The consequences of micropulsations on geomagnetically trapped particles

Non-adiabatic radiation belt dynamics is largely controlled by interactions between geomagnetically trapped particles and various modes of plasma turbulence. Long period electric field fluctuations act as a major source mechanism for the inner zone through the process of inward radial diffusion of particles injected into the convection dominated outer zone. Higher frequency turbulence provides a major loss mechanism by pitch-angle scattering into the atmospheric loss cone. The wave particle interactions may take the form of self induced instabilities or parasitic scattering. Examples of each will be given in this review.     

Cross Field Diffusion of Cosmic Rays in a Two-Dimensional Magnetic Field Turbulence

Cross field diffusion of energetic particles (cosmic rays) in a two-dimensional static magnetic field turbulence is studied performing test particle simulations. Qualitatively different diffusion processes are observed depending on the ratio of Larmor radius (ρ) to the correlation length (λ) of the magnetic field fluctuations. The diffusion is found to be composed of several regimes with distinct statistical properties, which can be characterized using Levy statistics. This revised version was published online in August 2006 with corrections to the Cover Date.     

Wave-particle interactions and their relevance to substorms

Wave-particle effects are implicit in most models of radial diffusion and energization of Van Allen belt particles; they were explicitly used in the wave turbulence model for trapped particle precipitation and trapped flux limitations by Kennel and Petschek, Cornwall and by many others. Liemohn used wave-particle interactions to work out a theory of path-integrated whistler amplification process to explain the lack of large per-hop attenuation of multiple-hop LF whistlers.Others have now used wave-particle interactions to construct theories of ELF and VLF chorus. In the present paper we shall review the observations and some of the pertinent theoretical interpretations of wave-particle effects as they relate to substorm and storm-time phenomena. If substorms develop as a result of magnetic merging, then it seems clear that wave-particle interactions in the dissipative or so-called diffusion region of the reconnection zone may be of great importance. The plasma sheet thinning and flow towards the Earth lead inevitably to the development of particle distribution functions that contain free energy in a pitch-angle anisotropy. Such free energy can be released via plasma wave instabilities. The subsequent wave-particle interactions can result in both strong and weak diffusion of particles into loss cones with consequent precipitation fluxes into the auroral zone. Ring current proton spectra also should be unstable against various plasma instabilities with consequent ring current decay and precipitations. Wave-particle interactions must play some important roles in auroral arcs, electrojets and other phenomena related to substorms. These aspects of wave-Paticle interaction will be covered     

The Cusp as a Source of Magnetospheric Energetic Particles, Currents, and Electric Fields: A New Paradigm

Energetic particle instrumentation on the Polar satellite has discovered that significant fluxes of energetic particles are continuously present in the region of the dayside magnetosphere where they cannot be stably trapped. This region is associated with either open magnetic field lines or a magnetic topology associated with pseudo-trapping. Two distinct features [Time-Energy Dispersion (TED) signatures and Cusp Energetic Particle (CEP) events] are observed in these energetic particle fluxes that strongly suggest a local acceleration of mostly shocked solar wind particles. As the solar wind particles ram themselves into the cusp geometry, they form diamagnetic cavities with strong turbulence that are capable of accelerating particles to energies of 100s and 1000s of kiloelectronvolts. This process forms a layer of energetic particles on the magnetopause as well as permits such particles to enter via drift the equatorial nightside magnetosphere to distances as close as six Earth radii under the influence of gradient and curvature effects in the local magnetic field. The fluxes of these particles have all of the properties associated with the ring current and can supply the magnitude of the cross tail current required. ISEE-1 energetic particle data and their pitch angle distributions [PAD] are examined at the magnetic equatorial plane on the night side to investigate and possibly validate the insights gains from the Polar data and energetic particle trajectory tracing in a realistic magnetic field. The existence and properties of butterfly-type PADs strongly supports the concept of a dayside high latitude source of energetic particle fluxes. Because the CEP process is impulsive and time variable the charge separation produced by the drifting electrons (eastward) and ions (westward) on the magnetospheric nightside may be responsible for the cross tail electric field that has been ascribed to the reconnection/convection process.     

Particle Scattering by Magnetic Fields

The need for a correct quantitative treatment of the interactions between cosmic rays and turbulent magnetic fields continues to be one of the fundamental problems of modern astrophysics. It is the aim of this paper to review new developments in the understanding of mechanisms involved in the scattering of charged particles by magnetic field fluctuations. Special emphasis is given to a comparison of transport parameters determined from the modeling of spacecraft and neutron monitor observation of solar particle events, with theoretical predictions derived from a spectral analysis of simultaneously measured fluctuation spectra. It appears that the traditional quasi-linear theory of particle scattering requires only a slight modification, and the major problem still is our lack of knowledge of the three-dimensional structure of the magnetic turbulence. Possibilities to better reconcile the theory with observations by properly taking into account the microphysics of wave and turbulence aspects of the fluctuations, and to use energetic particles as probes to study certain properties of the magnetic turbulence, are discussed. This revised version was published online in August 2006 with corrections to the Cover Date.     

