Quasi-monochromatic wave-particle interactions in magnetospheric plasmas

The natural waves observed within magnetospheres are often emitted over a very narrow spectral range. They thus can interact coherently with the charged particles forming the weakly collisional magnetospheric plasmas. In this review some aspects of these quasi-coherent Wave Particle Interactions, usually known as trapping processes, are underlined. A particular emphasis is here put on the situation effectively encountered within natural plasmas. Hence, the effects of plasma inhomogeneities on the resonant WPI are thoroughly studied. We focus on three effects:

1. The inhomogeneity of the medium changes the wave number and correspondingly the relative phase between the wave and the particle's motion. Thus, resonant conditions cannot be fulfilled over a large wave path, which tends to decrease the efficiency of the WPI. On the other hand, this effect leads a monochromatic wave to interact with a larger set of charged particles, which tends to restore a quasi linear-like diffusion process.
2. Even when trapping occurs, the inhomogeneity changes the saturation level of the kinetic instabilities.
3. Trapping can then be an efficient acceleration process.

     

Damping and nonlinear wave-particle interactions of Alfvén-waves in the solar wind

Since most Alfvén-waves in the solar wind are observed to come from the Sun, nonlinear wave-particle interactions can be expected to constitute their dominant dissipation process. The growth or damping of two circularly-polarized Alfvén-waves with wave vectors parallel to the ambient magnetic field is calculated using kinetic theory. If the waves are oppositely polarized they both damp proportional to their frequency. If the waves are of the same polarization, both the lower frequency wave and the plasma particles gain energy at the expense of the higher frequency wave. Thus, with increasing distance from the Sun, a steepening of the power spectrum is expected. For waves propagating in the same direction, the interaction is negligible for small , while it becomes appreciable for 10^–1. For conditions typical of the solar wind near 1 AU an observed half-hour linearly-polarized wave, for example, with B=0(B ₀) has a damping time of about 10 h.     

Fine structure of the ground-observed VLF chorus as an indicator of the wave-particle interaction processes in the magnetospheric plasma

The results of the investigations of chorus type VLF emissions both in the subauroral conjugate regions and along the meridional profile near the plasmapause projection are summarized in order to connect the peculiarities of ground-observed VLF chorus with the plasma processes in the magnetosphere during substorms development. The method for determination of the location of the instability region in the magnetosphere is suggested which is based on the measurement of the upper boundary frequency of the ground-observed VLF chorus (UBF-method). Dynamics of chorus spectra during the substorm development is investigated. On the basis of the revealed regularities the phenomenological model of the VLF chorus source development is constructed. The calculations of some magnetospheric plasma parameters such as plasma density, large-scale electric field etc. are carried out. The conformity between the calculated and typical measured parameters is shown. The diagnostic possibilities of VLF chorus are discussed.     

Replenishment of electrons lost in the south atlantic anomaly by gyroresonant pitch-angle diffusion

Experimental data describing the effect of the South Atlantic anomaly on E? 280 keV electron flux at L = 2 and high B values, are compared to the numerical solution of a pitch-angle diffusion equation with a varying loss cone. The diffusion coefficient needed to explain replenishment of the electrons lost over the anomaly is found to be 3.2 × 10^?2 sec^?1 Calculation of the diffusion coefficient due to cyclotron resonant interaction with VLF electro-magnetic waves leads to the conclusion that the observed wave spectral density can yield the needed diffusion coefficient.     

Rate coefficients for the chemi-ionization processes in sodium- and other alkali-metal geocosmical plasmas

The chemi-ionization processes in thermal and sub-thermal collisions of excited alkali atoms with atoms in ground and excited states were considered, with a particular accent to the applications for geocosmical plasma research. An improved version of semi-classical method for the rate coefficients calculation is presented. The method is applied to the cases of excited alkali atoms with the principal quantum numbers 5 ⩽ n ⩽ 25. The results of calculation of the considered chemi-ionization processes rate coefficients are compared to the existing experimental data. Their good agreement recommends to use the rate coefficients obtained for analysis of geocosmical plasma processes.     

