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Serpentine acceleration is typified by fixed radio frequency, fixed magnetic field and a near (but not) isochronous lattice, radial motion of the orbit, and two or more reversals of the motion in RF phase. This was discovered in 2003 for linear non-scaling FFAGs in the relativistic regime. In 2013, Kyoto University School of Engineering pointed out that serpentine acceleration is possible also in scaling FFAGs and may span the non-relativistic to relativistic regime. As a function of two key parameters, field index and synchronous energy, this paper shows how to optimize the extraction energy and the voltage per turn for the scaling case. Optimization is difficult, and typically leads to poor performance: either extreme voltage or small acceleration range. Nevertheless, designs with credible acceleration parameters can be obtained; and indicative examples are presented herein.
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