Hamiltonian mapping of magnetic reconnection during the crash stage of the sawtooth instability

Since the determination of the magnetic field topology and of the safety factor profile during the crash stage of the sawtooth instability is a difficult problem both theoretically and experimentally, a complementary approach based on a mapping technique usually referred to as the Tokamap [Balescu et al., Phys. Rev. E 58, 951 (1998)] is proposed to reconstruct the stochastic magnetic field evolution. It is shown that this method, when combined with the constraints on the magnetic fluxes provided by the theories of the sawtooth instability, is able to generate poloidal cross sections of the magnetic field topology during the crash phase of the instability that have behavior similar to the experimental ones. The method is applied to both the complete and the incomplete reconnection of the magnetic field.