Detailed magnetic structure and stochastic threshold

Non-linear evolution of reconnection is too slow to explain-by itself-fast phenomena such as internal disruptions in tokamaks or flares in the solar atmosphere. It has been proposed that the change in topology could lead to field line stochastization, and hence to highly increased transport. An important objection to this idea is that the increase of transport coefficients should smoothly follow the amplitude of the perturbation, while the observations show a catastrophic transition. We have shown 1) that the shape of the structures (and not only their size or amplitude) evolve during non-linear evolution 2) that the stochastic threshold can be strongly influenced by the detailed shape. Therefore, sharp transitions can appear during the evolution, due to the combination of these two effects. We will first consider an idealized situation, namely the two-waves problem in slab geometry, for which we will study the effect of the separatrix shape on the stochastic threshold. In the second part, we will present an application to the internal disruption in tokamaks, with an m=1 perturbation in a toroidal magnetic configuration. In the last part, we will discuss possible applications of the studies on shape effects to the behaviour of trapped particles in structures of the solar atmosphere.