Weak Chaos in the Plasma of a Fusion Device

It is known that the magnetic field which is used to confine hot plasmas in nuclear fusion devices can be described in Hamiltonian form. The time variable which appears in Hamilton equations is replaced by an angular variable around the torus. Small field errors applied on purpose, or naturally occurring instabilities of the plasma, often break good KAM surfaces and determine the presence of stochastic motion of magnetic field lines. This topic has practical implications, since particles follow magnetic field lines, and, if the former are chaotic, particles are rapidly lost towards the vacuum vessel of the device, and can damage the plasma facing components. From a theory point of view, various models have been applied to describe this experimental situation: the most common is the analysis of the connection length Lc of field lines to the wall, which can be directly compared to camera images of the damage caused by energetic particles hitting the wall of the device. More sophisticated tools have been applied recently, including the Lagrangian Coherent Structures (LCS) [1] and the Poincaré Recurrence Time, which map the presence of more or less chaotic regions inside the plasma [2].