bluuebunny/crossref_metadata_2025 huggingface dataset:
Convection in a plasma with opposed temperature and density gradients
Authors: Nocera Luigi
Published: March 2009

The stability of a viscous and heat-conducting plasma is considered, with temperature and density gradients arranged so that the resulting pressure is homogeneous, as suggested by some experiments on laser-plasma interactions. Gravity and magnetic field effects are ignored throughout. A non-dissipative fluid is considered first. Under the assumption of an Epstein profile for the equilibrium temperature, the dispersion curves for the propagation of sound waves are determined using a relaxation technique applied to a second-order spheroidal boundary-value problem for mode numbers 1,…, 5: it is found that these modes may be destablized by inhomogeneity. The dynamics of vorticity is analysed in the framework of the WKB approximation, which allows reduction to a fourth-order boundary-value problem: this is tackled in the ‘quasi-classical’ limit by solution of the relevant Bohr-Sommerfeld eigenvalue problem. Convective flows arise in the classically accessible layers and evanesce outside. For the same Epstein temperature profile as above, two such layers are formed, in agreement with observation. Given the growth rate of the unstable flow, the modified Rayleigh number, the width of the convective layer and the temperature drop across it are calculated as functions of the transverse wavenumber and for mode numbers 1–5. Conversely, given the modified Rayleigh number, the growth rate is calculated. The modified Rayleigh number and the growth rate thus found have a minimum and a maximum respectively as functions of the wavenumber of the perturbation. These can be taken as the most favourable values for convection to develop. The value of the wavenumber at which these extrema are attained can be used to determine the aspect ratio of the convective cells.
Magnetic fluctuations and kinetic equations in a two-species plasma
Authors: Di Vita Andrea
Published: March 2009

Some properties of the frequency spectrum of magnetic fluctuations in a tokamak two-species plasma are investigated. We start from the nonlinear resistive ballooning kinetic equation. A method based on the fluctuation-dissipation theorem of thermodynamics is employed. The frequency range |ωDe|/ω>|ω*e| is considered. The dependence of magnetic fluctuations on frequency and various macroscopic parameters is discussed. The influence of magnetic fluctuations on plasma thermodynamics is investigated.
An exact formula for the thermal and particle diffusivities based on the diffusive transport model in tokamak plasmas
Authors: Janicki Christian
Published: March 2009

An exact solution for the thermal (Xe) or particle (D) diffusivities is derived (up to a constant factor) for the diffusive model in terms of the Fourier coefficients of the perturbed Te (or ne) signals. The common assumptions of constant ne and Xe (or D) generally used in the standard analytical or semi-analytical solutions are not required, since their radial dependences are taken explicitly into account. The effect of a damping (sink) term in the heat equation can also be implemented easily.
General dispersion relation for surface waves on a plasma—vacuum interface: an image approach
Authors: Rowe G. W.
Published: March 2009

The image approach, used extensively to treat bounded unmagnetized plasmas, is extended to the case of an arbitrary homogeneous and non-magnetic medium. A general dispersion relation for electromagnetic surface waves on a plane plasma-vacuum interface is thus obtained, subject only to the suitability of the chosen boundary conditions. The boundary conditions used here are those of Barr and Boyd. It is emphasized that this dispersion relation is applicable to magnetized plasmas. The general dispersion relation is applied to the special case of an isotropie medium, and the dispersion relation of Barr and Boyd for an unmagnetized plasma is reproduced. A major assumption in the image approach is that the semi-infinite bounded medium can be described by the infinite-medium response. The validity of this assumption and of the boundary conditions is discussed. Two conditions are deduced that must be satisfied for the image theory to be self-consistent. It is argued that these can be satisfied in all situations for which the assumed boundary conditions are appropriate.
Nonlinear interaction of an intense electromagnetic wave with an unmagnetized electron—positron plasma
Authors: Berezhiani V. I. , Tsintsadze L. N. , Shukla P. K.
Published: March 2009

The nonlinear interaction of an arbitrarily large-amplitude circularly polarized electromagnetic wave with an unmagnetized electron-positron plasma is considered, taking into account relativistic particle-mass variation as well as large-scale density perturbations created by radiation pressure. It is found that the interaction is governed by an equation for the electromagnetic wave envelope, which is coupled with a pair of equations describing fully nonlinear longitudinal plasma motions. The dynamics of the nonlinear electromagnetic wave packet is studied.
Phase mixing and surface-wave decay in an inhomogeneous plasma
Authors: Cally P. S. , Sedláček Z.
Published: March 2009

The decay rate of an Alfvén or plasma surface wave propagating along an inhomogeneous layer of plasma is calculated. The inhomogeneous profile is thin and odd, but otherwise arbitrary. The wave's decay rate is determined using two fundamentally different methods, the integro-differential equation approach of Sedl´ček and the Sturm-Liouville expansion technique of Cally, and found by both to depend only on the slope of the Alfvén or plasma frequency profile at the ‘resonant point’, and not on other details of its shape. The result is verified numerically. This problem represents a good example with which to compare and contrast the two methods.
The kinetic theory of the nonlinear low-frequency response of a collisionless plasma to high-frequency electromagnetic radiation
Authors: Aliev Yu. M. , Bychenkov V. Yu. , Jovanović M. S. , Frolov A. A.
Published: March 2009