Jupiter's radiation belts

The recent close encounters of Pioneer-10 (December 1973) and Pioneer-11 (December 1974) with the planet Jupiter provided the first in situ observations of zenomagnetically trapped particle radiation. Such observations represented a major advance in planetary research. Prior estimates of radiation intensities (particle fluxes) at Jupiter had necessarily relied (in the case of electrons) upon inferences from Jovian decimetric radio emission observed at the Earth and (in the case of protons) upon postulates for the numerical scaling from terrestrial proton intensities. The Pioneer-10 and Pioneer-11 observations have stimulated continuing theoretical efforts to understand the reported findings and to extrapolate from them to other planets and other epochs. While the analysis of trapped-radiation data from the Pioneer spacecraft is far from being completed, a consensus has developed with respect to the physical mechanisms that must be considered. The observed radiation belts seem to be populated by radial diffusion from an external source. The diffusion coefficient seems to be that derived from fluctuations in the polarization electric field produced by neutral winds in the Jovian ionosphere, which is coupled to the magnetosphere by equipotential B-field lines. Radiation-belt electrons lose energy and change their equatorial pitch angles by virtue of synchrotron emission. Radiation-belt ions and electrons both may be subject to pitch-angle diffusion caused by waves that the respective particle anisotropies have created through plasma instabilities. Finally, radiation-belt ions and electrons seem to experience absorption by the inner Jovian satellites (moons) in a manner that may depend upon the species and energy of the incident radiation-belt particle. It is not yet known whether satellite-associated clouds of sodium and sulfur contribute substantially to the inferred particle absorption. Also still open is the question of whether the satellites provide a substantial source of radiation-belt particles. Moreover, there remains doubt concerning the configuration of the outer Jovian magnetosphere and the influence of this configuration on the zenomagnetic trapping of energetic charged particles.Proceedings of the Symposium on Solar Terrestrial Physics held in Innsbruck, May–June 1978.     

Dynamics of Radiation Belt Particles

This paper reviews basic concepts of particle dynamics underlying theoretical aspect of radiation belt modeling and data analysis. We outline the theory of adiabatic invariants of quasiperiodic Hamiltonian systems and derive the invariants of particle motion trapped in the radiation belts. We discuss how the nonlinearity of resonant interaction of particles with small-amplitude plasma waves, ubiquitous across the inner magnetosphere, can make particle motion stochastic. Long-term evolution of a stochastic system can be described by the Fokker-Plank (diffusion) equation. We derive the kinetic equation of particle diffusion in the invariant space and discuss its limitations and associated challenges which need to be addressed in forthcoming radiation belt models and data analysis.     

Inner-belt Van Allen radiation

A survey of the present state of knowledge about the inner radiation zone is presented. This includes a historical review of empirical data and theoretical considerations concerning electrons, protons, and heavier particles. Included are results obtained from the various high-altitude nuclear tests. Recent experimental results are presented and some newer theoretical ideas, such as pitch-angle scattering and radial diffusion, are discussed as applied to the data. Comparisons of the measured fluxes, spectra, and time variations with the theoretical calculations are made where possible.Some conclusions are drawn pertaining to the sources and loss processes for the trapped particles, and some comments are made regarding future measurements in the inner zone.     

Dynamics of the earth's ring current: Theory and observation

The development of currents within an arbitrary distribution of particles trapped in the geomagnetic field is described. These currents combine to form the earth's ring current and thus are responsible for the worldwide depressions of surface magnetic field strength during periods of magnetic activity known as magnetic storms. Following a brief review of trapped particle motion in magnetic fields, ring current development is described and presented in terms of basic field and particle distribution parameters. Experimental observations then are presented and discussed within the theoretical framework developed earlier. New results are presented which, in the area of composition and charge state observations, hold high promise in solving many long standing ring current problems. Finally, available experimental results will be used to assess our present understanding as to ring current sources, generation, and dissipation.     

