Study of Transient Ripple in Synchrotron

Beam ripples are one of the most important issues both in designs and operations of proton synchrotrons, and their magnitude should be suppressed in the order of 1e-6 to achieve stable beam accelerations. Despite various investigations, however, the sources of beam ripples are not sufficiently clarified yet. In this paper, ripples generated as transient responses in synchrotron magnet circuits are studied. A magnet circuit is modeled with an idealized current source with no ripples. When the ideal ramp pattern current is applied to the magnet circuit, the ripples intrinsically occur as oscillations among circuit inductance and capacitance, so-called LC oscillations. The ripples excited at the load circuits, which include magnets and interconnections, are obtained analytically and numerically. The circuit parameters of the magnets and the interconnections strongly affect to the intrinsic ripple amplitudes. The theoretical and empirical formulae for ripple amplitude estimation are also discussed.