Laboratory simulation of the physical processes occurring on and near the surfaces of comet nuclei

Abstract— Laboratory comet simulation experiments are discussed in the context of theoretical models and recent ground-based and spacecraft observations, especially the Giotto observations of P/Halley. The set-up of various comet simulation experiments is reviewed. A number of small-scale experiments have been performed in many laboratories since the early 1960s. However, the largest and most ambitious series of experiments were the comet simulation experiments known as KOSI (German = Kometen Simulation). These experiments were prompted by the appearance of Comet P/Halley in 1986 and in planning for the European Space Agency's Rossetta mission that was originally scheduled to return samples. They were performed between 1987 and 1993 using the German Space Agency's (DLR) space hardware testing facilities in Cologne. As with attempts to reproduce any natural phenomenon in the laboratory, there are deficiencies in such experiments while there are major new insights to be gained. Simulation experiments have enabled the development of methods for making comet analogues and for exploring the properties of such materials in detail. These experiments have provided new insights into the morphology and physical behavior of aggregates formed from silicate grains likely to exist in comets. Formation of a dust mantle on the surfaces and a system of ice layers below the mantle caused by chemical differentiation have been identified after the insolation of the artificial comet. The mechanisms for heat transfer between the comet's surface and its interior, the associated gas diffusion from the interior of the surface, and compositional, structural, and isotopic changes that occur near the surface have been described by modeling the experimental results. The mechanisms of the ejection of dust and ice grains from the surface and the importance of gas-drag in propelling grains have also been explored.     

Newtonian non-linear hydrodynamics and magnetohydrodynamics

We use covariant techniques to study the non-linear evolution of self-gravitating, non-relativistic media. The formalism is first applied to imperfect fluids, aiming at the kinematic effects of viscosity, before extended to inhomogeneous magnetized environments. The non-linear electrodynamic formulae are derived and successively applied to electrically resistive and to highly conductive fluids. By nature, the covariant equations isolate the magnetic effects on the kinematics and the dynamics of the medium, combining mathematical transparency and physical clarity. Employing the Newtonian analogue of the relativistic 1 + 3 covariant treatment also facilitates the direct comparison with the earlier relativistic studies and helps to identify the differences in an unambiguous way. The purpose of this work is to set the framework and take a first step towards the detailed analytical study of complex non-linear systems, like non-relativistic astrophysical plasmas and collapsing protogalactic clouds.     

Notes on transformations in non-linear systems

A comparative examination from the practical point of view is made of the methods of simultaneous elimination of fast and slow variables, accelerated elimination, and the non-canonical Lie transformation, that have been proposed in the literature. A non-canonical transformation defined by implicit functions is given and shown to be simpler than the Lie transformation.     

Thermodynamics in non-linear electrodynamics with anisotropic universe

In this work, we consider the framework of non-linear electrodynamics in Bianchi type I universe model composed of matter and electromagnetic field. We deal with electric and magnetic universe separately. In this scenario, we calculate the electric and magnetic fields and their corresponding matter densities using two particular types of interaction terms. We also check the validity of generalized second law of thermodynamics in both universe models enclosed by apparent horizon. It turns out that this law holds on the apparent horizon for a particular range depending upon the parameters. Finally, we discuss the deceleration and statefinder parameters to check the viability of these models.     

Linear and non-linear MHD wave propagation in steady-state magnetic cylinders

The propagation of linear and non-linear magnetohydrodynamic (MHD) waves in a straight homogeneous cylindrical magnetic flux tube embedded in a homogeneous magnetic environment is investigated. Both the tube and its environment are in steady state. Steady flows break the symmetry of forward (field-aligned) and backward (anti-parallel to magnetic field) propagating MHD wave modes because of the induced Doppler shifts. It is shown that strong enough flows change the sense of propagation of MHD waves. The flow also induces shifts in cut-off values and phase-speeds of the waves. Under photospheric conditions, if the flow is strong enough, the slow surface modes may disappear and the fast body modes may become present. The crossing of modes is also observed due to the presence of flows. The effect of steady-state background has to be considered particularly carefully when evaluating observation signatures of MHD waves for diagnostics in the solar atmosphere.     

Microwave background anisotropies arising from non-linear structures in open and universes

A new method arising from a gauge-theoretic approach to general relativity is applied to the formation of clusters in an expanding universe. The three cosmological models (₀=1, =0), (₀=0.3, =0.7) and (₀=0.3, =0) are considered, which extends our application in two previous papers. A simple initial velocity and density perturbation of finite extent is imposed at the epoch z =1000, and we investigate the subsequent evolution of the density and velocity fields for clusters observed at redshifts z =1, z =2 and z =3. Photon geodesics and redshifts are also calculated so that the cosmic microwave background (CMB) anisotropies arising from collapsing clusters can be estimated. We find that the central CMB temperature decrement is slightly stronger and extends to larger angular scales in the non-zero case. This effect is strongly enhanced in the open case. Gravitational lensing effects are also considered, and we apply our model to the reported microwave decrement observed towards the quasar pair PC 1643+4631 A&B.     

