• X. Huang, S.-Y. Lee
  IUCF, Bloomington, Indiana
• C.M. Ankenbrandt, E. Prebys
  Fermilab, Batavia, Illinois

The orbit response matrix (ORM) method* is applied to model the Fermilab Booster with parameters such as the BPM gains and rolls, and parameters in the lattice model, including the gradient errors and magnets rolls. We found that the gradients and rolls of the adjacent combined-function magnets were deeply correlated, preventing full determination of the model parameters. Suitable constraints of the parameters were introduced to guarantee an unique, equivalent solution. Simulations show that such solution preserves proper combinations of the adjacent parameters. The result shows that the gradient errors of combined-function magnets are within design limits.

*J. Safranek, Nucl. Instr and Meth. A, {\bf 388}, 27 (1997).

• X. Huang, S.-Y. Lee
  IUCF, Bloomington, Indiana
• E. Prebys, R.E. Tomlin
  Fermilab, Batavia, Illinois

The independent component analysis (ICA)* is applied to analyze simultaneous multiple turn-by-turn beam position monitor (BPM) data of synchrotrons. The sampled data are decomposed to physically independent source signals, such as betatron motion, synchrotron motion and other perturbation sources. The decomposition is based on simultaneous diagonalization of several unequal time covariance matrices, unlike the model independent analysis (MIA),** which uses equal-time covariance matrix only. Consequently the new method has advantage over MIA in isolating the independent modes and is more robust under the influence of contaminating signals of bad BPMs. The spatial pattern and temporal pattern of each resulting component (mode) can be used to identify and analyze the associated physical cause. Beam optics can be studied on the basis of the betatron modes. The method has been successfully applied to the Booster Synchrotron at Fermilab.

*A. Belouchrani et al., IEEE Trans. on Signal Processing, {\bf 45}, 434-444, (1997). **J. Irwin, et al., Phys. Rev. Lett. {\bf 82}, 1684 (1999); Chun-xi Wang, et al., Phys. Rev. ST Accel. Beams} {\bf 6}, 104001 (2003).