Simulations of Error-induced Beam Degradation in Fermilab’s Booster Synchrotron*

Individual particle orbits in a beam will respond to both external focusing and accelerating forces as well as internal space-charge forces. The external forces will reflect unavoidable systematic and random machine errors, or imperfections, such as jitter in magnet and radio-frequency power supplies, as well as translational and rotational magnet alignment errors. The beam responds in a self-consistent fashion to these errors; they continually do work on the beam and thereby act as a constant source of energy input. Consequently, halo formation and emittance growth can be induced, resulting in beam degradation and loss. We have upgraded the ORBIT-FNAL package and used it to compute effects of machine errors on emittance dilution and halo formation in the existing FNAL-Booster synchrotron. This package can be applied to study other synchrotrons and storage rings as well. INTRODUCTION Beam loss during the injection is a major concern regarding high-intensity circular accelerators. We investigate this phenomenon in Fermilab’s Booster synchrotron [1]. To do so, we use an upgraded ORBITFNAL 3D object-oriented simulation package [2] to compute beam dynamics calculations in the presence of time-dependent colored noise that is unavoidable in real machines. We find that this noise, coupled selfconsistently to the space-charge force, contributes to beam degradation, halo formation, and beam loss in the Booster synchrotron. This happens despite the fact that the Booster beam is relativistic; even though the spacecharge force is weak, both it and the noise act on the beam over a long time scale. Our motivations for performing realistic simulations involving colored noise and space-charge effects are: • To explore phenomena induced by unavoidable systematic and random machine errors/imperfections in the Booster that may generate continuous emittance growth and halo formation. • To search for other general sources of halo formation in synchrotrons or storage rings. • To augment analytic predictions and inferences arising from simple models [3, 4]. THE FERMILAB BOOSTER SYNCHROTRON The Fermilab Booster is an alternating-gradient, rapidcycling synchrotron containing 96 combined-function magnets. These magnets are excited with a 15-Hz biased sine wave. Capacitors are used to form a resonant network with the magnets. The proton-beam energy in the Booster ranges from 0.4 GeV at injection to 8.0 GeV at extraction. The parameters we use in simulating the Booster appear in Table 1. Table 1: Booster Parameters Ring Circumference [m] 474.2 Injection Kinetic Energy [MeV] 400.0 β at Injection 0.7131 γ at Injection 1.4263 Revolution Time at Injection [μsec] 2.2 γ at Transition 5.4696 |η| at Injection 0.458 Transverse Distribution Bi-Gaussian Longitudinal Distribution Uniform RF Peak Voltage ( V̂ ) [KV/Turn] 205.0 Maximum # of Macroparticles 110 K