A kinetic theory of nonlinear currents, quasi-stationary electric and magnetic fields and the ponderomotive effect of high-frequency electromagnetic radiation on a collisionless plasma is developed. General expressions for nonlinear current densities, fields and ponderomotive forces that are applicable in a broad range of space-time scales, characteristie of low-frequency motion in plasma, are obtained. These expressions are compared with the results of previous papers.
Thermodynamics of Vlasov equilibria
Authors: Minardi E.
Published: March 2009

This paper contains a systematic exposition of a statistical method leading to a characterization of relevant equilibrium and stability properties of col-lisionless Vlasov (collective) plasma configurations according to a formalism similar to that of the classical thermodynamics of Maxwellian systems. We reconsider a statistical model, proposed in earlier works, in which the basic objects of the statistics are volume elements in a configuration space of the charge or current density. The probability distribution in this space is calculated subject to a constraint expressing the existence of static equilibria involving only the smeared-out or collective part of the above densities, while the collective energy is uncorrelated with the fluctuations arising from the single-particle structure. It is one of the aims of this paper to show that the thermodynamic quantities arising automatically in the formalism, for instance the entropy, can be consistently inserted in the physical and conceptual context of classical thermodynamics. This is achieved by studying in detail a reversible energy interaction between the collective system and the external world, in order to identify the entropy variations calculated with the model with those of the entropy as conventionally defined. Our thermodynamic concepts are illustrated by applications to electrostatic Vlasov equilibria (in unstable situations and in the Maxwellian limit) and to magnetic systems, both in a case open to energy interaction with the external world (the tokamak) and in the case of an isolated system (a plasma enclosed in a perfectly conducting shell).
Waves with nonlinear polarization due to a self-generated magnetic field in a plasma
Authors: Aleksic N. B. , Aliev Yu. M. , Bychenkov V. Yu. , Vuković S.
Published: March 2009

We investigate a new mechanism of nonlinear wave interaction in a plasma with an electromagnetic wave, a Langmuir plasma wave and a self-generated quasi-stationary magnetic field involved in the three-wave process. It is demonstrated that magnetic field generation supports a new wave of hybrid polarization, which can be changed during the nonlinear evolution. Periodic regimes, as well as regimes of soliton (instanton) formation and kink-shaped transitions, can be realized.
Amplification of fast magnetosonic waves and the cut-off spectrum
Authors: Rutkevich I. M. , Mond M.
Published: March 2009

The propagation of fast magnetosonic waves in an inhomogeneous medium with planar flow in investigated. The equations describing the rays along which the waves propagate are derived, as well as the equations for the variations of the wave amplitude along the rays. These equations are solved for the case of steady flow that depends only on the radius. In addition, it is shown that a spectrum of eigenmodes may exist if the steady flow contains a shock. For that purpose, the reflection coefficient of a fast magnetosonic wave form a shock is derived, and it is shown that the waves can be localized in a region bounded by a shock and a critical surface. A criterion for stability of the spectrum is derived.
The influence of ion streaming and weak relativistic effects on the modulational instability of ion-acoustic waves
Authors: Parkes E. J.
Published: March 2009

The influence of ion streaming and weak relativistic effects on the modulational instability of ion-acoustic waves in a collisionless unmagnetized plasma is investigated. An averaging method is used to derive a weakly nonlinear dispersion relation, from which the instability criterion is deduced. Conflicting results in the literature are resolved.
Self-consistency in the interaction of magnetized electrons and ordinarily polarized electromagnetic waves
Authors: Rizzato F. B.
Published: March 2009

We use a Hamiltonian formalism to analyse the self-consistent wave–particle dynamical interaction involving magnetized electrons and ordinarily polarized electromagnetic waves. Considering first-harmonic cyclotron resonances, we show that there is a critical value of the electronic average density. For systems with lower than critical densities the saturation process is dictated by relativistic detuning effects, and wave dynamics may be disregarded. However, for systems with larger densities, saturation is governed by the available electromagnetic free energy, and the wave dynamics turns out to be essential.
Thermally driven magnetic turbulence in the presence of radiation cooling in plasmas
Authors: Bharuthram R. , Baboolal S. , Shukla P. K.
Published: March 2009

Instabilities of the flute-like magnetic fluctuations in the presence of radiation cooling in a non-uniform magnetoplasma are investigated. It is shown that magnetic turbulence can cause anomalous cross-field electron energy transport. The relevance of the investigation to magnetic and inertial fusion as well as to astrophysical plasmas is pointed out.
The gravitational interchange instability for perpendicular density gradients
Authors: Paris R. B.
Published: March 2009

