• 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).

• S.-Y. Lee, S. Breitzmann
  IUCF, Bloomington, Indiana
• K.Y. Ng
  Fermilab, Batavia, Illinois

Passive ferrite inserts were used to compensate the space charge impedance in high intensity space charge dominated accelerators. We study the narrowband longitudinal impedance of these ferrite inserts. We find that the shunt impedance and the quality factor for ferrite inserts are inversely proportional to the imaginary part of the permeability of ferrite materials. We also provide a receipe for truly passive space charge impedance compensation and, at the same time, avoiding the narrowband microwave instabilities.

• M. Bai, H. Huang, W. Mac Kay, V. Ptitsyn, T. Roser, S. Tepikian
  BNL, Upton, Long Island, New York
• S.-Y. Lee, F. Lin
  IUCF, Bloomington, Indiana

Siberian snakes now become essential in the polarized proton acceleration. With proper configuration of Siberian snakes, the spin precession tune of the beam becomes $\frac{1}{2}$ which avoids all the spin depolarizing resonance. However, the enhancement of the perturbations on the spin motion can still occur when the betatron tune is near some low order fractional numbers, called snake resonances, and the beam can be depolarized when passing through the resonance. The snake resonances have been confirmed in the spin tracking calculations, and observed in RHIC with polarized proton beam. Equipped with two full Siberian snakes in each ring, RHIC provides us a perfect facility for snake resonance studies. This paper presents latest experimental results. New insights are also discussed.

• 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).

• A.P. Shishlo, S.M. Cousineau, V.V. Danilov, S. Henderson, J.A. Holmes, Y. Sato
  ORNL, Oak Ridge, Tennessee
• S.-Y. Lee
  IUCF, Bloomington, Indiana
• R.J. Macek
  LANL, Los Alamos, New Mexico

The results of numerical electron-cloud simulations for long-bunch proton beams in accumulator rings are presented and compared with data from the Proton Storage Ring at LANL. The frequency spectra and growth rate of proton-bunch transverse instabilities are studied as functions of the RF cavity voltage, external magnetic fields, beam pipe surface properties, and other factors. We used the recently developed electron-cloud module in the ORBIT code. The model includes a fully self-consistent coupled treatment of the "proton bunch – electron-cloud" dynamics and the multipacting process with a realistic secondary emission surface model. Realistic lattices and proton bunch distributions are used. The efficiency of electron-cloud instability suppression has also been studied using a new ORBIT model.