Passive harmonic cavities for bunch shortening John Byrd Lawrence Berkeley National Laboratory

Voltage completely reactive (I.e. 90 phase shift w.r.t beam) Basic Idea Use reactive longitudinal focussing from beam-induced voltage in a cavity Use SC cavity so that Low beam losses Higher voltages Use at RF harmonic to get larger dV/dt Try to take advantage of developments in HOM-damped higher frequency SC cavities for rings Beam induced voltage V=jI(R/Q)fr/df Voltage completely reactive (I.e. 90 phase shift w.r.t beam) Original idea inspired by Yong Ho Chin

Basic idea (cont.) Voltage is either +-pi/2 with respect to beam: shortening or lengthening the bunch Limits to harmonic number given by bunch length and by vacuum chamber. Typical for 500 MHz main RF is third harmonic.

How to shorten bunches? Increase main RF voltage Add harmonic voltage Increase number of cells Additional HOMs Additional load on low-mode feedback Increase number of klystrons Further cost (equipment and wallplug) No hardware R&D required Add harmonic voltage Sqrt(n) gain per Volt effective in longitudinal focussing SC passive cavity operates reactively: very little power dissipation Passive operation requires no external power source (I.e. beam is the power source) Significant R&D required (cryo system, cryostat, etc.) Most colliders have existing cryo for solenoid.

Harmonic RF systems (cont.) The bunch shape can be calculated from the resulting distortion of the potential well. In the bunch lengthening case, the single particle motion is highly nonlinear and a large tune spread is introduced. bunch distribution potential potential and bunch distribution for optimal lengthening. The resulting tune spread is ~the original tune.

SC bunch shortening cavity for PEP-II The harmonic voltage can be phased to add the focussing of the main RF. Since the focussing is reactive, a passive (i.e. idling) cavity can be used to generate the voltage. Using 2 SC cells (R/Q=87 Ohms,Q=2e8), proper tuning can shorten the bunches by a factor of 2.5.

Elettra/SLS/CERN/CEA Based on Soleil 352 MHz design 2-cell w/HOM damping in between cells

Bessy-II design Based on Cornell design (cavity actually test prototype) HOM damping on external ferrite loads brazed to beam pipe

Summary Seems to be a feasible alternative for providing longitudinal focussing. Requires little beam/external power Higher harmonics give extra dV/dt Large voltages achievable in SC systems Voltage adjustable with tuning Existing designs for 1500 MHz systems. Cryostat designed Includes HOM damping Effects for large rings need to be evaluated (low mode excitation.)