Critical parameters for the nonlinear destabilization of double tearing modes in reversed shear plasmas

To investigate the nonlinear evolution of the double tearing mode (DTM) in reversed magnetic shear plasmas, characterized by a sudden and abrupt growth of the kinetic and magnetic energies, leading to full reconnection, we conduct a systematic study of the parameters based on the numerical resolution of the reduced magnetohydrodynamic equations in slab geometry. By introducing an instability parameter Delta(DTM)', we reveal three regimes for the evolution of the DTM: (1) a linearly stable regime (0 < Delta(DTM)' < Delta(1)'), (2) a linearly unstable regime but leading to the saturation of magnetic islands (Delta(1)' < Delta(DTM)' < Delta(2)') and (3) a linearly unstable regime leading to full reconnection (Delta(2)' < Delta(DTM)'). The critical value Delta(2)' delimiting regimes (2) and (3) corresponds to a critical island width w(c) above which the nonlinear destabilization is triggered. We successfully determine the critical threshold in (x(s), k(y)) space, which is fundamental for the prediction of explosive DTMs, as well as to understand the underlying mechanisms. Here, x(s) and k(y), respectively the distance between the two rational surfaces and the unstable wavenumber, determine the free energy contained in the equilibrium system. Moreover, w(c) calculated at the trigger of regime (3) is found to be independent of resistivity, supporting the idea that the nonlinear destabilization results from a structure-driven instability.