Beam Feedback Electronics for the Spear Storage Ring

The two beams of the 2 GeV Stanford electron-positron storage ring can exhibit, under certain modes of operation, coherent oscillations which have a rate of growth proportional to the beam current. Since this rate is much slower than the machine revolution tiequency, it is possible to produce damping by means of negative feedback, the beam itself being part of the feedback loop. Three systems have been built, two for the damping of transverse oscillations at the betatron frequency, and one for the damping of longitudinal oscillations at the synchrotron frequency. The electronics for these systems require wide band high power amplifiers and nanosecond circuitry. (Submitted to Nucl. Instr. and Methods. ) *Work supported by the U. S. Atomic Energy Commission. 2, Introduction The main parameters of the Stanford positron-electron storage ring SPEAR are found in Ref. I.. A theory for the damping of beam coherent instabilities has been studied by a number of authors, 2,3,4) and some machines have been equipped with systems of the same nature as the one we are about to describe. If one neglects phase shifts at the oscillation frequency and also radiation damping, a model for growing, coherent beam oscillations can be the RLC circuit of Fig. 1 where the resistance has been allowed to be negative in order to create antidamping. The differential equation for the closed loop circuit is c dv 1, 1 dt-R ‘f; s Vdt=-G; (1)