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The simple theory for the effect of gravity wave breaking on eddy diffusion and on mean stress is reviewed. Attempts are made to identify the magnitudes of known mechanisms for generating gravity waves. The relation between observed periods and unobserved horizontal wavenumbers is discussed. Finally the role of group velocity, wave packets and wave inhomogeneity is discussed.
High-frequency electrostatic microinstabilities in magnetospheric plasmas are considered in detail. Rather special plasma parameters are found to be required to match the theoretical wave spectrum with satellite observations in the magnetosphere. In particular, it is necessary to have a cold and a warm species of electrons such that (1) the warm component has an anomalous velocity distribution function that is nonmonotonic in the perpendicular component of velocity and is the source of free energy driving the instabilities, (2) the density ratio of the cold component to the hot component is greater than about 0.01, and (3) the temperature ratio of the two components for cases of high particle density is no less than 0.1. These requirements and the corresponding instability criteria are satisfied only in the trapping region; this is also the region in which the waves are most frequently observed. The range of unstable wavelengths and an estimate of the diffusion coefficient are also obtained. The wave are found to induce strong diffusion in velocity space for low-energy electrons during periods of moderate wave amplitude.
Rapid-double-exposure, diffuse-illumination holography is evaluated analytically and experimentally as a flow visualization method for time-varying shock waves. Conditions are determined that minimize the distance (localization error) between the surface or curve of interference-fringe localization and the shock surface. Treated specifically are the cases of shock waves in a transonic compressor rotor for which there is laser anemometer data for comparison and shock waves in a flutter cascade.
To understand the entry of the cool low‐latitude mantle ions into the tail plasma sheet near the flanks under persistent interplanetary magnetic field B y , we evaluate the role of the cross‐field diffusive transport by kinetic Alfvén waves (KAWs) by investigating two events observed by multiscale (MMS) spacecraft. Around the separatrix between the open and closed field‐line regions, a two‐component mixing of hot plasma sheet ions of a few keV with cool mantle ions of a few hundred eV was observed, indicating transport across the separatrix. The waves observed between 0.01 and 10 Hz around the separatrix had characteristics consistent with those of KAWs. The consistency allowed us to estimate the wave vectors as a function of frequency by fitting KAW dispersion to the observations. Using the observed wave powers, plasma moments, and the estimated wave vectors, we computed the cross‐field diffusion rates associated with KAWs. The diffusion rates were found to be comparable to or larger than the Bohm diffusion rates during the intervals when the two‐component mixing was observed, indicating that the KAW diffusive transport can play a role in the entry of low‐latitude mantle ions into the plasma sheet.
An instability analysis is presented for parallel and antiparallel propagating electromagnetic waves generated by reflected and diffuse suprathermal ions upstream of the earth's bow shock. Calculations are performed on the basis of upstream particle observations made by the ISEE 1 Quadrispheric Lepedea instrument and low-energy electron measurements made by the ISEE 1 electron spectrometer for a single period. The electromagnetic dispersion relation is computed and the unstable modes and growth times of the fastest growing waves are determined. It is found that the reflected ions destabilize the plasma most strongly at a wave frequency 0.1 that of the ion gyrofrequency by a resonant ion beam instability for waves propagating upstream and by a nonresonant firehose-like instability for waves propagating downstream. The diffuse ions also destabilize the plasma most strongly at the same frequency by means of resonant instabilities of both right- and left-hand polarized waves propagating away from the bow shock.
An equation governing the combined radial diffusion and stochastic acceleration of super-Alfvenic ions by magnetohydrodynamic waves in Jupiter's outer magnetosphere is derived. The formulation is based upon a total energy invariant of the adiabatic transport which applies to an isotropic distribution undergoing rapid pitch angle scattering by waves. An analytic solution to the double diffusion equation is obtained and numerical results are presented for two models of ion injection. The first model assumes S(+) and O(+) are injected throughout a broad region of space through photoionization of Jupiter's magnetospheric neutral wind and obtain an initial energy corresponding to the local corotation energy after pickup by the planetary magnetic field. The second model assumes a monoenergetic distribution of energetic protons is implanted in the middle magnetosphere by the action of field-aligned potential drops in Jupiter's auroral ionosphere. For both light and heavy ions the injection process creates a seed population of particles which are further accelerated nonadiabatically by the MHD waves and adiabatically through radial diffusion. A comparison of the theoretical results with a recent data analysis of Voyager low-energy charged particle measurements is made with very good agreement, thus providing a rigorous quantitative account of and definitive explanation for the high-energy ion component of Jupiter's magnetosphere.
