Numerical construction of the Poincare map, with application to accelerators

摘要

We show how to construct a symplectic approximation to the Poincar(prime)e map, using data from a symplectic integrator. We illustrate by producing a full-turn map for a realistic model of the Large Hadron Collider. Mapping of one turn is typically faster by a factor of 60 than direct integration. This allows one to follow orbits over times comparable to the required storage time of the beam, on a workstation computer. Fast mapping also allows the construction of quasi-invariant actions, which aid in estimates of long-term stability.