Table of contents

The "International Topical Conference on Plasma Physics: New Plasma Horizons" was held at the University of Algarve, Faro, Portugal, during the period 3–7 September 2001. The conference was organized by P. K. Shukla, R. Bingham, J. I. Mendonça and L. Stenflo with the help of an international advisory board and a program committee that included well known scientists from all over the world. The conference enters into a series of previous activities that we have held at the Abdus Salam International Centre for Theoretical Physics, Trieste (Italy) since 1989 and at the University of Algarve (UA), Faro (Portugal) since 1999.

The purpose of this meeting was to provide an informal forum for scientists who have a broad experience/knowledge in science including, for example, nonlinear optics and nonlinear waves and structures in fluids and plasmas. The selected topics represented new horizons in areas that were interdisciplinary. They spanned from basic physics to many applied aspects in diverse areas, and described new trends of research in optics, fluids, as well as in several sub-branches of plasma physics and associated fields arising in the twenty-first century.

The response of the conference, which was attended by approximately ninety delegates from Europe, USA, Japan, and the developing countries, was excellent. The participants were an admixture of young and senior researchers. This helped to disseminate knowledge between these two generations of plasma and fluid dynamics physicists.

The scientific program was structured into five review talks (45 minutes) and thirty-seven invited topical lectures (30 minutes) covering the history, theory/simulations, experiments and observations. In addition, there were about fifty poster papers in two sessions. The latter gave opportunities to younger physicists to display the results of their recent work and to obtain comments from the other participants. During the five days at the UA, we focused on fundamental and applied aspects of:

(i) various nonlinearities in sciences

(ii) plasmas in space and astrophysics

(iii) plasma turbulence in laboratories

(iv) collective processes in dusty plasmas

(v) some exotic topics.

In his keynote address, Professor Akira Hasegawa described the physics of localized pulse propagation through optical fibers, and emphasized the success of optical solitons for ultra-high speed communications to very long distances. His presentation revealed that the Kerr nonlinearity is indeed useful for practical purposes. Following Hasegawa's speech there were many talks dealing with new aspects of the statistical description of partially incoherent optical wave dynamics in nonlinear media, solitons and radiating quasi-solitons, solitons in Madelung fluids, mutual interaction between laser beams, formation and dynamics of vortices in fluids and plasmas, as well as axisymmetric plasma equilibria in general relativity. The new horizons in space plasmas and astrophysics covered solar system plasmas and their diagnostic power (a lucid presentation by Professor Ruedi von Steiger), nonlinear structures in our solar system, lamentation of Alfvén beams, transonic MHD flows, stochastic ion heating by large amplitude Alfvén waves, topical phase transitions, and the physics of numerous solitary structures in the Earth ionosphere/magnetosphere. Professor Pat Diamond took a broad view on nonlinear theories and observations of drift wave turbulence and zonal flows in association with transport barriers in magnetic fusion devices. Several papers also dealt with novel aspects of zonal excitation and transport modulation by radially coherent flow structures and fast magnetic field explosions. A symposium on complex plasmas was dedicated to the late Nagesha Rao and Anatoly Nefedov who were among the pioneers in the new field of dusty plasma physics. Here, the lectures were focused on charging, shielding and dynamics of dust grains, formation and melting dynamics of ordered Coulomb crystals, image tracking of particle fluctuations, three-dimensional wake potentials in magnetized plasmas, waves in nonideal plasmas, electrostatic solitary waves, shocks, etc. An exotic lecture discussed a method for detecting vacuum nonlinearities due to the quantum electrodynamic terms in the Maxwell equations. Extended discussions were held in order to emphasize on future developments and on the impact of one field to others. The discussions were intense (sometimes even heated) and successful. Most of the invited papers and a few poster papers from the Faro meeting appear in this Topical Issue of Physica Scripta, which will be distributed to all the participants. We expect that the papers of the present proceedings shall be useful for understanding the many complex phenomena that are common in numerous branches of physics.

The organizers are grateful to Professor Adriano Pimpão, the President of the University of Algarve for his generous support and warm hospitality in Faro. The editors express sincere gratitude to their colleagues and co-organizers Professors R. Bingham and J. T. Mendonça for their constant and wholehearted support in our endeavours. We appreciate the excellent work of the scientific secretary Dr. Tahir Farid as well as of Mrs. Anabela Gonçalves. Thanks are also due to the European Commission for supporting our activity through the Research Training Network entitled "Complex Plasmas: The Science of Colloidal Plasmas and Mesospheric Charged Aerosols".

