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Shock wave formation due to nonlinear vibrations in tube containing fluid subjected to transverse magnetic field with plane heater at midsection and externally supplied energy
The emissions in the chorus frequency band which were detected on the Voyager 1 inbound pass between about ten and six Jupiter radii are surveyed. An overview of the plasma and wave observations during the inbound pass is presented and the spatial regions in which chorus band signals were observed are discussed. A series of wide-band frequency-time frames which characterize the onset of two observed intervals of chorus band activity is displayed. A detailed examination is made of the spectra for rising chorus which sweeps upward in frequency from 0.2 to 0.5 times the electron cyclotron frequency f(c). Two temporally successive wide-band frames in which several types of chorus band emissions were observed are discussed. The spatial morphology of chorus is discussed in terms of the electron energies which resonate with whistler mode waves. A recent theory of chorus generation is reviewed along with theories and a model explaining the narrow-band emissions above f(c)/2.
The "Supercritical Pile" GRB model is an economical model that provides the dissipation necessary to convert explosively the energy stored in relativistic protons in the blast wave of a GRB into radiation; at the same time it produces spectra whose luminosity peaks at ~1 MeV in the lab frame, the result of the kinematics of the proton-photon - pair production reaction that effects the conversion of proton energy to radiation. We outline the fundamental notions behind the "Supercritical Pile" model and discuss the resulting spectra of the prompt emission from optical to gamma-ray energies of order Gamma^2 m_ec^2, (Gamma is the Lorentz factor of the blast wave) present even in the absence of an accelerated particle distribution and compare our results to bursts that cover this entire energy range. Particular emphasis is given on the emission at the GLAST energy range both in the prompt and the afterglow stages of the burst.
The two-fluid solar-wind model is extended by including the collisionless dissipation of hydromagnetic waves originating at the sun. A series of solar wind models is generated, parameterized by the total energy flux of hydromagnetic waves at the base of the model. The resulting properties of propagation and dissipating of hydromagnetic waves on this model are presented.
Observations and theory of convectively-coupled equatorial waves suggest that they can be categorized into two distinct groups. Moisture modes are waves whose thermodynamics are governed by moisture fluctuations. The thermodynamics of the gravity wave group, on the other hand, are rooted in buoyancy (temperature) fluctuations. On the basis of scale analysis it is found that a simple nondimensional parameter –akin to the Rossby number– can explain the processes that lead to the existence of these two groups. This parameter, defined as Nmode, indicates that moisture modes arise when anomalous convection lasts sufficiently long so that dry gravity waves eliminate the temperature anomalies in the convective region, satisfying weak temperature gradient (WTG) balance. This process causes moisture anomalies to dominate the distribution of moist enthalpy (or moist static energy), and hence the evolution of the wave. Conversely, convectively-coupled gravity waves arise when anomalous convection eliminates the moisture anomalies more rapidly than dry gravity waves can adjust the troposphere towards WTG balance, causing temperature to govern the moist enthalpy distribution and evolution. Spectral analysis of reanalysis data indicates that slowly-propagating waves (cp ~ 3 m s-1) are likely to be moisture modes while fast waves (cp ~ 30 m s-1) exhibit gravity wave behavior, with "mixed moisture-gravity" waves existing in between. While these findings are obtained from a highly idealized framework, it is hypothesized that they can be extended to understand simulations of convectively-coupled waves in GCMs and the thermodynamics of more complex phenomena.
Electrons are accelerated to nonthermal energies at shocks in space and astrophysical environments. While shock drift acceleration (SDA) has been considered a key process of electron acceleration at Earth’s bow shock, it has also been recognized that SDA needs to be combined with an additional stochastic process to explain the observed power-law energy spectra. Here, we show mildly energetic (∼0.5 keV) electrons are locally scattered (and accelerated while being confined) by magnetosonic-whistler waves within the shock transition layer, especially when the shock angle is large (θ(sub Bn) approximately equal or greater than 70°). When measured by the Magnetospheric Multiscale mission at a high cadence, ∼0.5 keV electron flux increased exponentially in the shock transition layer. However, the flux profile was not entirely smooth and the fluctuation showed temporal/spectral association with large-amplitude (δB/B ~ 0.3), low-frequency (approximately equal or less than 0.1 Ω(sub ce) where Ω(sub ce) is the cyclotron frequency), obliquely propagating (θ(sub kB) ~ 30°–60°, where θ(sub kB) is the angle between the wave vector and background magnetic field) whistler waves, indicating that the particles were interacting with the waves. Particle simulations demonstrate that, although linear cyclotron resonances with ∼0.5 keV electrons are unlikely due to the obliquity and low frequencies of the waves, the electrons are still scattered beyond 90° pitch angle by (1) resonant mirroring (transit-time damping), (2) non-resonant mirroring, and (3) subharmonic cyclotron resonances. Such coupled nonlinear scattering processes are likely to provide the stochasticity needed to explain the power-law formation.
