Charged-Particle Transport Libraries: ASC/PEM Level-2 Milestone Review [Slides]
Abstract not provided.
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
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Nuclear Data Evaluation Improvements for Charged Particle Transport [Slides]
Abstract not provided.
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
Fokker-Planck equations for charged-particle transport with a discussion of some higher-order effects
A derivation of the Fokker-Planck equation, based on the central limit theorem, is presented which clearly illustrates the conditions for its validity. It is reiterated that previous use of the Fokker-Planck equation in cosmic-ray transport is correct. Higher-order effects associated with magnetic mirroring and field line random walk at low energies are discussed heuristically.
Jokipii, J. R.↗
Analytical description of charged particles transport along arbitrary guiding-field configurations
A new description of focused transport was developed which is valid for arbitrary spatial dependences of both the scattering mean free path and the focusing length. In particular, it describes the supercoherent transition from the coherent modes that occurs when focusing is strong compared to scattering to the diffusive mode that occurs when focusing is weak. Because it specifies the pitch angle distribution in terms of relatively simple functions, the new formulation facilitates not only the detailed interpretation of solar particle events, but also the qualitative understanding of focused transport. In the steady state, it predicts that the angular distribution consists of a highly collimated 'strahl' which is superimposed on an anisotropic 'halo'. This picture provides new insight into observed configurations of steady-state particle fluxes.
Earl, J. A.↗
Analytical description of charged particle transport along arbitrary guiding-field configurations
Focused particle transport is analyzed in terms of partial differential equations which are applicable to arbitrary spatial variations of the mean free path and the focusing length. A distribution function for transport is written in two forms of the Boltzmann equation and a coefficient of spatial diffusion is defined. Changes from a nearly coherent propagation of flare particles in regions of strong focusing near the sun to ordinary diffusion in the outer solar system are described as supercoherent transitions. A solution to the steady state problem is developed and results are presented for a monopolar guiding field configuration with isotropic diffusion gradually giving way to anisotropy in a region suggestive of a collimated beam of particles streaming away from its source.
Earl, J. A.↗
The effect of convection upon charged particle transport in random magnetic fields
In a coordinate system moving with the plasma and random magnetic fields of a wind that blows with constant velocity in the direction of the guiding field, transport of energetic particles is described by a Boltzmann equation which is similar to the one that describes unconvected transport. Although this formulation is mathematically identical to that developed by Luhmann, which refers to the system where the guiding field is static, there are both practical and fundamental reasons to adopt the new approach. It leads to first-order approximate transport equations which are similar to those that apply in the absence of convection. However, these equations are more general than Parker's description of diffusion and convection, for they describe the coherent modes of transport that appear when the mean free path is large compared to the scale length for spatial variations of the guiding field, and they are valid for arbitrary wind velocity. The latter characteristic opens up new possibilities for analyzing particle transport in relativistic flows seen in some astronomical objects.
Earl, J. A.↗
The effect of solar-wind convection on charged particle transport in interplanetary space
In the formulation of focused transport without convection, approximate solutions of the Boltzmann equation are described in terms of small perturbations of its two fundamental steady-state solutions. In the presence of convection, the same approach is applicable, provided that the analysis is carried out in a system moving with the solar wind. The approximate transport equations that apply in this system are very similar to those that apply in the absence of convection. The new equations assume that the wind blows in the direction of the guiding field and is constant in space and time. Nevertheless, these equations are more general than existing formulations, for they retain their validity when the solar wind velocity is large, and they describe the coherent modes of transport that appear when the mean free path is greater than 1 AU. An interesting implication of the new formulation is that coherent disturbances are swept along with the wind. In this respect, they differ from truly scatter-free modes, which are not affected by the wind.
Earl, J. A.↗
Simulation of charged particle transport on the MPP
Computations of cosmic ray transport based upon finite difference methods are afflicted by instabilities, inaccuracies, and artifacts. To avoid these problems, a Monte Carlo formulation was developed which is closely related not only to the finite difference formulation, but also to the underlying physics of transport phenomena. Implementations of this approach are currently running on the Massively Parallel Processor at Goddard, whose enormous computing power overwhelms the poor statistical accuracy that usually limits the use of stochastic methods. In a Monte Carlo simulation of rectilinear transport, the coherent and diffusive effects that appeared are in good quantitative agreement with both finite difference and analytical calculations.