Finally, we would like to express our gratitude to the Universidade do Algarve for providing the venue and for administrative support, the Universidade Técnica de Lisboa for secretarial support, and the FCT-Fundação para a Ciência e a Tecnologia for a limited financial support to our conference at the UA, Faro. Besides, the organizers cordial thanks are extended to the speakers and the attendees for their contributions which resulted in the success of the Faro conference. Specifically, we appreciate the speakers for delivering excellent talks, supplying well prepared manuscripts for publication, and enhancing the plasma physics activity at the UA, Faro.

Optical soliton is a by-product of research in cyclotron waves in plasmas. After more than a quarter of a century, the optical soliton is now pursued as a most promising mean for over Tera-bit per second ultra-high speed communications. After a brief introduction, the talk presents what is going on in the practical soliton transmission format, its merits and demerits, with a particular emphasis on the concept of the dispersion managed soliton. It also covers unsolved problems, which arise from the polarization mode dispersion (PMD) and inter-channel interactions in wavelength division multiplex (WDM) systems.

A novel statistical approach based on the Wigner transform method is proposed for the description of partially incoherent optical wave dynamics in nonlinear media. The Wigner–Moyal equation is derived for the Wigner distribution of the optical wave field governed by the nonlinear Schrödinger equation with an arbitrary nonlinearity. An application to incoherent light propagation in dispersive Kerr media shows that random phase fluctuations of a plane wave solution lead to a linear Landau-like damping effect, which can stabilize the nonlinear modulational instability. A similar effect is shown to occur in the case of the two-stream instability of two partially incoherent optical waves interacting with each other through cross-phase modulation initiated by the nonlinearity. In the limit of the geometrical optics approximation, it is shown that 1D and 2D self-trapped, stationary and incoherent wave pulse structures may exist for a wide class of nonlinear media. Furthermore, time-dependent self-similar 1D and 2D structures have been found in the case of the Kerr nonlinearity.

We review the results of recent investigations dealing with a connection between the envelope soliton-like solutions of a wide family of nonlinear Schrödinger equations (NLSEs) and the soliton-like solutions of a wide family of Korteweg-de Vries equations (KdVEs). The investigation is carried out within the context of the Madelung's fluid picture, which plays the role of the fluid counterpart of the NLSE. In two different fluid motion regimes (uniform current velocity and stationary-profile current velocity variation, respectively), bright and gray/dark soliton-like solutions of both modified NLSE and modified KdVE are found. Remarkably, the present approach represents an alternative key of reading for the envelope soliton theory of the NLSE. In particular, the well known envelope soliton solutions and soliton solutions of the cubic NLSE and the standard KdVE, respectively, are recovered from the general approach and in terms of the fluid language presented in this paper.

Axisymmetric plasma equilibria near a rotating black hole are considered within the multifluid description. An isothermal two-component plasma with electrons and positrons or ions is determined by four structure functions and the boundary conditions. These structure functions are the Bernoulli function and the toroidal canonical momentum per mass for each species; they remain arbitrary if no gain and loss processes are considered, in close analogy to the free flux functions in ideal magnetohydrodynamics. Several simplifying assumptions allow the reduction of the basic equations to one single scalar equation for the stream function χ of positrons or ions, respectively, playing the ŕle of the Grad/Shafranov equation in magnetohydrodynamics; in particular, Maxwell's equations can be solved analytically for a quasineutral plasma when both the charge density and the toroidal electric current density are negligible (in contrast to the Tokamak situation). The basic smallness parameter is the ratio of the skin depth of electrons to the scale length of the metric and fluid quantities, and, in the case of an electron-ion plasma, the mass ratio m_e/m_i. The χ-equation can be solved by standard methods, and simple solutions for a Kerr geometry are available; they show characteristic flow patterns, depending on the structure functions and the boundary conditions.

