Energetic particle reservoirs: 1. Derivation of the transport equation.

A transport equation is derived and discussed that describes the post-maximum phase of solar energetic particle (SEP) events, when the combination of nearly scatter-free propagation along field lines and magnetic mirroring inside 1AU with back-scatter beyond 1AU reduces both the field-aligned intensity gradient and field-aligned pitch-angle anisotropy to small values, producing a particle "reservoir". The mathematical de-coupling of parallel and transverse propagation is the key element in this description of "reservoir" transport, which also has applications beyond the description of the decay of SEP events. [ABSTRACT FROM AUTHOR]