Trans-sonic cusped shaped, periodic waves and solitary waves of the electrostatic ion-cyclotron type

By adopting an essentially fluid dynamic viewpoint we derive the wave structure equation for stationary, fully nonlinear, electrostatic, ion-cyclotron waves. The existence of two fundamental constants of the motion, namely, conservation of momentum flux parallel to the ambient magnetic field, and energy flux parallel to the direction of wave propagation, enables the wave structure equation to be reduced to a first order differential equation, which has solutions that are physically transparent. The analysis shows that sufficiently oblique waves, propagating at sub-ion acoustic speeds, form soliton pulse-like solutions whose amplitudes are greatest for perpendicular propagation. Waves that propagate supersonically have periodic cnoidal waveforms, which are asymmetric about the compressive and rarefactive phases of the wave. It is also shown that there exist critical driver fields for which the end point of the compressive phase goes sonic (in the wave frame), with the consequence that the wave form develops a cusp. It is possible that this trans-sonic, choked flow feature provides a mechanism for the 'spiky' waveforms observed in auroral electric field measurements

Trans-sonic cusped shaped, periodic waves and solitary waves of the electrostatic ion-cyclotron type

International audienceBy adopting an essentially fluid dynamic viewpoint we derive the wave structure equation for stationary, fully nonlinear, electrostatic, ion-cyclotron waves. The existence of two fundamental constants of the motion, namely, conservation of momentum flux parallel to the ambient magnetic field, and energy flux parallel to the direction of wave propagation, enables the wave structure equation to be reduced to a first order differential equation, which has solutions that are physically transparent. The analysis shows that sufficiently oblique waves, propagating at sub-ion acoustic speeds, form soliton pulse-like solutions whose amplitudes are greatest for perpendicular propagation. Waves that propagate supersonically have periodic cnoidal waveforms, which are asymmetric about the compressive and rarefactive phases of the wave. It is also shown that there exist critical driver fields for which the end point of the compressive phase goes sonic (in the wave frame), with the consequence that the wave form develops a cusp. It is possible that this trans-sonic, choked flow feature provides a mechanism for the "spiky" waveforms observed in auroral electric field measurements

Evidence from satellite altimetry for small-scale convection in the mantle

Small scale convection can be defined as that part of the mantle circulation in which upwellings and downwellings can occur beneath the lithosphere within the interiors of plates, in contrast to the large scale flow associated with plate motions where upwellings and downwellings occur at ridges and trenches. The two scales of convection will interact so that the form of the small scale convection will depend on how it arises within the large scale flow. Observations based on GEOS-3 and SEASAT altimetry suggest that small scale convection occurs in at least two different ways

Electronic and magnetic properties of the ionic Hubbard model on the striped triangular lattice at 3/4 filling

We report a detailed study of a model Hamiltonian which exhibits a rich interplay of geometrical spin frustration, strong electronic correlations, and charge ordering. The character of the insulating phase depends on the magnitude of Delta/|t| and on the sign of t. We find a Mott insulator for Delta >> U >> |t|; a charge transfer insulator for U >> \Delta >> |t|; and a correlated covalent insulator for U >> \Delta ~ |t|. The charge transfer insulating state is investigated using a strong coupling expansion. The frustration of the triangular lattice can lead to antiferromagnetism or ferromagnetism depending on the sign of the hopping matrix element, t. We identify the "ring" exchange process around a triangular plaquette which determines the sign of the magnetic interactions. Exact diagonalization calculations are performed on the model for a wide range of parameters and compared to the strong coupling expansion. The regime U >> \Delta ~ |t| and t<0 is relevant to Na05CoO2. The calculated optical conductivity and the spectral density are discussed in the light of recent experiments on Na05CoO2.Comment: 15 pages, 15 figure

A current driven instability in parallel, relativistic shocks

Recently, Bell has reanalysed the problem of wave excitation by cosmic rays propagating in the pre-cursor region of a supernova remnant shock front. He pointed out a strong, non-resonant, current-driven instability that had been overlooked in the kinetic treatments, and suggested that it is responsible for substantial amplification of the ambient magnetic field. Magnetic field amplification is also an important issue in the problem of the formation and structure of relativistic shock fronts, particularly in relation to models of gamma-ray bursts. We have therefore generalised the linear analysis to apply to this case, assuming a relativistic background plasma and a monoenergetic, unidirectional incoming proton beam. We find essentially the same non-resonant instability noticed by Bell, and show that also under GRB conditions, it grows much faster than the resonant waves. We quantify the extent to which thermal effects in the background plasma limit the maximum growth rate.Comment: 8 pages, 1 figur

A Unified Picture of the FIP and Inverse FIP Effects

We discuss models for coronal abundance anomalies observed in the coronae of the sun and other late-type stars following a scenario first introduced by Schwadron, Fisk & Zurbuchen of the interaction of waves at loop footpoints with the partially neutral gas. Instead of considering wave heating of ions in this location, we explore the effects on the upper chromospheric plasma of the wave ponderomotive forces. These can arise as upward propagating waves from the chromosphere transmit or reflect upon reaching the chromosphere-corona boundary, and are in large part determined by the properties of the coronal loop above. Our scenario has the advantage that for realistic wave energy densities, both positive and negative changes in the abundance of ionized species compared to neutrals can result, allowing both FIP and Inverse FIP effects to come out of the model. We discuss how variations in model parameters can account for essentially all of the abundance anomalies observed in solar spectra. Expected variations with stellar spectral type are also qualitatively consistent with observations of the FIP effect in stellar coronae.Comment: 25 pages, 4 figures, submitted to Ap