The stability of charged-particle motion in sheared magnetic reversals

We consider the motion of charged particles in a static magnetic reversal with a shear component, which has application for the stability of current sheets, such as in the Earth's geotail and in solar flares. We examine how the 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 stochastic 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 surfaces changes. We use multiple-timescale perturbation theory to predict this variation analytically. We, also find that for some values of b(y), all the KAM surfaces are destroyed owing to a resonance effect between two timescales, making the phase space globally chaotic. By investigating the stability of the solutions in the vicinity of the fixed point, we are able to predict for what values of b(y) this happens and when the KAM surfaces reappear.