  Hamiltonian dynamics has been applied to study the slip-stacking dynamics.
The canonical-perturbation method is employed to obtain the second-harmonic
correction term in the slip-stacking Hamiltonian. The Hamiltonian approach
provides a clear optimal method for choosing the slip-stacking parameter and
improving stacking efficiency. The dynamics are applied specifically to the
Fermilab Booster-Recycler complex. The dynamics can also be applied to other
accelerator complexes.
