bluuebunny/crossref_metadata_2025 huggingface dataset:
Ion plasma waves in dusty plasmas: Halley's comet
Authors: de Angelis U. , Formisano V. , Giordano M.
Published: March 2009

We investigate ion waves in a plasma in the presence of massive charged dust particles, a common space-plasma component now known to exist also in planetary rings and comets. We derive an equation describing low-frequency electrostatic perturbations on a non-homogeneous background, where the inhomogeneity is due to a distribution of charged grains, each surrounded by an equilibrium statistical distribution of plasma particles. This model is then applied to propose an interpretation of some recent data from the Vega and Giotto space probes to Halley's comet the increase of the low-frequency electrostatic noise (ion-acoustic waves) in the region of increased dust.
Linear and nonlinear coupled Alfvén-Varma modes
Authors: Shukla P. K. , Stenflo L.
Published: March 2009

Starting from the particle continuity equation and the guiding-centre model for the particle velocity, using an equation of state in the form of the conservation of the ion magnetic moment, as well as Ohm's and Ampère's laws, a set of four coupled nonlinear equations has been derived to investigate the properties of magnetic turbulence in plasmas with hot ions and cold electrons. It is shown that finite-β effects can cause a linear coupling between the Alfvén and Varma modes in a weakly non-uniform plasma immersed in an inhomogeneous magnetic field. In the nonlinear regime the stationary solutions of the four field equations are found to be double vortices. Implications of our results for enhanced magnetic fluctuation and anomalous transport in a mirror reactor are pointed out.
Early onset of dissipative electrostatic drift-wave turbulence
Authors: Katou K.
Published: March 2009

The nonlinear dynamics of a low-frequency electrostatic dissipative inhomogeneous plasma in an external magnetic field is studied for conditions above the critical point. The diffusion flux and the saturation level are self-consistently calculated from first principles, i.e. from the Braginskii equation.
Analytical properties and numerical solutions of the derivative nonlinear Schrödinger equation
Authors: Dawson Silvina Ponce , Fontán Constantino Ferro
Published: March 2009

From the analysis of the symmetries of the derivative nonlinear Schrödinger (DNLS) equation, we obtain a new constant of motion, which may be formally considered as a charge and which is related to the helicity of the physical System. From comparison of these symmetries and those of the soliton solutions, we draw conclusions about the number of constraints that must be imposed and the way a Liapunov functional must be constructed in order to study the solitons' stability. We also examine the relationship between the stability with respect to form and the symmetries that are broken by the soliton solutions. We complete the analysis with some numerical simulations: we solve the DNLS equation taking a slightly perturbed soliton as an initial condition and study its temporal evolution, finding that, as expected, they are stable with respect to form.
Corrigendum
Authors: Faghihi M. , Scheffel J.
Published: March 2009

A minor correction, having no major influence on our results, is reported here. The coefficients in the equations of state (16) and (17) should read

The set of equations (13)–(20) now comprise the correct, linearized and Fourierdecomposed double adiabatic equations in cylindrical geometry. In addition, there is a printing error in (15): a factor bz should multiply the last term of the left-hand side. Our results are only slightly modified, and the discussion remains unchanged. We wish, however, to point out that the correct stability criterion for isotropic pressure, (26), should be

This is the double adiabatic counterpart to the m ╪ 0 Kadomtsev criterion of ideal MHD.
Dynamical evolution of three-dimensional kinetic electron-beam instabilities
Authors: Abdel-Gawad H. I.
Published: March 2009

We present a method of solution of the quasi-linear diffusion equation for the averaged distribution function. The criterion for its validity is discussed. Using the solution obtained, we study the dynamics of the relaxation of a weak kinetic electron-beam instability and show that it saturates asymptotically at zero energy level. In a self-consistent manner, the distribution function for the beam particles will be shown to deform to a flat shape.
Wavenumber shift of an obliquely propagating ion-cyclotron whistler
Authors: Paul S. N. , Sur A. K. , Pakira G.
Published: March 2009

An expression for the nonlinear wavenumber shift of an obiquely propagating ion-cyclotron whistler in the presence of negative ions are derived. The effects of the intensity of the wave, the ion-cyclotron frequency, the negative-ion concentration and the propagation angle on the wavenumber shift of whistlers is discussed. Numerical estimations are also made of the wavenumber shift.
A quasi-static equilibrium model of the rotamak
Authors: Bertram W. K.
Published: March 2009

An equilibrium model for a spherical field reversed configuration in the presence of a transverse rotating magnetic field is presented. It is shown that this quasi-static equilibrium is an exact solution of the time-dependent ideal magneto-hydrodynamic equations.
Forced Alfvén-wave turbulence and subgrid-scale closure
Authors: Zhou Ye , Vahala George
Published: March 2009

The renormalization-group method is applied to the problem of forced turbulence in the simplified Alfvén model of Chen and Mahajan. The effects of small unresolvable subgrid modes on the large-scale turbulence leads to a renormalized response function ε. In certain limits, the resulting recursion relation for the response function can be converted into a differential equation that can be solved analytically. For Gaussian forcing terms satisfying a power-law wavenumber correlation k–y but white-noise frequency spectrum, it is found that the response function exhibits second-harmonic generation of waves at frequency ω = 2ΛvA for all exponents y ≥ 0, where Λ is the wavenumber separating the subgrid and supergrid modes.
Nonlinear ion-acoustic waves in a magnetized plasma and the Zakharov-Kuznetsov equation
Authors: Shivamoggi Bhimsen K.
Published: March 2009

