• 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).

• V.S. Kashikhin, D.J. Harding, J.A. John, J.R. Lackey, A. Makarov, W. Pellico, E. Prebys
  Fermilab, Batavia, Illinois

Since its initial operation over 30 years ago, most correction magnets in the Fermilab Booster Synchrotron have only been able to fully correct the orbit, tunes, coupling, and chromaticity at injection (400MeV). We have designed a new correction package, including horizontal and vertical dipoles, normal and skew quadrupoles, and normal and skew sextupoles, to provide control up to the extraction energy (8GeV). In addition to tracking the 15Hz cycle of the main, combined function magnets, the quadrupoles and sextupoles must swing through their full range in 1ms during transition crossing. The magnet is made from 12 water-cooled racetrack coils and an iron core with 12 poles, dramatically reducing the effective magnet air gap and increasing the corrector efficiency. Magnetic field analyses of different combinations of multipoles are included.

• J.R. Lackey, D.J. Harding, J.A. John, V.S. Kashikhin, A. Makarov, E. Prebys
  Fermilab, Batavia, Illinois

The beam from the Fermilab Linac is injected onto a bump in the closed orbit of the Booster Synchrotron where a carbon foil strips the electrons from the Linac’s negative ion hydrogen beam. Although the Booster itself runs at 15Hz, heat dissipation in the orbit bump magnets has been one limitation to the fraction of the cycles that can be used for beam. New, 0.28T pulsed window frame dipole magnets have been constructed that will fit into the same space as the old ones, run at the full repetition rate of the Booster, and provide a larger bump to allow a cleaner injection orbit. The new magnets use a high saturation flux density Ni-Zn ferrite in the yoke rather than laminated steel. The presented magnetic design includes two and three dimensional magnetic field calculations with eddy currents and ferrite nonlinear effects.

• E. Prebys
  Fermilab, Batavia, Illinois

The demands of the Fermilab neutrino program will require the 30 year old Fermilab 8 GeV Booster to deliver higher intensities than it ever has. Total proton throughput is limited by radiation damage and activation due to beam loss in the Booster tunnel. Of particular concern is the insulation in the 96 combined function lattice magnets. This poster describes a study of the potential radiation damage to these magnets from extended running at the planned intensities.

• 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).