Bunch Tiltmeter Steve Smith SLAC Snowmass July 16, 2001 Update date Multibunch (ATF) results) Chip status Delete costs Get better drawing of cavity More details of cavity BPM scheme Bunch Tiltmeter Snowmass July 16, 2001

BPM Sensitive to Bunch Tilt Observation at ASSET: BPM Cavity power vs. beam position has minimum which depends on bunch tilt There is a small tilt signal in quadrature with position signal Add to other signals

Response of Cavity BPM to Point Charge Q d

Response of BPM to Tilted Bunch Centered in Cavity q q/2 Treat as pair of macroparticles: d/2 d/2 st q/2

Tilted bunch Point charge offset by d Centered, extended bunch tilted at slope d/st Tilt signal is in quadrature to displacement The amplitude due to a tilt of d/s is down by a factor of: with respect to that of a displacement of d (~bunch length / Cavity Period )

Example Bunch length st = 200 mm/c = 0.67 ps Tilt tolerance d = 200 nm Cavity Frequency F = 11.424 GHz Ratio of tilt to position sensitivity ½ft = 0.012 A bunch tilt of 200 nm / 200 mm yields as much signal as a beam offset of 0.012 * 200 nm = 2.4nm Need BPM resolution of ~ 2 nm to measure this tilt Challenging! Getting resolution Separating tilt from position Use higher cavity frequency?

Cavity BPM Parameters nm Parameter Value Comments Dipole frequency 11.4 GHz   Monopole frequency 7.17 GHz Cavity Radius 16 mm Wall Q ~6000 Ignoring beam duct, etc Cavity coupling  = 2 Loaded Q 2000 Bandwidth 6 MHz Beam aperture radius 6 mm Sensitivity 6 mV/nC/nm Bunch charge 1010 e- Per bunch Signal power @ 1mm -28 dBm Peak power Decay time 56 ns Required resolution  = 2 nm Noise Figure Budget 25 dB For  = 2 nm, thermal only Wakefield Kick 0.5 volt/pC/mm Long range Structure wakefield kick 1.8 volt/pC/mm Per structure Short-range wakefield ~1/200th of structure

Cavity Comments Signal adequate Wakefields OK Beam centering tolerance 1/10th of sturctures May want higher frequency Better position resolution More favorable tilt / position sensitivity ratio

Position-Tilt Discrimination Phase-sensitive detection Position jitter or dithering measures phase of position signal Quadrature part of signal is tilt + background One phase of residual common mode RF interference/leakage The higher the frequency the better!

What’s Next? Simulate signal, background Optimize cavity Does this sensitivity to bunch tilt lead to increased sensitivity in an RF bunch length monitor? Transverse cavity upstream of tilitmeter Titlemeter measures slope*bunch length Transverse cavity, detuned by maybe 8 MHz, provides internal calibration of tiltmeter.

Cavity BPM Calculation