The Fermilab Booster accelerates beam from 400 MeV to 8 GeV at 15 Hz. In the PIP (Proton Improvement Plan) era, it is required that Booster deliver 4.2 x $10^$ protons per pulse to extraction. One of the obstacles for providing quality beam to the users is the longitudinal quadrupole oscillation that the beam suffers from right after transition. Although this oscillation is well taken care of with quadrupole dampers, it is important to understand the source of these oscillations in light of the PIP II requirements that require 6.5 x $10^$ protons per pulse at extraction. This paper explores the results from machine studies, computer simulations and solutions to prevent the quadrupole oscillations after transition.

The demand in high intensity and low emittance of the beam extracted from the Booster requires a better control over the momentum spread growth and bunch length shortening at transition crossing, in order to prevent beam loss and coupled bunch instability. Since the transition crossing involves both longitudinal and transverse dynamics, the recently modified 3-D STRUCT code provides an opportunity to numerically investigate the different transition crossing schemes in the machine environment, and apply the results of simulation to minimize the beam loss and emittance growth operationally.

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.

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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.

Over the past decade, Fermilab has focused efforts on the intensity frontier physics and is committed to increase the average beam power delivered to the neutrino and muon programs substantially. Many upgrades to the existing injector accelerators, namely, the current 400 MeV LINAC and the Booster, are in progress under the Proton Improvement Plan (PIP). Proton Improvement Plan-II (PIP-II) proposes to replace the existing 400 MeV LINAC by a new 800 MeV LINAC, as an injector to the Booster which will increase Booster output power by nearly a factor of two from the PIP design value by the end of its completion. In any case, the Fermilab Booster is going to play a very significant role for nearly next two decades. In this context, I have developed and investigated a new beam injection scheme called "early injection scheme" (EIS) for the Booster with the goal to significantly increase the beam intensity output from the Booster thereby increasing the beam power to the HEP experiments even before PIP-II era. The scheme, if implemented, will also help improve the slip-stacking efficiency in the MI/RR. Here I present results from recent simulations, beam studies, current status and future plans for the new scheme.

The Fermilab Booster is a bottleneck limiting the proton beam intensity in the accelerator complex. A study group has been formed in order to have a better understanding of this old machine and seek possible improvements. The work includes lattice modeling, numerical simulations, bench measurements and beam studies. Based on newly obtained information, it has been found that the machine acceptance is severely compromised by the orbit bump and dogleg magnets. This, accompanied by emittance dilution from space charge at injection, is a major cause of the large beam loss at the early stage of the cycle. Measures to tackle this problem are being pursued.