Hamiltonian formalism in the problem on the modification of the current density profile during the development of tearing instability in a tokamak

The formation of a magnetic island as a result of tearing instability can be interpreted as the bifurcation of an axisymmetric equilibrium configuration at which nested magnetic surfaces are preserved. The modification of the current density profile due to such bifurcation is studied using the Hamiltonian formalism. In the case of a long narrow island, the gradient profile changes to a profile with an extremum on the axis of the magnetic island.