The dynamics and interaction of like-signed vortex structures in two dimensional flows are investigated by means of direct numerical solutions of the two-dimensional Navier–Stokes equations. Two vortices with distributed vorticity merge when their distance relative to their radius, d/R₀, is below a critical value, a_c. Using the Weiss-field, a_c is estimated for vortex patches. Introducing an effective radius for vortices with distributed vorticity, we find that 3.3 < a_c < 3.5 independently of the vorticity distribution. The evolution of spiral vorticity filaments in the merging process is effectively producing small scale structures and the relation to the enstrophy "cascade" in developed 2D turbulence is discussed. The influence of finite viscosity on the merging is also investigated. Additionally, we examine vortex interactions on a finite domain, and discuss the results in connection with the formation of "vortex crystals".

Two-dimensional vortex dynamics is characterized by motion of coherent vortices or clumps in a rugged distribution of background vortices. We study eminent features in this process by using a magnetized pure electron plasma starting from highly controlled initial density distribution. The topics included are (1) relaxation of many-clump dynamics states to crystallization, (2) single clump dynamics in a background vorticity distribution, (3) two-clump interaction in a low-level background vorticity distribution, and (4) accelerated crystallization of three clumps in a low-level background vorticity distribution.

The magnetosphere and the heliosphere constitute a magnificent laboratory for plasma wave phenomena, some of which have been studied in situ by ingenious spacecraft instrumentation, on board satellites probing interplanetary space as well as planetary and cometary environments. In several of these missions nonlinear structures have been observed. On the theoretical side, there are well known paradigms for nonlinear waves and solitons, like the different versions of the Korteweg-de Vries or nonlinear Schrödinger equations in multi-ion plasmas. We give a brief overview of how some of the more recent observations can be connected to the archetypical mathematical descriptions, in particular for magnetospheric boundary layer waves, nonlinear Alfvén waves in interplanetary space and solitary waves in cometary plasmas.

Magnetohydrodynamic (MHD) waves control the dynamics of plasma, the main constituent of the universe. They occur as the natural response to global excitation. Frequency and wave forms are determined by the magnetic confinement geometry and distribution of background equilibrium variables. Hence, measurement of the spectrum of MHD waves gives direct information on the internal state of the plasma, provided a theoretical model is available to solve the forward and inverse spectral problems. This activity has been called MHD spectroscopy, [1, Goedbloed et al. Phys. Control. Fusion 35 B277 (1993)] in analogy with quantum mechanical spectroscopy which also involves eigenvalue problems of linear operators. The terminology also entails a program, viz. to improve the accuracy of our knowledge of plasmas, both in the laboratory and in astrophysics.

While such a program is highly desirable a new angle to the study of MHD waves coming from the effects of transonic background flows requires a complete revision of all previous spectral results. Transonic flows in laboratory plasmas result from neutral beam heating (causing toroidal rotation) whereas they are commonplace for astrophysical plasmas (flows in coronal flux tubes, stellar winds, rotating accretion disks, jets emitted from radio galaxies, etc.). Such flows upset the standard theoretical approach to plasma dynamics, consisting of a separate study of equilibrium state and of the perturbations of this background. We will discuss a new approach to the dichotomy consisting of a study of the similarities of the nonlinear stationary flow patterns and the different linear waves structures that occur when the background speed traverses the full range of critical speeds (from "slow magnetosonic" to "Alfvén" to "fast magnetosonic"). This requires the development of new computational tools which yield a plethora of new waves and instabilities. We will illustrate this with results on tokomak and accretion disk plasmas.

Observations indicate that the magnetotail convection is turbulent and bi-modal, consisting of fast bursty bulk flows (BBF) and a nearly stagnant background. We demonstrate that this observed phenomenon may be understood in terms of the intermittent interactions, dynamic mergings and preferential accelerations of coherent magnetic structures under the influence of a background magnetic field geometry that is consistent with the development of an X-point mean-field structure.

We present a new class of solitary structures in plasmas consisting of two or more ion populations. They give rise to extremely coherent waves and arise from the electromagnetic momentum coupling between the different ion species having different mass, temperature or flow speeds. These so-called "oscillitons" are characterized by a spatial oscillation superimposed on the spatial growth and decay associated with the usual single-ion solitons. The type of stationary structures which may appear can be deduced from the dispersion relation of the stationary waves of the system D(ω = kU,k) = 0, where U is the soliton velocity. In certain regions of U, where mode splitting results in a throat-like shape of the dispersion curves, the corresponding complex solution k = k(U) indicates the existence of this new type of soliton. Examples of the solution of the full nonlinear stationary Hall-MHD equations are given. For the particular case of a cold bi-ion plasma with relative drift it is shown how oscillitons are formed in space and time and how they are related to coherent waves generated by solar wind mass loading at planets and comets.

