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One may well ask: at this late stage, what more do we need to learn about the old subject of beam breakup instabilities (BBU) in linear accelerators? The physical mechanism is well-understood. Various stabilization mechanisms have been explored and implemented. The theoretical techniques that have been developed in treating the instabilities have become standard tools, and except for the cases where the focusing force is a nonlinear function of the beam's transverse displacement, the governing equations are linear. On the other hand, BBU is perhaps the most fundamental instability in a linear accelerator——its excitation requires no more than the passage of a charged particle beam through a sequence of cavities. The resurgence of interest in this instability naturally accompanied the construction of high current accelerators. In fact, our interest in this instability was originally stimulated by the two— beam accelerator experiment that was recently conducted at the Naval Research Laboratory. As we gained more experience with BBU, we are confronted with various nagging issues. Some of these are well-known and are, in fact, generic to all stability theories. Others are of a more specific nature. We shall describe them in this paper. A key issue, in our opinion, is the adequacy of the "conventional" models and the confidence in their use to assess the danger of BBU growth in a given experimental situation. The predictive capability is very important, as BBU growth depends on many parameters: beam current, beam energy, pulse length, pulse separation, cavity separation, machine length, acceleration gradients, focal strength breakup mode frequency and their spectra, their Q values, and transverse shunt impedances. Half of these parameters span over four orders of magnitudes, depending on the machine. Some important ones cannot even be determined accurately. Below, we shall discuss the various issues which arose in the course of our research. We provided answers to a small fraction of them, while the others await future investigation. Needless to say, the list is not exhaustive.
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