Minimizing Chaos During the Reconnection Process G. CORSO, G. ODA and I. L. CALDAS lnstituto de Fisica, (Jniversidade de SBo Paulo, Caixa Postal 66318, 05389-970 Slo Paula. Brazil lAccrpred 7 March lY97) Abstract-Chaos around the separatrices of resonant chains during the reconnection process in Tokamaks with non-monotonic profiles is analysed. To characterize the extension of chaos in the system, we estimate the convergence of the chaotic lines by computing the winding number profiles in the neighborhood of the separatrices. Some simulations were performed and we have detected. for these non-twist mappings, a reduction of chaos during the reconnection process. A theoretical interpretation based on the overlapping of resonance pictures is proposed in order to explain the decrease of chaos. These results may contribute to interpret the recently observed improvement in reversal magnetic shear in Tokamaks. 0 1997 Elsevier Science Ltd 1. INTRODUCTION Reconnection in a phase space is defined as a process where the number and the index of the fixed points remain the same, but the trajectories assume a new arrangement [l-3]. In this paper we focus attention on the relation between the reconnection process and chaos. As we shall see, the stochastic layer diminishes during the reconnection process. We present a theoretical interpretation in order to explain the decrease of chaos during the reconnection based on the overlapping of resonance pictures (ORP). The paper of Chirikov [4] presents a method to obtain an analytical estimate of the transition to chaos established in the ORP. The creation of a stochastic layer can be understood in the Chirikov picture; according to that picture, chaos in nonlinear Hamiltonian systems is originated from overlapping of adjacent resonant island chains in the phase space. Whenever the amplitude of the resonant islands increases, they will become larger and overlap each other. The ORP will be used in order to understand chaos during the reconnection. Two papers have already treated the relationship between reconnection process and chaos. One of these [5] deals with a continuous Hamiltonian that represents a reconnection process, but in this work the reconnection is generated by increasing the amplitude of the islands. As one increases the island amplitude the stochastic layer naturally increases [4], hiding the most important phenomenon. The reconnection picture we use in this paper, contrary to Ref. [5], is that caused by the approximation of the island chains without increasing the amplitude. The other paper [6] deals with a non-twist map and uses the residue criterion to compute the critical value for the destruction of the KAM curves. It is concluded that the transition to chaos in this class of systems is different from the twist maps. In this work we emphasize the behavior of the stochastic layer, keeping the island amplitude constant. The physical reconnection model used in this work is extracted from the magnetic confined plasma context. MHD equilibrium plasmas with central hole current density profiles confined in Tokamaks present reconnection of the magnetic field lines when perturbed by resonant fields. Although these perturbations can be due to natural plasma 1891