The magnetic field in Hall plasmas is frozen in the electron component and is advected not only with the plasma motion but also with the electrical current flow. Its coupling with the plasma may be not as strong as characteristic of the MHD approximation. The rotation and slipping of the magnetic field result in a very different and less efficient magnetic field generation by dynamo-rotating plasma disk in magnetic field. We found some exact analytical solutions of nonlinear equations describing the dynamo. In particular, the dynamo may not dissipate the energy in the steady state limit. The 3-component magnetic field and magnetic energy are generated and accumulated during the transition time only. An electrical jet is another unusual phenomenon for MHD. It was investigated theoretically and experimentally for laboratory plasmas during the last 15 years and now is used for fast current switching. We found periodical or shock-like nonlinear wave traveling along a Hall plasma column and not associated with plasma motion. A nonlinear equation describing a possible steady state magnetic field distribution and current flow in a Hall plasma conductor is derived, which differs from the Grad-Shafranov equation. In conclusion we discuss how transfer our results onto astrophysical plasmas. This physics could be important for understanding the evolution of dusty plasma disks and jets around new stars.

An analogy between sandpile relaxation and the evolution of the drift wave spectrum by zonal flow induced shearing is used to characterize the probability distribution function of fluctuations in the drift wave population density Ñ, and thus address the predictability of intermittency in drift wave-zonal flow turbulence. Basic conservation and symmetry properties are used to derive a generalized Burgers equation for Ñ in the radial wave number k_r. Shocks are symptomatic of shearing events, which are analogous to avalanches in the sandpile. The pdf P(ΔÑ) is shown to be intrinsically asymmetric in k_r and the asymptotic behaviors of both left and right tails are determined. The implications of these results for transport are discussed.

A new mechanism for the excitation of zonal flows by a finite amplitude monochromatic drift wave is presented. It does not require any initial symmetry breaking, and thus provides an efficient triggering for the L–H transition in tokamaks. The nonlinear process consists in the self focusing of a drift-wave pump, governed by the nonlinear interaction with the second harmonic reactive quasimodes, which determines the steady-state profile of the shear flow. In a tokamak geometry, this mechanism is relevant in the regime when the variation of the effective parallel wavenumber of drift-waves, due to toroidal effects, turbulent decorrelation etc., prevents the exact beating of the drift waves along the entire torus, and yields a component of adiabatic electrons associated with the zero-frequency nonlinear mode.

The numerical results indicate that, in a tokomak geometry, the magnetic shear does not affect the basic configuration of zonal flows, which remain restricted to the critical region in which the second harmonic is evanescent. The configuration of the zonal flows appears to be robust, while the distribution of the short-scale (both in x and y) quasimodes is very sensitive to the small changes of the phase of the pump wave, and cannot be effectively controlled by the asymptotic boundary condition. As they are also rather slowly converging with large k_y, the behavior of the short-scale quasimodes indicates also the possibilities of the intermittency and chaos.

Collisionless magnetic field line reconnection exhibits important similarities under widely different physical conditions, ranging from the magnetohydrodynamic regime, of interest for space and high temperature magnetically confined plasmas, to the electron-magnetohydrodynamic regime, of interest for the interaction of ultraintense, ultrashort laser pulses with a plasma. Analytical and numerical results are presented that illustrate the nonlinear evolution of the reconnection instability in a two dimensional configuration with a neutral line in fluid and in kinetic plasma regimes. The importance of plasma anisotropy is stressed for the case of laser plasma interaction.

The microscopic dynamical responses of a two dimensional circular Coulomb cluster to thermal excitations and to the external force along a narrow band through its center are studied. The strong competition between the cirular boundary and the inner domain with triagular lattice leads to the nonuniform melting of the cluster. With the increasing temperature, the surface particles exhibit anisotropic motions along the circular shells. No abrupt melting transition is observed for the outer region. The intrinsic defects around the domain boundary initiate the continuous core melting transition and also the fluidization under the external stress. The fluidization shows a non equilibrium second order transition with stick-slip type motion at the transition point.

