Impedance optimization of small gap chambers for the high single bunch current operation at the undulator based light sources

In the undulator based light sources the intensity limit of single bunch is often determined by the strong vertical instability caused by the wake field in the ring, where the undulator itself is large impedance source. The optimization of transition from the large aperture to undulator’s small-gap chamber is on-going research topic in an effort to reduce the vertical impedance; at the same time, the demand on single-bunch current is high from the timingmode x-ray user community. In this paper, after showing the results obtained by exploring the parameter space guided by Stupakov’s formula, we propose the linearlysegmented transition which can reduce the impedance down to 60% or less of the original linear taper. The reduction can be utilized either to increase the bunch current substantially or to install a smaller gap chamber without impacting the bunch current limit. For the definite result we considered the transition between two ellipses, namely, (a, b) = (42 mm, 21 mm) and (18 mm, 4 mm) over the length 15-30 cm in beam direction. INTRODUCTION In the 3rd generation light source the demand in high single bunch current often requires a strict control of impedance. The moderate change in impedance can have significant impact on the single bunch current limit. Main impedance source is insertion device (ID) chamber with a small gap. In this paper we present the impedance optimization of ID chamber taking into account of linear and nonlinear transition, width and gap of ID chamber, superellipse parameter of cross section, and the symmetry breaking of upstream and downstream transition. Specifically, we like to make vertical impedance of the transition between two ellipses, namely, (a, b) = (42 mm, 21 mm) and (18 mm, 4 mm) to be small. This is the reference configuration with the transition length equal to 18 cm. Most of the optimization result is normalized by this reference case. LINEAR TAPER OPTIMIZATION WITH CONSTRAINT Let’s consider a transition between arc and ID chamber as shown in Fig. 1. We firstly set the value of b to 17 mm or 21 mm. For each value of b, we varied the horizontal aperture a in wide range from 42 mm down to 10 mm. The vertical kick factor computed by the program GdfidL [1] is shown in Fig. 2 as a function of a. The results are normalized by the reference case. There is a significant reduction in Ky as the upstream aperture of taper gets smaller. However, this design makes rf heating large because of the abrupt change in aperture. The new design is proposed in Fig 3, which results in the significantly reduced rf heating. Overall reduction in vertical impedance is 45% when a=b=17 mm is used. Figure 1: The linear taper connecting arc and ID chambers showing the horizontal plane (top) and the vertical plane (bottom). Black curve represents the profile of the reference chamber and the red curve indicates a new profile with optimization parameters a and b. Figure 2 : The reduction of vertical kick factor as the horizontal aperture, a, reduces from the original 42 mm down to 10 mm for a given vertical aperture, b. Figure 3 : The optimized linear taper which is similar to Fig. 1 but with two segmented transitions. ___________________________________________ † yong-chul.chae@desy.de 9th International Particle Accelerator Conference IPAC2018, Vancouver, BC, Canada JACoW Publishing ISBN: 978-3-95450-184-7 doi:10.18429/JACoW-IPAC2018-TUPMF073