Merit Functions for the Linac Optics Design for Colliders and Light Sources

Optics matching and transverse emittance preservation are key goals for a successful operation of modern high brightness electron linacs. The capability of controlling them in a real machine critically relies on a properly designed magnetic lattice. Conscious of this fact, we introduce an ensemble of optical functions that permit to solve the often neglected conflict between strong focusing, typically implemented to counteract coherent synchrotron radiation and transverse wakefield instability, and distortion of the transverse phase space induced by chromatic aberrations and focusing errors. A numerical evaluation of the merit functions is applied to the Pohang Accelerator Laboratory free electron laser. INTRODUCTION Strong focusing is typically prescribed in modern high brightness electron linacs to avoid beam break up along the accelerator and to minimize coherent synchrotron radiation (CSR) effects in bunch length magnetic compressors [1]. Additional constraints are typically due to the optimization of the performance of diagnostics and beam collimation, with the additional advantage of cumulating the desired betatron phase advance in short distances, so as to save space and finally minimize the cost of the facility. Unfortunately, it may also hamper the main goal of emittance preservation through the excitation of optical aberrations and potentially leads, through focusing errors, to beam optics mismatch that can in turn corrupt the optics scheme adopted for the suppression of the instabilities. Based on these often conflicting requirements and on the partial lack, in the archival literature, of established strategies to design and optimize the optics of linear colliders and linac-driven free electron lasers (FELs), we introduce an ensemble of merit functions that offer, to our knowledge for the first time, a guidance to the definition of quadrupole strengths and Twiss functions in high brightness electron linacs. In particular, this work applies methods already published in [2] and partially revised in [1], to the PAL XFEL in Pohang, South Korea [3]. The baseline optics and other parameters of the electron beam in the PAL XFEL are shown in Fig. 1. The PAL-XFEL is designed to generate 0.1-nm hard X-ray FEL using a 10 GeV electron linac with a switch line at 3-GeV point for 1~3 nm soft X-ray FEL. The target slice emittance is 0.4 mm-mrad at 0.2 nC. A three-bunch compressor lattice is chosen so as to make more electrons in a bunch meet the requirements of emittance and correlated energy spread for SASE-FEL. The lattice also minimizes the emittance growth due to CSR. Figure 1: Baseline Twiss functions and energy dispersion from the injector end to the undulator entrance (top), mean energy, rms energy spread (middle) and rms bunch length (bottom) along the beam line. OPTICS SENSITIVITY TO FOCUSING ERRORS Our treatment basically applies well known concepts of linear and nonlinear accelerator physics. Some of them however, like the tune-shift-with-amplitude and the chromaticity, are not suited to describe local sources of phase space distortion. This fact justifies a less conventional approach in which we define a sensitivity coefficient that identifies sources of optics mismatch along the lattice. We adopt the definition of the mismatch parameter introduced in [4]. In addition, we assume a relative focusing error k, due to a perturbation  in the quadrupole strengths, so that the final mismatch parameter is computed in each plane as follows: ___________________________________________ #[email protected] Proceedings of IPAC2014, Dresden, Germany TUPRO056 05 Beam Dynamics and Electromagnetic Fields D01 Beam Optics Lattices, Correction Schemes, Transport ISBN 978-3-95450-132-8 1159 C op yr ig ht © 20 14 C C -B Y3. 0 an d by th e re sp ec tiv e au th or s