Earl, James A.↗
Stochastic simulation of charged particle transport on the massively parallel processor
Computations of cosmic-ray transport based upon finite-difference methods are afflicted by instabilities, inaccuracies, and artifacts. To avoid these problems, researchers developed a Monte Carlo formulation which is closely related not only to the finite-difference formulation, but also to the underlying physics of transport phenomena. Implementations of this approach are currently running on the Massively Parallel Processor at Goddard Space Flight Center, whose enormous computing power overcomes the poor statistical accuracy that usually limits the use of stochastic methods. These simulations have progressed to a stage where they provide a useful and realistic picture of solar energetic particle propagation in interplanetary space.
Earl, James A.↗
The telegraph equation in charged particle transport
We present a new derivation of the telegraph equation which modifies its coefficients. First, an infinite order partial differential equation is obtained for the velocity space solid angle-averaged phase-space distribution of particles which underwent at least a few collisions. It is shown that, in the lowest order asymptotic expansion, this equation simplifies to the well-known diffusion equation. The second-order asymptotic expansion for isotropic small-angle scattering results in a modified telegraph equation with a signal propagation speed of v(5/11) exp 1/2 instead of the usual v/3 exp 1/2. Our derivation of a modified telegraph equation follows from an expansion of the Boltzmann equation in the relevant smallness parameters and not from a truncation of an eigenfunction expansion. This equation is consistent with causality. It is shown that, under steady state conditions in a convecting plasma, the telegraph equation may be regarded as a diffusion equation with a modified transport coefficient, which describes a combination of diffusion and cosmic-ray inertia.
Gombosi, T. I.↗
Radial evolution of the solar wind turbulence with application to charged particle transport
The proposed research efforts funded by the Pioneer-Venus Guest Investigator Grant to the Bartol Research Institute center on a study of the radial and temporal variation of the large-scale interplanetary magnetic field (IMF) and include a study of the radial variation of the observed north-south asymmetry of the IMF spiral based on the previous results of Bieber (1988). The preliminary results of Bieber demonstrated that at Earth orbit there exists an asymmetry between the yearly average winding angles of toward and away sector fields that can be as large as 10 degrees. The Bieber (1988) analysis employed the NSSDC omnitape data set of 1 AU measurements. When the observed asymmetry is related to the state of the solar magnetic dipole, it is possible to conclude that the IMF north of the heliospheric current sheet is more tightly wound than the IMF spiral south of the current sheet. The average difference in the winding angle as measured over a 21 year period spanning 1965 through 1985 was 3.1 degrees + 1.1 degrees. The Bieber analysis was able to rule-out several possible sources for the observed behavior including a possible asymmetry in the solar wind speed or the observed hemispherical dependence of solar rotation. The object of this research was to extend this previous result to include observations within the inner and outer heliosphere, to examine the radial dependence of the reported asymmetry, and to better resolve the possible source of the observations. The Pioneer-Venus Orbiter has proven to be the perfect monitor for the inner heliospheric observations. It has provided 9 years of continuous observations at a fixed heliocentric distance (except for those periods when the spacecraft was within the region of space where the magnetic field is influenced by the presence of the planet). Comparisons between the 1 AU observations recorded on the NSSDC omnitape and the 0.7 AU observations of the Pioneer-Venus Orbiter have greatly improved our understanding of the IMF winding angle asymmetry. Further comparison with outer heliospheric measurements have proven interesting, although less conclusive.
Smith, Charles W.↗
Charged Particle Transport Code Verification
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Riedel, Sean M.↗
Coherent pulses in the diffusive transport of charged particles`
We present exact solutions to the diffusive transport of charged particles following impulsive injection for a simple model of scattering. A modified, two-parameter relaxation-time model is considered that simulates the low rate of scattering through perpendicular pitch-angle. Scattering is taken to be isotropic within each of the foward- and backward-pointing hemispheres, respectively, but, at the same time, a reduced rate of sccattering is assumed from one hemisphere to the other one. By applying a technique of Fourier- and Laplace-transform, the inverse transformation can be performed and exact solutions can be reached. By contrast with the first, and so far only exact solutions of Federov and Shakov, this wider class of solutions gives rise to coherent pulses to appear. The present work addresses omnidirectional densities for isotropic injection from an instantaneous and localized source. The dispersion relations are briefly discussed. We find, for this particular model, two diffusive models to exist up to a certain limiting wavenumber. The corresponding eigenvalues are real at the lowest wavenumbers. Complex eigenvalues, which are responsible for coherent pulses, appear at higher wavenumbers.