The analouge of the Reyleigh–Taylor instability (the gravitational interchange mode) for an infinitely conducting, approximately one-dimensional plane plasma slab is examined when the gravitational acceleration g is taken to be perpendicular to the equalibrium density gradient δp0. In contrast with the ‘classical’ situation (where g is aligned with δp0), it is found for a current layer with Magnetic shear that there is no instability threshold equivalent to the ‘classical’ situation (where g is aligned with δp0), it is found for a current layer with magnetic shear that there is no instability threshold equivalent to the Suydam criterion: the mode is unstable for all values of |δp0|. In the weak shear limit the growth rate of the instability is shown to exhibit the familiar (g|δp0|/p0)img; scaling characteristic of the gravitational interchange mode.
Exact algebraic dispersion relations for wave propagation in hot magnetized plasmas
Authors: Fichtner Horst , Sreenivasan S. Ranga
Published: March 2009

A new model is presented for the treatment of wave propagation along an external magnetic field in a hot collisionless plasma. The analysis is based on the so-called polynomial distribution functions along the magnetic field, and takes account of enhanced fractions of high-energy particles, which are characteristic of rarefied and magnetized astrophysical plasmas, in comparison with the bi-Maxwellian distributions. These new distributions permit the derivation of general dispersion relations that are exactly valid for waves with Im (ω) > 0, and represent good approximations for those with Im (ω) > 0. Furthermore, the explicit form of the dispersion relations is shown to be valid for distribution functions of different shapes. Because of their algebraic structure, the solution of the dispersion relations can be shown to be equivalent to the determination of the roots of complex-valued polynomials. The cold plasma, the Maxwellian plasma and the so-called quasi-Maxwellian plasma appear in this formalism as asymptotic and special cases. The reliability of the model is demonstrated with the calculation of dispersion curves, growth and damping rates for several standard modes, and by comparing it with previous calculations carried out using explicit Maxwellian distributions. Finally, the tendency of the solar wind to generate ion-cyclotron waves is investigated as a first, new application.
Theory of modulational interaction of two coupled waves. Part 1. General formulae for a nonlinear medium
Authors: Vladimirov Sergey V. , Tsytovich Vadim N.
Published: March 2009

The modulational interaction of two waves propagating in a cubically nonlinear medium is considered. It is shown that the correct theory operates with ‘renormalized’ equations for the linear dielectric function and for an effective third-order medium response. This renormalization is due to so-called interference terms. The appearance of interference terms is a specific feature of the two-mode modulational instability in comparison with the well-known instability of a single mode.
Two-fluid electromagnetic instability in a self-consistent inhomogeneous plasma with saturated magnetic shear
Authors: Katou K. , Mamada H.
Published: March 2009

The stability of an inhomogeneous finite-β plasma confined by a sheared magnetic field is analysed in the two-fluid slab approximation. The stationary plasma involves an electron plasma current that is self-consistently generated by magnetic shear through Ampère's law. Magnetic shear is found to be stabilizing (destabilizing) if the electron drift consistent with it is antiparallel (parallel) to the propagation direction of drift waves. Mode stability arises from competition between the Doppler shifts resulting from both the electron diamagnetic drift and the electron drift related to magnetic shear, and the wave frequency. The finite-β effects reduce the growth rate but do not stabilize the mode. In contrast with the hydromagnetic tearing instabilities, the growth rate is proportional to the electron-ion collision frequency, which is regarded as the lowest-order term in powers of the electron-ion collision frequency by Taylor's theorem.
Self-focusing and filamentation of laser beams in collisional plasmas with finite thermal conduction
Authors: Ghanshyam  , Tripathi V. K.
Published: March 2009

A Gaussian laser beam propagating through a plasma heats the electrons and creates a low-density duct via ambipolar diffusion. Thermal conduction plays an important role in temperature equilibrium when the electron mean free path λm is greater than the beam radius (λm ≥ ro). For λm ≫ ro thermal conduction suppresses any non-uniformities in electron temperature, and nonlinearity is dominated by the ponderomotive force. The plasma duct traps and focuses the laser radiation above a threshold power. As the beam size shrinks, thermal conduction becomes stronger, leading to periodic self-focusing of the beam. The laser beam is also susceptible to filamentation instability. The spatial growth rate is a monotonically increasing and saturating function of the incident intensity of the beam.
Nonlinear sausage-wave propagation in a magnetic slab in an incompressible fluid
Authors: Ruderman M. S.
Published: March 2009

Long nonlinear sausage-wave propagation in a magnetic slab in an incompressible plasma is considered. The governing equation is derived with the aid of the reductive perturbation method. The solutions of this equation in the form of periodic waves of permanent shape are found numerically.
Nonlinear stability of surface waves in magnetic fluids: effect of a periodic tangential magnetic field
Authors: El-Dib Yusry O.
Published: March 2009

Nonlinear wave propagation on the surface between two superposed magnetic fluids stressed by a tangential periodic magnetic field is investigated using the method of multiple scales. A stability analysis reveals the existence of both nonresonant and resonant cases. From the solvability conditions, three types of nonlinear Schrodinger equation are obtained. The necessary and sufficient conditions for stability are obtained in each case. Formulae for the surface elevation are also obtained in both the non-resonant and the resonant cases. It is found from the numerical calculation that the tangential periodic magnetic field plays a dual role in the stability criterion, while the field frequency has a destabilizing influence.
Solitons in a magnetized ion-beam plasma system
Authors: Kalita B. C. , Kalita M. K. , Bhatta R. P.
Published: March 2009

