Higher Order Dispersion and Momentum Compaction in MAD-X/PTC using NormalForm

Dispersion and the momentum compaction factor have been treated since ages in the literature of accelerator physics to first order. Since quite some time dispersion and the momentum compaction factor can be derived via PTC and thereby in MAD-X to arbitrary order (presently hard-wired to fourth order in MAD-X). It was realized that little is known about this high order derivation in the community. This paper attempts to clarify how the higher order momentum compaction factors are derived from first principle allowing for an alternative way to calculate them.