Demand of high luminosity in the Tevatron collider in Fermilab makes the small beam emittance coming out of the 8 GeV Booster a highly desirable feature. This is because Booster bunches with small emittance, when eventually coalesced into Main Ring bunches, will ensure a high luminosity in the collider. Efforts have been made to identify factors limiting the phase space density in both transverse and longitudinal dimensions. The experimental result points to space charge induced tune spread at low energy as the main factor limiting the transverse phase space density, and the space charge induced phase space dilution at transition and longitudinal coupled bunch instability as the factors limiting the longitudinal phase space density. To counteract these factors, a set of harmonic correction sextupoles and skew sextupoles were implemented to reduce the third order resonances in the transverse case. In the longitudinal case a .gamma./sub t/-jump system was implemented to ease the bunch tumbling after transition, and various schemes to damp the longitudinal coupled bunch instability are either implemented or being reviewed. Future plans and efforts will be mentioned briefly at the end of this article. 3 refs., 8 figs., 1 tab.

Abstract Not Provided.

Multi-particle simulations are performed to study emittance growth in the Fermilab Booster. Analysis shows that the source of vertical emittance growth comes mostly from random errors in skew quadrupoles in the presence of a strong transverse space-charge force. [1] Random errors in dipole rolls and the Montague resonance do contribute but to lesser extent. The effect of random errors in the quadrupoles is small because the betatron envelope tunes are reasonably far away from the half-integer stopband.

The Fermilab booster accelerator was originally conceived for acceleration of protons with an injection energy of 200 MeV to an extraction energy of ten GeV (to the 500 GeV main accelerator). Early booster operation has been limited to eight GeV. The booster beam will be more acceptable to the main accelerator if extraction is at ten GeV, thus the booster magnet system is now being modified for ten GeV acceleration. Regulation of the booster magnetic field for injection at 200 MeV was a task even when operating to eight GeV. An outline is given of the approach which was adopted and how it relates to the ten GeV attempt. Problems encountered in the design of any ac magnet system are discussed.