Periodic phenomenon caused by unstable overventilated laminar jet diffusion flame with traveling sound wave, primarily burning rate
At Uranus, the Voyager 2 plasma wave investigation observed very significant phenomena related to radio emissions, dust impacts, and magnetospheric wave-particle interactions. On January 19, 1986 (R = 270 R-sub U) the plasma wave investigation detected an intense radio burst at 31 and 56 kHz, and this provided the first indication that Uranus had a magnetosphere. During the encounter, more of these sporadic bursts were observed along with relatively continuous radio emissions extending down to 10 kHz, and a sporadic narrowband radio signal with f near 5 kHz. As Voyager passed through the ring plane, the plasma wave investigation recorded a large number of dust impacts. The Voyager 2 plasma wave instrument also detected many strong electromagnetic and electrostatic plasma waves, with intensity peaks in the region within 12 Uranus radii. These waves have characteristics that can interact strongly with the local plasma and with the trapped energetic particles, leading to precipitation into the atmosphere, charged particle acceleration, and charged particle diffusion. In addition, strong wave activity was detected in the region of the bow and shock and moderate levels in the magnetic tail.
The density of ions in the Io plasma torus and the scattering of these ions by low frequency electromagnetic emissions detected by Voyager 1 were studied. The ion density profile was investigated using whistler dispersion measurements provided by the Voyager plasma instrument. The scale height and absolute density of H+ ions in the vicinity of the plasma torus were determined by combining the measured plasma densities with the whistler dispersion measurements. A theoretical analysis of the modes of propagation of low frequency electromagnetic emissions in the torus was undertaken. Polarization reversal effects and rough estimates of the ion diffusion coefficient were utilized. Numerical evaluation of the ion diffusion coefficients in the torus were made using the observed Voyager 1 wave intensities. Results show that the observed wave intensities produce significant ion diffusion effects in the ion torus.
A theory of quasilinear diffusion for obliquely propagating electromagnetic waves was developed in the 1960's and applied in the 1970's to model scattering of relativistic electrons by a prescribed distribution of waves. In the latter work, a transformation of variables, from wavevector space to the temporal frequency and tangent of the wave normal angle, was used so that simple Gaussian functions of frequency and tangent of the wave normal angle could be multiplied together to define the distribution of wave power, although arbitrary distributions of power in these two variables is also permitted. Finally, in 2005, previous work was consolidated and has been widely used in heliophysics studies that require computation of quasilinear diffusion coefficients. Here it is shown that this transformation is inppropriate when the precise wave vector distribution is known. The correct transformation is derived and used to produce diffusion coefficients that can differ by orders of magnitude from those computed using the inappropriate transformation. The differences are largest when the distribution of wave power extends to wave normal angles near the resonance cone. When the ratio of the plasma frequency to the gyrofrequency is large, only low energies (keV) are affected, but as the ratio decreases higher energies (MeV) also show differences. It is also shown that the derivation from the 1960's uses a notation that results in the diffusion coefficients depending on the distribution of wave power with respect to the wave azimuthal angle whereas there should be no such dependence.
The magnetic reconnection experiment has recently seen short wavelength ([Formula: see text]) lower-hybrid waves near the electron diffusion region in strong guide field reconnection. Based on plasma parameters from the experiment, we perform a three-dimensional fully kinetic simulation in order to investigate the generation of the lower-hybrid waves and their effects on the reconnection process. We find that the low-beta regions around the reconnection site are unstable to the lower-hybrid drift instability propagating in the outflow direction, driven by the difference between the electron and ion outflows. The waves modify the electron distributions, leading to periodic opening and closing of gaps in electron velocity space, and provide a small contribution to the anomalous resistivity. Finally, the simulation results are discussed in the context of space observations and laboratory experiments.
The magnetic reconnection experiment has recently seen short wavelength (kp (e)(1) lower-hybrid waves near the electron diffusion region in strong guide field reconnection. Based on plasma parameters from the experiment, we perform a three-dimensional fully kinetic simulation in order to investigate the generation of the lower-hybrid waves and their effects on the reconnection process. We find that the low-beta regions around the reconnection site are unstable to the lower-hybrid drift instability propagating in the outflow direction, driven by the difference between the electron and ion outflows. The waves modify the electron distributions, leading to periodic opening and closing of gaps in electron velocity space, and provide a small contribution to the anomalous resistivity. Finally, the simulation results are discussed in the context of space observations and laboratory experiments.