Parametric excitation of a dust particle, trapped in the plasma-sheath boundary'of a dc argon plasma at a low gas pressure, has been investigated experimentally and theoretically. The Mathieu equation, which is a well-known formula to describe parametric excitation in a harmonic oscillator, was directly derived from the equation of motion of a dust particle, oscillating in an externally driven ion sheath potential. Experimental observations give the growth rates and threshold values of the amplitude of the externally applied periodic perturbation for the parametric excitation. The measured growth rates and threshold values are compared with theoretical values calculated using the derived Mathieu equation to indicate that the parametric excitation occurs in the experiments much easier than the theoretical predictions of the Mathieu equation.

Recently the dynamics of dust grains trapped in the sheath region of radio-frequency (rf) or dc plasma discharges under low pressure conditions has attracted the attention of the dusty plasma community. Several experiments have been performed in order to explore the dynamics of dust grains levitating above the negatively biased electrode. Under very low pressures, several experimental groups have observed the generation of self excited large amplitude vertical oscillations which arise by lowering either the background pressure or the plasma number density. In other experiments, the vertical oscillations have been driven by an external sinusoidal voltage applied to a wire in the sheath region. A theoretical model is presented that successfully describes the phenomenology in these various experiments including the observed self excited oscillations and nonlinear resonance oscillations.

In previous calculations of the shielding around a dust grain in a plasma, the ion and electron currents to the grain, and the charge acquired by the grain, the plasma ions have typically been assumed collisionless. We show that the inclusion of ion charge-exchange collisions enormously changes this physics, by creating a class of negative-energy trapped ions. Under typical dusty plasma conditions, these trapped ions slowly accumulate, and in steady state they dominate the shielding cloud in the nonlinear region near a dust grain, greatly increase the ion current to the grain, and reduce the negative charge acquired by the grain. We present a self-consistent analytic calculation of the grain charge, plasma currents, and shielded potential.

A space-charge sheath near a negative surface in a plasma composed of dust grains of a variable positive charge, electrons, and neutral particles, is considered. The limiting case of large ratio of the electron Debye radius to the length scale of variation of the charge of a dust grain is treated. The charging of dust grains in the sheath is quasi-equilibrium in such a case, i.e. the current of the electrons emitted by a dust grain is approximately equal to the current of the plasma electrons collected by the grain. An analytical solution decribing the sheath is found for this limiting case. A further simplification may be achieved in cases when the mean energy of electrons emitted by the dust grain is much smaller than the surface potential of the grain.

Photoemission experiments with UV radiation have been performed to investigate the microphysics and charge characteristics of individual isolated dust grains of various compositions and sizes by using the electrodynamic balance facility at NASA Marshall Space Flight Center. Dust particles of 2–10 µm diameter are levitated in a vacuum chamber at pressures ∼10^-5 torr and exposed to a collimated beam of UV radiation in the 120–200 nm spectral range from a deuterium lamp source with a MgF₂ window. A monochromator is used to select the UV wavelength with a spectral resolution of 8 nm. The electrodynamic facility permits measurements of the charge and diameters of particles of known composition, and monitoring of photoemission rates with the incident UV radiation. Experiments have been conducted on test particles of silica and polystyrene to determine the photoelectric yields and surface equilibrium potentials when exposed to UV radiation. A brief description of an experimental procedure for photoemission studies is given and some preliminary laboratory measurements of the photoelectric yields of individual dust particles are presented.

The potential distributions between charged dust grains in dusty plasma condensates (dust crystals) are derived analytically. The profiles of the intergrain potential distributions are such that dust grains form regular periodic structures. In the dust crystals, the charge of a given grain is not only determined by its own potential, but it also strongly depends on the potential of other dust grains that are participating in the dust crystallization. It means that although short range interaction is provided by the Debye–Hückel potential, a long range interaction contributes to the formation of a dust crystal. For cubic symmetry and small dust grain (when the dust grain sizes are smaller than the inter-grain spacing), the calculation of the potential has been performed analytically. We also discuss the possibility of both longitudinal (or compressional) and transverse oscillations of our cubic dust lattice.

We present a rigorous theoretical investigation of electrostatic solitary and shock structures that may exist in dusty plasmas, by employing the reductive perturbation technique as well as the pseudo-potential approach. We have focused on dust acoustic solitary waves (DASWs) in a plasma whose constituents are negatively charged cold dust fluid and Boltzmann electrons and ions. We have also investigated the effects of adiabatic dust fluid temperature, non-isothermal (trapped and nonthermal) ion distributions, non-planer (spherical and cylindrical) geometries, strong dust correlation, etc. It is shown that such effects do not only significantly modify the dust acoustic solitary structures, but also introduce some important new features to the DASWs. Furthermore, we have considered the nonlinear propagation of dust acoustic and dust ion-acoustic waves in a dissipative dusty plasma and have shown that they can propagate as shock waves. The implications of our results to space and laboratory dusty plasmas are briefly mentioned.