The formation of ion-acoustic solitary waves in a magnetized plasma with stationary ions and beam ions together with inertia-less electrons is investigated. The generation of waves in a plane is assumed to be one-dimensional, in a direction inclined at an angle θ to the direction of the magnetic field, with constant drift velocity of the ion beam. Remarkably, the amplitudes of the solitons are found to attain a maximum value at a particular beam-ion velocity γ, and then decrease slightly and remain almost constant for higher γ. The width of the waves is large at small y for small beam-ion density Nb, but it attains a constant minimum value at a particular value of γ. The amplitude decreases sharply to zero with decreasing y, whereas it remains almost constantly high for larger y. It is observed that as a wave approaches the direction of the magnetic field, its amplitude increases to a constant maximum value, which is larger for higher beam-ion velocities.
Determination of the growth rate for the linearized Zakharov—Kuznetsov equation
Authors: Allen M. A. , Rowlands G.
Published: March 2009

Studies of the Zakharov—Kuznetsov equation governing solitons in a strongly magnetized ion-acoustic plasma indicate that a perturbed flat soliton is unstable and evolves into higher-dimensional solitons. The growth rate γ = γ(k) of a small sinusoidal perturbation of wavenumber k to a flat soliton has already been found numerically, and lengthy analytical work has given the value of We introduce a more direct analytical method in the form of an extension to the usual multiple-scale perturbation approach and use it to determine a consistent expansion of γ about k = 0 and the other zero at k2 = 5.By combining these results in the form of a two-point Padé approximant, we obtain an analytical expression for γ valid over the entire range of k for which the solution is unstable. We also present a very efficient numerical method for determining the growth rate curve to great accuracy. The Padé approximant gives excellent agreement with the numerical results.
Oblique nonlinear Alfvén waves in strongly magnetized beam plasmas. Part 1. Nonlinear vector evolution equation
Authors: Deconinck Bernard , Meuris Peter , Verheest Frank
Published: March 2009

Nonlinear MHD waves propagating obliquely to the external magnetic field in warm multi-species plasmas with anisotropic pressures and different equilibrium drifts are treated without imposing the customary quasi-neutrality between the different species or neglecting the displacement current in Ampère's law. The wave magnetic field obeys a vector nonlinear evolution equation, which in the limits of parallel propagation or of both the neglect of the displacement current and the imposition of quasi-neutrality reduces to the vector formulation of the well-known derivative nonlinear Schrödinger equation.
Nonlinear growth of strongly unstable tearing modes
Authors: Waelbroeck F. L.
Published: March 2009

Rutherford's theory of the tearing instability is extended to cases where current nonlinearities are important, such as long-wavelength modes in current slabs and the m = 1 instability in tokamaks with moderately large aspect ratios. Of particular interest is the possibility that the associated magnetic islands, as a result of secondary instabilities, have a singular response to the Ohmic diffusion of the current. A family of islands is used to test this possibility; it is found that the response remains bounded.
Contribution of higher-order nonlinearity to nonlinear ion-acoustic waves in a weakly relativistic warm plasma. Part 1. Isothermal case
Authors: El-Labany S. K.
Published: March 2009

The contribution of higher-order nonlinearity to nonlinear ion-acoustic waves in a weakly relativistic plasma consisting of warm ion-fluid and hot isothermal electrons is investigated using reductive perturbation theory. A Korteweg-de Vries-type equation, with temperature- and relativistic-parameter-dependent coefficients is obtained. The renormalization method is applied to the equations obtained from the different orders of perturbation theory to obtain a stationary solution. Relativistic cold and non-relativistic warm plasma limits are considered in order to make comparisons with previous results.
Entropy of Vlasov equilibria and Hamilton's principle
Authors: Minardi E.
Published: March 2009

The following property is shown of the entropy functional constructed in previous work and associated with a Vlasov electrostatic or magnetostatic collective equilibrium (a static solution of the Vlasov equation): the vanishing of the first variation of the functional is equivalent to Hamilton's principle applied to a Lagrangian describing motion of the underlying system of particles compatible with the collective equilibrium, provided that the variations are associated withreversibleprocesses. This property is shown in two cases: (i) a system of particles in Coulomb interaction admitting a collective (Vlasov) equilibrium in the presence of a scalar pressure; and (ii) a system of independent electrons in a background of fixed ions subject to an external electric field and to a magnetic field (created in part by electron currents) associated with a cylindrically or toroidally symmetric equilibrium in the presence of the electron–ion friction force and an anisotropic pressure.
Refined theory of tearing growth rates. Part 1. Plasma model without stability threshold
Authors: Barbulla W. , Rebhan E.
Published: March 2009