We consider here the nonlinear development of ion-acoustic waves in a magnetized plasma, and give a further discussion of the analytical properties of the Zakharov-Kuznestov equation that governs the latter problem. First we discuss the solitary-wave solutions and show that they give a good description of recent experimental results about the manner in which the magnetic field influences the solitary waves. We then exhibit recurrence and Lagrange stability of solutions of the Zakharov-Kuznestov equation.
Absolute stability in a collisionless electron-heat-conducting plasma in strong magnetic fields
Authors: de la Torre A. , Duhau S.
Published: March 2009

The dispersion relation obtained from a linear analysis of the hydrodynamic system of equations of Duhau is used to study the behaviour of the fast and slow magnetosonic and entropy modes in an electron-heat-flux-conducting plasma. The evolution of the hydrodynamic modes different from the Alfvén mode are studied as the electron heat flux is increased from zero as well as around the borders of overstable regions, for any anisotropy condition of the ions. The development of the domains of mirror and electron-heat-flux overstabilities are established and the regions of absolute stability are shown
Ion-acoustic solitons in magnetized multi-component plasmas including negative ions
Authors: Das K. P. , Verheest Frank
Published: March 2009

A study is made of ion-acoustic solitons in a low-β magnetized plasma consisting of any number of adiabatic positive and negative ion species in addition to the presence of isothermal electrons. A KdV equation in three dimensions or KdV-ZK equation is derived. This equation admits comprehensive or rarefactive solitons propagating in any oblique direction with respect to the direction of the external magnetic field, depending on the density of the negative ion species. When the nonlinear coefficient of this equation vanishes, the nonlinear ion-acoustic wave is described by a modified KdV equation in three dimensions. This equation is also derived and its solitary-wave solutions are discussed. Both compressive and rarefactive solitons are possible. Finally, the three-dimensional stability of these solitons is investigated by the small-k perturbation expansion method of Rowlands and Infeld. Stability criteria and growth rates of instabilities are derived.
Asymptotic state of the finite-Larmor-radius guiding-centre plasma
Authors: Knorr G. , Pécseli H. L.
Published: March 2009

The equilibrium properties of a two-dimensional plasma are examined theoretically, using a model where the finite-Larmor-radius corrections to the simple guiding-centre description are included. The analysis is carried out in a truncated Fourier representation of the resulting equations. This system has three ‘rugged’ quadratic invariants. A canonical-ensemble probability distribution characterized by three temperatures is derived. The resulting partition function is obtained and the equilibrium spectral energy density is calculated. The possibility of negative-temperature states leading to an inverse energy cascade is pointed out.
Propagation characteristics and reflection of an ion-acoustic soliton in an inhomogeneous plasma having warm ions
Authors: Singh Sanjay , Dahiya R. P.
Published: March 2009

The problem of propagation of an ion-acoustic soliton and its reflection in a weakly inhomogeneous plasma is considered, taking into account the effect of finite ion temperature. A reductive perturbation analysis is carried out to obtain expressions for the local speed, amplitude and width of the soliton. The peak value of the soliton amplitude increases and the soliton width decreases with increasing ion temperature. An equation describing the dependence of the reflected-wave amplitude on ion temperature is obtained. The amplitude of the reflected wave is observed to decrease with increasing ion temperature on account of Landau damping.
Reflection of ion-acoustic waves from bipolar potential structures
Authors: Nakamura Y. , Chutia Joyanti
Published: March 2009

Reflection of ion-acoustic waves from the ion sheath in front of the separation grid in a double-plasma device has been investigated experimentally. The plasma potential φ of the source plasma was controlled relative to that of the target plasma. When eφ < κΤe, where Τe is the electron temperature, no reflection was observed. The reason for this is that ions are drifting towards the grid with the Bohm velocity, i.e. the ion-acoustic velocity. When eφ > κΤe the reflected wave consists of the ion-acoustic wave and the ion beam mode. The reflection coefficient for the ion-acoustic wave is about unity. This high efficiency is due to reflection of the ions themselves.
Weakly relativistic nonlinear orbit dynamics for intense ordinary-mode propagation near electron cyclotron resonance
Authors: Davidson Ronald C. , Yang Tser-Yuan , Aamodt Richard E.
Published: March 2009

