Linda told us about the progress of inertial stabilization simulations. Details are here. So far simulations are done for a rigid block with 6 degrees of freedom. Sensors (accelerometers) located on the block can successfully distinguish all 6 modes of motion and the pushers can act on each mode separately. The PID feedback loop was implemented and were able to respond on step like disturbance. These looks nice so far. Next necessary step should include more real characteristic of the sensors with roll-off and corresponding phase-lag at low and high frequency. At the same time proper filtering of the sensor signal should be implemented. The ground motion model should also eventually be incorporated into these tests. Also, the inertial sensor signals should be eventually combined in the simulations with signals that would carry DC information (beam-beam deflection, optical or capacitive references).
Andrei addressed the question of forces that act on a final quadrupole in the inhomogeneous field of detector. To get feeling of scale: as Andrew Ringwall reported, for the PEP-II permanent final quads the net axial force was about 1000 lb because the permeability of the permanent magnet material is about 1.05 and not exactly 1.0. This was not foreseen in PEP-II design, but did not produce much harm since the supports were strong enough.
We need to evaluate this force for NLC case and see is it possible design the system so that it will compensate for the net force while having properties required for inertial stabilization.
Another potential complication arise due to horizontal crossing angle which is about 20 mrad. Since the final quadrupole (regardless, permanent or superconducting) is placed not exactly on axis of the magnetic field, the fringe filed of the detector acting on current in the quad (or the effective current for permanent quad) will produce some uncompensated vertical force Fy. Since Fy=0 if the quad placed on axis, then Fy = F0 x/a and therefore there will be created some coupling of horizontal and vertical motion of the quad. Very rough estimations show that coupling can be large, of the order of 1-10 at 1Hz (decreasing with frequency as 1/f^2). This and similar effects and their possible harm need to be carefully evaluated.
A.Seryi
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November 15, 2000
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