A survey of solar wind ion velocity distributions and derived parameters (temperature, ion differential speed, heat flux, adiabatic invariants) is presented with emphasis on the heliocentric distance range between 0.3 and 1 AU traversed by the Helios solar probe. The radial evolution of nonthermal features are discussed which are observed to be most pronounced at perihelion. Within the framework of quasilinear plasma theory, wave particle interactions that may shape the ion distributions are considered. Some results of a self consistent model calculation are presented accounting for ion acceleration and heating by resonant momentum and energy exchange with ion cyclotron and magnetosonic waves propagating away from the Sun along the interplanetary magnetic field. Another tentative explanation for the occurrence of large perpendicular proton temperatures is offered in terms of heating by Landau damping of lower hybrid waves.
The possibility that ion beams could provide a free energy source for driving an ion/ion instability responsible for the ULF wave occurrence is investigated. For this, the wave dispersion relation with the observed parameters is solved. Secondly, it is shown that the ring-like distributions could then be produced by a coherent nonlinear wave-particle interaction. It tends to trap the ions into narrow cells in velocity space centered around a well-defined pitch-angle, directly related to the saturation wave amplitude in the analytical theory. The theoretical predictions with the observations are compared.
Whistler waves propagating nearly parallel to the ambient magnetic field experience a nonlinear instability due to transverse currents when the background plasma has a population of sufficiently low energy electrons. Intriguingly, this nonlinear process may generate oblique electrostatic waves, including whistlers near the resonance cone with properties resembling oblique chorus waves in the Earth’s magnetosphere. Focusing on the generation of oblique whistlers, earlier analysis of the instability is extended here to the case where low-energy background plasma consists of both a “cold” population with energy of a few eV and a “warm” electron component with energy of the order of 100 eV. This is motivated by spacecraft observations in the Earth’s magnetosphere where oblique chorus waves were shown to interact resonantly with the warm electrons. The main new results are: 1) the instability producing oblique electrostatic waves is sensitive to the shape of the electron distribution at low energies. In the whistler range of frequencies, two distinct peaks in the growth rate are typically present for the model considered: a peak associated with the warm electron population at relatively low wavenumbers and a peak associated with the cold electron population at relatively high wavenumbers; 2) overall, the instability producing oblique whistler waves near the resonance cone persists (with a reduced growth rate) even in the cases where the temperature of the cold population is relatively high, including cases where cold population is absent and only the warm population is included; 3) particle-in-cell simulations show that the instability leads to heating of the background plasma and formation of characteristic plateau and beam features in the parallel electron distribution function in the range of energies resonant with the instability. The plateau/beam features have been previously detected in spacecraft observations of oblique chorus waves. However, they have been attributed to external sources and have been proposed to be the mechanism generating oblique chorus. In the present scenario, the causality link is reversed and the instability generating oblique whistler waves is shown to be a possible mechanism for formation of the plateau and beam features.