This effort involved the analysis of low frequency waves as observed by the Galileo spacecraft near the Galilean moon, Io. Io is a significant source of material, especially SO2, and various products of dissociation, and further these atoms and molecules are readily ionized. The initial velocity of the ions is essentially that of the neutral species, i.e., the Keplerian velocity. The plasma, on the other hand is co-rotating, and there is a differential flow of the order 57 km/s between the plasma and the neutral particles. Thus pick-up ion instabilities are Rely to occur within the Jovian magnetosphere. Indeed, magnetometer observations from the Galileo spacecraft clearly show ion cyclotron waves that have been identified with a large variety of plasma species, such as O+, S++ (which has the same gyro-frequency as O+), S+, and SO2+. Typically, however, the dominant frequency is near the SO2+ gyro-frequency. The research effort was originally planned to be a team effort between Robert J. Strangeway as the Principal Investigator, and Debbie Huddleston, who was an Assistant Research Geophysicist at UCLA. Unfortunately, Dr. Huddleston took a position within Industry. The effort was therefore descoped, and Dr. Strangeway instead pursued a collaboration with Dr. Xochitl Blanco-Cano, of the Instituto de Geofisica, Universidad Nacional Autonoma de Mexico. This has proved to be a productive collaboration, with several papers and publications arising out of the effort. The magnetic field oscillations near lo generally fall into two types: ion cyclotron waves, with frequencies near an ion gyro-frequency, and lower frequency mirror-mode waves. The ion cyclotron waves are mainly transverse, and frequently propagate along the ambient magnetic field. The mirror-mode waves are compressional waves, and they have essentially zero frequency in the plasma rest frame. One of the purposes of our investigation is to understand what controls the types of wave modes that occur, since both wave modes can be drive unstable by the pressure anisotropy associated with the pick up ions. The pick ion velocity is perpendicular to the ambient magnetic field, and is generally much larger than the thermal velocity, at least initially. At its simplest, we found that the ion cyclotron waves are controlled by the parameters of the species in gyro-resonance with the wave. Thus, while the growth rates for the lower mass (higher gyro-frequency) pick-up ions are generally larger, we found that the heavier SO2+ ion cyclotron waves are generally preferred. This is because one of the effects of the wave instability is to diffuse the ions in pitch angle and energy. The lower mass ions therefore consist of both a ring of recently created pick-up ions, and a thermal background. This thermal background quenches the ion cyclotron instability. SO2+ is different, however. Being a molecule, the species can also dissociate. Our analysis suggests that the dissociation acts on a time scale comparable to or faster than the velocity space diffusion time scale. There are consequently no thermal SO2+ ions to quench the instability. We have also investigated the mirror-mode. This mode can at times grow more rapidly than the individual ion cyclotron waves. This is mainly because the mirror-mode can grow off the pressure anisotropy of the individual species with which the waves are in resonance. Lastly, as part of this effort we have begun to investigate the instability for obliquely propagating modes. Galileo observations show that at times the ion cyclotron waves are significantly elliptically polarized, and further the wave vector is at a large angle to the field, significant growth can occur for oblique propagation. Depending on the group velocity of the waves, it is possible that obliquely propagating modes have higher advective growth rate, but this has yet to be determined.
Electromagnetic ion cyclotron (EMIC) waves are widely believed to play an important role in influencing the radiation belt and ring current dynamics. Most studies have investigated the effects or characteristics of EMIC waves by assuming their left-handed polarization. However, recent studies have found that the reversal of polarization, which occurs at higher latitudes along the wave propagation path, can change the wave-induced pitch angle diffusion coefficients. Whether such a polarization reversal can influence the global ring current dynamics remains unknown. In this study, we investigate the ring current dynamics and proton precipitation loss in association with polarization-reversed EMIC waves by using the ring current–atmosphere interactions model (RAM). The results indicate that the polarization reversal of H-band EMIC waves can truly decrease the scattering rates of protons of 10 to 50 keV or >100 keV in comparison with the scenario in which the EMIC waves are considered purely left-handed polarized. Additionally, the global ring current intensity and proton precipitation may be slightly affected by the polarization reversal, especially during prestorm time and the recovery phase, but the effects are not large during the main phase. This is probably because the H-band EMIC waves contribute to the proton scattering loss primarily at E < 10 keV, an energy range that is not strongly affected by the polarization reversal.
