Particle dynamics in 3-D reconnecting current sheets in the solar atmosphere

The orbits of charged particles (electrons and protons), in a Harris-type 3D field topology of a reconnecting current sheet (RCS), are analyzed by dynamical systems methods. The focus is on values of the magnetic and electric fields relevant to RCSs in the solar atmosphere. First, a perturbative form of the equations of motion is used to determine the stability perpendicularly to the plane of reconnection, which is crucial in the efficiency of the RCS as an accelerator. The problem is shown to correspond to a case of "parametric resonance". The orbits are then studied with the complete form of the equations of motion. These can be reduced to a two degrees of freedom Hamiltonian nonlinear system by exploiting the existence of an additional integral of motion besides the energy. The orbits are studied analytically by normal form theory. Regular and chaotic orbits are identified by the use of appropriate Poincare surfaces of section. The kinetic energy gain for escaping particles is calculated as a function of the initial conditions of injection of an orbit in the sheet. Formulae relating the kinetic energy gain to the physical parameters of the sheet and the initial conditions of the orbits are given both for electrons and protons.