A Method of Transfer Maps for Linear and Nonlinear Beam Elements

Transfer matrix methods are widely used to calculate properties of particle orbits as they pass through linear beam elements such as drif t spaces, bending magnets, and quadrupoles. A new method of "transfer maps" has been developed to also include nonlinear transformations that result from nonlinear beam elements such as sextupoles, octupoles, etc. The method of transfer maps therefore provides a complete theory of beam transport through both linear and nonlinear elements. In particular, it is possible to use transfer maps in the context of circular machines to study tune shifts, structure resonances, stop band widths, emittance growth rates, etc. Consequently, the method of transfer maps provides an alternative to the method of Hamiltonian perturbation theory usually employed for this purpose.