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The data needed in the future for trapped particle modeling are summarized. A short summary of past and future modeling activities and a list of satellite data that have not yet been considered in the modeling efforts is included.
Calculations concerning the pitch-angle diffusion resulting from resonant wave-particle interactions can lead to definitive predictions of equatorial pitch-angle distributions and rates of particle loss as a function of particle energy and L-value. Thus, given simultaneous high-altitude measurements of pitch-angle distributions and low-altitude measurements of precipitating fluxes as a function of energy and L, the importance of proposed wave-particle interactions can be verified or discarded. Since many wave-particle phenomena occur over large spatial and temporal scales, exact simultaneity in longitude and time is not necessary. Simultaneous low and high altitude (preferably nearly equatorial) particle measurements could thus greatly increase our understanding of trapped particles and their effects on the ionosphere. Furthermore, given a verified pitch-angle diffusion mechanism and simultaneous low- and high-altitude measurements, accurate lowto high-altitude mappings of field lines and magnetospheric boundaries (such as the plasmapause) could be obtained.
At a tangential discontinuity between two constant magnetic fields a layer of trapped particles can exist, this work examines the conditions under which the current carried by such particles tends to maintain the discontinuity. Three cases are examined. If the discontinuity separates aligned vacuum fields, the only requirement is that they be antiparallel. With arbitrary relative orientations, the field must have equal intensities on both sides. Finally, with a guiding center plasma on both sides, the condition reduces to a relation which is also derivable from hydromagnetic theory. Arguments are presented for the occurrence of such trapped modes in the magnetopause and for the non-existence of specular particle reflection.
Anomalous LF plasma oscillation by particles trapped in potential well behind satellite applied to ionospheric measurements
Currents of quasi-trapped particles having discontinuities on earths day and night sides
Trapped particle radiation study of selected trajectories for low altitude Skylab missions
Dipole representations of the earth's magnetic field have been found to have insufficient accuracy for the study of magnetically trapped particles. A coordinate system consisting of the magnitude of the magnetic field B, and the integral invariant I has been found to adequately organize, measurements made at different geographic locations. It is shown in the present paper, that a parameter L = f(B,I) can be defined which retains most of the desirable properties of I and which has the additional property of organizing measurements along lines of force. Since the parameter L is the analog of a physical distance in a dipole field (the equatorial radius of a magnetic shell), it is usually found to present fewer conceptual difficulties than the integral invariant I.
Observational and theoretical evidence that the polar cap can expand rapidly enough during the growth phase of a substorm to release geomagnetically trapped particles from previously closed drift shells, enabling the particles to escape into the tail, are examined. Observations show that the moving separatrix can overtake convecting nightside plasma during intervals of polar-cap expansion. Models of this phenomenon suggest that closed nightside field lines can be evaculated of their particle populations, and it is noted that such evacuations can account for the occurrence of energetic-particle bursts in the tail.
We have been assessing the effects of background radiation in low-Earth orbit for the next generation of X-ray and Cosmic-ray experiments, in particular for International Space Station orbit. Outside the areas of high fluxes of trapped radiation, we have been using parameterizations developed by the Fermi team to quantify the high-energy induced background. For the low-energy background, we have been using the AE8 and AP8 SPENVIS models to determine the orbit fractions where the fluxes of trapped particles are too high to allow for useful operation of the experiment. One area we are investigating is how the fluxes of SPENVIS predictions at higher energies match the fluxes at the low-energy end of our parameterizations. I will summarize our methodology for background determination from the various sources of cosmogenic and terrestrial radiation and how these compare to SPENVIS predictions in overlapping energy ranges.
The "Van Allen belts" of the trapped energetic particles in the Earth's magnetosphere were discovered by the Explorer I satellite in 1958. In addition, in 1959, it was observed that UHF radio emissions from Jupiter probably had a similar source -- the Jovian radiation belts. In this paper, the global characteristics of these two planets' trapped radiation environments and respective magnetosphere are compared and state-of-the-art models used to generate estimates of high-energy electron and proton populations - the dominate particles in these environments.
Motion of particles in magnetosphere
Near-forward scattering of an optically trapped 5 m radius polystyrene latex sphere by the trapping beam was examined both theoretically and experimentally. Since the trapping beam is tightly focused, the beam fields superpose and interfere with the scattered fields in the forward hemisphere. The observed light intensity consists of a series of concentric bright and dark fringes centered about the forward scattering direction. Both the number of fringes and their contrast depend on the position of the trapping beam focal waist with respect to the sphere. The fringes are caused by diffraction due to the truncation of the tail of the trapping beam as the beam is transmitted through the sphere.
Three possible sources of particle species important to the energy balance of the magnetosphere are discussed, with special emphasis on particles with different charge-to-mass ratios. Possibilities for various experimental tests are pointed out. Some recent experimental data on geomagnetically trapped alpha particles are compared with relevant results of current theoretical work. An experiment is proposed that is likely to provide quantitative indications for the energization and loss processes affecting ionic particle species in the magnetosphere.
Adiabatic theory of distorted motion of charged particles in geomagnetic field, showing dependence on equatorial pitch angle
The interaction of trapped radiation with the ring of Jupiter is investigated. Because it is an identical problem, the rings of Saturn and Uranus are also examined. Data from the Pioneer II encounter, deductions for some of the properties of the rings of Jupiter and Saturn. Over a dozen Jupiter magnetic field models are available in a program that integrates the adiabatic invariants to compute B and L. This program is to label our UCSD Pioneer II encounter data with the most satisfactory of these models. The expected effects of absorbing material on the trapped radiation are studied to obtain the loss rate as a function of ring properties. Analysis of the particle diffusion problem rounds out the theoretical end of the ring absorption problem. Other projects include identification of decay products for energetic particle albedo off the rings and moons of Saturn and a search for flux transfer events at the Jovian magnetopause.
The equations of motion for a particle in resonance with a small finite amplitude wave are solved approximately, using secularity free perturbation theory. The wave propagates at an arbitrary angle to a uniform background magnetic field in an infinite collisionless plasma. The wave fields include a longitudinal electrostatic component and elliptically polarized transverse electric and magnetic components. The trajectories of trapped and resonant untrapped particles are described, for each of the possible wave-particle resonances. These trajectories are used to construct an estimate of the nonlinear time dependent Landau damping rate of the wave.
Resonant magnetic-moment-violating interactions effect on high energy particle loss from radiation belts determined from quasi-linear diffusion equation
The discovery of a microsignatury of trapped radiation in the Amalthea orbit as detected by Pioneer 11 in a flyby of Juptier in 1974 is reported and its implications for the radial diffusion coefficient in Jupiter's inner magnetosphere are discussed. A low energy telescope registered the absorption of low-energy protons as a function of the magnetic L shell durig inbound and outbound trajectories. Drift velocities of the 1 MeV particles were calculated. No correspondingly heightened effects were observed from high-energy electrons or heavier nuclei. Further analysis of the 0.5-8.7 MeV protons showed data to be consistent erosion of the particle drift shadows by a diffusion process. A limit was calculated for the highest diffusion coefficient value for the 1 MeV protons at the Amalthea orbit. The results indicate that the diffusion is driven by fluctuating electric or magnetic fields.