V.Vogel presented his idea of IP-BPM (2nm resolution) under large beam divergence (about 300 urad) at the ATF2 focal point.

First, he explained general properties of a cavity BPM with 6426MHz, which has f_010=4.4GHz,Q_ex=2600, f_110=6.426GHz,Q_load=3300 and f_020=10.2GHz, Q_ex=5800. With a 1nm displacement, the peak ratio of P_010(020)/P_110=135(125)dB. Since TM110 (dipole mode of position signal) has a resonant frequency far from those of TM010 and TM020, i.e. +2.2GHz and -3.8GHz, these frequency differences reduce the ratios by 60 and 65 dB, respectively (Frequency filter). The space mode selection of signals further reduce the ratios by 40 and 25dB, respectively, where the magic-T is used for combining signals, i.e. canceling the common/monopole modes. Therefore, the net total gains of TM010 and TM020 are both 35dB, which correspond to +60nm and -60nm, respectively, in the electrical center shift. Further reduction of the common modes can be done with the time filter by using different quality factors; i.e. the time dependence of EXP( - t omega/(2 Q) ), omega=2pi freq. . Another constraint of the Q-value comes from bunch spacing in multi-bunch operation, which will be 150 -300nsec for ILC. In the multi-bunch operation, the Q-values must be smaller for faster damping signals. He also presented the principle of electronics based on the above design considerations.

He proposed a set of cavity-BPMs with nanometer resolution at FP (focal point) of the ATF2. It consists of a reference cavity and two narrow gap cavities with damped cavities for x and y position measurements. Total length is 450mm. The reference cavity measures phase, bunch length and bunch angle/tilt. To compensate a gain-loss due to the narrow gap (2mm, effective 4mm) , beam pipe must be small diameter of 6mm, where necessary length is 250mm with the small pipe. Since this gap is 1/5 of the present cavity-BPMs, the beam angular (divergence) dependence is expected to decrease by 1/5. He estimated the BPM output voltage as a function of frequency ( 4 < f < 14GHz) with this geometry. The peak voltage is at the frequency of about 10GHz, whose magnitude is comparable to thermal noise (band width of 3MHz, 300K), i.e. 1.57uV.

We discussed on his questions for detailed design work in future. In summary, we fixed the following parameters in the meantime;

- (1) Bunch length to be 8mm
- (2) Single bunch operation for the first goal of the ATF2
- (3) Electronics based on digital technique; the cost estimation is necessary with comparison with that of analog circuit, so SLAC will estimate it.
- (4) Dynamic rage can be 10^4, corresponding to 10um/1nm, with mover system, so 14 bit ADC; further reduction will be discussed in future.
- (5) 6mm diameter of beam pipe, 250mm long, to be checked by optics designers (A.Seryi, S.Kuroda, D.Kalinin et.al.) and ask the minimum value.
- (6) For the calibration, three BPMs are preferable in the space of 450mm length, precise x and y movers with about 10nm step, and steering the beam with nanometer level which is also necessary for the Shintake monitor.
- (7) To reduce the thermal noise further, the electronics could be cooled down at liq.N2 temperature.

In order to discuss on some of the above issues, we will have a video meeting on 17th or 24th February, 9-10am Thursday morning in Japanese time. We will also have a meeting in March, i.e. between 3 and 16 March, for the draft design.