The nonlinear orbit equations are investigated analytically and numerically for a constant-amplitude electromagnetic wave (ωs, ks) with ordinary-mode polarization propagating perpendicular to a uniform magnetic field B0 êz. Relativisitic electron dynamics are essential in determining the maximum orbit excursion when the incident wave frequency ωs is near the nth harmonic of the electron cyclotron frequency Ωc. Coupled nonlinear equations are obtained for the slow evolution of the amplitude A(т) and phase ø(t) of the perpendicular orbit when ωs ≈ nΩc. The dynamical equations are reduced to quadrature and simplified analytically. At exact resonance (ωs = nΩc), if relativistic effects are (incorrectly) neglected, the maximum orbit excursion Amax approaches the unacceptably large value determined from the first (non-zero) solution to Jn(ns ΩsAmax) = 0, which totally invalidates the non-relativistic approximation. (Here ns Ωs = cks/Ωc.) As a contrasting illustrative example, for n = 1, ωs = Ωc and moderate pump strength, weak relativistic effects limit the maximum orbit excursion to the approximate value , where єs = ns ωs (Vz/c) Vq/c ≪ 1, and Vq is the axial quiver velocity in the applied oscillatory field. Physically, relativistic effects produce a nonlinear frequency shift that dynamically ‘detunes’ the particle motion from exact cyclotron resonance, thereby limiting amplitude growth.
Self-focusing of nonlinear ion-acoustic waves and solitons in magnetized plasmas. Part 3. Arbitrary-angle perturbations, period doubling of waves
Authors: Frycz P. , Infeld E.
Published: March 2009

Nonlinear waves, solutions of the Zakharov–Kuznetsov (ZK) equation for a dilute plasma immersed in a strong magnetic field, are studied numerically. It is found that the most unstable mode rides with the carrier wave and leads to period doubling. Owing to the simplicity of the ZK equation, this and other phenomena, similar to those observed for gravity waves on a water surface, can be fully investigated. Analytical methods are also explored. An expansion in the carrier-wave amplitude leads to good estimates for growth rates, a result so far unobtainable for water waves. This paper can be read independently of parts 1 and 2, but a brief summary of all three parts is given at the end.
Coupling between Varma, modified-convective-cell and Alfvén modes in an inhomogeneous plasma
Authors: Shukla P. K. , de Angelis U. , Jovanović D.
Published: March 2009

The effect of parallel electron dynamics is incorporated in the study of the Varma mode, which is a flute-like electrostatic ion drift perturbation in an inhomogeneous magnetic field. Starting from the electron and ion continuity equations, an equation for the conservation of the ion magnetic moment, the generalized Ohm's law, and Faraday's and Ampère's laws, we derive a set of four nonlinearly coupled differential equations. The nonlinearities arising from the E × B0 convection of the density and magnetic-moment variations, nonlinear ion polarization drift and Lorentz force, and the coupling of the parallel electron flow to the perturbed magnetic field are included. In the linear limit we find that the Varma mode becomes coupled with the modified-convective-cell and Alfvén modes. The instability of the coupled system is analysed and an expression for the growth rate is obtained. In the nonlinear regime we present the localized dipole vortex solution of the coupled Varma and convective-cell modes as well as the coupled Varma and Alfvén modes. It is found that for the former case the nonlinear structure is a solution of a second-order partial differential equation, whereas for the coupled Varma and inertial Alfvén waves the dipole vortex belongs to a family of fourth-order differential equations. Our results can be useful in understanding the electrostatic and electromagnetic fluctuations in mirror reactors, tokamaks and astrophysical plasmas.
On the dependence of the efficiency of lower-hybrid current drive on the wave spectrum
Authors: Nocentini Aldo
Published: March 2009

The dependence of the efficiency of current drive by lower-hybrid waves on the shape and intensity of the wave spectrum is discussed in the case where no d.c. electric field is present. The discussion is based on a simple formula arising from a one-dimensional kinetic treatment of the problem.
A catastrophe-theory study of a two-chamber model for a tokamak scrape-off and divertor
Authors: Punjabi Alkesh
Published: March 2009

The two-chamber model (TCM) of Singer and Langer is employed to study the plasma transport in the scrape-off and divertor regions of a tokamak. Collisiondominated transport along the field lines is considered, with a. geometric-mean flux-limited expression for parallel electron heat conduction. An analytic method for the catastrophe-theory study of the TCM is developed. Maxwell convention for the catastrophes is adopted. Catastrophes occur when the energy flux entering the divertor chamber from the main plasma scrape-off, the recycling coefficient and the ratio of electron temperatures in the scape-off to that in the divertor exceed some threshold values. It is seen that the behaviour of the plasma during these catastrophes is in qualitative agreement with the experimentally observed features of the plasma during the H-mode transition.
Numerical investigation of a plasma beam entering transverse magnetic fields
Authors: Koga J. , Geary J. L. , Fujinami T. , Newberger B. S. , Tajima T. , Rostoker N.
Published: March 2009

We study plasma-beam injection into transverse magnetic fields using both electrostatic and electromagnetic particle-in-cell (PIC) codes. In the case of small beam momentum or energy (low drift kinetic β) we study both large- and small-ion-gyroradius beams. Large-ion-gyroradius beams with a large dielectric constant ε ≫ (M/m)½ are found to propagate across the magnetic field via E × B drifts at nearly the initial injection velocity, where and M/m is the ion-to-electron mass ratio. Beam degradation and undulations are observed, in agreement with previous experimental and analytical results. When ε is of order (M/m)½ the plasma beam propagates across field lines at only half its initial velocity and loses its coherent structure. When ε is much less than (M/m)½ the beam particles decouple at the magnetic field boundary, scattering the electrons and slightly deflecting the ions. For small-ion-gyroradius beam injection a flute-type instability is observed at the beam-magnetic-field interface. In the case of large beam momentum or energy (high drift kinetic β) we observe good penetration of a plasma beam by shielding the magnetic field from the interior of the beam (diamagnetism). However, we observe anomalously fast penetration of the magnetic field into the beam and find that the diffusion rate depends on the electron gyroradius of the beam.
Numerical determination of the ambipolar electric field in a stellarator-reactor plasma
Authors: D'Haeseleer W. D. , Hitchon W. N. G. , Shohet J. L.
Published: March 2009

