Particle Motion in Collapsing Magnetic Traps in Solar Flares. I. Kinematic Theory of Collapsing Magnetic Traps

We present a model of collapsing magnetic traps in magnetic field configurations associated with solar flares. The model is based on a kinematic description of the magnetic field obeying the ideal Ohm's law. The dynamic evolution of the models is given in terms of a time-dependent transformation from Eulerian to Lagrangian coordinates. The transformation can be used to determine the corresponding flow field, the magnetic field, and the electric field from given initial conditions. The theory is formulated for translationally invariant situations, but a fully three-dimensional version is also given. The effect of various transformations and initial conditions is discussed with a view to calculating charged particle orbits in the given electromagnetic fields.