1. Bunch Tiltmeter Steve Smith SLAC Snowmass July 16, 2001 Update date
Multibunch (ATF) results)
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More details of cavity BPM scheme
Bunch Tiltmeter
Snowmass July 16, 2001

2. 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

3. Response of Cavity BPM to Point ChargeQ d

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

5. 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 )

6. Example Bunch length st = 200 mm/c = 0.67 ps Tilt tolerance d = 200 nm
Cavity Frequency F = 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 * 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?

7. 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 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

8. 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

9. 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!

10. 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.

12. Cavity BPM Calculation