The effects of density gradients on the convective amplification of upper hybrid waves in the magnetosphere

Intense (? 10 mVm^?1) electrostatic plasma waves near the upper hybrid frequency have been observed between ± 50° magnetic latitude during spacecraft plasmapause crossings. We present wave growth rate and three-dimensional convective amplification calculations which suggest how intense upper hybrid (IUH) events can occur over such a wide range of latitudes. The effects of wave refraction are shown to be crucial to the proper calculation of convective amplification.We first calculate upper hybrid wave growth for an IUH event at 10° MLAT during which a complete electron distribution function with a loss cone feature was measured simultaneously with the waves. We show that a parallel density gradient may be necessary to account for the observed amplification. Without such a density gradient, the dipole magnetic field gradient would quickly refract the wave vector component parallel to the local field lines out of the unstable region in wave vector space. Upon mapping the distribution function observed at 10° MLAT to other latitudes by conserving the electrons' magnetic moments, we then find that the mapped distribution could produce large amplification at higher latitudes only if there is an appropriate parallel density gradient. At the equator, the long magnetic field gradient scale length enables large amplitudes to be attained without a density gradient.The results of our UH ray tracing analysis are related to theories and observations of magnetospheric continuum radiation.     

An implementation of radiative transfer in the cosmological simulation code gadget

We present a novel numerical implementation of radiative transfer in the cosmological smoothed particle hydrodynamics (SPH) simulation code gadget . It is based on a fast, robust and photon-conserving integration scheme where the radiation transport problem is approximated in terms of moments of the transfer equation and by using a variable Eddington tensor as a closure relation, following the Optically Thin Variable Eddington Tensor suggestion of Gnedin & Abel. We derive a suitable anisotropic diffusion operator for use in the SPH discretization of the local photon transport, and we combine this with an implicit solver that guarantees robustness and photon conservation. This entails a matrix inversion problem of a huge, sparsely populated matrix that is distributed in memory in our parallel code. We solve this task iteratively with a conjugate gradient scheme. Finally, to model photon sink processes we consider ionization and recombination processes of hydrogen, which is represented with a chemical network that is evolved with an implicit time integration scheme. We present several tests of our implementation, including single and multiple sources in static uniform density fields with and without temperature evolution, shadowing by a dense clump and multiple sources in a static cosmological density field. All tests agree quite well with analytical computations or with predictions from other radiative transfer codes, except for shadowing. However, unlike most other radiative transfer codes presently in use for studying re-ionization, our new method can be used on-the-fly during dynamical cosmological simulation, allowing simultaneous treatments of galaxy formation and the re-ionization process of the Universe.     

Quantum relativistic theory of the synchrotron/cyclotron radiation in a strongly-magnetized plasma: The case of longitudinal propagation

Full quantum relativistic treatment of the cyclotron/synchrotron emission and absorption in tenuous plasmas with superstrong magnetic field is developed for the case when the radiation wave-vector is parallel to the magnetic field. The emissivities and absorption coefficients for a plasma with arbitrary distribution function of particles are presented in terms of simple sums over the Landau levels. On the basis of these expressions, the negative absorption (maser amplification) is shown to be impossible for the longitudinal propagation in a tenuous plasma. The summation over the Landau levels is performed analytically, and the quantum effects are analysed in detail, for the thermal distribution of plasma particles. A new type of quantum relativistic oscillations is predicted in the emission and absorption spectra for a plasma with anisotropic temperature. The results obtained are useful for an interpretation of the X-ray and gamma-ray observations of the objects associated with strongly magnetized neutron stars (particularly of the gamma-ray bursters).     

The derivation of temperature gradient and electron density maps from EUV spectroheliograms

We discuss spatial variations in electron density at the base of the corona and in the temperature gradient in the chromospheric-coronal transition layer as determined from analysis of maps constructed from Mgx and OVI spectroheliograms. Both the mapping techniques and results of analyzing EUV spectra from OSO 6 observations are presented. Comparisons of these maps with photospheric magnetograms and spectroheliograms made in chromospheric EUV lines and continua indicate that the electron density and temperature gradient in the transition layer tend to be enhanced in areas where the photospheric magnetic field and chromospheric EUV emission are enhanced. Relationships among the coronal electron density, transition-layer temperature gradient, chromospheric emission, and photospheric magnetic field strength are derived.     

