Longitudinal stability in multi-harmonic accelerating cavities

Accelerating cavities that excite multiple modes at integer harmonics of the fundamental frequency can potentially be used to limit the effects of rf breakdown and pulsed surface heating at high accelerating gradients. Understanding the longitudinal stability and the acceptance of such a cavity is important to their development and use. The general Hamiltonian for longitudinal stability in multi harmonic cavities is derived and the particle dynamics are explored.