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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 todoi:10.1051/0004-6361:20042288 fatcat:xzandtybgrah7kbwg3y6g3wthe