BBU in microtrons with subharmonic injection

It is pointed out that the current in recirculating electron accelerators is limited by the recirculating regenerative type of beam breakup (BBU). Existing calculations of the BBU threshold current, I _s, average over the relative phase between the beam bunch and the RF mode causing the blowup. This averaging is invalid if the BBU frequency is an integral or half-integral multiple of the beam frequency, in which case I_s may be substantially reduced. This effect is not important when the beam frequency equals the accelerating mode frequency, f₀, because the RF structure can be designed to avoid the harmonic condition. When the beam frequency is a large submultiple of f₀, this may not be possible. Calculations for the NIST RTM, which will inject at the 36 ^th subharmonic of f₀, are presented. The calculations include the effects of the reversed first return orbit and the variable return-path focusing of the RTM