Propagation of solar-flare cosmic rays along corotating interplanetary flux-tubes

The propagation of solar-flare cosmic rays along a corotating spiral mean interplanetary magnetic flux-tube is investigated under a variety of initial, inner and outer boundary conditions, by solving the transport equations numerically. The inner boundary condition is shown to have negligible effects on the redistribution of the cosmic rays in interplanetary space, apart from a proportionality constant. The diffusion coefficients have been classified into type I and type II: for type I the peakalong-spiral stays at a finite heliocentric distance, while for type II it travels to infinity. The time dependence of the anisotropy vector is characteristically different in each type and in the case of type I is a function of the observation point. The general propagation characteristics with a free-escape outer boundary are like those of type I. It is shown that closely exponential decay can be produced without a free-escape boundary. The concept of an ‘equilibrium shape’ at late time is introduced. With a source that decays slowly, a maximum and minimum pair appears in the spatial distribution; the maximum subsequently propagates outward and the minimum inward. The impulsive models given do not reproduce satisfactorily all the observed characteristics of solar burst events and a solar source extended in time appears to be indicated.