An Overview of Existing Algorithms for Resolving the 180° Ambiguity in Vector Magnetic Fields: Quantitative Tests with Synthetic Data

We report here on the present state-of-the-art in algorithms used for resolving the 180° ambiguity in solar vector magnetic field measurements. With present observations and techniques, some assumption must be made about the solar magnetic field in order to resolve this ambiguity. Our focus is the application of numerous existing algorithms to test data for which the correct answer is known. In this context, we compare the algorithms quantitatively and seek to understand where each succeeds, where it fails, and why. We have considered five basic approaches: comparing the observed field to a reference field or direction, minimizing the vertical gradient of the magnetic pressure, minimizing the vertical current density, minimizing some approximation to the total current density, and minimizing some approximation to the field's divergence. Of the automated methods requiring no human intervention, those which minimize the square of the vertical current density in conjunction with an approximation for the vanishing divergence of the magnetic field show the most promise.     

Linear wave conversion processes in the theory of the proton whistler

The linear coupling between the different kinds of waves propagating in a warm plasma inhomogeneous along thex direction is investigated in order to locate the regions (,k) space where two of the roots of the characteristic equation coalesce. Firstly, using the approximation of geometrical optics the differential equation is derived and wave propagation at fixed wave numberk _z is studied in these special cases for which the characteristic equation reduces to a biquadratic. When the density gradient is parallel to the magnetic field, a detailed analysis of the different properties of the waves shows that the mechanism proposed by Gurnett and others to explain the characteristics of the proton whistler is unlikely to operate, even if a wave coupling occurs at the so called cross over frequency for small incidence angles. The only relevant process occurs when the density gradient is perpendicular to the magnetic field for waves propagating at small incidence angles. It is shown that, close to a coalescence point, but within the limit of the geometrical optics approximation, one of the WKB solutions is a mixed (transverse-longitudinal) mode which becomes purely longitudinal in the limit of large wave numbers. Consequently, as this wave has E almost parallel tok, coalescence implies that the waves are nearly longitudinal at the singular point, in agreement with other results. Next, application of the theory is made to some relevant space observations. It is shown that the proton whistler could be the result of a linear coupling between the extraordinary and the slow ion cyclotron waves close to the Buchsbaum resonance in ionospheric regions above 300 to 400 km where the H⁺ density begins to grow. Transformation conditions are given which favour the coupling mechanism in regions of strong latitudinal gradients. Finally, a comparison is made with experiment which confirms the principal features of the present theory.     

The Electron Firehose and Ordinary-Mode Instabilities in Space Plasmas

Self-generated wave fluctuations are particularly interesting in the solar wind and magnetospheric plasmas, where Coulomb collisions are rare and cannot explain the observed states of quasi-equilibrium. Linear theory predicts that firehose and ordinary-mode instabilities can develop under the same conditions, which makes it challenging to separate the role of these instabilities in conditioning the space-plasma properties. The hierarchy of these two instabilities is reconsidered here for nonstreaming plasmas with an electron-temperature anisotropy T _∥>T _⊥, where ∥ and ⊥ denote directions with respect to the local mean magnetic field. In addition to the previously reported comparative analysis, here the entire 3D wave-vector spectrum of the competing instabilities is investigated, with a focus on the oblique firehose instability and the relatively poorly known ordinary-mode instability. Results show a dominance of the oblique firehose instability with a threshold lower than the parallel firehose instability and lower than the ordinary-mode instability. For stronger anisotropies, the ordinary mode can grow faster, with maximum growth rates exceeding those of the oblique firehose instability. In contrast to previous studies that claimed a possible activity of the ordinary-mode in the low β [<?1] regimes, here it is rigorously shown that only the high β [>?1] regimes are susceptible to these instabilities.     

Rayleigh-Taylor instability of a Hall plasma with arbitrary density gradient

The Rayleigh-Taylor instability of a plasma layer in the presence of a horizontal magnetic field is investigated, taking into account the effects of Hall-currents and an arbitrarily large density gradient. It is shown for the general case that if the density decreases vertically upward, the system is thoroughly stable.For a plasma layer with exponentially varying density an approximate dispersion relation is obtained using the Galerkin's method. An analysis of the roots of the dispersion relation reveals that the Hall-currents loosen the stabilizing influence of the magnetic field and impart instability to the system. For sufficiently large values of the density gradient and the Hall currents the system is throughly destabilized for all perturbations.     

Normal forms for the epicyclic approximations of the perturbed Kepler problem

We compute the normal forms for the Hamiltonian leading to the epicyclic approximations of the (perturbed) Kepler problem in the plane. The Hamiltonian setting corresponds to the dynamics in the Hill synodic system where, by means of the tidal expansion of the potential, the equations of motion take the form of perturbed harmonic oscillators in a rotating frame. In the unperturbed, purely Keplerian case, the post-epicyclic solutions produced with the normal form coincide with those obtained from the expansion of the solution of the Kepler equation. In all cases where the perturbed problem can be cast in autonomous form, the solution is easily obtained as a perturbation series. The generalization to the spatial problem and/or the non-autonomous case is straightforward.     

