Identification of symmetry breaking and a bifurcation sequence to chaos insingle particle dynamics in magnetic reversals

Regular and stochastic behaviour in single particle orbits in static magnet ic reversals have wide application in laboratory and astrophysical plasmas and have been studied extensively. In a simple magnetic reversal of the for m B = B-0(f(z), 0, b(1)) with an odd function f(z) providing the reversing field component and a constant bl providing linking field component, the sy stem has three degrees of freedom but only two global (exact) constants of the motion, namely the energy, h, and the canonical momentum in the y-axis, P-y. Hence, the system is non-integrable and the particle motion can, unde r certain conditions, exhibit chaotic behaviour. Here we consider the dynam ics when a constant shear field, bz, is added so that B = B-0(f(z), b(2), b (1)). In this case, the form of the potential changes from quadratic to vel ocity dependent. We use numerically integrated trajectories to show that th e effect of the shear held is to break the symmetry of the system so that t he topology of the invariant tori of regular orbits is changed. This has se veral important consequences: (1) the change in topology cannot be transfor med away in the case of b(2) not equal 0 and hence the system cannot be tra nsformed back to the more easily understood shear free case (b(2) = 0); (2) invariant tori take the form of nested Moebius strips in the presence of t he shear field. The route to chaos is via bifurcation (period doubling) of the Moebius strip tori. (C) 2000 Elsevier Science B.V. All rights reserved.