Emittance measurement and modeling for the Fermilab Booster

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.

Simulations of beam envelope dynamics in circular accelerators

“…10 in Ref. [4], show that the emittance growth arises from linear coupling resonances from random skew quadrupoles.…”

“…COSY INFINITY has also been proposed to expand its code to deal with space charge force [10,11]. A few systematic emittance evolution experiments were done in LINACs [12], and fewer in circular accelerators [4,13]. Systematic measurements and analysis of the emittance evolution with different injection turns at the Fermilab Booster, see e.g., Fig.…”

“…Important candidates for the emittance growth in circular accelerators include the half-integer stop band that can perturb the beam envelope function, the Montague resonance, and other systematic space charge resonances [3][4][5]. Many numerical simulation codes, such as TRACE [6], PARMILA [7], ORBIT [8], WARP [9], etc., were developed to study the mechanism of emittance growth.…”

“…Thus the bunch length change is small [4]. The effect of transverse space charge effect can be approximated by a two-dimensional potential, characterized by the beam sizes σ x and σ z which also depend on s. Combining both the scalar and vector space charge potentials, we find the space charge potential in the Frenet-Serret coordinate system as [20] …”

Influence of chaos on resonance crossings

“…al [1]. However, before extra complications such as sextupole errors and dynamic noise could be introduced, important dynamical phenomena were observed, aided by the new complexity algorithmin the presence of only space-charge and focusing.…”