From the circular to the spatial elliptic restricted three-body problem

We deal with the study of the spatial restricted three-body problem in the case where the small particle is far from the primaries, that is, the so-called comet case. We consider the circular problem, apply double averaging and compute the relative equilibria of the reduced system. It appears that, in the circular problem, we find not only part of the equilibria existing in the elliptic case, but also new ones. These critical points are in correspondence with periodic and quasiperiodic orbits and invariant tori of the non-averaged Hamiltonian. We explain carefully the transition between the circular and the elliptic problems. Moreover, from the relative equilibria of elliptic type, we obtain invariant 3-tori of the original system.     

Plasma boundaries at 6.6 RE as observed by GEOS-2: Large plasmapause discontinuity and injection event. Discussion of diamagnetic effects

An impulsive event observed from the nightside geostationary orbit by the GEOS-2 European satellite is analysed in detail in the case of a very quiet magnetosphere. It is characterized by a very sharp and steep plasma density gradient observed near 2230 L.T. A quite detailed picture of the situation can be sketched as a result of the GEOS-2 set of experiments. The observations roughly organize themselves as follows along the geostationary orbit: an intense and well localized d.c. electric field appeared between the outbound crossing of the plasmapause and local midnight; at the same time a sudden ULF activity arose probably indicating the presence of field-aligned currents; GEOS-2 then entered a quieter plasmasheet where clear diamagnetic effects are evidenced. These observations are consistent with a stabilization of a possible interchange instability, which would maintain the density gradient at the plasmapause. The validity of the plasma density measurements which are made through an active wave method is discussed in connection with the 2 keV mean energy of the plasmasheet particles. The macroscopic evolution equation of the plasma bulk velocity is considered. It appears that the gradients of the macroscopic drift velocity of the plasma may have a non-negligible effect rendering invalid the unsophisticated scheme of a balance between kinetic and magnetic pressures.     

Kinetic Alfvén waves in extended radio sources

Electric current generation by kinetic Alfvén waves (KAW) is discussed for the case of extended radio sources (ERS), in particular, extragalactic jets (EJ). These currents are generated parallel to the background magnetic field due to Landau damping by which KAW accelerate electrons. We find that the KAW generated currents are in excess of the currents necessary for an EJ to be magnetically self-confined. We address the problem of determining the process that can maintain ERS inhomogeneous. We study the stability of a plasma which has: (1) the average local current density due to KAW given by our calculations; (2) the average local electrical conductivity (anomalous) due to KAW indicated by our calculations and the calculations of Hasegawa and Mima (1978); and (3) wave heating by surface Alfvén waves, independent of plasma temperature. We show that this plasma is subject to the thermal Joule instability. We suggest the thermal Joule instability as the process that maintains ERS inhomogeneous. Our KAW analysis correlates the important problems of ERS of (re)acceleration, current generation, collimation, and maintenance of inhomogeneities.     

Super-reflection in fluid discs: corotation amplifier, corotation resonance, Rossby waves and overstable modes

In differentially rotating discs with no self-gravity, density waves cannot propagate around the corotation, where the wave pattern rotation speed equals the fluid rotation rate. Waves incident upon the corotation barrier may be super-reflected (commonly referred to as corotation amplifier), but the reflection can be strongly affected by wave absorptions at the corotation resonance/singularity. The sign of the absorption is related to the Rossby wave zone very near the corotation radius. We derive the explicit expressions for the complex reflection and transmission coefficients, taking into account wave absorption at the corotation resonance. We show that for generic discs, this absorption plays a much more important role than wave transmission across the corotation barrier. Depending on the sign of the gradient of the vortensity of the disc,  ζ=κ²/(2ΩΣ)  (where Ω is the rotation rate, κ is the epicyclic frequency and Σ is the surface density), the corotation resonance can either enhance or diminish the super-reflectivity, and this can be understood in terms of the location of the Rossby wave zone relative to the corotation radius. Our results provide the explicit conditions (in terms of disc thickness, rotation profile and vortensity gradient) for which super-reflection can be achieved. Global overstable disc modes may be possible for discs with super-reflection at the corotation barrier.     

Generalized hill's problem Lagrangian Hill's case

In this paper, we investigate a generalization of the Hill's problem to the case where no restriction is made about the nature of the field of force perturbing two small bodies in gravitational interaction. We apply the general equations obtained to the dynamics of two bodies located in the vicinity of the triangular lagrangian points of the restricted three-body problem.     

Forward Symplectic Integrators for Solving Gravitational Few-Body Problems

We introduce a class of fourth order symplectic algorithms that are ideal for doing long time integration of gravitational few-body problems. These algorithms have only positive time steps, but require computing the force gradient in addition to the force. We demonstrate the efficiency of these Forward Symplectic Integrators by solving the circular restricted three-body problem in the space-fixed frame where the force on the third body is explicitly time-dependent. These algorithms can achieve accuracy of Runge–Kutta, conventional negative time step symplectic and corrector symplectic algorithms at step sizes five to ten times as large.     

