Abstract
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.
Highlights
Revolution x10003, 5, 7, etc., injection turns
Transition-energy loss is visible at the transition energy at about revolution
Since the horizontal beam width is a quadrature of contributions from the betatron motion and the rms offmomentum oscillation, we cannot directly calculate the normalized horizontal emittance unless we can isolate and remove the contributions of the off-momentum contribution
Summary
The measured rms beam profiles and widths are used to deduce the emittances of the beam. We build a realistic lattice model to analyze measured IPM data and deduce the horizontal and vertical emittances and the rms off-momentum width [7,8,9]. The space-charge force of our model is based on the potential derived from a Gaussian beam distribution, where the horizontal and vertical rms beam radii are updated in each revolution. We employ this particle tracking model to evaluate the effects of random errors in dipole, quadrupole, skew-quadrupole fields on the beam emittances.
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