Magnetometer and thermal plasma instruments on the polar-orbiting Dynamics Explorer 1 satellite observed a small-amplitude ultralow frequency pulsation event at the outer edge of the plasmapause near the geomagnetic equator in the midafternoon sector on August 10, 1982, during the recovery phase of a magnetic storm. Transverse pulsations of 30-50 s period were observed throughout the event, and a 270-s period, purely compressional Pc 5 pulsation with several shifts in phase occurred within + or - 5 deg of the geomagnetic equator. Electric fields and the motion of thermal ions appeared to be in quadrature with pulsations in magnetic field magnitude throughout the event. This suggests that the net Poynting flux for the compressional waves was zero, consistent with their being standing waves. Large fluxes of trapped 90 deg pitch angle 10-eV protons, also symmetric about the geomagnetic equator, were observed in conjunction with the waves. These may serve as a source of free energy for the pulsations. These observations lend support to recent studies suggesting that many dayside compressional wave events are related to localized field line resonance near plasmapauselike boundaries, but also include features that cannot be explained by existing theories.
Various electrical phenomena have been reported prior to or concurrent with earthquakes such as resistivity changes, ground potentials, electromagnetic (EM), and luminous signals. Doubts have been raised as to whether some of these phenomena are real and indeed precursory. One of the reasons for uncertainty is that, despite decades of intense work, there is still no physically coherent model. Using low- to medium-velocity impacts to measure electrical signals with microsecond time resolution, it has now been observed that when dry gabbro and diorite cores are impacted at relatively low velocities, approximately 100 m/s, highly mobile charge carriers are generated in a small volume near the impact point. They spread through the rocks, causing electric potentials exceeding +400 mV, EM, and light emission. As the charge cloud spreads, the rock becomes momentarily conductive. When a dry granite block is impacted at higher velocity, approximately 1.5 km/s, the propagation of the P and S waves is registered through the transient piezoelectric response of quartz. After the sound waves have passed, the surface of the granite block becomes positively charged, suggesting the same charge carriers as observed during the low-velocity impact experiments, expanding from within the bulk. During the next 2-3 ms the surface potential oscillates, indicating pulses of electrons injected from ground and contact electrodes. The observations are consistent with positive holes, e.g., defect electrons in the O(2-) sublattice, traveling via the O 2p-dominated valence band of the silicate minerals. Before activation, the positive holes lay dormant in the form of electrically inactive positive hole pairs (PHP), chemically equivalent to peroxy links, O3X/OO\XO3, with X=Si(4+), Al(3+), etc. PHPs are introduced into the minerals by way of hydroxyl,O3X-OH, which all nominally anhydrous minerals incorporate when crystallizing in H2O-laden environments. The fact that positive holes can be activated by low-energy impacts, and their attendant sound waves, suggests that they can also be activated by microfracturing. Depending on where in the stressed rock volume the charge carriers are activated, they will form rapidly moving or fluctuating charge clouds that may account for earthquake-related electrical signals and EM emission. Wherever such charge clouds intersect the surface, high fields are expected, causing electric discharges and earthquake lights.
A closed-form solution for cylindrical thermal waves in metals is given based on the nonlinear hyperbolic system of energy-conservation and heat-flux relaxation equations. It is shown that heat released from a line source propagates radially outward with finite speed in the form of a thermal wave which exhibits a discontinuous wave front. Unique nonlinear thermal-wave solutions exist up to a critical amount of driving energy, i.e., for larger energy releases, the thermal flow becomes multivalued (occurrence of shock waves). By comparison, it is demonstrated that the parabolic thermal-wave theory gives, in general, a misleading picture of the profile and propagation of thermal waves and leads to physical (infinite speed of heat propagation) and mathematical (divergent energy integrals) difficulties. Attention is drawn to the importance of temporal heat-flux relaxation for the physical understanding of fast transient processes such as thermal waves and more general explosions and implosions.
Test particle calculations are used to compute the effects of gravity and ponderomotive acceleration by shear Alfven wave oscillations on the distribution function of O(+) ions along auroral field lines, assuming an ionospheric Maxwellian source of the ions at 2000 km altitude with approximately 0.5 eV of thermal energy in the parallel component of velocity. The electric field model corresponds to a standing wave oscillation with a frequency approximately 1 Hz in the azimuthal direction superimposed on the background dipole field, in which the wave amplitude is either increasing or decreasing in time. The electric field is taken to be primarily in the perpendicular direction. The time varying wave produces broad distributions with widths of 2 to 10 times the initial 0.5-eV thermal energy of the Maxwellian source, and the density and flux of upward going O(+) ions at one Earth radius are both enhanced in this model. The oxygen ion distribution functions at 1 R(sub E) altitude resulting from interaction with waves whose amplitudes are increasing in time have a more gradual lower energy cutoff than do the distribution functions resulting from decaying waves. The high-energy part of the distribution functions in growing waves reflects the temperature of the Maxwellian source, while the high-energy part of the distributions resulting from decaying waves steepens with time, independent of the source temperature.
