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 [1]. 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.

In beams which are suf®ciently close to the linear stability limit, a variety of nonlinear wave phenomena are readily observed which can be used to diagnose aspects of the beam dynamics and the machine impedance. We have found that debunched beams in both the Fermilab Main Ring and the Tevatron are marginally stable to longitudinal oscillations and exhibit nonlinear three-wave coupling as well as nonlinear Landau damping and the formation of soliton-like perturbations. In addition, we have generated classical nonlinear echoes using twofrequency excitation in the Fermilab Accumulator. These phenomena can be used as diagnostic tools to determine diffusion rates in the beam as well as the longitudinal impedance. Moreover, aspects of these effects are likely involved in the approach to equilibrium as a longitudinal instability saturates under the in¯uence of a driving impedance. We present experimental results and analytical models based on perturbation techniques. In addition, we describe particle simulations which model the fully nonlinear evolution of these phenomena.

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