Stochastic acceleration of solar cosmic rays in an expanding coronal magnetic bottle

Several key features of the coronal propagation of solar cosmic rays have previously been explained by a ''magnetic bottle'' model proposed by Schatten and Mullan. The major apparent difficulty with that model is that expansion of the closed bottle might have a severe cooling effect on the cosmic rays trapped inside. In the present paper, we examine this difficulty by applying the equation for stochastic acceleration to an expanding bottle. Following our earlier suggestion, the scattering centers are taken to be small-scale magnetic inhomogeneities which are present in the corona prior to the flare, and which are set into turbulent motion when a flare-induced shock passes by. We identify the inhomogeneities with the collapsing magnetic neutral sheets discussed by Levine in the context of normal coronal heating. We find that the acceleration efficiencies can indeed be high enough to offset expansive cooling: within the time intervals that are typically available for closed bottle evolution (1000--3000 s), protons can be accelerated from 1 keV to 100 MeV and more. Our results indicate that the flux of particles which are accelerated to (say) 100 MeV is very sensitive to shock speed if this speed is less than about 103 km s-1