Alignment and precession of a black hole with a warped accretion disc

We consider the shape of an accretion disc whose outer regions are misaligned with the spin axis of a central black hole and calculate the steady state form of the warped disc in the case where the viscosity and surface densities are power laws in the distance from the central black hole. We discuss the shape of the resulting disc in both the frame of the black hole and that of the outer disc. We note that some parts of the disc and also any companion star maybe shadowed from the central regions by the warp. We compute the torque on the black hole caused by the Lense–Thirring precession, and hence compute the alignment and precession time-scales. We generalize the case with viscosity and hence surface density independent of radius to more realistic density distributions for which the surface density is a decreasing function of radius. We find that the alignment time-scale does not change greatly but the precession time-scale is more sensitive. We also determine the effect on this time-scale if we truncate the disc. For a given truncation radius, the time-scales are less affected for more sharply falling density distributions.     

Is Cyclotron Maser Emission in Solar Flares Driven by a Horseshoe Distribution?

Since the early 1980s, decimetric spike bursts have been attributed to electron cyclotron maser emission (ECME) by the electrons that produce hard X-ray bursts as they precipitate into the chromosphere in the impulsive phase of a solar flare. Spike bursts are regarded as analogous to the auroral kilometric radiation (AKR), which is associated with the precipitation of auroral electrons in a geomagnetic substorm. Originally, a loss-cone-driven version of ECME, developed for AKR, was applied to spike bursts, but it is now widely accepted that the measured distribution function is horseshoe-like (an isotropic distribution with a one-sided loss cone), and that a horseshoe-driven version of ECME applies to AKR. We explore the implications of the assumption that horseshoe-driven ECME also applies to spike bursts. We develop a 1D model for the acceleration of the electrons by a parallel electric field, and show that under plausible assumptions it leads to a horseshoe distribution of electrons in a solar flare. A second requirement for horseshoe-driven ECME is an extremely low plasma density, referred to as a density cavity. We argue that a coronal density cavity should develop in association with a hard X-ray burst, and that such a density cavity can overcome a long-standing problem with the escape of ECME through the second-harmonic absorption layer. Both the horseshoe distribution and the associated coronal density cavity are highly localized, and could not be resolved in the statistically large number of local precipitation regions needed to explain a hard X-ray burst. The model highlights the “number problem” in the supply of the electrons needed to explain a hard X-ray burst.     

Comparison of solutions to the thirteen-moment and standard transport equations for low speed thermal proton flows

We have compared solutions obtained from the general 13-moment system of transport equations with those obtained from the standard collision-dominated transport equations for conditions corresponding to low speed thermal proton flow in the topside ionosphere in the vicinity of the plasmapause. In general, the solutions obtained from the 13-moment system of equations, which allows for different species temperatures parallel and perpendicular to the geomagnetic field and non-classical heat flows, are different from those obtained from the standard transport equations, which account for isotropic temperatures and classical collision-dominated heat flows. Within the plasmasphere, where the electron density is high, the differences between the 13-moment and standard solutions are typically small. However, outside the plasmasphere where the electron density is lower and in the ionosphere above SAR-arcs, where substantial electron and proton heat flows occur, there can be significant differences between the 13-moment and standard solutions. Generally, the differences are much larger for the protons than for the electrons. Our 13-moment solutions indicate that the proton and electron distributions are anisotropic with the difference between parallel and perpendicular temperatures approaching 4000 K for the protons and 2500 K for the electrons in the ionosphere above SAR-arcs. Also, above SAR-arcs the 13-moment heat flow equations yield proton heat flows as much as a factor of 10 lower and electron heat flows as much as a factor of 2 lower than those predicted by the classical collision-dominated heat flow expressions for the same boundary conditions.     

Symmetry, bifurcation and stacking of the central configurations of the planar 1+4 body problem

In this work we are interested in the central configurations of the planar $1+4$ body problem where the satellites have different infinitesimal masses and two of them are diametrically opposite in a circle. We can think of this problem as a stacked central configuration too. We show that the configurations are necessarily symmetric and the other satellites have the same mass. Moreover we prove that the number of central configurations in this case is in general one, two or three and, in the special case where the satellites diametrically opposite have the same mass, we prove that the number of central configurations is one or two and give the exact value of the ratio of the masses that provides this bifurcation.     

A model for solar oscillations at cm and mm wavelengths

It is suggested that large scale oscillations of the Sun give rise to the periodic fluctuations observed in the quiet Sun at radio wavelengths. These fluctuations would be most readily observed from regions where there is a large gradient of electron temperature with electron density, and are thus more readily observed at cm wavelengths than at millimetre wavelengths.