Steady-state cosmic-ray propagation in interplanetary space

This thesis is a theoretical investigation of the steady-state propagation of galactic and solar cosmic-rays in the inter-planetary medium. The study is carried out by means of analytic, steady-state solutions of the equation of transport for cosmic-rays in the interplanetary medium, including the effects of convection, diffusion and energy changes. In Chapters 2-6, analytic monenergetic-source and mono-energetic-spectrum solutions of the steady-state equation of transport are obtained and these solutions are related to previously obtained analytic solutions. In Chapter 7, three proofs are given of a result first noted by Gleeson (1972), for the mean-time-rate-of-change of momentum for cosmic-rays in interplanetary space, reckoned for a fixed volume in a reference frame fixed in the solar system. Also discussed in Chapter 7, are the proper role of: (i) the adiabatic deceleration momentum rate <¬¿œÄv=>\\(_{ad}\\) introduced by Parker (1965), and (ii) the mean-time-rate-of-change of momentum, <¬¿œÄv='>, of particles with momentum p' specified relative to the solar wind frame of reference, and with position ¬¿œÄvº specified in the fixed frame of reference. The physical significance of the momentum rate <¬¿œÄv='> has not been understood previously, and it is derived (for the first time) in Appendix G, from the transformation of momentum between the fixed and solar wind frames of reference. It is shown that Parker (1965) and Jokipii and Parker (1970) have misinterpreted the energy change term in the comic-ray continuity equation associated with <¬¿œÄv='>, due to an insufficient distinction between the two momentum rates <¬¿œÄv=>\\(_{ad}\\) and <¬¿œÄv='>. The cosmic-ray particle flow and momentum changes are related to each other via the continuity or transport equation. In order to elucidate this relation we introduce the concept of a flow line in position momentum space. The flow line is defined as the curve whose tangent in position momentum space is given by the ratio of the stream-ing velocity to the mean-time-rate-of-change-of-momentum in the fixed frame of reference. In Chapters 8-10, the solutions developed in Chapters 2-6, are used to verify most of the principal known features of steady-state propagation in the solar cavity. Some of these are: the energy changes; the relative exclusion of low energy galactic particles; the origin within the galactic spectrum of particles of given kinetic energy at 1 A.U. say; and the flow of particles in the solar cavity. Flow lines for monoenergetic galactic and solar comic-rays are con-structed by using the monoenergetic-source and monowlergetic-spectrum solutions of the equation of transport derived in Chapters 2-6. The flow lines show, in some detail, the radical differences in the energy changes and flow of galactic and solar cosmic-rays. In brief, Chapter 8 deals with galactic cosmic-ray propagation, Chapter 9 deals with the propagation of monoenergetic solar cosmic-nays, and Chapter 10 concerns the propagation of galactic cosmic-rays for a special model In which a monoenergetic spectrum of particles is specified at the boundary of the solar cavity which is located at a finite distance from the sun.