Beam Dynamics in NS-FFAG EMMA with Dynamical Maps

The Non Scal­ing Fixed Field Al­ter­nat­ing Gra­di­ent EMMA has a com­pact lin­ear lat­tice. Ef­fect of Fringe Field on the beam has to be stud­ied care­ful­ly. A nu­mer­i­cal mag­net­ic field map is gen­er­at­ed by mag­net mea­sure­ments or mag­net de­sign soft­wares. We de­vel­oped a tech­nique that pro­duces from the nu­mer­i­cal field map, a dy­nam­i­cal map for a par­ti­cle trav­el­ling in the en­tire EMMA cell for a ref­er­ence en­er­gy with­out ac­cel­er­a­tion. Since the beam dy­nam­ics change with en­er­gy, a set of maps have been pro­duce with dif­fer­ent ref­er­ence en­er­gies be­tween 10 and 20MeV. For each ref­er­ence en­er­gy, sim­u­lat­ed tune and time of flight (TOF) have been com­pared with re­sults in Zgoubi - track­ing di­rect­ly through nu­mer­i­cal field map. The range of va­lid­i­ty of a sin­gle map has been in­ves­ti­gat­ed by track­ing par­ti­cle with large en­er­gy de­vi­a­tion. From that, a sen­si­ble ac­cel­er­a­tion scheme has been im­ple­ment­ed.