A non-linear theory of vertical resonances in accretion discs

An important and widely neglected aspect of the interaction between an accretion disc and a massive companion with a coplanar orbit is the vertical component of the tidal force. As shown by Lubow, the response of the disc to vertical forcing is resonant at certain radii, at which a localized torque is exerted, and from which a compressive wave (p mode) may be emitted. Although these vertical resonances are weaker than the corresponding Lindblad resonances, the   m =2  inner vertical resonance in a binary star is typically located within the tidal truncation radius of a circumstellar disc.
In this paper I develop a general theory of vertical resonances, allowing for non-linearity of the response, and dissipation by radiative damping and turbulent viscosity. The problem is reduced to a universal, non-linear ordinary differential equation with two real parameters. Solutions of the complex non-linear Airy equation are presented to illustrate the non-linear saturation of the resonance and the effects of dissipation. It is argued that the   m =2  inner vertical resonance is unlikely to truncate the disc in cataclysmic variable stars, but contributes to angular momentum transport and produces a potentially observable non-axisymmetric structure.     

Thermodynamic study of non-linear electrodynamics in loop quantum cosmology

In this work, we have discussed the Maxwell’s electrodynamics in non-linear forms in FRW universe. The energy density and pressure for non-linear electrodynamics have been written in the electro-magnetic universe. The Einstein’s field equations for flat FRW model in loop quantum cosmology have been considered if the universe is filled with the matter and electro-magnetic field. We separately assumed the magnetic universe and electric universe. The interaction between matter and magnetic field have been considered in one section and for some particular form of interaction term, we have found the solutions of magnetic field and the energy density of matter. We have also considered the interaction between the matter and electric field and another form of interaction term has been chosen to solve the field equations. The validity of generalized second law of thermodynamics has been investigated on apparent and event horizons using Gibb’s law and the first law of thermodynamics for magnetic and electric universe separately.     

Field-aligned currents and auroral acceleration by non-linear MHD waves

This paper examines the consequences of the assumption that substorm-associated growth of magnetosphere-ionosphere current systems is triggered by the incidence, on the ionosphere, of a large amplitude Alfvén wave generated in the distant magnetotail. It is pointed out that there is a large body of evidence suggesting that, in the acceleration region near 1 R_E, one is likely to find a major discontinuity in mass density. Following the approach of Cohen and Kulsrud (1974) who studied the steepening of large amplitude hydromagnetic waves into shocks, we demonstrate that the character of the background plasma and magnetic field in the auroral acceleration region near 1 R_E can be ideal for the generation of MHD shocks and that these shocks can lead to the acceleration of ions and electrons as reported by investigators using S3-3 satellite data.     

Magnetoconvection in an inclined magnetic field: linear and weakly non-linear models

Recent observations of sunspots have revealed a rich range of behaviour and a complicated magnetic field structure; magnetoconvection is the key physical process underlying these phenomena. Traditional studies of magnetoconvection have considered vertical, or sometimes horizontal, imposed fields. Tilted fields have received less attention, and yet these are crucial to sunspot dynamics, particularly in the penumbra where field lines are inclined at a variety of angles to the vertical. Tilting the field is also interesting from a purely theoretical viewpoint since it breaks many of the symmetries usually associated with convection problems. In this paper we study the linear stability of a layer permeated by an inclined magnetic field and go on to set up model equations in order to study the patterns formed in the weakly non-linear regime. Possible applications of the results to sunspots are discussed.     

Evolution of peaks in weakly non-linear density field and dark halo profiles

Using the two-point Edgeworth series up to second order in the linear rms density fluctuation we construct the weakly non-linear conditional probability distribution function for the density field around an overdense region. This requires calculating the two-point analogues of the skewness parameter S ₃. We test the dependence of the two-point skewness on distance from the peak for scale-free power spectra and Gaussian smoothing. The statistical features of such a conditional distribution are given as the values obtained within linear theory corrected by the terms that arise as a result of weakly non-linear evolution. The expected density around the peak is found to be always below the linear prediction while its dispersion is always larger than in the linear case. For large enough overdensities the weakly non-linear corrections can be more significant than the peak constraint introduced by Bardeen et al. We apply these results to the spherical model of collapse as developed by Hoffman & Shaham and find that in general the effect of weakly non-linear interactions is to decrease the scale from which a peak gathers mass and therefore also the mass itself. In the case of an open universe this results in steepening of the final profile of the virialized proto-object.