Nonlinear longitudinal dynamics studies at the ALS

Abstract

Nonlinear longitudinal dynamics studies at the ALS J. M. Byrd † , W-H Cheng, S. DeSantis, D. Li, LBNL, G. Stupakov, F. Zimmermann, SLAC Abstract We present a summary of results for a variety of stud- ies of nonlinear longitudinal dynamics in the Advanced Light Source, an electron storage ring. These include observation of decoherence at injection, decay of an injected beam, forced synchrotron oscillations and dif- fusion from one bunch to the next. All of the mea- surements were made using a dual–scan streak camera which allowed the real-time observation of the longi- tudinal distribution of the electron beam. Introduction Synchrotron oscillations are inherently nonlinear, mostly because of the sinusoidal radiofre- quency (RF) voltage used to longitudinally focus the beam. When the bunch length is small compared to the RF wavelength, the RF voltage over the length of the bunch can be considered as linear, minimizing nonlinear effects. In electron storage rings, this is al- most always the case. However, as the performance demands on electron rings grow, it becomes increas- ingly important to understand several of the subtle effects caused by the nonlinearities. These effects are also fascinating unto themselves and their study con- stitutes a contribution to the physics of beams. This paper presents a summary of results of experimen- tal studies of several nonlinear effects in longitudinal beam dynamics in the Advanced Light Source (ALS), an electron storage ring optimized for producing high brightness synchrotron radiation. Machine parameters relevant to our experiments are listed in Table 1. Due to space considerations, only a qualitative description of the results are presented here. More theoretical and experimental details can be found elsewhere[2, 5, 6]. Section II describes the streak camera used for all of the results in this paper. Section III presents a study of injection transients with and without beam capture. Section IV presents measurements of diffu- sion from one bunch to another. Section V describes measurements of forced nonlinear synchrotron oscilla- tions. Section VI summarizes the paper. Dual scan streak camera To make a detailed study of the longitudinal beam dynamics, we used a streak camera (SC) to observe the evolution of the longitu- dinal bunch distribution. A schematic diagram of the Hamamatsu C5680 SC is shown in Figure 1. The SC converts the time structure of a pulse of synchrotron radiation at optical wavelengths from a bend magnet ∗ This work was supported by the U.S. Dept. of Energy under Contract Nos. DE-AC03-76SF00098 and DE-AC03-76SF00515. † JMByrd@lbl.gov Parameter E C f rf V rf h Q s λ rad Description Beam energy Circumference RF frequency RF voltage Harmonic number Momentum compaction Synchrotron tune Long. rad. damping rate RMS natural bunch length RMS δE/E Value 1.5 GeV 196.8 m 499.664 MHz 1.1 MV 4.5 mm Table 1: Nominal ALS longitudinal parameters. Fast 125 MHz vertical sweep slow horz sweep A B C E D F slow time G time time Figure 1: Schematic diagram of the streak camera in synchroscan mode with dual sweep. A: photocathode, B: accel. mesh, C: vert. deflection electrode, D: horz. defl. electrode, E: microchannel plate F: phosphor screen, G: CCD camera. into vertical deflection at the CCD camera. In our experiments, the vertical deflection plates are driven by a 125 MHz sinusoidal voltage synchronized to the RF frequency. In addition, there is an optional slow horizontal deflection which allows observation of the longitudinal profile as a function of time. The time scale of the horizontal sweep can be adjusted to ob- serve several turns or thousands of turns and can be triggered to coincide with an event such as injection. For sweep times longer than several hundred turns, individual turns can no longer be resolved and so the longitudinal profile appears as a continuous line across the image. The synchroscan principle is illustrated in Fig. 2 which shows the 125 MHz vertical deflecting volt- age with respect to the arrival times of 4 storage ring bunches. Only deflections within the marked bands appear on the microchannel, allowing an effec- tive means of gating a particular bunch. The phase of the deflecting voltage can be adjusted to place the arrival of a single bunch on the center of the screen.