A numerical parametric study of the radial ambipolar electric field in a stellarator reactor has been undertaken. With the numerical neoclassical code FLOCS (Flow Code for Stellarators), which is capable of handling both ions and electrons of all relevant kinetic energies, the radial ambipolar field (Er)AMB is determined from the algebraic condition that ion and electron fluxes are equal. As expected, the potential is of the same order of magnitude as the temperature. Somewhat surprisingly at first sight, however, the potential does not change much with the temperature (in the parameter range under consideration), being somewhat insensitive to moderate variations of T. An explanation for this behaviour is presented. Finally, the radial particle fluxes, consistent with the obtained (Er)AMB, and the particle confinement time are computed.
Waves in a cold plasma with spatially periodic sheared fields
Authors: Diver D. A. , Laing E. W. , Sellar C. C.
Published: March 2009

We have studied wave propagation in a cold plasma, in the presence of a spatially rotating magnetic field of constant magnitude. New features introduced by this variation include streaming velocities and a plasma current in equilibrium and density fluctuations. We present only the case of wave propagation along the axis of rotation of the magnetic field. A set of ordinary differential equations for the electric field components is obtained, which may be combined into a single fourth-order ordinary differential equation with periodic coefficients. Solutions are obtained in closed form and their nature is determined in terms of the physical parameters of the System, magnetic field strength, number density and wave frequency.
Excitation of long-wave quasi-perpendicular electrostatic ion-cyclotron waves in multi-species weakly ionized plasmas
Authors: Milić B. S.
Published: March 2009

It is shown, using kinetic equations with BGK model collision integrals, that in a multi-species weakly ionized plasma the quasi-perpendicular ion-cyclotron instability (waves of growing amplitude) excited by the electron drift parallel to the background magnetic field first sets in for long waves (modal wavelengths much larger than the electron mean free path) as the drift is gradually increased, much as in plasmas with only one ion species. Only waves with modal frequencies close to some cyclotron harmonics of some of the ion species present are taken into account in the present work. Owing to the mutual commensurability of all the ion-cyclotron frequencies, more than one species of ions may be ‘resonant’ with any mode of the type considered. The role of ‘resonant’ and ‘non-resonant’ ion species is investigated, both in general and for some particular plasmas. Some numerical details are also given. It is shown that although in most instances the threshold drifts vary monotonically (but not linearly) as the plasma composition is varied, there are cases in which maxima or minima (often depending on the degree of non-isothermality) of the threshold drift magnitude are predicted for some specific plasma compositions. These are usually encountered in plasmas containing ions with different charge numbers.
An approach to the collisional heating rates of an anisotropic plasma
Authors: Hernández R.
Published: March 2009

An approach to the evaluation of the collisional transfer rates of the components of the temperature tensor between drifting tri-Maxwellians for an arbitrary central interaction force between the particles is given. We describe an explicit calculation of the transfer rates of the parallel and perpendicular temperatures of test particles in an isotropie background gas. With a concise form for the transfer rates, we also find the time-independent solution of the transport equation for the anisotropic temperature of ions, as test particles in a drifting neutral background with an external magnetic field.
Alternative representation of the dielectric tensor for a relativistic magnetized plasma in thermal equilibrium
Authors: Yoon Peter H. , Davidson Ronald C.
Published: March 2009

An alternative representation of the dielectric tensor εij(k, ω) for a relativistic magnetized plasma in thermal equilibrium is presented. This representation involves an infinite series expansion in powers of , as well as an asymptotic expansion for large Here ωc = eB0/mc is the nonrelativistic cyclotron frequency, k⊥ is the wavenumber perpendicular to the magnetic field B0êz, and α is the dimensionless parameter defined by α = mc2/KBT. The present work generalizes Shkarofsky's (1966) representation. Moreover, unlike Trubnikov's (1958) formal result, in which the k⊥ and kz dependences of εij(k, ω) are inexorably coupled, the present representation naturally separates the k⊥ and kz dependences of εij(k, ω). As an application, the general expression is simplified for the case of a weakly relativistic plasma, and the dispersion relation is obtained for electromagnetic waves, including first-order relativistic effects. The method developed in this paper can be used for other non-thermal distributions.
Compact toroid formation, dynamics and lifetime in collisional plasmas generated at high fill pressures
Authors: Dooling J. C. , York T. M. , Niimura M. , Aghamir F. , Mead F. B. , Shieh D. R.
Published: March 2009