The relativistic cyclotron resonance condition for right-handed extraordinary mode waves defines an ellipse in velocity space. The position of the center and size of the semiminor axis of this ellipse are functions of the plasma frequency, gyrofrequency, wave frequency, and wave normal angle. The effect of varying these parameters on the position and size of the resonance contour is analyzed. The results show that as the wave normal angle decreases, the semiminor axis increases in size and as the plasma frequency to gyrofrequency ratio decreases, the minimum energy for resonating electrons decreases and the maximum wave normal angle allowed by the resonance condition increases. Also, as the wave frequency to gyrofrequency ratio increases, the center of the resonance ellipse moves away from the origin. The relativistic resonance condition and the electron distribution in velocity space obtained by the S3-3 satellite are used to calculate numerically growth rates for the terrestrial auroral kilometric radiation. It is shown that the loss cone region of the electron distribution can give rise to growth rates for the extraordinary mode that are sufficiently large to account for the observed radio emission intensities.
The effects of long-wavelength dissipation on beam-driven Langmuir turbulence are investigated using numerical simulations that include both weak and strong turbulence effects. Strong-turbulence wave collapses occur concurrently with weak-turbulence energy cascades if the long-wavelength damping is sufficiently small relative to the growth rate of the beam-unstable waves. Above a threshold damping level, only the weak-turbulence backscatter cascade is observed, and it becomes increasingly truncated as the damping increases, eventually consisting of only a single backscatter. A simple Lotka-Volterra model gives an excellent description of the periodic evolution observed in the weak-turbulence regime. Suppression of the usual backscatter cascade by long-wavelength damping enables intense beam-aligned density troughs to form, which trap and duct Langmuir waves.
We present Magnetospheric Multiscale observations of an electron-scale current sheet and electron outflow jet for asymmetric reconnection with guide field at the subsolar magnetopause. The electron jet observed within the reconnection region has an electron Mach number of 0.35 and is associated with electron agyrotropy. The jet is unstable to an electrostatic instability which generates intense waves with E(sub parallel lines) amplitudes reaching up to 300 mV/m and potentials up to 20% of the electron thermal energy. We see evidence of interaction between the waves and the electron beam, leading to quick thermalization of the beam and stabilization of the instability. The wave phase speed is comparable to the ion thermal speed, suggesting that the instability is of Buneman type, and therefore introduces electron-ion drag and leads to braking of the electron flow. Our observations demonstrate that electrostatic turbulence plays an important role in the electron-scale physics of asymmetric reconnection.
The oscillation of differential fluxes of energetic ions modulated by a ULF wave often shows a phase shift between measurements in back-to-back detectors with look directions perpendicular to the ambient magnetic field. In a plasma of a single ion species, the phase difference is caused by displacement of the effective measurement positions by one ion gyroradius to each side of the detector. As the wave phase is periodic, the observed phase shift can correspond to a family of possible wavelengths. Simultaneous measurements of the flux modulations in different energy channels, which are equivalent to measurements of the wave phase at different positions, may make it possible to single out a unique wavelength consistent with all the measurements. Using the medium-energy-particle experiments ISEE-1 and 2, each of which may serve as a back-to-back detector, the above method was applied to a compressional Pc 5 wave observed near the equatorial plane at L between about 7 and 11. The transverse propagation properties of the wave were determined unambiguously.
The removal of radiation belt electrons through pitch-angle scattering by the observed obliquely propagating plasmaspheric whistler wave band is investigated. Electron lifetimes are calculated as a function of L and energy. The effects of high latitude interactions and of oblique wave propagation with the resulting diffusion at all cyclotron harmonics are quantitatively incorporated into the calculations. The inclusion of these effects appears to extend the role of whistler-driven electron pitch-angle diffusion to provide an explanation of the positioning of the quiet time radiation belt electron slot and the electron losses within the slot region.