An extension of the theory of kinematic MHD models of collapsing magnetic traps to 2.5D with shear flow and to 3D

Context. During solar flares a large number of charged particles are accelerated to high energies, but the exact mechanism responsible for this is, so far, still unclear. Acceleration in collapsing magnetic traps is one of the mechanisms proposed. Aims. In the present paper we want to extend previous 2D models for collapsing magnetic traps to 3D models and to 2D models with shear flow. Methods. We use analytic solutions of the kinematic magnetohydrodynamic (MHD) equations to construct the models. Particle orbits are calculated using the guiding centre approximation. Results. We present a general theoretical framework for constructing kinematic MHD models of collapsing magnetic traps in 3D and in 2D with shear flow. A few illustrative examples of collapsing trap models are presented, together with some preliminary studies of particle orbits. For these example orbits, the energy increases roughly by a factor of 5 or 6, which is consistent with the energy increase found in previous 2D models.