Confinement of solar flare cosmic rays to sectors of the corotating solar magnetic field

A method is presented for solving the problem of confining solar flare particles to definite sectors of the solar magnetic field by the use of Laplace transform coordinates. An analysis of solar events dating back to 1956 indicates that the radial diffusion coefficient Dr = Mrrβ is applicable in all cases for a value of β ≃ 1. A lateral diffusion coefficient Dθ = Mθra is postulated for the interplanetary medium with α = 1, 2. It is shown that the ratio of Mθ/Mr must be of the order of 0.01 or less for both power laws in order to confine the particles to an initial ejection angle θ0. The concept of a solar flare, initially confined to a small ejection angle, developing into a large-scale flare later in the event is found to be untenable. The theoretical equations predict that large-scale flares must originate with large ejection angles. The maximum value of the ejection angle is estimated to be about 90°. The theoretical equations predict that the graph of log (nt3/(2-β)) versus 1/t yields a straight line similar to the simple isotropic model, and this is confirmed by the experimental evidence. The theory further predicts the existence of sharp flare boundaries that have been experimentally detected for very low energy flares. It is shown that failure to adopt a suitable boundary condition at the sun in the mathematical solution leads to erroneous results.