Design of a triple-bend isochronous achromat with minimum coherent-synchrotron-radiation-induced emittance growth

PHYSICAL REVIEW ACCELERATORS AND BEAMS 19, 064401 (2016) Design of a triple-bend isochronous achromat with minimum coherent-synchrotron-radiation-induced emittance growth M. Venturini Lawrence Berkeley National Laboratory, University of California, Berkeley, California 94720, USA (Received 8 April 2015; revised manuscript received 15 April 2016; published 9 June 2016) Using a 1D steady-state free-space coherent synchrotron radiation (CSR) model, we identify a special design setting for a triple-bend isochronous achromat that yields vanishing emittance growth from CSR. When a more refined CSR model with transient effects is included in the analysis, numerical simulations show that the main effect of the transients is to shift the emittance growth minimum slightly, with the minimum changing only modestly. DOI: 10.1103/PhysRevAccelBeams.19.064401 I. INTRODUCTION II. FORMALISM It is desirable for acceleration and transport of high- brightness electron bunches to occur without degradation of the beam quality. Unfortunately, a number of processes can spoil the beam transverse emittance and among these one of the most prevalent is coherent synchrotron radiation (CSR). As the electrons in a bunch travel through a bend, synchro- tron radiation at the low end of the frequency spectrum is emitted coherently, perturbing the particle energy, inducing transverse offsets both in the spacial and angular coordi- nates, and therefore causing projected emittance growth. One way to contain the adverse effects of CSR is to reduce overall bending; however, to eliminate bending altogether is usually not an option. For instance, in single-pass systems for free electron lasers (FELs) dipole magnets are required for bunch compression and often to distribute the electrons to off-axis beamlines. In multipass systems, such as energy recovery linacs, bending is integral to the machine topology. Here we consider the problem of minimizing CSR effects on the transverse emittance in a triple-bend isoch- ronous achromat, a lattice unit widely used in accelerator design. We adopt a 1D steady-state free-space model of CSR [1] and a method of analysis first introduced in [2] for the study of CSR in bunch compressors. We show that within the approximation of the model it is possible to specify a lattice design that yields vanishing CSR-induced emittance growth. Our approach has some similarities with [3,4] and in particular [5]. We refer to the Introduction in [5] for a review of various approaches to the problem of minimizing CSR-effects on the emittance. For additional related work see also [6–12]. Consider a dispersive beam line from s ¼ s i to s ¼ s f with bending occurring in the horizontal plane and no acceleration. In a 1D approximation, the effect of CSR on a particle of the bunch at location s along the beam line is to induce a relative-energy change δ s ðzÞ depending on the arclength coordinate s and particle longitudinal coordinate z. In the linear approximation, the particle orbit in the horizontal plane following the energy kick evolves according to s →s f x ¼ R 11 i s →s f x 0 ¼ R 21 i s →s f 0 x i þ R 26 f δ s ðzÞ; s→s s→s where R ij are the entries of the linear transport matrix while x i , x i 0 and x, x 0 are the particle coordinates at the entrance and exit of the beam line respectively. Notice that the entries R 11 , R 12 , R 21 , and R 22 are for the transport matrix from s i to s f , whereas the entries R 16 an R 26 are for transport starting from s i ≤ s ≤ s f , where the CSR energy kick occurs. Integrating the effect of CSR through the whole dis- persive section, the particle coordinates at the exit of the beam line become x ¼ x β þ x ˆ ðzÞ and x 0 ¼ x β 0 þ x ˆ 0 ðzÞ with s →s s →s s →s s →s x β ¼ R 11 i f x i þ R 12 i f x 0 i and x 0 β ¼ R 21 i f x i þ R 22 i f x 0 i , and Z x ˆ ðzÞ ≡ s f dδ s ðzÞ s→s f R 16 ds; ds s f dδ s ðzÞ s→s f R 26 ds: ds s i Z s i þ R 16 f δ s ðzÞ; x i þ R 22 i x ˆ 0 ðzÞ ≡ Published by the American Physical Society under the terms of the Creative Commons Attribution 3.0 License. Further distri- bution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. s →s f 0 x i x i þ R 12 i If the beam is initially centered, hx i i ¼ hx i 0 i ¼ 0, where h·i represents averaging over the bunch population in phase-space, we can think of (ˆ x ðzÞ, x ˆ 0 ðzÞ) as the centroid Published by the American Physical Society