Autocorrelation is applied to analyze sets of finite-sampling data such as the turn-by-turn beam position monitor (BPM) data in an accelerator. This method of data analysis, called the independent component analysis (ICA), is shown to be a powerful beam diagnosis tool for being able to decompose sampled signals into its underlying source signals. We find that the ICA has an advantage over the principle component analysis (PCA) used in the model-independent analysis (MIA) in isolating independent modes. The tolerance of the ICA method to noise in the BPM system is systematically studied. The ICA is applied to analyze the complicated beam motion in a rapid-cycling booster synchrotron at the Fermilab. Difficulties and limitations of the ICA method are also discussed.
The necessary condition for minimizing the emittance of the three-and multiple-bend achromat lattices is derived. For isomagnetic three-or multiple-bend achromat lattices, the minimum emittance can only be attained if the length of the dipoles is a factor of 3 1/3 longer than that of outer dipoles. For the threeor multiple-bend achromat with equal length dipoles the minimum emittance can also be achieved by increasing the magnetic field of middle dipoles by a factor of ͱ3 larger than that of outer dipoles. The minimum emittance formula for the isomagnetic three-bend achromat with equal length dipole has also been derived.
The vertical-beam emittance in an electron storage ring is mainly determined by two factors: the linear betatron coupling and the spurious vertical dispersion generated by magnet errors. We find that the contribution of spurious vertical dispersion is larger than that generated by the linear betatron coupling. Using the independent component analysis (ICA) method, we develop stop band corrections to reduce the vertical emittance. We demonstrate our method by making ICA and correction to a quadruple-bend achromatic low emittance lattice. Six families of skew quadrupoles can effectively minimize both the vertical dispersion and the linear betatron coupling.
Turn-by-turn beam profile data measured at the Fermilab Booster are studied. Lattice models with experimental accelerator ramping parameters are used to obtain the lattice functions for data analysis. We studied the horizontal and vertical emittance growth behavior in different stages of a booster ramping cycle and its relation to the beam intensity. The transverse and longitudinal components in the horizontal beam width are separated by a fitting model which makes use of the different scaling rules of the beam momentum. We analyze the post-transition horizontal beam size oscillation based on a model where the longitudinal phase-space mismatch has resulted from rf voltage mismatch during the transition-energy crossing. We carried out systematic multiparticle simulation to show that the source of the vertical emittance growth is a combination of the random errors in skew-quadrupole and dipole fields, and the systematic Montague resonance. The effect of random quadrupole field is small for the Fermilab Booster because the betatron envelope tunes are reasonably far away from the half-integer stop band.
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