A 0·50 m long compact-toroid transport experiment (CTTX) has been studied with a number of diagnostics, including Thomson scattering, to determine local plasma properties and gradients indicative of transport processes. The CTTX bias and main field strengths were –0·09 and 0·35 T. Compact toroid formation and lifetime were studied at static fill pressures of 20, 100 and 150 mTorr deuterium, between 3 and 30μs after firing of the main bank. Thomson-scattering diagnosis was carried out using a Q-switched Nd: glass laser operated at both fundamental (1053 nm) and second-harmonic wavelengths (527 nm). For each pressure, scattering tests were conducted at radii r of 0·1, 1·0, 1·85 and 2·60 cm and axial positions z of 6·7, 13·0 and 19·0 cm (1054 nm); supplementary data were obtained at r = 0·1, 1·35 and 2·10 cm at z = 6·7 cm (527 nm). Electron densities and temperatures were in the ranges 1021–1022 m-3 and 2–20 eV. Thomson-scattering results are compared with diamagnetic loop, inter-ferometry, luminosity and piezoelectric pressure-probe data. Axial behaviour of the formation CT plasma varies significantly with initial fill pressure: continuous axial contraction occurs at ISOmTorr; whereas the 20 mTorr plasma appears first to contract then expand. Particle loss times are found to decrease from 70 μs at 20 mTorr to 24 μs at 100 mTorr and 12 μs at 150 mTorr. Energy decay times are 6, 7 and 5 μs for 20, 100 and 150 mTorr respectively. Flux-decay times are approximately 20 μs for 20 mTorr, 12 μs for 100 mTorr and 20 μs for 150 mTorr fill pressure. These values are two to four times longer than would be expected from theory using classical transport. In order to explain the sustained magnetic flux, the role of electric fields within the compact toroid is considered.
The effect of a static magnetic field on the growth of a rippled electromagnetic beam
Authors: Singh Arvinder , Singh Tarsem
Published: March 2009

This paper presents an investigation of the growth of a radially symmetrical ripple, superimposed on a Gaussian electromagnetic beam in a collisionless magnetized plasma. On account of the non-uniform intensity distribution of the main beam, the d.c. component of the ponderomotive force becomes finite and leads to modification of the background density. There is feedback from the main beam to the ripple, which subsequently grows at the cost of the pump wave. The effect of the plasma and pump parameters is studied in detail. An interesting feature is that the ripple always grows, irrespective of the phase relationship of the main beam and the ripple. This is due to strong self-focusing of the main beam for the chosen set of parameters.
Main-signal filamentation in free-electron lasers with deeply trapped particles
Authors: Rizzato F. B.
Published: March 2009

The filamentation of electromagnetic waves in a free-electron laser with deeply trapped electrons is analysed. This instability is the result of particle bunching along transverse directions (with respect to the fast wave vector), as opposed to the untrapped-electron case, where it is a result of longitudinal bunching. Two cases are considered: (i) the non-resonant or reactive one, with purely imaginary growth rates; and (ii) the resonant one, with large (small) values of the real (imaginary) part of the perturbing frequency. In particular, we find that the reactive instability occurs only when the wiggler amplitude is unusually large. On the other hand, we show that the resonant process (with frequencies close to the synchrotron frequency) may be relevant for conventional free-electron lasers and that the growth rate for quasi-trans verse perturbations may be larger than that corresponding to longitudinal perturbations. Owing to the inhomogeneity and anisotropy of our system, low-frequency magnetic fields are generated. These fields, as well as the transverse electric fields, are analysed, and their role in the low-frequency dynamics is clarified.
Weakly multi-dimensional cosmic-ray-modified MHD shocks
Authors: Zank G. P. , Webb G. W.
Published: March 2009

The multi-dimensional structure of weak, energetic-particle-modified shocks is investigated by means of appropriate perturbation techniques. The time-dependent shock-structure equation is found to be a generalized form of the well-known one-dimensional Burgers equation, whose steady state, in the absence of cosmic rays, is shown to be related to an equation modelling steady transonic flow in several dimensions. The time-dependent (1 + 2)- and (1 + 3)-dimensional Burgers equations are integrated exactly by means of Hirota's technique for one-shock solutions. On the basis of the exact solutions, a discussion relating the various length scales associated with the shock is presented.
Plasma waves in hot relativistic beam-plasma systems. Part 2. Kinetic and hydrodynamic instabilities
Authors: Magneville Alain
Published: March 2009

Temporal and spatial hydrodynamical instabilities and kinetic instabilities of plasma waves are considered for a relativistic beam–plasma System. The beam and plasma temperatures, and the beam velocity, may be relativistic. Instability conditions and growth rates are evaluated. An unusual case of kinetic stability inversion, for relativistic or dense beams, is discussed.
Laser beat wave in a relativistic plasma
Authors: Magneville Alain
Published: March 2009

A relativistic study of the beat wave of two laser beams in a hot plasma is presented in the case where the modifications of the distribution function due to this beat wave are much smaller than the equilibrium distribution function. This situation corresponds to small laser energies or high plasma temperatures. The power-conversion efficiency of the laser beams is evaluated for different values of temperatures, laser energies and frequencies.
MHD stagnation-point flows at a current sheet including viscous and resistive effects: general two-dimensional solutions
Authors: Phan T. D. , Sonnerup B. U. Ö.
Published: March 2009