In the theory of tearing modes analytical expressions for the growth rate y are only known for large y > 1/TR. However, since resistive instabilities cannot be externally stabilized, they will rather be observed at small growth rates, which are also the ones that matter in a bifurcation analysis. In this paper the described gap in the tearing theory is closed for the model of a convected resistivity in a sheet pinch. The analytical expressions obtained from an asymptotic perturbation analysis for small growth rates are as simple as those for large growth rates. However, they differ from them appreciably, and also show a marked difference between symmetric and asymmetric perturbations. Specifically, for asymmetric modes in contrast to the symmetric ones, no stability threshold exists, i.e. all asymmetric modes are at least weakly unstable. In addition to the results for small growth rates, an implicit analytical formula is presented that bridges the regime between small and large growth rates. The high quality of the analytical results is confirmed by numerical solution of the full tearing equations
Parametric decay instability of an upper-hybrid wave in a two-temperature plasma
Authors: Konar S. , Rai V.
Published: March 2009

Parametric decay of an upper-hybrid pump into another upper-hybrid wave and a low-frequency lower-hybrid mode is considered in a two-electron temperature plasma. Expressions for the nonlinear dispersion relation and growth rate are obtained. It is found that the growth rate is quite sensitive to the hot-electron temperature and the density ratio of the hot and the cold components only when the side-band frequency is close to the second or third harmonic of the cyclotron frequency. The relevance of our investigation to Q machines and the ELMO bumpy torus is pointed out.
A necessary condition for omnigenity in stellarators
Authors: Dommaschk Walter
Published: March 2009

A lower bound for the total variation Bmax/Bminof the field strength B on a toroidal vacuum magnetic surface with finite twist (rotational transform) of the field is given as a necessary (not sufficient) condition for the field lines to be geodesics on it. If such a surface existed, it would be omnigenous with respect to the local gradient-B and centrifugal guiding-centre drift approximation, which means that the normal components of these drift velocities would be zero. It is found that the lower bound on Bmax/Bmindepends on the maximum of – (r/B) ∂B/∂r within the surface. Hereris the distance from the origin of the torus. The lower bound is large if this maximum is small, and vice versa. For some more recent stellarator configurations the condition is found to be satisfied at outer magnetic surfaces. It is obtained without the use of expansion techniques, under the assumption that there is a nested system of magnetic surfaces within the omnigenous one.
Kinetic theory for a distribution of ionized dust particles
Authors: Aslaksen T. K. , Havnes O.
Published: March 2009

Dust particles, assumed to be of one size and to exhibit a discrete distribution of electric charges, are treated as heavy ions with a large number of ionization levels. The average of the discrete particle effects on the kinetic equations is approximated by the Lénard–Balescu collision term and by detailed counting to describe transport in velocity space and transitions between the differentionization levels respectively. We estimate analytically and numerically the relaxation times for the dust particles both towards a Maxwellian velocity distribution and towards an equilibrium distribution for the ionization levels. We sum over the ionization levels to obtain a hierarchy of ‘charge-moment’ equations for the single dust density function, and estimate the importance of terms originating from the ionization distribution. Similar terms are also present in the hydrodynamic equations for a dust plasma, and we briefly discuss these.
Obliquely propagating ion-acoustic nonlinear periodic waves in a magnetized plasma with two electron species
Authors: Yadav L. L. , Tiwari R. S. , Sharma S. R.
Published: March 2009

Obliquely propagating ion-acoustic nonlinear periodic waves in a magnetized plasma consisting of warm adiabatic ions and two Maxwellian electron species are studied. Using the reductive perturbation method, the Korteweg–de Vries (KdV) equation is derived and its cnoidal wave solution is discussed. It is found that as the amplitude of the cnoidal wave increases, so does its frequency. The effects of variations in the density and temperature ratios of the two electron species, the ion temperature, the angle of obliqueness and the magnetization on the characteristics of the cnoidal wave are discussed in detail. When the coefficient of the nonlinear term of the KdV equation, a1, vanishes, the modified Korteweg–de Vries equation is derived, and its periodic-wave solutions are discussed in detail. In the limiting case these periodic-wave solutions reduce to soliton or double-layer solutions.
Structures of reconnection layers based on the ideal magnetohydrodynamic equations
Authors: Dai Wenlong , Woodward Paul R.
Published: March 2009

A Riemann solver is used, and a set of numerical simulations are performed, to study the structures of reconnection layers in the approximation of the one- dimensional ideal MHD equations. Since the Riemann solver may solve general Riemarin problems, the model used in this paper is more general than those in previous investigations on this problem. Under the conditions used in the previous investigations, the structures we obtained are the same. Our numerical simulations show quantitative agreement with those obtained through the Riemann solver.
Bifurcation of BGK waves in a plasma of cold ions and electrons
Authors: Hannibal L. , Rebhan E. , Kielhorn C.
Published: March 2009

