First Observation of Simultaneous Alpha Buckets in a Quasi-Isochronous Storage Ring

Abstract

We present the first experimental evidence confirming the theoretical predictions of alpha buckets in an electron storage ring. By controlling both the first-and second-order momentum compaction factors, we succeeded in storing electrons simultaneously in a pair of alpha buckets or in either bucket alone. The two electron bunches are separated in energy by slightly less than 1% and the energy is tunable over a narrow range. The energy difference was directly measured using synchrotron light from an undulator. Simultaneous two-color light beams from an undulator were generated. By changing the rf voltage, we were able to vary the normally fixed longitudinal bunch separation. The physics of nonlinear longitudinal phase space has been understood for some time in proton accelerators, where crossing the so-called transition energy (vanishing phase slip factor) during acceleration can cause a loss of beam [1]. Electron accelerators do not have this problem since the velocity dependent term in the phase slip factor is usually negligible compared to the path lengthening term characterized by the momentum compaction factor, a ϵ a 1 1 a 2 d. As a result, electron rings nearly always operate well above the transition energy. Until now, a vanishing phase slip factor has been a concept to be avoided. However, recently several attempts have been made to generate short bunches in electron storage rings by reducing the first-order momentum compaction factor for the lattice and operating close to transition in a "quasi-isochronous mode" [2-4]. As the first-order term a 1 is reduced, the effect of the second-order term becomes important in determining the physics of the electron bunches. Additional stable fixed points, so-called alpha buckets, develop where electrons could be stored [2]. We present the first experimental evidence of the existence of these alpha buckets in an electron storage ring and we explore their dependence on the radio frequency system (rf) and lattice parameters. We also demonstrate a potential application of the alpha buckets by creating two-color light beams from an undulator.The longitudinal equations of motion for an electron of energy E in a high energy electron storage ring are given bywhere V rf , v rf ϵ 2ph͞T 0 , and h are the rf voltage, frequency, and harmonic number; E 0 , T 0 , and U 0 are the energy, revolution period, and radiated energy loss per turn of the synchronous electron in the ring. The damping term has been neglected in Eqs.(1) as it does not play a role in the discussion which follows. f and d are the phase deviation and the fractional energy deviation of an electron from the synchronous electron with phase, f s . The momentum compaction factor is expanded to second order in d. The fixed points of the equations of motion are given by the condition that ᠨ f ᠨ d 0. Under normal operating conditions, only the first-order term in the momentum compaction, a 1 , is considered nonzero. In this case, there is one stable and one unstable fixed point at ͑f 0, d 0͒ and ͑p 2 2f s , 0͒, respecti...

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