Exact solutions are presented of two-dimensional steady-state incompressible stagnation point flows at a current sheet separating two colliding plasmas. They describe the process of resistive field annihilation (zero reconnection) where the magnetic field in each plasma is strictly parallel to the current sheet, but may have different magnitudes and direction on its two sides. The flow in the (x, y) plane toward the current sheet, located at x = 0, may have an arbitrary angle of incidence and an arbitrary amount of divergence from or convergence towards the stagnation point. We find the most general form of the solution for the plasma velocity and for the magnetic field. For the z compenents of the flow and field, solutions in the form of truncating power series in y are found. The cases obtained in this study contain the solutions obtained by Parker, Sonnerup & Priest, Gratton et al. and Besser, Biernat & Rijnbeek as special cases. The role of viscosity in determining the flow and field configurations is examined. When the two colliding plasmas have the same viscosity and density, it is shown that viscous effects usually are important only in strongly divergent or convergent viscous flows with viscous Reynolds number of the order of unity or smaller. For astrophysical applications the viscous Reynolds number is usually high and the effects of viscosity on the interaction of plasmas of similar properties are small. The formulation of the stagnation-point flow problem involving plasmas of different properties is also presented. Sample cases of such flows are shown. Finally, a possible application of the results from this study to the earth's magnetopause is discussed briefly.
Asymptotic solution of the Vlasov and Poisson equations for an inhomogeneous plasma
Authors: Croci Riccardo
Published: March 2009

The purpose of this paper is to derive the asymptotic solutions to a class of inhomogeneous integral equations that reduce to algebraic equations when a parameter ε goes to zero (the kernel becoming proportional to a Dirac δ function). This class includes the integral equations obtained from the system of Vlasov and Poisson equations for the Fourier transform in space and the Laplace transform in time of the electrostatic potential, when the equilibrium magnetic field is uniform and the equilibrium plasma density depends on εx, with the co-ordinate z being the direction of the magnetic field. In this case the inhomogeneous term is given by the initial conditions and possibly by sources, and the Laplace-transform variable ω is the eigenvalue parameter.
Parametric decay of a whistler wave at the difference frequency of two electromagnetic waves in a plasma
Authors: Guha S. , Sarkar Ruby
Published: March 2009

A large-amplitude whistler wave excited at the difference frequency of two high-frequency electromagnetic pump waves is shown to decay parametrically into a lower-hybrid wave (LHW) and a low-frequency ion–Bernstein wave (IBW) in a collisionless magnetized multi-ion-species plasma,. A nonlinear dispersion relation describing this parametric interaction process is derived. The low-frequency ponderomotive force along the direction of the external magnetic field leads to the dominant coupling. Possible applications to ion heating in the ionosphere, in the earth's magnetosphere and in laboratory plasmas are discussed.
Generation and radiation of third harmonics by an electrostatic wave in a narrow inhomogeneous layer of a warm plasma
Authors: Hussein A. M.
Published: March 2009

An investigation is made of wave generation and the radiation of third harmonics by an electrostatic wave in a narrow inhomogeneous layer of a warm plasma. The amplitudes of the third-harmonic wave are calculated. It is found that they depend both on the nonlinear interaction of the initial waves and on the interaction of second harmonics with the initial wave. The generation of third harmonics by interaction of the initial waves is a four-wave process, i.e. a higher-order nonlinearity.
Aspects of subgrid modelling and large-eddy simulation of magnetohydrodynamic turbulence
Authors: Zhou Ye , Vahala George
Published: March 2009

Subgrid-scale closures for magnetohydodynamic (MHD) turbulence are examined using the filtering technique. From the similarities between incompressible MHD turbulence and its hydrodynamic counterpart, as well as ideas from dynamo theory, a subgrid model is constructed from the large-eddy simulation (LES) of MHD turbulence. This model should find applicability in treating LES of the reversed-field pinch.
Phase-mixing and surface waves: a new interpretation
Authors: Cally P. S.
Published: March 2009

The classical incompressible MHD or cold plasma phase mixing problem, which involves Alfvén or plasma waves in inhornogeneous media, is re-examined using a spatial Fourier series rather than the usual temporal Fourier or Laplace transform approach. A number of exact and near-exact analytic and numerical results are derived which reveal an attractive picture of energy cascading to smaller length-scales in a manner reminiscent of turbulence. Furthermore, we present a simple and unambiguous description of how a surface wave arises in the limit in which the inhomogeneity becomes a discontinuity.
Helicity waves propagating in a plasma
Authors: Yoshida Z.
Published: March 2009

There exist plasma waves that transport helicity although they do not propagate electromagnetic energy. The dispersion relations of such helicity waves are studied. The electric field of the waves is parallel to the perturbed magnetic field, and both are perpendicular to the perturbed current. In cross-field propagation, a helicity wave is decomposed into two transverse modes with different polarizations and a longitudinal part. The helicity waves are principally Alfvénic in the low-frequency limit. At high frequencies, the Faraday effect comes into the polarization.
A physical description of magnetic helicity evolution in the presence of reconnection lines
Authors: Wright Andrew N. , Berger Mitchell A.
Published: March 2009

