The longitudinal phase space program ESME, modified for space charge and wall impedance effects, has been used to simulate transition crossing in the Fermilab Booster. The simulations yield results in reasonable quantitative agreement with measured parameters. They further indicate that a transition jump scheme currently under construction will significantly reduce emittance growth, while attempts to alter machine impedance are less obviously beneficial. In addition to presenting results, this paper points out a serious difficulty, related to statistical fluctuations, in the space charge calculation. False indications of emittance growth can appear if care is not taken to minimize this problem.

The transition crossing is space charge dominated in the Fermilab Booster. Since the longitudinal space charge forces are defocusing below transition and focusing above transition, they generate the mismatch at transition, which causes the longitudinal emittance growth above transition. It's proved by numerical simulation that such mismatch can be partially compensated by a particular radial motion at transition, which is operationally favored by the high intensity beam. The transition crossing in Booster is space charge dominated. Usually, the nonlinear chromatic effect can cause the emittance growth during transition because particles with different energies cross transition at different times. The transition time is set by the synchronous particle; below transition, particles with positive energies relative to the synchronous particle become unstable since they are in the wrong phase, and above transition, particles with negative energies are unstable. The dependence of the transition energy upon the momentum deviation can be adjusted via different sextupole corrector settings such that the emittance growth due to the chromatic nonlinear effect can be greatly reduced. Fortunately, at the corrector setting of I{sub sextl} = -97 A and I{sub sexts} = 97 A, the dependence can be removed, see Figure 1. Space charge forces are mainly responsible for the longitudinal emittance growth at transition.

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We have studied space charge effects in the Fermilab Booster. Our studies include investigation of coherent and incoherent tune shifts and halo formation. We compare experimental results with simulations using the 3-D space charge package Synergia.

The stable region of the Fermilab Booster beam in the complex coherent-tune-shift plane appears to have been shifted far away from the origin by its intense space charge making Landau damping appear impossible. Simulations reveal a substantial buildup of electron cloud in the whole Booster ramping cycle, both inside the unshielded combined-function magnets and the beam pipes joining the magnets, whenever the secondary-emission yield (SEY) is larger than (almost equal to)1.6. The implication of the electron-cloud effects on the space charge and collective instabilities of the beam is investigated.

A longitudinal phase-space simulation (ESME) of the transition crossing is carried out (including various collective and single particle effects contributing to the longitudinal emittance blow up). The simulation takes into account the longitudinal space-charge force (bunch length oscillation), the transverse space-charge (the Umstateter effect) and finally the dispersion of the momentum compaction factor (the Johnsen effect). As a result of this simulation one can separate relative strengths of the above mechanisms and study their individual effects on the longitudinal phase-space evolution, especially filamentation of the bunch and formation of a galaxy-like'' pattern. Finally, a simple scheme of the [gamma]{sub t}-jump is implemented as a cure. 14 refs.

The Fermilab Project X plan for future high intensity operation relies on the Main Injector as the engine for delivering protons in the 60-120 GeV energy range. Project X plans call for increasing the number of protons per Main Injector bunch from the current value of 1.0 x 1011 to 3.0 x 1011. Space charge effects at the injection energy of 8 GeV have the potential to seriously disrupt operations. We report on ongoing simulation efforts with Synergia, MARYLIE/Impact, and IMPACT, which provide comprehensive capabilities for parallel, multi-physics modeling of beam dynamics in the Main Injector including 3D space-charge effects.