Journal ArticleDOI
Green's theorem and Green's functions for the steady-state cosmic-ray equation of transport
G. M. Webb,L. J. Gleeson +1 more
TLDR
In this paper, the spherically-symmetric steady-state cosmic-ray equation of transport in interplanetary space was developed for the Spherically Symmetric Stochastic Equation of Transport (SSTEOT).Abstract:
Green's Theorem is developed for the spherically-symmetric steady-state cosmic-ray equation of transport in interplanetary space. By means of it the momentum distribution functionFo(r,p), (r=heliocentric distance,p=momentum) can be determined in a regionra≤r≤rbwhen a source is specified throughout the region and the momentum spectrum is specified on the boundaries atraandrb. Evaluation requires a knowledge of the Green's function which corresponds to the solution for monoenergetic particles released at heliocentric radiusro, Examples of Green's functions are given for the casera=0,rb=∞ and derived for the cases of finiteraandrb. The diffusion coefficient κ is assumed of the form κ = κo(p)rb. The treatment systematizes the development of all analytic solutions for steady-state solar and galactic cosmic-ray propagation and previous solutions form a subset of the present solutions.read more
Citations
More filters
Journal ArticleDOI
Reviews - Eigenfunction Expansions Associated with Second-Order Differential Equations. By E. C. Titchmarsh Pp. 175. 20s. 1946. (Oxford University)
Journal ArticleDOI
A perturbation approach to cosmic ray transients in interplanetary space
Ping Ping Chih,Martin A. Lee +1 more
TL;DR: In this article, a perturbation approach is used to model the linear response of the cosmic ray distribution as a function of perturbations in the solar wind transport parameters, i.e., velocity, drift velocity and the diffusion tensor, which are additive.
Journal ArticleDOI
A general time-dependent stochastic method for solving Parker's transport equation in spherical coordinates
TL;DR: In this paper, the authors presented a 3D stochastic approach for solving Parker's transport equation with time dependence in 3D, evolving from their 3-D steady state approach, which is valid for any type of heliospheric magnetic field, although they choose the standard Parker field to illustrate the steps to calculate the transport of galactic cosmic rays.
Journal ArticleDOI
A Hitch-hiker's Guide to Stochastic Differential Equations. Solution Methods for Energetic Particle Transport in Space Physics and Astrophysics
TL;DR: An overview of the recent history of stochastic differential equations (SDEs) in application to particle transport problems in space physics and astrophysics is given in this paper, where the authors present a helpful working guide to the literature and at the same time introduce key principles of the SDE approach via "toy models".
Journal ArticleDOI
Theory and Modeling of Galactic Cosmic Rays: Trends and Prospects
TL;DR: In this paper, past and future trends in the theory and modeling of galactic cosmic rays in the heliosphere, and select some of the outstanding issues where future progress is anticipated are discussed.
References
More filters
Journal ArticleDOI
Handbook of Mathematical Functions
Book
Table of Integrals, Series, and Products
TL;DR: Combinations involving trigonometric and hyperbolic functions and power 5 Indefinite Integrals of Special Functions 6 Definite Integral Integral Functions 7.Associated Legendre Functions 8 Special Functions 9 Hypergeometric Functions 10 Vector Field Theory 11 Algebraic Inequalities 12 Integral Inequality 13 Matrices and related results 14 Determinants 15 Norms 16 Ordinary differential equations 17 Fourier, Laplace, and Mellin Transforms 18 The z-transform
Journal ArticleDOI
The passage of energetic charged particles through interplanetary space
TL;DR: In this article, a general expression for the particle diffusion coefficient kij, including both scattering in magnetic irregularities and systematic pressure drifts, was derived from the condition that energetic solar particles in interplanetary space random walk in the irregularities in the large-scale inter-planetary magnetic field, and the observed fields show that the diffusion coefficient is of the order of 1021-1022 cm2/sec.
Related Papers (5)
On the convection, diffusion, and adiabatic deceleration of cosmic rays in the solar wind
J. R. Jokipii,Eugene N. Parker +1 more