High-Voltage Breakdown Penalties for the Beam-Breakup Instability

The strength of the dangerous beam breakup (BBU) instability in linear induction accelerators (LIAs) is determined by the transverse coupling impedance Z_⊥ of the induction cell cavity. For accelerating gap width w less than the beam pipe radius b, the transverse impedance is theoretically proportional to w/b, favoring narrow gaps to suppress BBU. On the other hand, cells with narrow gaps cannot support high accelerating gradients, because of electrical breakdown and shorting of the gap. Thus, there is an engineering trade-off between BBU growth and accelerating gradient, which must be considered for next generation LIAs now being designed. In this article this tradeoff is explored, using a simple pillbox cavity as an illustrative example. For this model, widening the gap to reduce the probability of breakdown increases BBU growth, unless higher magnetic focusing fields are used to further suppress the instability.