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

2. 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

3. 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.

4. 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.

5. 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.

6. 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.

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

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

9. 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.)