Effect of Centrifugal Transverse Wakefield for Microbunch in Bend.

摘要

We calculate centrifugal force for a short bunch in vacuum moving in a circular orbit and estimate the emittance growth of the beam in a bend due to this force. Many of the basic features of the coherent synchrotron radiation (CSR) of short bunches and its effect on beam dynamics in accelerators are now well established. The effect is usually described in terms of the longitudinal force, or wakefield, that causes the energy loss in the beam, and also redistributes the energy between the particles by accelerating the head and decelerating the tail of the bunch. Coherent radiation becomes most important for short bunches and high currents. More subtle features of CSR such as transition effect due to the entrance to and exit from the bend, CSR force in the undulator, and shielding due to the close metallic boundaries have been also studied. Much less is known about the transverse force in a short bunch moving on a circular orbit. The problem has been treated in several papers beginning from R. Talman's work, who pointed out that the centrifugal force of a rotating bunch can result in a noticeable tune shift of betatron oscillations. Later, an important correction to the Talman paper has been added, where it was shown that due to the energy variation in the bunch, the effect of the transverse force proportional to R(sup -1) is canceled, and the residual effect is of the order of R(sup -2), that is much smaller than originally predicted. Recently, however, Derbenev and Shiltsev found the centrifugal force of the order of R(sup -1) that differs from Talman's result by a logarithmic factor only. Taking into account the existing controversy in the literature, in this paper, we consider the transverse force in a bunch based on simple physical arguments, starting from a dc beam. We will derive the centrifugal force for a relativistic coasting beam in vacuum, and then generalize the result for a short bunch, and estimate its effect on the emittance growth in a bend.