The linear as well as the nonlinear propagation of dust–acoustic waves (DAWs), dust–charge–density waves (DCDWs) and dust–coulomb waves (DCWs) in non-ideal dusty plasmas comprising of electrons, ions and dust grains has been studied by self-consistently including the grain charge variations. The non-ideal effects are incorporated through the van der Waals equation of state for the dust fluid, while the charge fluctuation effects come in through the current balance equation. The real frequency and the damping rate for the linear DAWs, DCDWs and DCWs are investigated over a range of dust fugacity, defined through f = 4πn_doλ²_DR, where n_do is the dust number density, R is the grain size (radius) and λ_D is the effective plasma (electron and ion) Debye length. The reductive perturbation approach has been used to derive the governing equation for the nonlinear evolution of the various modes. The combined effects of the non-ideal contributions and the grain charge fluctuation in the linear as well as the nonlinear regimes of wave propagation have been analyzed.

The results of experimental observations of two types of dust vortices (vertical and horizontal) in the presence of an additional electrode in a planar radio frequency (rf) discharge are presented. It is shown that the occurrence of these vortices can be explained by dissipative instability in the dust cloud due to a dust charge gradient. This gradient occurs due to the disturbance of electro-neutrality or the variation of electron temperature caused by the extra electrode in the rf-plasma. The observed motion of dust particles has been compared with the results of molecular dynamic simulations. Good qualitative and quantitative agreement was found.

In quantum electrodynamics, photon–photon scattering can be the result of the exchange of virtual electron–positron pairs. Effectively, this gives rise to self-interaction terms in Maxwell's equations, similar to the nonlinearities due to polarisation in nonlinear optics. These self-interaction terms vanish in the limit of parallel propagating waves. However if instead the modes generated in waveguides are used, there will be a non-zero total effect. Based on this idea, we calculate the nonlinear excitation of beat wave modes and estimate the strength of this nonlinear mechanism.

The three dimensional structure of the wake potential due to ion cyclotron waves in a dusty magnetized plasma with streaming ions is studied. We focused our attention to the situation when the test dust particulate is stationary, because it corresponds to the real laboratory experiment on plasma crystal. The role of the external magnetic field on the periodic attractive forces is clarified. In this paper, we consider the externally applied uniform magnetic field parallel to the sheath plane in Case A, and perpendicular to the sheath plane in Case B, separately. In Case A, the analysis includes the E × B drift effect in addition to the ion flow with a constant velocity u_io perpendicular to the magnetic field. In case B, the ion flow with a constant velocity uio parallel to the magnetic field. The result shows that the magnitude of the wake potential due to the ion cyclotron wave in Case A behind a dust particulate is much increased for strongly magnetized plasma when λ_D/ρ_e ≥ 1.77, where λ_D, ρ_e are the Debye length and the Larmor radius of electrons, respectively. On the other hand, in Case B, the amplitude of the wake potential for the magnetized plasma is small compared with that of unmagnetized plasma.

We experimentally observe a high-contrast intensity modulation in the multimode CW output of a Titanium:Sapphire laser. This modulation has a very low frequency (in the hundreds of Hz range), being stable and self-sustaining, unlike previously reported regimes which require external perturbations such as a periodic change in the resonant cavity length. This effect results from the nonlinear coupling of several longitudinal modes with very large frequency spacing (of the order of tens of THz) which arise due to mode competition violation (promoted by dispersion control within the laser cavity), associated with the large gain bandwidth of Ti:Sapphire. To our knowledge, this is a previously unreported phenomenon, for which we are currently developing an adequate theoretical model. These results may prove useful in the further understanding of the onset of mode-locked operation in ultrashort lasers and other highly nonlinear systems.

The nonlinear evolution of low frequency electrostatic waves in a magnetised plasma is investigated for parameters characteristic of the auroral acceleration region. Our model consists of Boltzmann electrons and warm ions. Using fluid theory, a nonlinear evolution equation is derived for the wave potential. Numerical solutions show the existence of sinusoidal, sawtooth or bipolar waveforms. The effects of plasma parameters on the wave amplitude are examined, in particular the effect of a finite ion temperature.

