Charged Particle Beam Transport Using Lie Albegraic Methods

Methods have recently been developed enabling one to describe charged particle beam transport in terms of a Lie algebraic representation. We show how this formulation may be applied to the problem of computing transfer maps (including aberrations) for the beam-line elements common in accelerator physics. In addition, explicit calculations are carried out for a variety of common elements including drift sections, static magnetic dipole, quadrupole, and sextupole lengths, and dynamic sectons such as bunchers. The resultant mappings are displayed, and provide a succinct basis for efficient numerical computation of charged particle beam behavior during transport.