Phase space distribution of particles near an isolated difference resonance

The phase space distribution of beam particles near an isolated difference resonance was studied. The numerical simulation has shown that the distribution can quickly settle down to a final state if its initial state is Gaussian. The final state can be treated as a stationary state as long as the high order fluctuation can be neglected. From the Liouville equation, the emittances of beam particles are calculated approximately. There is a good agreement between analytical and numerical results.<>