Minimizing longitudinal distortion in a nearly isochronous linear nonscaling fixed-field alternating gradient accelerator

Linear nonscaling FFAGs (fixed-field alternating gradient accelerators) are machines that use linear magnets to achieve an extremely large energy acceptance (generally a factor of 2 or more). This paper examines the longitudinal dynamics in such a machine, focusing on the longitudinal acceptance, the phase space area that is transmitted without excessive distortion. The paper shows how to compute the distortion in two ways: computing the emittance growth, and computing the distortion of an initial ellipse from an elliptical shape. The paper will describe a model for the longitudinal dynamics in a linear nonscaling FFAG, show how to compute the longitudinal distortion in such a machine using a Dragt-Finn factorization, examine the accuracy of the calculation, and describe how longitudinal acceptance can interact with other performance criteria for an FFAG.