Longitudinal instability caused by long driftsin the C-ADS injector-Ⅰ

The period length is usually much larger than the cavity effective length in a low energy superconducting linac.The long drifts between cavities will not only decrease the acceptance of the linac, but also lead to possible instability. The linac will be more sensitive to mismatch and other perturbations. From the longitudinal motion equation, the function which describes the parametric resonance is deduced and the relation between the instability region and the cavity filling factor is discussed. It indicates that if the zero current phase advance per period is kept below 90°, instability driven by parametric resonance will never occur. The space charge effect will enhance the instability, so that a stricter limitation on the phase advance per cell is required. From the numerical simulation results for two different schemes of Injector-Ⅰ of the C-ADS driver linac, one can find that even with just three cells in the unstable region, significant emittance growth can be observed. Further investigations show that it is apt to produce halo particles under resonance, and the machine becomes more sensitive to errors and mismatches. Therefore, it is important to keep all cells in the stable region throughout the linac of very high beam power to minimize beam losses.