The formation of a stationary non equilibrium (s.n.e.) distribution function is studied numerically. To describe a weakly collisional space uniform plasma the non linear Landau–Fokker–Planck kinetic equation is used. A local (in momentum space) s.n.e. distribution can be formed inside the energy interval between the source and the sink of particles. The results can be used for the prediction of the semiconductor behaviour with an intrinsic as well as an extrinsic conductivity under the bombardment by fast ion beams.

The rotation of Coulomb clusters with different numbers of micron-sized particles is studied experimentally in inductively coupled magnetised dusty plasma. When an external axial magnetic field was applied to dust Coulomb clusters, the clusters were observed to be rotating as a rigid body in the left-handed direction. We found the cluster rotation to be dependent on the particle number and configuration. Thus, the threshold magnetic field strength B_th at which the cluster would rotate decreased as the number of particles N increased and can be expressed by B_th = 200/N². We also show that angular velocity ω depends on the magnetic field strength B as exp(–23/N)B^8.3/N1.5.

A fully non-linear theory for stationary waves, propagating obliquely to an ambient magnetic field in a cold plasma, is developed. In the cold case soliton solutions, representing both compressions and rarefactions in the magnetic field, exist if the flow is sub-fast and sufficiently oblique, but in the case of compressions not too oblique. The maximum attainable compression is 3 (when the soliton number m is unity) and there is a complete rarefaction when m = 4. The properties of these stationary waves are described both in terms of magnetic hodographs and a spatial structure equation, whose equilibrium points yield the maximum compression and rarefaction at the centre of the waves. The existence of an analytic solution in terms of elementary transcendental functions highlights the role played by the soliton number m in determining the speed, strength and width of the solitons. The effects of thermal pressure on solitons structures is briefly described. In general pressure effects weaken the fast soliton, but give rise to a new slow soliton.

In this paper we investigate the effects of a diamagnetic frequency peaking and velocity shear on a two-dimensional drift mode structure. Previous study made by Horton et al. showed that a strong diamagnetic frequency peaking can trap the wave energy both radially and along the magnetic field lines. We show that the localising effect of the diamagnetic frequency peaking can be suppressed by a strong velocity shear in the edge plasma. The same phenomenon is present in the bulk plasma, but due to the velocity shear not being as pronounced there, the effect is nominal.

Response of nonuniform magnetized plasma to strongly nonlinear electromagnetic perturbations driven by nonuniform flows is studied. Various types of coherent structures with spatial scales of the order of the electron skin depth are found carried by the flow or propagating through the plasma, with spatial scales measured in tens of kilometers for the magnetotail region.

In this paper, we discuss a new cyclotron maser type instability driven by a crescent or horseshaped electron distribution function. Such distribution functions are easily created by an electron beam moving into a stronger magnetic field region, where conservation of the first adiabatic invariant causes an increase in their pitch angle. This produces a broad region on the distribution function where ∂f_e/∂v_⊥ > 0. Planetary dipole magnetic fields are examples of where these types of distributions can be found. We examine the stability of these electron horseshoe distribution functions for right-hand extraordinary mode (R–X mode) radiation close to the electron cyclotron frequency propagating perpendicular to the magnetic field using both non-relativistic and relativistic beams.

Scattering and transformation of high frequency waves in plasmas are due to electron density inhomogeneities. These are the thermal fluctuations in ordinary plasmas but in dusty plasmas two additional scattering sources are present: the electrons in the shielding clouds around the charged dust particles and induced electron density fluctuations discreteness.

The comet C/LINEAR 1999 S4 was observed by the ACIS-S instrument on the Chandra X-ray Observatory (CXO) in July 2000, and the resultant spectrum was by far the clearest cometary X-ray spectrum to date. It is the aim of this paper to see if the spectrum can be reproduced directly from atomic data using the ADAS (the Atomic Data and Analysis Structure) system to try and reproduce the conditions of the comet's interaction with the solar wind. This is accomplished by calculating the atomic rate coefficients for a simplified cometary plasma over a range of likely temperatures and combining the resultant predicted emission line spectrum with a pure bremsstrahlung continuum. The outcome is a model spectrum which can be compared to that Chandra observation.