For the simple model of cold electrons streaming against cold ions the complete set of nonlinear stationary waves is expressed in terms of elliptic functions. The conditions for their dynamical connection to a uniform neutral plasma state are taken into account, and the conditions for the neglect of the magnetic field are analysed. The range of existence of stationary waves is found to be confined to the stable regime of the two-stream instability, but covers only part of it. All nonlinear BGK waves that are found within the limits of the model can be shown to bifurcate from the two-stream instability, some of them also exhibiting secondary and further bifurcations. As an exceptional case, all bifurcations can be treated exactly. Close to the linear regime, all nonlinear modes turn out to be unstable. The corresponding instability is caused by a wave decay that transports energy from low to high wavenumbers of the Fourier modes constituting the wave. From the two-stream solutions four- stream solutions with exactly vanishing magnetic field are derived.
Magnetohydrodynamic instability driven by cosmic rays
Authors: Ko Chung-Ming , Jeng An-Tzong
Published: March 2009

Magneto-acoustic instability driven by cosmic rays and the waves that they excite was first studied by McKenzie and Webb and by Zank. In the present paper this instability is reconsidered. In general, the cosmic-ray plasma system is unstable. However, depending on how the time scale is chosen, the results and interpretation may be different from those of McKenzie and Webb and of Zank, particularly in the long- and short-wavelength limits. To illustrate this instability in an astrophysical context, we take our Galaxy and supernova remnants as examples. In those examples, length scales shorter than 2.5 kpc and 1.5 pc respectively are susceptible to this instability, and the growth times are of the order of 4 × 108 and 1.5 × 104 yr respectively.
Steady MHD flows with an ignorable co-ordinate and the potential transonic flow equation
Authors: Webb G. M. , Brio M. , Zank G. P.
Published: March 2009

The paper explores the interrelationship between the generalized Grad-Shafranov equation, or trans-field force balance equation, for steady MHD flows with an ingnorable co-ordinate, and work by Imai on field-aligned MHD flows. The development of Imai, assumes at the outset that the fluid velocity V is parallel to the magnetic field B, and exploits an analogy with steady compressible irrotational flow in ordinary fluid dynamics. In Imai's analysis the magnetic induction B is written in the form B = σb, where , and MA is the appropriate Alfvén Mach number. Gauss' law Δ. B = Δ. (σb) = 0 then plays a role analogous to the mass continuity equation in ordinary fluid dynamics, where σ corresponds to the density of the pseudo-fluid. Imai's analysis leads to a transonic equation for the field potential φ defined by b = Δφ. For a restricted class of flows the trans-field force balance equation formulation also leads to the transonic potential flow equation, but the assumption of an ignorable co-ordinate allows for the possibility of non-field-aligned flows with non-zero electric field potential ΦE The characteristics of the generalized Grad—Shafranov equation are related to the Mach cone and the group velocity surface for linear magnetosonic waves. The corresponding forms of the characteristics for the potential transonic flow equation in the (x, y) plane and in the (bx, by) hodograph plane are discussed. Sample solutions of the potential transonic flow equation for radial, helical and spiral flows are obtained by means of the hodograph transformation, and are used to illustrate the differences between hyperbolic and elliptic flows. The potential transonic flow equation is obtained for the case of an ignorable co-ordinate z of a rectangular Cartesian co-ordinate system (x, y, z), and also for the case of flows with an ignorable co-ordinate of a spherical polar co-ordinate system (r, θ, ω). Astrophysical applications are briefly discussed.
Acceleration of charged particles by large-amplitude electromagnetic waves
Authors: Kuo S. P. , Lee M. C.
Published: March 2009

The fundamental process of acceleration of charged particles by large-amplitude electromagnetic waves is investigated. Exact analytical solutions can be derived from the nonlinear equations that govern the motion of charged particles in wave fields. It is found that circularly polarized electromagnetic waves can act on the charged particles via α d.c. Lorentz force imposed by the wave fields. This process can effectively energize charged particles that may initially have low energies.
Systematic approximations for magnetized transit-time interactions
Authors: Melatos A. , Robinson P. A.
Published: March 2009

A systematic procedure is given for generating analytic approximations to the wave–particle energy transfer in magnetized transit-time interactions. The procedure can be applied to any wave-packet field structure, and yields especially simple results in the physically important limits of (i) small and large Larmor radius and (ii) small and large values of the ratio of the wave frequency to the cyclotron frequency. In many applications, the approximations developed here are the only viable means of calculating the wave—particle energy transfer, because the exact analytic theory and numerical test-particle calculations are too demanding computationally.
Evolution of wave packets in magnetohydrodynamics
Authors: Pusri Anju , Malik S. K.
Published: March 2009

The propagation of wave packets on the surface of an electrically conducting fluid of uniform depth in the presence of a tangential magnetic field is investigated in (2 + 1) dimensions. The evolution of wave envelope is governed by two coupled partial differential equations with cubic nonlinearity. The stability analysis reveals the existence of different regions of instability. The effect of the applied magnetic field is not only significant but also different for different regions of stability. ‘Envelope soliton’ and ‘waveguide’ solutions of the amplitude equation are also discussed. The self-focusing phenomenon that arises when the amplitude of the wave becomes infinite in finite time is also examined. It is found that in a certain region of the stability diagram it may be easier to observe this phenomenon in the presence of a magnetic field. The Rayleigh-Taylor problem is also studied and various criteria for the existence of instability are obtained.
Plasma microinstabilities driven by loss-cone distributions
Authors: Summers Danny , Thorne Richard M.
Published: March 2009