Nonclassical Transport and Particle-Field Coupling: from Laboratory Plasmas to the Solar Wind

Understanding transport of thermal and suprathermal particles is a fundamental issue in laboratory, solar-terrestrial, and astrophysical plasmas. For laboratory fusion experiments, confinement of particles and energy is essential for sustaining the plasma long enough to reach burning conditions. For solar wind and magnetospheric plasmas, transport properties determine the spatial and temporal distribution of energetic particles, which can be harmful for spacecraft functioning, as well as the entry of solar wind plasma into the magnetosphere. For astrophysical plasmas, transport properties determine the efficiency of particle acceleration processes and affect observable radiative signatures. In all cases, transport depends on the interaction of thermal and suprathermal particles with the electric and magnetic fluctuations in the plasma. Understanding transport therefore requires us to understand these interactions, which encompass a wide range of scales, from magnetohydrodynamic to kinetic scales, with larger scale structures also having a role. The wealth of transport studies during recent decades has shown the existence of a variety of regimes that differ from the classical quasilinear regime. In this paper we give an overview of nonclassical plasma transport regimes, discussing theoretical approaches to superdiffusive and subdiffusive transport, wave–particle interactions at microscopic kinetic scales, the influence of coherent structures and of avalanching transport, and the results of numerical simulations and experimental data analyses. Applications to laboratory plasmas and space plasmas are discussed.     

Theoretical studies of interplanetary propagation and acceleration

Studies evaluating the transport coefficients for energetic particles in interplanetary space are described in relation to particle data.In position space, the main mode of propagation is along field lines but perpendicular diffusion and drift motion is also possible. Diffusion coefficients based on interplanetary magnetic field data are either derived from quasi-linear, adiabatic theory or this theory corrected for finite scattering near 90° pitch angle or by numerical techniques. Relevant particle data includes solar proton event time profile and anisotropy measurements. In general, when Fokker-Planck transport equation solutions are fitted to particle data, the parallel diffusion coefficients obtained still appear rather larger than those given by theoretical estimates. Perpendicular diffusion is shown to be due to field line wandering and random drift motion effects. The importance of drift motion in cosmic ray modulation theory is mentioned.Although much emphasis is currently placed upon shock acceleration in CIR's, statistical acceleration in interplanetary space must be considered. Energetic particles may gain energy from longitudinal waves and cyclotron resonance interactions. Analytical and numerical estimates of the energy space diffusion coefficients are considered. Some reveal a surprising importance to this statistical acceleration and can explain a variety of data.Presented at the Fifth International Symposium on Solar-Terrestrial Physics, held at Ottawa, Canada, May 1982.     

The Localization of Particle Acceleration Sites in Solar Flares and CMES

We review the particular aspect of determining particle acceleration sites in solar flares and coronal mass ejections (CMEs). Depending on the magnetic field configuration at the particle acceleration site, distinctly different radiation signatures are produced: (1) If charged particles are accelerated along compact closed magnetic field lines, they precipitate to the solar chromosphere and produce hard X-rays, gamma rays, soft X-rays, and EUV emission; (2) if they are injected into large-scale closed magnetic field structures, they remain temporarily confined (or trapped) and produce gyrosynchrotron emission in radio and bremsstrahlung in soft X-rays; (3) if they are accelerated along open field lines they produce beam-driven plasma emission with a metric starting frequency; and (4) if they are accelerated in a propagating CME shock, they can escape into interplanetary space and produce beam-driven plasma emission with a decametric starting frequency. The latter two groups of accelerated particles can be geo-effective if suitably connected to the solar west side. Particle acceleration sites can often be localized by modeling the magnetic topology from images in different wavelengths and by measuring the particle velocity dispersion from time-of-flight delays.     

Radiation belts in the region of the South-Atlantic magnetic anomaly

Conclusion The difference of the geomagnetic field from the field of the idealized dipole not only creates certain difficulties for studying the geomagnetically trapped radiation but also presents new possibilities for studying the processes which control the particle movement in the magnetosphere. It will be remembered that the fact that the geomagnetic field is not a dipole played a decisive role in the very beginning of the formation of our ideas about the nature of the intense fluxes of the penetrating radiation detected during the satellite flights.In fact, the longitude dependence of the lower boundary of the penetrating radiation in the region of low latitudes according to the properties of the geomagnetic field made it possible to conclude immediately that the detected radiation was caused by the geomagnetically trapped particles.As to the difficulties in the trapped radiation study caused by the existence of the anomalies, they, first of all, result in the original and, at the first glance, incomprehensible form of the particle intensity contours drawn in geographical coordinates for low altitudes. However, when turning to the McIlwain coordinate system, which is naturally connected with the real magnetic field, the seeming chaos in the radiation distribution disappears being unexpectedly replaced by harmony and order. But even in this coordinate system some ambiguities are observed connected with the distortion of the adiabatic invariants during the time comparable with the period of the particle drift around the earth.The thorough analysis of these effects in combination with the observations of the radiation at high altitudes may answer such a principle question as the question about the velocity of the movements of the mirror points.It should be noted that some information has been obtained to date on the movement of the electron-mirror points only and similar information about protons is absent.It is possible that new aspects of the use of the magnetic anomalies for studying the geomagnetosphere will appear in due time.     

