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.

Simulations of the Fermilab Booster reveal a substantial electron-cloud buildup both inside the unshielded combined-function magnets and the beam pipes joining the magnets, when the second-emission yield (SEY) is larger than (almost equal to)1.6. The implication of the electron-cloud effects on space charge and collective instabilities of the beam is discussed.

For Project X, the Fermilab Main Injector will be required to operate with 3 times higher bunch intensity. The plan to study the space charge effects at the injection energy with intense bunches will be discussed. A multi-MW proton facility has been established as a critical need for the U.S. HEP program by HEPAP and P5. Utilization of the Main Injector (MI) as a high intensity proton source capable of delivering in excess of 2 MW beam power will require a factor of three increase in bunch intensity compared to current operations. Instabilities associated with beam loading, space charge, and electron cloud effects are common issues for high intensity proton machines. The MI intensities for current operations and Project X are listed in Table 1. The MI provides proton beams for Fermilab's Tevatron Proton-Antiproton Collider and MINOS neutrino experiments. The proposed 2MW proton facility, Project X, utilizes both the Recycler (RR) and the MI. The RR will be reconfigured as a proton accumulator and injector to realize the factor 3 bunch intensity increase in the MI. Since the energy in the RR and the MI at injection will be 6-8 GeV, which is relatively low, space charge effects will be significant and need to be studied. Studies based on the formation of high intensity bunches in the MI will guide the design and fabrication of the RF cavities and space-charge mitigation devices required for 2 MW operation of the MI. It is possible to create the higher bunch intensities required in the MI using a coalescing technique that has been successfully developed at Fermilab. This paper will discuss a 5 bunch coalescing scheme at 8 GeV which will produce 2.5 x 1011 protons in one bunch. Bunch stretching will be added to the coalescing process. The required RF parameters were optimized with longitudinal simulations. The beam studies, that have a goal of 85% coalescing efficiency, were started in June 2010.

Space-charge effects on beam stabilities are studied for the proposed two-ring high-intensity Fermilab booster destined for the muon collider. This includes microwave instabilities and rf potential-well distortions. For the first ring, ferrite insertion is suggested to cancel the space-charge distortion of the rf wave form. To control the inductance of the ferrite during ramping and to minimize resistive loss, perpendicular biasing to saturation is proposed.

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 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.

We calculate the impedance and the wake functions for laminated structures with parallel-planes and circular geometries. We critically examine the approximations used in the literature for the coupling impedance in laminated chambers and find that most of them are not justified because the wall surface impedance is large. A comparison between the flat and the circular geometry impedance is presented. We use the wake fields calculated for the Fermilab Booster laminated magnets in realistic beam simulations using the Synergia code. We find good agreement between our calculation of the coherent tune shift at injection energy and the experimental measurements. In this paper we calculate the impedance and the wake functions for laminated structures with parallel-planes and circular geometries. First the coupling impedance is derived as a function of the wall surface impedance. Then the surface impedance is calculated by solving Maxwell's equations inside the lamination and the crack regions. We find that the commonly used resistive-wall approximations, good for metallic pipes with small surface impedance, are not valid in the laminated structures where the surface impedance is large. Realistic Synergia simulations of the Booster machine with wake fields predict transverse coherent tune shifts in good agreement with the experiment.