Description
A new analytic model is developed for tearing modes valid over their linear and nonlinear growth, and ultimately their saturation. The model includes full toroidal geometry, encapsulating Glasser-Greene-Johnson effects, accounting for low-n ballooning corrections in a continuous way from the linear to the non-linear stage, while the mode width evolves from the linear resistive layer width associated with the electrostatic potential, to the non-linear magnetic island separatrix width. Bootstrap current effects are also added for completeness. The model allows for sheared toroidal plasma rotation, thus enabling calculation of double tearing modes in realistic tokamak equilibria. Double tearing modes are of great importance for advanced scenario operation, for example in MAST-U, when the minimum of a non-monotonic q-profile drops below m/n=2. A tractable model that accounts for sheared plasma rotation should now available for double tearing modes during the nonlinear regime. In particular this paper aims to develop a significantly modified Rutherford equation for that purpose.