We discuss the role of neoclassical resistivity and local magnetic shear in the triggering of the sawtooth in tokamaks. When collisional detrapping of electrons is considered the value of the safety factor on axis, q(0, t), evolves on a new time scale, , where τη = 4πa2/[c2η(0)] is the resistive diffusion time, ν* = νe/(3/2ωte) is the electron collision frequency normalized to the transit frequency and = a/R0 is the tokamak inverse aspect ratio. Such an evolution is characterized by the formation of a structure of size around the magnetic axis, which can drive rapid evolution of the magnetic shear and decrease in q(0, t). We investigate two possible trigger mechanisms for a sawtooth collapse corresponding to crossing the linear threshold for the m = 1, n = 1 instability and non-linear triggering of this mode by a core resonant mode near the magnetic axis. The sawtooth period in each case is determined by the time for the resistive evolution of the q-profile to reach the relevant stability threshold; in the latter case it can be strongly affected by ν*.
Bifurcations of the magnetic axis and the alternating-hyperbolic sawtooth