The dissipation of relative magnetic helicity due to the presence of a resistive reconnection region is considered. We show that when the reconnection region has a vanishing cross-section, helicity is conserved, in agreement with previous studies. It is also shown that in two-dimensional systems reconnection can produce highly twisted reconnected flux tubes. Reconnection at a high magnetic Reynolds number generally conserves helicity to a good approximation. However, reconnection with a small Reynolds number can produce significant dissipation of helicity. We prove that helicity dissipation in two-dimensional configurations is associated with the retention of some of the inflowing magnetic flux by the reconnection region, vr. When the reconnection site is a simple Ohmic conductor, all of the magnetic field parallel to the reconnection line that is swept into vr is retained. (In contrast, the inflowing magnetic field perpendicular to the line is annihilated.) We are able to relate the amount of helicity dissipation to the retained flux. A physical interpretation of helicity dissipation is developed by considering the diffusion of magnetic field lines through vr. When compared with helicity-conserving reconnection, the two halves of a reconnected flux sheet appear to have slipped relative to each other parallel to the reconnection line. This provides a useful method by which the reconnected field geometry can be constructed: the incoming flux sheets are ‘cut’ where they encounter vr, allowed to slip relative to each other, and then ‘pasted’ together to form the reconnected flux sheets. This simple model yields estimates for helicity dissipation and the flux retained by vr in terms of the amount of slippage. These estimates are in agreement with those expected from the governing laws.
Scattering of circularly polarized electromagnetic waves off a straight electron beam propagating along a constant magnetic field
Authors: Bogdanov Alexander
Published: March 2009

The stability of straight field-aligned electron beams, immersed in an external magnetic field of finite magnitude, with respect to the excitation in them of circularly polarized (spiral) electromagnetic waves is a problem calling for detailed investigation, particularly in the context of the study and development of free-electron lasers. Traditionally the problem is treated using the theory of electromagnetic waves scattering off electron-beam density oscillations. This is done, however, without considering the inverse influence of the beam on the dispersion properties of the electromagnetic waves. On the other hand, it is well known that the presence of the beam introduces substantial changes in the characteristics of the electromagnetic waves interacting with the beam, and, moreover, this results in the appearance of radically new types of waves that are entirely absent in free space. The paper is dedicated to the study of the nonlinear dynamics of the interaction of such radically changed electromagnetic waves with the beam density oscillations.
Modulational instability produced by Alfvénic turbulence in a collisionless plasma
Authors: Hamabata Hiromitsu
Published: March 2009

Using first-order smoothing theory, Fourier analysis and perturbation methods, we obtain the evolution equation of the wave spectrum as well as the nonlinear forces generated by Alfvénic turbulence in a finite-β plasma with dispersion and phenomenological Landau-damping effects. The stability of Alfvénic turbulence is then analysed by solving the derived mean-field equations. It is shown that parallel-propagating turbulent Alfvén waves with dispersion can be modulationally unstable, leading to amplification of large-scale Alfvén waves and acoustic waves when Landau-damping effects are strong and weak respectively.
Amplification of nonlinear surface waves in an inhomogeneous transition layer
Authors: Brodin G. , Gradov O. M.
Published: March 2009

A plasma with a boundary transition layer of variable depth in the presence of a powerful electromagnetic field is considered. It is shown that a displacement of the boundary will grow, and will propagate as a nonlinear surface wave in the direction in which the depth of the transition layer decreases.
Guiding-centre orbits for particles in cross-field devices
Authors: Riyopoulos Spilios
Published: March 2009

The motion of a particle driven by a slow RF wave inside crossed electrostatic and magnetostatic fields is examined. A time-scale separation exists in the synchronous frame, moving at the slow-wave phase velocity, where all fields appear static in time and the cyclotron motion is much faster than the guidingcentre drift. The averaging of the periodic gyromotion is performed systematically with canonical transformations up to second order in the smallwave amplitude. The first-order guiding-centre drift follows the equipotential surfaces of the transformed electric field. The second-order effects, due to the field-line curvature, and/or the nonlinear variation in the wave phase velocity, cause departures from the parapotential flow. The topology of the trajectories depends on the departure of the drift velocity from synchronism with the wave. Various flow topologies corresponding to different values of the control parameters are examined.
Intense propagation in a magnetized cold plasma: modulational instabilities of fully relativistic electromagnetic waves
Authors: Kates Ronald E. , Kaup D. J.
Published: March 2009

This paper studies modulational instabilities of intensely propagating, circularly polarized, plane electromagnetic plasma waves in the presence of an external magnetic field pointing exactly in the direction of propagation. By ‘intense propagation’, we mean that eEo/mw (where Eo is the amplitude of the wave's transverse electric field) is comparable to unity, so that the problem is fully nonlinear and cannot be solved by regular perturbation methods. The positive component may consists of either positrons or singly charged ions. The plasma is assumed to be fully ionized and cold. Modulated intensely propagating electromagnetic waves couple (in general) to longitudinal motions via the ponderomotive force. For given wavenumber, the frequency of the wave depends on the amplitude not only via the obvious mechanism of relativistic mass increase but also via the density inhomogeneities induced by the ponderomotive force. This coupling effectively involves derivatives of the envelope, and the effect of longitudinal motions is comparable to that of relativistic nonlinearities. For this reason, a proper expansion procedure requires verification that one has obtained a self-consistent solution of all the field equations up to the appropriate order, including the longitudinal equations. This is best accomplished using the well-known two-timing approach. Modulational instability arises in the case of an ion-electron plasma with relativistic electrons but non-relativistic ions. However, for parameter values appropriate to pulsar magnetospheres, where the electron-cyclotron frequency is much larger than the frequency of the wave, there is no instability on the time scale of a micropulse.
Quasi-one-dimensional model equations for plasma flows in high-pressure discharges in ablative capillaries
Authors: Zoler D. , Cuperman S.
Published: March 2009

