Transient beam loading and rf power evaluation for future circular colliders

Abstract

Interaction of the beam with the fundamental impedance of the accelerating cavities can limit the performance of high-current accelerators. It can result in a significant variation of bunch-by-bunch parameters (bunch length, synchronous phase, etc.) if filling patterns contain gaps that are not negligible compared with the cavity filling time. In the present work, this limitation is analyzed using the steady-state time-domain approach for the high-current option (Z) of the future circular electron-positron collider and for the future circular hadron-hadron collider. Mitigation of transient beam loading by direct rf feedback is addressed with evaluation of additional required generator power.

Beam gap transient analysis and mitigations in high-current storage rings for an electron-ion collider

“…As shown in [22,23] for the case of constant cavity voltage, the cavity phase modulation that minimizes the klystron power is given by…”

“…where F b is the relative bunch form factor [25], ϕ b is the beam stable phase (electron machine convention), and ω rf is the rf angular frequency. As shown in [23], the constraint on the cavity voltage results in excessive required power when the stable phase differs from π=2. Therefore, a tradeoff exists between some modulation of the cavity voltage and the available rf power, for the electron ring.…”