Electromagnetic and electrostatic instabilities driven by loss-cone particle distributions have been invoked to explain a variety of plasma phenomena observed in space and in the laboratory. In this paper we analyse how the loss- cone feature (as determined by the loss-cone index or indices) influences the growth of such instabilities in a fully ionized, homogeneous, hot plasma in a uniform magnetic field. Specifically, we consider three loss-cone distributions: a generalized Lorentzian (kappa) loss-cone distribution, the Dory—Guest—Harris distribution and the Ashour-Abdalla-Kennel distribution (involving a subtracted Maxwellian). Our findings are common to all three distributions. We find that, for parallel propagation, electromagnetic instabilities are only affected by the loss-cone indices in terms of their occurrence in the temperature anisotropy. However, for oblique propagation, even including propagation at small angles to the ambient magnetic field, the loss-cone indices do independently affect the growth of instabilities for electromagnetic waves, in contrast to certain claims in the literature. For electrostatic waves such that 1, where kx is the component of the wave vector perpendicular to the ambient magnetic field and pLa is the Larmor radius for particle species <r, we find that the loss-cone indices only enter the dispersion equation via the temperature anisotropy, and so in this case the loss-cone feature and perpendicular effective thermal speed do not independently affect wave growth.
Magnetoacoustic modes in a magnetized dusty plasma
Authors: Rao N. N.
Published: March 2009

The existence of various types of (fast) magnetoacoustic modes in different frequency regimes in a magnetized dusty plasma consisting of electrons, ions and dust particles is investigated. The analysis is carried out using an effective two-fluid MHD-like model which allows for the non-frozen motion of the component fluids. For frequencies much smaller than the dust particle gyro- frequency, we obtain a magnetoacoustic mode that is a generalization of the usual compressional fast hydromagnetic wave in an electron—ion plasma. In the higher-frequency regimes, we show the existence of two new types of modes called ‘Dust-magnetoacoustic waves’. Both modes are accompanied by compressional magnetic field and plasma number density perturbations, and are the electromagnetic generalizations of the dust-acoustic waves in an unmagnetized dusty plasma with thermal electrons and ions. For a two- component plasma, all three modes degenerate into the same fast magneto- acoustic wave found in the usual electron—ion plasmas. We also obtain another novel type of magneto-acoustic mode called a ‘dust—ion-magneto- acoustic wave’, which is an electromagnetic generalization of the dust—ion- acoustic wave. The dispersion relations as well as the frequency regimes for the existence of the various modes are explicitly obtained. An alternative derivation of the relevant governing equations using an approach similar to that employed in so-called ‘electron magnetohydrodynamics’ (EMHD) is also presented.
Raman scattering of photons in the solar interior
Authors: Tsytovich V. N. , Bingham R. , de Angelis U.
Published: March 2009

We reconsider the transport equation in the solar interior and calculate the effects on the opacity of photon scattering near the Raman resonance. Both spontaneous and stimulated scattering on thermal photons and thermal plasmons are taken into account, and changes in opacity (with respect to previous calculations) are calculated numerically and found to be negligible with respect to relativistic corrections to photon scattering.
The unbounded two-dimensional guiding-centre plasma
Authors: Kiessling Michael K. -H.
Published: March 2009

The thermal mean-field equilibrium of a translation-invariant, unbounded one- component guiding-centre plasma is studied by analytical techniques. A variational principle is constructed. It is shown that only radial symmetric, decreasing density profiles occur. Prescribing the total number of gyro centres N ∈ (0, ∞), the energy E ∈ (E0, ∞) and the canonical angular momentum M ∈ (0, ∞]) uniquely determines a profile. Metastable or unstable profiles do not exist. A simple algebraic relation between N, M, the guiding-centre temperature β−1 and the characteristic Larmor frequency ω is derived. This explains Williamson's computer-based observations.
Tokamak transport based on the 13-moment model
Authors: Tippett Michael K.
Published: March 2009

A new model for collisional transport in a tokamak plasma is analysed. This model is obtained from Grad's 2-fluid 13-moment equations by estimating the order of magnitude of the various effects and neglecting those that are small. The model includes small particle flows, pressure anisotropy and temperature variation within flux surfaces. A formal solution is calculated that satisfies the model equations to O(me/mi). These solutions are found to evolve on a time scale Temi/me ≈ 50 ms.
Emission of extraordinary waves from an inhomogeous plasma
Authors: Croci R.
Published: March 2009

The asymptotic solution of the system of Vlasov and Maxwell equations for a plasma slab with a given current distribution is derived for weak absorption and weak equilibrium density inhomogeneity, but without the usual restriction that the perpendicular wavelengths be larger than the Larmor radii of the thermal particles. The equilibrium magnetic field is homogeneous. No model equations or phenomenological assumptions are introduced, except that the interaction of the components of the electric field parallel and perpendicular to the equilibrium magnetic field (corresponding to the ordinary and extraordinary waves in a homogeneous plasma) has been neglected. The electric field in vacuum is determined by a condition on the analytical form of the Fourier transform of the field that must necessarily also apply to the exact solution. The example presented to illustrate the results considers the emission at the harmonics of the electron gyrofrequency of a population of fast electrons in a plasma with cold ions; the theoretical results are in a very good qualitative agreement with experiment.
Propagation of ion-acoustic solitons in a warm ion-beam—plasma system
Authors: El-Labany S. K.
Published: March 2009

