Frequency jump in an ion linac

Frequency jumps in an ion linac use to be made in order to provide a large transverse acceptance in the low-energy part and a high accelerating gradient in the high-energy part. This frequency jump may induce a discontinuity in the average longitudinal force per focusing period and shrink the longitudinal acceptance of the linac if this transition is not performed carefully. In this paper, three techniques are developed which produce a ''certain'' continuity of the channel at the transition between. The continuity type is discussed. It is demonstrated that the longitudinal acceptance can be preserved whatever the frequencies of the cavities in the linac. This point is very important when comparisons between different cavity types are made (spoke and elliptical cavities for, instance). A few examples are shown to illustrate the performances of the three techniques. Frequency jumps in ion linacs use to be made in order to provide a large transverse acceptance (physical aperture) in the low-energy part and a high accelerating gradient and/or a better shunt impedance in the high-energy part. The minimization of the size of the cavities in the high-energy section is also interesting to reduce the cost because these cavities are the most numerous in the accelerator. Smaller cavities help to reduce the cryogenic load and induce a cheaper fabrication. This frequency jump may induce a discontinuity in the average longitudinal force per focusing period and shrink the longitudinal acceptance of the linac if this transition is not performed carefully. In Ref. (1), tech- niques are shown to manage the transition an radio fre- quency quadrupole operating at 350 MHz and a coupled cavity drift tube linac (CCDTL) operating at 700 MHz. It is explained that as the frequency is doubled in the CCDTL, a conservative synchronous phase of � 60 degrees is re- quired at the beginning of the structure to capture all particles. The concept of the continuity of the phase ad- vance per unit length is discussed for the transverse plane in order to provide a current and emittance independent design. This continuity simplifies significantly the match- ing at the transition. In this paper, we propose to develop techniques for designers to tune the phase and the field at frequency transitions in an ion linac which include accep- tance and phase advance per unit length issues. During the European Spallation Source studies in 2000 (2), we devel- oped a first technique to keep constant the confinement potential shape at the frequency jump. The goal was to maintain the beam in the achieved equilibrium state. Later, we proposed a different approach based on the continuity of the acceptance of the system. More recently, a third technique which is a mix of the first two has been proposed. In this paper, these three techniques are developed and compared to the classical method which is a matching at the transition (tuning of the focusing elements to maintain a smooth evolution of the phase advance per meter in the following section) keeping a high accelerating efficiency. II. CONSTANT POTENTIAL SHAPE