The topology of guiding center orbits in a linear magnetic cusp

Particle orbits for a linear magnetic cusp configuration, characteristic for magnetic reconnection, are analyzed within the guiding center approximation. A class of particle orbits encircling the magnetic X-line is identified and the orbit phase space partition is obtained and characterized as a function of dimensionless parameters controlling the orbit topology. The large majority of particles are found to be trapped in the direction of the X-line implying large neoclassical corrections to the plasma resistivity. This may be the key in explaining the high rates of collisionless magnetic reconnection observed in nature.