Review of dynamic aperture studies. Yiton Yan SLAC. Dynamic aperture (DA) studies. tracking Default method: symplectic element by element tracking – however, attention will be more on nonlinear maps. Taylor-map tracking – accurate, but not exactly symplectic
But 10th-order Taylor map tracking shows biased artificial diffusion due to not syplectic.
Can be trasnferred back to Taylor map with one-order (or more orders) higher
The 10th-order Taylor map is re-expanded to the 11th-order Taylor map and works!
Direct iteration will do.
Very elegant idea. Very fast. However, Spurious terms present unknown accuracy concern
Symplectic integrator is then used for separating the integrable polynomials.
Lower homogeneous order terms uses higher order symplectic integrator while higher homogenous order terms uses lower order symplecticintegrator or even just separate them.
Computation time is slower than minimized-term Irwin factorization. However, it is more naturally close to the original Lie map and therefore generally less concerns about accuracy.
This is a goal-moving soccer game
nPB converge very fast.
Not exactly symplectic.
OK for PEP-II HER and LER tracking
1000 turns are needed for PEP-II due to damping
otherwise the direct dynamic aperture optimization is not analytical and so must use GA which usually take longer time.
All done. Thanks.