Signals of cavity BPM come from beam displacement(x), beam tilt(x'), common mode and thermal noise. The signals are proportional to total charge of beam-bunch. The tilt and common mode are out of phase in 90 degree while the displacement is in phase. In general, the tilt should be removed by phase detection, or precise cavity alignment and beam orbit tuning are necessary. The common mode should be cancelled out by 180 degree combiner with two opposite signals. The thermal noise should be minimized by low noise circuit.

The common mode signal can be estimated by an error in a pill-box cavity with outer wall coupling, that is 0.305 lamda_110/ Q_110, where lamda_110 and Q_110 are wave length and Q-value of TM_110 mode. ATF-BPM has an error of 1.65um with lamda_110=0.046 m and Q_110=8500. The 180 deg. combiner has 20~40dB (1/10~1/100) reduction. The phase detection would have additional 20~40dB. Therefore, the error would be 16.5 ~ 0.165nm.

The title signal is proportional to tilt angle and power of bunch length. The ATF beam has an angle jitter of 4 urad, which produces 43nm signal with "scalar" detection. The phase, i.e. vector, detection will provide 20~40dB reduction. Therefore, a tilt mover must be necessary to calibrate the phase detection for proper phase position,

Ultimate resolution must be limited only by thermal noise. However, actual resolution comes from electronics circuit unless noise figure (NF) is zero. A good example is the FFTB cavity BPM called as Shintake BPM. The displacement signal is produced at 25uV/nm/nC accompanied by 9 uV thermal noise with 100MHz band width (BD). Since the electronics has 30dB total gain with 4dB NF, the signal would be 790 uV/nm/nC with noise of 451uV ( 9 x 10^{4/20} x 10 ^{30/20} ). So, the "electronics" error (resolution) would be 0.57nm, while the measured one was 20~30nm. Since a dynamic range of the electronics was 2 V, a measurable range was estimated to be 2.5 um.

Usually the resolution can be estimated by three BPMs aligned linearly. If they are equally spaced with the same resolution (sigma), the resolution of middle BPM is obtained by SQRT(3)/2 sigma, where sigma is projected one.

BPM mover has a role of;

- capture beam into measurable range at high gain, so three BPM's must be moved independently.
- calibrate position response.
- adjust tilt of cavity to beam by phase de-tuning.
- adjust detection phase by minimizing tilt sensitivity.

Specification of the mover is;

- Dynamic range:capture beam within 2.5um (rough mover)
- Position calibration; need 1nm resolution for 2.5 um range (precise mover)
- Tilt tuning and phase tuning: need < 1urad resolution for > 100urad range, assuming initial tilt < 100 urad.

There was a discussion on single and three V-blocks for supporting BPM's. Since the specification requires independent movement of the three BPMs, the three V-blocks must be used.