rf acceleration with harmonic number jump

We have recently considered acceleration of protons and heavy ions in a fixed-field alternating-gradient accelerator with nonscaling lattice and linear field profile. To avoid the problem of frequency modulation for acceleration of low-energy beams over a too short period of time, and to boost the acceleration rate, the method of harmonic number jump (HNJ) was proposed. This method allows the use of constant frequency acceleration, for instance using superconducting cavities, despite the fact that the beam velocity may vary considerably. Of course in this case the accelerating voltage and rf phase will need to be programmed accordingly as we shall show. We shall study first the motion of synchronous particles, and then of those with deviating initial conditions. We estimate the area and height of the rf buckets that are to contain the beam bunches with the added condition of the HNJ. We finally investigate methods to allow the program of energy gain as required by the HNJ method, including the effect of the cavity transit time factor.