Periodic Approach to Space Charge Limit in Proton Linear Accelerators

The analytical approach to space charge effect in drift tube linacs has been mainly divoted to estimating how the potential well is filled up by some given distribution. This paper describes a different analytical approach to this problem. Eventhough the structure of a drift tube linac is not uniform geometically, it is considered periodic from the rf point of view. Thus the equation of oscillation can be expressed in the same way as the AG focusing theory, longitudinally as well as transversely. This matrix treatment allows closer approximation of the physical gaps and drift spaces where the external field to the beam is so different. The results so obtained yields somewhat higher limits than those obtained by conventional method for drift tube linacs. The upper limits of the current for KEK proton linac and PIGMI APF structure predicted by this theory are discribed.