The ANSYS calculations of the cantilever (20tx100wx695Lmm^{3}) and the both-end
support system with a single plate (case 0; 10tx50wx1520L mm^{3}) have very good
agreements with measurements on resonant(eigen) frequencies at 3 - 1000Hz.
The agreements can be quantified by Modal Assurance Criteria (MAC) values, where the MAC
values are evaluated on each grid of measured and calculated resonant frequencies.
Looking at the MAC values in details, they has least magnitude at the twisting oscillation
mode.
At the same time, damping ratios(D) were also obtained by resonant shapes,
i.e. D=(f1-f2)/2/fn, where FFT-powers decreases at f1 and f2 by 1/sqrt(2) from a resonant
peak(fn). The first modes have the damping ratios of 1.68% and 0.11% for the cantilever and
the case-0, respectively.

In addition to the case-0, two more different structures were studied for the two end support.
These structures have two cantilevers connecting with thinner plates in order to simulate
the support tube in the JLC detector.
First case (case-1) used two plates of 5t x 70w x 200L mm^{3} bolted to the
cantilevers. The two plates can be "mechanically" equivalent to a single plate of
27tx70wx200L mm^{3}. So, the calculation assumed such a plate in the case-1.
Measurements have additional resonant patterns compared to the calculation which
resembles the case-0.
The second case (case-2) used a plate of 1tx98wx200L mm^{3}. Although the
calculation shows more resonances than the case-0 and the comparable number of resonances
to measured one, the resonant shapes were very different except for the 1st and 2nd modes.
For these two cases, the two cantilevers shows independent oscillations as many as
the cantilever support.

In conclusions, our models of case-1 and -2 in calculations are inadequate partially due to difficulties of putting precise geometries in the ANSYS. However, we observed that thinner plates connecting between two cantilevers were not so rigid compared with that of the case-0.

The system comprises a fast position monitor (BPM), a kicker and a feedback regulator. The BPM and kicker are located at 4m downstream and upstream of IP in the same side. So, the round-trip time of flight to the IP is 27nsec. The cable delay between the BPM- and kicker- system is 6nsec.

The BPM is a conventional stripline-type of 20mm diameter, 10cm length and 4.4mm width, and
it is a 50 Ohm line. Using 714MHz bandpass filter and lowpass-filter, an output rise time of
less than 3 nsec and position resolution of sub-micron level can be achieved. Tolerable
imbalances of intercepted spray into the striplines are on the order of
10^{5} particles per bunch.

The kicker has curved striplines at a 6mm radius (12mm full gap) and a length of 75cm (round
trip time of 5nsec). The step response of the kicker is a linear ramp with 0-100% rise time
of 5 nsec. The necessary drive voltage is listed to be 250mV/nm,
which is probably for +/- 250mV applied to top and bottom
striplines and two kickers for electron and positron beams,
since 0.25x2x0.75/12x10^{-3}x2/250x10^{9}=1nm.

The feedback regulator must consider a non-linear character of beam-beam deflection versus the large beam-beam offsets and the round trip lag, which may require opposite gain factors, i.e. high and low gains, respectively. The system has been modeled in Simulink, which shows very rapid correction of beam-beam offsets. For an example, a 8nm (~3 sigma) offset can converge to the original position within 42nsec, which is the same recovery time of full luminosity. For a large offset of 100nm in "non-linear" region, the full luminosity can be restorated in 120nsec which means that about 50% luminosity is recovered at 37 sigma offset. The present calculation has not been optimized for a speedup.

Although angle jitters may mimic the beam-beam offset, they can be corrected by steering magnets upstream of IP.

We discussed on a possible geometry of this system at IP for JLC. Three dimensional layout must be necessary.

The 2001 NLC optics has the collimation system of 1.5km length which is 2 times longer than a present one (2002 optics). So, he will update the optics with the 2002 ones.

Configurations of magnets (kind, position, strength etc. ) is available in a home page of the JLC-BDS. These lists shall be reviewed if they are enough informations for background simulations by a group of JLC Beam-Detector Simulation Study.

The next meeting will be on 30 May (Thu.), 2002 13:30 - 15:00 at 3 gokan, 425.