce a substantial second-order azimuthal field, in addition to the axial field predicted by earlier work which neglected these factors. In some circumstances this azimuthal field is much larger than the axial field.
On the evolution and enhanced relaxation of a homogeneous isotropic two-dimensional plasma in a uniform magnetic field
Authors: Haggerty M. J.
Published: March 2009

An enhancement of evolution rates in two-dimensional plasma models by a large factor containing the square root of the coupling parameter is known to occur. It is shown here to persist even when all collective effects are removed from weak-coupling calculations, under a simplified boundary condition preserving the isotropy of the system. Long-range vorticity is shown to develop. A careful treatment of time integrals allows irreversibility to be discussed with fewer ambiguities than usual with respect to limit ordering. Applications to three- dimensional laboratory plasmas are tentatively suggested. Future computer simulations should determine the usefulness of the comparatively simple relationships found among moments of the pair correlation. The new effects are shown to be qualitatively similar to some found in other approaches to plasma interactions in uniform magnetic fields.
The collisionless flow of unmagnetized plasmas around bodies
Authors: Könemann Bernd
Published: March 2009

The ion density in the wake of extended bodies in collisionless flows of unmagnetized plasmas is qualitatively investigated. Both the deflexion of the ions in a surface potential field, and the collective response of the ambient plasma are incorporated in a model which reveals the connexion between the wakes of extended bodies and those of point charges. The differences between the wake features of small and large bodies in strongly non-isothermal plasmas (Te » Ti) are related to the excitation of different types of waves. In isothermal plasmas no sharp wake features can be expected, because the appropriate waves are heavily damped, and other features are smoothed by the thermal motion of the ions.
Numerical parameter study of stability against resistive axisymmetric modes for doublets
Authors: Jensen Torkil H. , McClain F. W.
Published: March 2009

Stability and growth rates of resistive axisymmetric modes for doublets have been studied numerically. Because of the many parameters entering the problem this study has the form of a survey of features that are believed to be most important for stability. In general it is found that the most dangerous mode is one that either elongates or contracts the plasma in the vertical direction. Stability, and in the case of instability, the growth rate, depends on the proximity of a conducting wall surrounding the plasma. Numerical examples of this are given both for cases of a rectangular wall shape and an indented wall shape. Examples are also given that indicate the sensitivity to parameters characterizing the equilibrium. Finally, an example is given for the case of a wall with a finite resistivity. It is shown that such a wall does not affect the stability, but decreases the growth rate relative to a case where the wall is absent.
On the theory of Buneman's instability in hot ion plasma
Authors: El-Naggar I. A. , Khalil Sh. M. , Sizonenko V. L.
Published: March 2009

The development of Buneman's kinetic-type instability in plasma with hot ions and cold electrons is investigated. Expressions for the frequencies and growth rates of oscillations when the current velocity slightly exceeds the instability threshold velocity have been derived in the linear approximation. The quasilinear theory of instabilities has been developed, and it has been shown that the quasi-linear effects lead to the amplification of the instability.
Resonant wave–particle interaction at the half-integer cyclotron harmonics
Authors: Schmitt J. P. M. , Lapierre Y.
Published: March 2009

A single particle is subjected to the combined action of a static uniform magnetic field and an electromagnetic wave. The equations of motion are solved using the perturbation method up to second order. In the results, two different types of second-order effects appear: (i) the always present non-resonant effects, resulting in a ponderomotive drift and a nonlinear cyclotron frequency shift, and (ii) the resonant effects appearing at the half-integer harmonics of the gyrofrequency and leading to perpendicular heating and diffusion.