Analytical evaluation of the second order momentum compaction factor and comparison with MAD results

Author

Shan, J.P. ; Peggs, S.G. ; Borgacz, S.A.

Author_Institution

Fermi Nat. Accel. Lab., Batavia, IL, USA

fYear

1993

fDate

17-20 May 1993

Firstpage

74

Abstract

The second order momentum compaction factor α₁ is a critical lattice parameter for transition crossing in hadron synchrotrons and for the operation of quasi-isochronous storage rings, which have been proposed for free electron lasers, synchrotron light sources and recently for high luminosity e⁺e^- colliders. First the relation between the momentum compaction factor and the dispersion function is established, with the “wiggling effect” included. Then an analytical expression of α₁ is derived for an ideal FODO lattice by solving the differential equation for the dispersion function. A numerical calculation using MAD is performed to show excellent agreement with the analytical result. Finally, a more realistic example, the Fermilab Main Injector, is shown not far away from the ideal lattice

Keywords

particle beam diagnostics; Fermilab Main Injector; MAD results; differential equation; dispersion function; free electron lasers; hadron synchrotrons; ideal FODO lattice; numerical calculation; quasi-isochronous storage rings; second order momentum compaction factor; synchrotron light sources; transition crossing; wiggling effect; Compaction; Differential equations; Dispersion; Free electron lasers; Laser transitions; Lattices; Light sources; Ring lasers; Storage rings; Synchrotrons;

fLanguage

English

Publisher

ieee

Conference_Titel

Particle Accelerator Conference, 1993., Proceedings of the 1993

Conference_Location

Washington, DC

Print_ISBN

0-7803-1203-1

Type

conf

DOI

10.1109/PAC.1993.309011

Filename

309011