The reductive perturbation method is employed to investigate the excitation of ion-acoustic solitons in an ion-beam—plasma system consisting of warm ions and isothermal electrons through which a warm ion beam is propagating. Korteweg—de Vries and Korteweg–de Vries-type equations are obtained for the first- and second-order perturbed potentials respectively. The renormalization method is used to remove the secular terms. It is found that both the amplitude and the width of the soliton are strongly affected by the ion temperatures as well as the velocity of the ion beam. An alternative method is used to make a comparison with the solution obtained by the perturbation method.
Modifications of plasma edge electric field and confinement properties by limiter biasing on the KT-5C tokamak
Authors: Gao Hui , Zhai Kan , Wen Yi-Zhi , Wan Shu-De , Wang Gui-Ding , Yu Chang-Xun
Published: March 2009

Experiments using a biased multiblock limiter in the KT-5C tokamak show that positive biasing is more effective than negative biasing in modifying the edge electric field, suppressing fluctuations and improving plasma confinement. The biasing effect varies with the limiter area, the toroidal magnetic field and the biasing voltage. By positive biasing, the edge profiles of the plasma potential, the electron temperature and the density become steeper, resulting in a reduced edge particle flux, an increased global particle confinement time and lower fluctuation levels of the edge plasma.
Velocity correlations in two-dimensional electrostatic turbulence in low-β plasmas
Authors: Pécseli H. L. , Trulsen J.
Published: March 2009

The Eulerian and Lagrangian correlation functions in low-frequency electrostatic turbulence in strongly magnetized plasmas are studied in two spatial dimensions. In this limit the ion velocity in the direction perpendicular to a homogeneous magnetic field is approximated by the E × B/B2velocity. For strictly flute-type fluctuations, a similar model is also used for the electron dynamics. Allowing, on the other hand, for a small B-parallel component of the perturbations, an isothermal Boltzmann distribution for the electrons can be justified while the two-dimensional ion description is retained. The present analysis is based on an approximation of the actual two-dimensional flow in terms of an autonomous system consisting of many overlapping and mutually convecting vortices. Simple analytical expressions for the full space—time-varying Eulerian correlation are derived solely in terms of plasma parameters. it is demonstrated that an extension of the arguments giving the foregoing results also allows for derivation of analytical expressions for the Lagrangian correlation function. The results are supported by a Monte Carlo simulation based on the model.
Nonlinear dynamics of low-frequency drift waves
Authors: Beckmann M. , Frank P. , Himmel G.
Published: March 2009

The nonlinear behaviour of unstable drift waves in magnetized plasmas is analysed analytically. Most attention is paid to low-frequency waves created in electron density and temperature gradients of opposite sign. This situation is typically encountered in radiofrequency-produced discharges. The model developed explains nonlinear features such as mode competition, amplitude saturation and magnetic field hysteresis, which are observed experimentally.
Analytical description of low-frequency electron density and temperature oscillations
Authors: Frank P. , Beckmann M. , Himmel G.
Published: March 2009

Low-frequency density and temperature oscillations (ω « νj, ωcj, where νj is the collision frequency with neutrals and ωcj is the cyclotron frequency; j = i, e) observed in magnetized radiofrequency-produced plasmas with electron density and temperature gradients across the magnetic field are analysed using a local two-fluid model. This model incorporates the electron energy equation. The resulting dispersion relation permits study of the parameter dependence of the complex angular wave frequency. Instability is found in the case where the election density and temperature gradients have opposite signs. This instability is classified as a low-frequency drift wave, and the criteria for its onset are obtained.
Ponderomotive effects on the expansion of a photoplasma in the microwave range
Authors: Leloutre B. , Furtlehner J. -P. , Camus P.
Published: March 2009

An increase in the expansion rate towards vacuum of a plasma column with density of order 108 cm−3 and radius 0·5–2·0 mm produced by photoionization in the presence of a 9·4 GHz microwave field is found. The microwave field imposed by the TEM005 Gaussian mode of a spherical Fabry–Pérot resonator acts on the plasma through its ponderornotive force. First, the use of a potential barrier spectrometer allows us to measure the increase, in the number and energy of escaping electrons compared with the same plasma without microwave field. Secondly, the expansion of the modified photoplasma is checked by applying a small polarization voltage on the Fabry-Pérot mirrors to collect the ions. In the presence of the microwave field the time-resolved ion peak. Which presents a two-lobe profile faster than the single one observed without the field, indicates strong modification of the plasma dynamics. All these observations are interpreted by a simple model including the ponderomotive microwave force and the electrostatic plasma force, which act in opposite directions.