Control of stochasticity in magnetic field lines

We present a method of control which is able to create barriers to magnetic field line diffusion by a small modification of the magnetic perturbation. This method of control is based on a localized control of chaos in Hamiltonian systems. The aim is to modify the perturbation (of order epsilon) locally by a small control term (of order E 2) which creates invariant tori acting as barriers to diffusion for Hamiltonian systems with two degrees of freedom. The location of the invariant torus is enforced in the vicinity of the chosen target (at a distance of order E due to the angle dependence). Given the importance of confinement in magnetic fusion devices, the method is applied to two examples with a loss of magnetic confinement. In the case of locked tearing modes, an invariant torus can be restored that aims at showing the current quench and therefore the generation of runaway electrons. In the second case, the method is applied to the control of stochastic boundaries allowing one to define a transport barrier within the stochastic boundary and therefore to monitor the volume of closed field lines.