Quasi-one dimensional hydrodynamic continuity, momentum and energy equations describing the plasma flow in high-pressure-discharge ablative capillaries are derived. To overcome the formidable difficulties arising in the solution of a fully two-dimensional system of equations, experimental information on the structure (geometry) of the generated plasma is used. Thus the two-dimensional hydrodynamic equations are averaged over the cross-section of the capillary to obtain a quasi-one-dimensional system of equations in which, however, the essential two-dimensional features are present. These include the radial outwards radiative transfer of energy and the radial inwards ablative mass flow. Some particular cases, including their thermodynamical aspects, are discussed. Illustrative analytical and numerical solutions of the equations are also presented.
Nonlinear MHD waves in a dissipative plasma with Hall dispersion and the modified Burgers—Schrödinger equation
Authors: Korsunsky Sergei V.
Published: March 2009

We consider the nonlinear propagation of magnetosonic waves along an unperturbed magnetic field in a plasma of high but finite conductivity when the Hall effect is taken into account, and we give a discussion of the analytical solutions of the nonlinear evolution equation that governs the latter problem. This equation is a generalization of the well-known modified Schrödinger equation and of the modified Burgers equation (it is referred to here as the modified Burgers-Schrödinger equation). Explicit analytical expressions for both a stationary kink-type solution and circularly polarized quasi-periodic waves are obtained and investigated.
Magnetohydrodynamic stability of a streaming gas jet
Authors: Elazab Samia S.
Published: March 2009

The MHD stability of a gas jet surrounded by a streaming radially finite liquid cylinder (with solid cylindrical edge) is studied. The system is acted upon by capillary, electromagnetic and inertial liquid forces. The eigenvalue relation is established to all kinds of perturbations. The streaming has a strong destabilizing influence that is independent of all problem parameters. The capillary force is destabilizing only for small axisymmetric modes and stable for the rest. The electromagnetic force is strongly stabilizing whatever the intensities of the magnetic field. If the influence of the latter is sufficiently strong, the influence of the streaming can be completely suppressed. It is found that for an axisymmetric perturbation the domain of instability is the same whatever the value of the liquid radial distance.
Net inverse-bremsstrahlung (NIB) acceleration of a high-energy electron beam in an axial electrostatic wave
Authors: Kim S. H.
Published: March 2009

It is shown that stimulated emission is an intrinsically incoherent-phase phenomenon arising from the uncertainty principle, and that therefore the laser gain cannot be described by any classical model, which must be coherent in all aspects. The force due to the net inverse-bremsstrahlung (‘NIB force’) acting on a high-energy electron beam travelling in an undulating field whose wave vector is collinear with the electron beam (‘collinear wiggler’) is found by extending the quantum kinetic theory of the free-electron laser. In the case that an axial electrostatic wave is used as the catalysing field for the net multi- photon inverse bremsstrahlung, it is shown that NIB acceleration is practical only when the potential amplitude (in terms of the electron energy) of the laser wave, [eA0], is comparable to or larger than the electron rest energy mc2.
Anomalous absorption of a radio wave in the ionosphere
Authors: Tripathi V. K. , Sawhney B. K. , Singh S. V.
Published: March 2009

A radio wave transmitted into the ionosphere in the presence of a lower-hybrid drift wave excites a Langmuir wave, which is then damped by electrons, thereby heating them. This constitutes an important absorption mechanism. We evaluate the potential of the Langmuir wave and obtain an expression for the ratio Pr of the power of the Langmuir wave to that of the incident radio wave in the inhomogeneous ionosphere. It is found that the radio wave suffers an absorption of about 8% for a density fluctuation n1/n0 = 5%, but the electric field of the Langmuir wave becomes about 11.7 times that of the radio wave, which can lead to the excitation of parametric instabilities in the ionosphere.
Nonlinear electrostatic waves in equal-mass plasmas
Authors: Stewart G. A.
Published: March 2009

A study is made of electrostatic waves in a cold equal-mass plasma. Numerical simulation reveals that cold equal-mass plasmas are fundamentally unstable to such oscillations, in contrast to the behaviour of these waves in electron-ion plasmas. A quasi-linear analysis of the problem is performed and an analytic solution found that duplicates the early evolution of the plasma.
Three-dimensional stability of solitary kinetic Alfvé waves and ion-acoustic waves
Authors: Ghosh G. , Das K. P.
Published: March 2009

Starting from a set of equations that lead to a linear dispersion relation coupling kinetic Alfvén waves and ion-acoustic waves, three-dimensional KdV equations are derived for these waves. These equations are then used to investigate the three-dimensional stability of solitary kinetic Alfvén waves and ion-acoustic waves by the small-k perturbation expansion method of Rowlands and Infeld. For kinetic Alfvén waves it is found that there is instability if the direction of the plane-wave perturbation lies inside a cone, and the growth rate of the instability attains a maximum when the direction of the perturbation lies in the plane containing the external magnetic field and the direction of propagation of the solitary wave.