The Solution to the Magnetohydrodynamic Trigger Problem
The trigger problem in magnetohydrodynamics (MHD) concerns the timescale for the release of a large fraction of the energy in a magnetic eld. The specic problem of the `tokamak sawteeth' is here treated in terms of classical dynamics in potential wells, and can be explained by the appearance of an in exion point in such wells. However, the trigger problem is posed primarily as an abstract mathematical problem, so its solution has to be presented in the same terms. Translating from the physical language of potential wells, triggering is found to be a consequence of homoclinic bifurcation in Hamiltonian dynamical systems.