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- Yu.A. Kubyshin
UPC, Barcelona
- A.V. Poseryaev, V.I. Shvedunov
MSU, Moscow
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Implementation of low energy injection schemes in the race-track microtron (RTM) design requires a better understanding of the longitudinal beam dynamics. Differently to the high energy case a low-energy beam will slip in phase relative to the accelerating structure phase. We generalize the concept of equilibrium or synchronous particle for the case of non-relativistic energies and introduce the notion of transition energy for RTMs. An analytical approach for the description of the synchronous phase slip is developed and explicit, though approximate, formulas which allow to define the equilibrium injection phase and fix the parameters of the accelerator are derived. The approximation can be improved in a systematic way by calculating higher order corrections. The precision of the analytical approach is checked by direct numerical computations using the RTMTrace code and was shown to be quite satisfactory. Explicit examples of injection schemes and fixing of RTM global parameters are presented.
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