气固两相湍流场纳米颗粒演变特性综述

含纳米颗粒的气固两相湍流场在包括航空等众多领域中很常见,以单体、聚集体和团聚体不同形式存在的纳米颗粒在流场中经过生成、对流、扩散、凝并、破碎等过程,其数密度、尺度、尺度分散度等将发生变化。本文就以上相关研究状况进行了回顾,说明颗粒生成是气相化学反应产生的可冷凝蒸汽物质因表面冷却、绝热膨胀或混合、湍流混合或化学过程产生的过饱和所导致;导致颗粒凝并的原因包括布朗运动、湍流剪切、速度梯度、差异沉降;颗粒的凝并取决于颗粒的尺度和流场的特性,并受初始颗粒分布及湍流扩散控制;湍流场对颗粒凝并的影响除了湍流强度的因素外,还体现在由湍流脉动所引发的颗粒数密度的脉动;颗粒凝并后形成尺度较大的团聚体容易在流场剪切和其他因素作用下发生破碎;剪切破碎是导致颗粒破碎的主要因素,有效破碎系数取决于剪切率和颗粒的体积分数;颗粒的沉降取决于颗粒尺度、形状和流体性质等因素;导致颗粒沉降的因素有重力、扩散、惯性撞击、电场和热迁移等;当存在温度梯度时,热泳力对颗粒沉降也起到重要作用。本文最后提出了有待进一步研究的若干问题。     

Large eddy simulation of turbulent diffusion flame combustion using a conserved scalar methodology

The present paper describes an LES prediction of turbulent diffusion flame combustion in a simplified axi-symmetric combustor geometry.The calculations are carried out using a well-tested finite volume incompressible LES code which has been modified to handle variable density and reacting flows.The basic mixture fraction conserved scalar method is used with the chemical state relationships described by fast chemistry.The turbulence-chemistry interaction is modelled by a sub-grid PDF method and the PDF is assumed to follow a Beta-function shape.The LES predictions have been time-averaged over 3.5 flow-through times to generate the mean radial profiles of mixture fraction,product mass fraction,temperature,axial velocity and axial rms.The agreement of the LES predictions with the experimental data is good for all the above quantities at four different axial positions with largest differences at the first measurement plane.The LES method also provides information on the unsteady nature of turbulent diffusion combustion. For turbulent reacting flows with large density ratio,it was found necessary to use a relaxation method in order to remove unphysical high-frequency fluctuations and to maintain numerical stability.      

Stochastic Acceleration of Energetic Particles in the Heliosphere

In this paper we assess possible roles of stochastic acceleration by random electric field and plasma motion in the production and transport of energetic particles in the heliosphere. Stochastic acceleration can occur in the presence of multiple small-scale magnetohydrodynamic waves propagating in different directions. Usually, this type of stochastic acceleration is closely related to particle pitch angle scattering or parallel diffusion. Given the values of the parallel diffusion coefficient inferred from the observations of cosmic ray modulation or other energetic particle phenomena in the heliosphere, stochastic acceleration by small-scale waves is much slower than acceleration by shock waves and it is also much slower than adiabatic cooling by the expansion of the solar wind; thus it is considered as inefficient for producing heliospheric energetic particles or for the modulation of cosmic rays. Another type of stochastic acceleration occurs when particles go through random compressions or expansions due to large-scale plasma motion. This acceleration mechanism could be very fast when the correlation time of the fluctuations in plasma compression is short compared to the diffusion time. Particle acceleration by an ensemble of small shock waves or intermittent long wavelength compressible turbulence belongs to this category. It tends to establish an asymptotic p ^?3 universal distribution function quickly if there is no or little large-scale adiabatic cooling. Such a particle distribution will contain an infinite amount of pressure. Back reaction from the pressure is expected to modify the amplitude of plasma waves to an equilibrium state. At that point, the pressure of accelerated particles must remain finite and the accelerated particles could approach a p ^?5 distribution function.     

