Transient beam loading in electron-positron storage rings

In this note the fundamental of transient beam loading in electron-positron storage rings will be reviewed. The notation, and some of the material, has been introduced previously. The present note is, however, more tutorial in nature, and in addition the analysis is extended to include the transient behaviour of the cavity fields and reflected power between bunch passages. Since we are not bound here by the rigid space limitations of a paper for publication, an attempt is made to give a reasonably coherent and complete discussion of transient beam loading that can hopefully be followed even by the uninitiated. The discussion begins with a consideration of the beam-cavity interaction in the ''single-pass'' limit. In this limit it is assumed that the fields induced in the cavity by the passage of a bunch have decayed essentially to zero by the time the next bunch has arrived. The problem of the maximum energy that can be extracted from a cavity by a bunch is given particular attention, since this subject seems to be the source of some confusion. The analysis is then extended to the ''multiple-pass'' case, where the beam-induced fields do not decay to zero between bunches, and to a detailed consideration of the transient variation of cavity fields and reflected power. The note concludes with a brief discussion of the effect of transient beam loading on quantum lifetime