CONTROL OF CLOSED ORBIT DEVIATION DUE TO SYNCHROTRON RADIATION* sLAc-PuB-15yo

Stanford Linear Accelerator Center Stanford University, Stanford, California 94305 Introduction The energy loss by synchrotron radiation in elec- tron-positron storage rings occurs in every bending mag- net and is thus distributed around the ring, while the energy gain occurs at the rf cavities, which are usually lumped in only a few locations.' This type of orbit distortion is usually negligibly small compared to the design allowance in existing synchrotrons and storage rings; however, in the case of the larger storage rings now being contemplated, the distortion can be substan- tial in comparison to beam size and is different for electrons and positrons. This difference between the two closed orbits can produce horizontal separations and crossing angles between the two beams at the inter- action regions. For example, for several of the possi- ble PEP operating configurations concentrating the rf cavities symmetrically about one insertion region, hori- zontal separations are produced which are of the order of the horizontal beam size at some interaction points and are unacceptable. There are at least three possible solutions to this problem. The first is to use a lattice in which the dispersion and its derivative are zero at the interac- tion regions and at the locations of the rf system. The second is to use transverse electric fields to produce the necessary corrections in the orbits of the two beams. The last is to distribute the rf accelerating system around the ring in such a way that the closed orbit deviations are within acceptable limits. For studying this problem, the thin-lens lattice design program MAGIC has been modified to compute the closed orbit distortion for any distribution of the rf system operating at any configuration.2 In the next section, we discuss the computation of the closed orbit and in the latter sections, we discuss the different options and give the reasoning that we have used to de- cide on the solution of distributing the rf system for PEP. Orbit Computation Consider the case where the energy change due to the radiation in the bending magnets is adiabatic; i.e., Lp..&, with B(s) the usual betatron function and'E(s)/E, the ratio of the beam energy to the design energy at a point 5. The prime denotes differentiation with respect to s. The closed orbit solution can then be.approximated by the sum of two terms. The first is equal to the dispersion n(s) times the quantity c E(s) - Eo Eo I * Because this first term is discontinuous between the entrance and exit of an rf cavity, the se- cond term must be a normal betatron oscillation chosen to make the closed orbit continuous. The closed orbit x(s) in the regions between cavities can be written as