ATS-6 UCSD Auroral Particles Experiment

The University of California at San Diego (UCSD) Auroral Particles Experiment on the Applications Technology Satellite-6 (ATS-6) consists of five electrostatic charged particle detectors. The features which contribute to the uniqueness of the UCSD data include a rotation capability which often allows sampling very near the direction of the magnetic field, an energy range of five orders of magnitude with a lower extreme of less than 1 eV, and a very large geometric factor which results both from a postenergy analysis electrostatic lens and from the unique ovoidal shape of the analyzing plates. A preliminary look at a subset of UCSD magnetospheric data emphasizes those phenomena which are observed as a result of the new features described. These phenomena include intense magnetic field aligned auroral particles, a persistent and very low energy dusk region enhancement, and low energy 1-10-s fluctuations tentatively identified as Alfven waves.     

Geomagnetically trapped radiation

This review covers the major developments in radiation-belt phenomenology of the past four years (1970–1973). This has been a period characterized by consolidation and refinement of ideas and measurements related to geomagnetically trapped particles. Significant progress has been made in understanding ion and electron pitch-angle distributions within the context of radial diffusion and pitch-angle diffusion, respectively. Comparison of alpha-particle and proton distributions has helped to clarify the relative strengths of known radial-diffusion mechanisms. Careful measurements have indicated the directional flux of cosmic-ray-albedo neutrons, which constitute (through beta decay) a major source of high-energy ( 20 MeV) inner-belt protons. Inclusion of radial-diffusion and geomagnetic-secular effects has brought the theory of the inner proton belt into reasonable agreement with observation. At very lowL values (L 1.2) atmospheric collisions have been found to facilitate the radial transport of 40 keV protons and 2 MeV electrons. The plasmapause has been identified as an important boundary for plasma instabilities (wave-particle interactions) that lead to particle precipitation and red-arc excitation. Suggestions have followed for artificially simulating such plasmaspheric effects by magnetospheric injection of cold barium or lithium plasma.     

Solar modulation of galactic cosmic radiation

In this review an attempt is made to present an integrated view of the solar modulation process that cause time variation of cosmic ray particles. After briefly surveying the relevant large and small scale properties of the interplanetary magnetic fields and plasma, the motion of cosmic ray particles in the disordered interplanetary magnetic fields is discussed. The experimentally observed long term variations of different species of cosmic ray particles are summarised and compared with the theoretical predictions from the diffusion-convection model. The effect of the energy losses due to decelaration in the expanding solar wind are clearly brought out. The radial density gradient, the modulation parameter and their long term variation are discussed to understand the dynamics of the modulating region. The cosmic ray anisotropy measurements at different energies are summarised. At high energies (E 1 GeV), the average diurnal anisotropy is shown to be energy independent and along the 18.00 h direction consistent with their undergoing partial corotation with the sun. The average semi-diurnal anisotropy seems to vary with energy as E ⁺¹ and incident from a direction perpendicular to the interplanetary field line, consistent with the semi-diurnal component being produced by latitudinal gradients. Both the diurnal and semi-diurnal components are shown to be practically time invariant. On a day to day basis, however, the anisotropy characteristics such as the exponent of variation, the amplitude and the phase show very high variability which are interpreted in terms of convection and variable field aligned diffusion due to the redistribution of the galactic cosmic ray density following transient changes in the interplanetary medium. The anisotropy observation at low energies (E 100 MeV) are, however, not explained by the theory.The rigidity dependence and the anisotropies during short term variations such as Forbush decreases are discussed in terms of the proposed field models for the interplanetary field structure and are compared with the observed rigidity dependence of long term variations. The data pertaining to the 27 day corotating Forbush decreases and their association with enhanced diurnal variation are also presented. The relationship between the energetic storm particle events which are caused by the acceleration of particles in the shock fronts and the Forbush decreases which are caused by the exclusion of galactic particles by the enhanced field structure in the same fronts are clearly brought out. Thus the recurrent increases at low energies and recurrent decreases at high energies may both be caused by the field structure in the shock front. In conclusion, the properties of the very short period fluctuations (18–25 cph) are summarised.     

Pickup Ion Acceleration at the Termination Shock and in the Heliosheath

We discuss pickup ion acceleration and transport near the solar wind termination shock from the perspective of their spectral, spatial, and pitch-angle distributions. Our study is performed in the framework of a recently developed anisotropic transport model based on a Legendre polynomial expansion technique. Voyager 1 LECP angular distributions of 1 MeV protons, represented in the form of an expansion in spherical harmonics in the frame aligned with the measured interplanetary magnetic field, are used as benchmarks for our theory. We find the observed distributions consistent with our model predictions for particle acceleration and reflection at a highly oblique shock wave. It is shown that first-order (field aligned) anisotropy is a measure of shock obliquity while the second-order (transverse) anisotropy reflects the energy dependence of the particle scattering mean free path. We also discuss the role of enhanced scattering and momentum diffusion on the spectral properties of energetic charged particles.