Do electromagnetic ion cyclotron (EMIC) waves cause strong pitch-angle diffusion of RC ions? This question is the primary motivation of this paper and has been affirmatively answered from the theoretical point of view. The materials that are presented in the Results section show clear evidence that strong pitch-angle diffusion takes place in the inner magnetosphere indicating an important role for the wave-particle interaction mechanism in the formation of RC ions and EMIC waves.
A theory is presented to predict the occurrence of weak rotating waves in a centrifugal compression system with a vaneless diffuser. As in a previous study of axial systems, an undisturbed performance characteristic is assumed known. Following an inviscid analysis of the diffuser flow, conditions for a neutral rotating disturbance are found. The solution is shown to have two branches; one with fast rotation, the other with very slow rotation. The slow branch includes a dense set of resonant solutions. The resonance is a feature of the diffuser flow, and therefore such disturbances must be expected at the various resonant flow coefficients regardless of the compressor characteristic. Slow solutions seem limited to flow coefficients less than about 0.3, where third and fourth harmonics appear. Fast waves seem limited to a first harmonic. These fast and slow waves are described, and effects of diffuser-wall convergence, backward blade angles, and partial recovery of exit velocity head are assessed.
A self-consistent theory is set forth for the excitation of hydromagnetic waves and the acceleration of 'diffuse' ions upstream of the earth's bow shock in the quasi-equilibrium that results when the solar wind velocity and the interplanetary magnetic field are nearly parallel. For the waves, the quasi-equilibrium derives from a balance between excitation by the ions, which stream relative to the solar wind plasma, and convective loss to the magnetosheath. For the diffuse ions, the quasi-equilibrium derives from a balance between injection at the shock front, confinement to the foreshock by pitch angle scattering on the waves, and acceleration by compression at the shock front. It also results from loss to the magnetosheath, loss due to escape upstream of the foreshock, and loss via diffusion perpendicular to the average magnetic field onto field lines that do not connect to the shock front. Diffusion equations describing the ion transport and wave kinetic equations describing the hydromagnetic wave transport are solved self-consistently to give analytical expressions. These describe (1) the differential wave intensity spectrum as a function of frequency and distance from the bow shock and (2) the ion omnidirectional distribution functions and anisotropies as functions of energy and distance from the bow shock.
A careful examination of the effects of collisions on resonant wave–particle interactions leads to an alternate interpretation and deeper understanding of the quasilinear operator originally formulated by Kennel & Engelmann ( Phys. Fluids , vol. 9, 1966, pp. 2377–2388) for collisionless, magnetized plasmas, and widely used to model radio frequency heating and current drive. The resonant and nearly resonant particles are particularly sensitive to collisions that scatter them out of and into resonance, as for Landau damping as shown by Johnston ( Phys. Fluids , vol. 14, 1971, pp. 2719–2726) and Auerbach ( Phys. Fluids , vol. 20, 1977, pp. 1836–1844). As a result, the resonant particle–wave interactions occur in the centre of a narrow collisional boundary when the collision frequency $\unicode[STIX]{x1D708}$ is very small compared to the wave frequency $\unicode[STIX]{x1D714}$ . The diffusive nature of the pitch angle scattering combined with the wave–particle resonance condition enhances the collision frequency by $(\unicode[STIX]{x1D714}/\unicode[STIX]{x1D708})^{2/3}\gg 1$ , resulting in an effective resonant particle collisional interaction time of $\unicode[STIX]{x1D70F}_{\text{int}}\sim (\unicode[STIX]{x1D708}/\unicode[STIX]{x1D714})^{2/3}/\unicode[STIX]{x1D708}\ll 1/\unicode[STIX]{x1D708}$ . A collisional boundary layer analysis generalizes the standard quasilinear operator to a form that is fully consistent with Kennel–Englemann, but allows replacing the delta function appearing in the diffusivity with a simple integral (having the appropriate delta function limit) retaining the new physics associated with the narrow boundary layer, while preserving the entropy production principle. The limitations of the collisional boundary layer treatment are also estimated, and indicate that substantial departures from Maxwellian are not permitted.