Kota, J.↗
Analysis of a model for transport of charged particles in a random magnetic field
A model for the transport of charged particles in a random magnetic field is a Volterra integrodifferential equation with a long-range kernel. The integrodifferential equation is solved numerically with the method of Bellman, Kalaba, and Lockett (1966). The results are shown to be in excellent agreement with analytical asymptotic results.-
Hanson, F. B.↗
Simple Integral Transport for Charged Particles
A short description of the simple integral transport (SIT) design, framework, and code is given. Explicit details are given for problems with spherical symmetry, as an explanation of the general features in context. This discussion sets up a simple calculation of alpha particle transport in inertial confinement fusion systems, as a proof of concept.
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
BEAMR: An interactive graphic computer program for design of charged particle beam transport systems
A computer program for a PDP-15 is presented which calculates, to first order, the characteristics of charged-particle beam as it is transported through a sequence of focusing and bending magnets. The maximum dimensions of the beam envelope normal to the transport system axis are continuously plotted on an oscilloscope as a function of distance along the axis. Provision is made to iterate the calculation by changing the types of magnets, their positions, and their field strengths. The program is especially useful for transport system design studies because of the ease and rapidity of altering parameters from panel switches. A typical calculation for a system with eight elements is completed in less than 10 seconds. An IBM 7094 version containing more-detailed printed output but no oscilloscope display is also presented.
Leonard, R. F.↗
Radiation Protection Effectiveness of Polymeric Based Shielding Materials at Low Earth Orbit
Correlations of limited ionizing radiation measurements onboard the Space Transportation System (STS; shuttle) and the International Space Station (ISS) with numerical simulations of charged particle transport through spacecraft structure have indicated that usage of hydrogen rich polymeric materials improves the radiation shielding performance of space structures as compared to the traditionally used aluminum alloys. We discuss herein the radiation shielding correlations between measurements on board STS-81 (Atlantis, 1997) using four polyethylene (PE) spheres of varying radii, and STS-89 (Endeavour, 1998) using aluminum alloy spheres; with numerical simulations of charged particle transport using the Langley Research Center (LaRC)-developed High charge (Z) and Energy TRaNsport (HZETRN) algorithm. In the simulations, the Galactic Cosmic Ray (GCR) component of the ionizing radiation environment at Low Earth Orbit (LEO) covering ions in the 1< or equals Z< or equals 28 range is represented by O'Neill's (2004) model. To compute the transmission coefficient for GCR ions at LEO, O'Neill's model is coupled with the angular dependent LaRC cutoff model. The trapped protons/electrons component of LEO environment is represented by a LaRC-developed time dependent procedure which couples the AP8min/AP8max, Deep River Neutron Monitor (DRNM) and F10.7 solar radio frequency measurements. The albedo neutron environment resulting from interaction of GCR ions with upper atmosphere is modeled through extrapolation of the Atmospheric Ionizing Radiation (AIR) measurements. With the validity of numerical simulations through correlation with PE and aluminum spheres measurements established, we further present results from the expansion of the simulations through the selection of high hydrogen content commercially available polymeric constituents such as PE foam core and Spectra fiber(Registered TradeMark) composite face sheet to assess their radiation shield properties as compared to generic PE.
Badavi, Francis F.↗
Transport of charged particles in the earth's magnetosphere
A review of recent data on and conceptions of processes in which high energy particles are transported across magnetic shells in the earth's magnetosphere is presented. The processes discussed include adiabatic processes (with conservation of all three adiabatic invariants of charged particle motion in the magnetic field), diffusion processes (with violation of only the third or third and second invariants), and the so-called fast nonadiabatic processes, which appear to result from the action of strong electric fields.
Shalimov, V. P.↗