The stability of charged-particle motion in sheared magnetic reversals

We consider the motion of charged particles in a static magnetic reversal w ith a shear component, which has application for the stability of current s heets, such as in the Earth's geotail and in solar flares. We examine how t he topology of the phase space changes as a function of the shear component b(y). At zero b(y), the phase space may be characterized by regions of sto chastic and regular orbits (KAM surfaces). Numerically, we find that as we vary b(y), the position of the periodic orbit at the centre of the KAM surf aces changes. We use multiple-timescale perturbation theory to predict this variation analytically. We, also find that for some values of b(y), all th e KAM surfaces are destroyed owing to a resonance effect between two timesc ales, making the phase space globally chaotic. By investigating the stabili ty of the solutions in the vicinity of the fixed point, we are able to pred ict for what values of b(y) this happens and when the KAM surfaces reappear .