Chaos in trapped particle orbits

An analytic expression is obtained for the threshold for stochastic transport of high energy trapped particles in a tokamak due to toroidal field ripple. The result permits a rapid evaluation of energetic particle loss in general equilibria. The approach to chaos has two limiting cases: island overlap from neighboring precession resonances, and the overlap of bounce resonance webs extending from resonant surfaces. In both cases the physical resonance consists of motion through a distance which is an integer multiple of the field coil separation in one bounce.