S. Di Mitri, Elettra Sincrotrone Trieste

Transcription

1 S. Di Mitri, Elettra Sincrotrone Triete CBB Workhop at UoC, 7-8/10 017, Chicago, IL 1

2 Prologue Thi i a review with an accent on analytical modelling, and accuracy of prediction relative to eperimental evidence. I will kip theoretical derivation and computational algorithm. I will report about a election of cae tudie for linac-driven FEL. CSR will be analyed in term of tranvere emittance and longitudinal intability energy pread, microbunching. New path of reearch on CSR intability could be identified. CBB Workhop at UoC, 7-8/10 017, Chicago, IL

3 CSR Tail-Head Interaction P receive photon tet particle in the q emit photon r r r t bunch head The longitudinal E-field come from ource particle in the bunch tail n r Curved path in a dipole magnet geometricalconideration. CSR intability i primarily a chromatic &r effect. Effect on tranvere emittance can be Two particle on ame circular path 1-D model, decribed through linear optic. γ 3 /R >> 1 teady-tate approimation, ENERGY CHANGE ALONG BUNCH, per METER: Current pike or fat rie enhance the z-csr field. CBB Workhop at UoC, 7-8/10 017, Chicago, IL 3

4 C. Hall et al., PRST-AB 18, Energy Lo Eample: Gauian bunch in teady-tate emiion: Total energy lo We hould be able to reolve Relative mean energy lo energy lo at thi level Relative rm energy pread Arc TBA or Bate cell 0.1 GeV, 0.1 nc, < 1 ka Dicrepancy i at δ 0.1% level CBB Workhop at UoC, 7-8/10 017, Chicago, IL 4

5 CBB Workhop at UoC, 7-8/10 017, Chicago, IL CBB Workhop at UoC, 7-8/10 017, Chicago, IL Collaping the Phyic onto RMS Value R R + + = + + = δ δ Particle coordinate tranform according to: Energy diperion function Change of longitudinal momentum by aborption of radiation ε = RMS EMITTANCE Since and from CSR field are correlated, thi goe to 0.,0, = γ α ε ε ε I thi implified picture good enough? At which level of accuracy?

6 S. Di Mitri et al., PRL 110, Horizontal Emittance T. FEL 17 and NOCE 17 Dogleg almot iochronou σ X α, 1, CSR f ε = ε + ε H, µ δ,0,0 Accuracy of prediction i at ε n, 0.1µm level, 3 µ = π 0.5 nc, 1 GeV, 0.5 ka 0. nc, 7 GeV, 3 ka w #5 η, η +η, + η #1 η, + η w = 1, µ = π #3 #7 +η, η µ = π 3, p rm 0. p rm CBB Workhop at UoC, 7-8/10 017, Chicago, IL 6

7 Y. Jiao et al., PRST-AB 17, S. Di Mitri, NIM A Tranient Effect Steady-tate model doen t account for tranient effect, which are relevant over m length dipole Are thee contribution noticeable in the overall CSR energy budget? Chicane Steadytate 1 Particle i not affected while 1 i till outide Particle continue to be affected after leaving bend 1 dipole Arc 6 DBA 0.5 nc, 1 GeV, 1 ka + Tranient CBB Workhop at UoC, 7-8/10 017, Chicago, IL Contribution i at εn, 0.1 chicane 1.0 µm level long arc. 7

8 I. Akkerman et al., PRST-AB 0, Eample: Compact ERL UV FEL CSR kick are calculated analytically at each dipole: THEORY: 0.6 µm 1-D CODE: 0.73 µm elegant Analytical can of final emittance v. initial Twi parameter: imulation, including tranient effect CBB Workhop at UoC, 7-8/10 017, Chicago, IL 8

9 S. Di Mitri et al., NIM A D Code K. Bane et al., PRST-AB 1, FERMI Team, P. William, A. Bryne & ASML, in progre 1-D code agree for mild compreion 0.3 GeV, 0.3 nc, < 1 ka 0.3 GeV, 0.8 nc, 0.5 ka 1-D code agree at full compreion even??. 1-D appro. till eem to be good for 0.3 GeV, 0.7 nc, < 3 ka CBB Workhop at UoC, 7-8/10 017, Chicago, IL 9

10 H. Owen et al. for NLS 008,3-D Code C. Prokop et al., NIM A D model doen t account for CSR field radial dependence: Forcing θ 1 θ lead to the o-called Derbenev criterion: tranvere effect become important when 0.7 GeV, 0.3 nc, ka elegant P.84 µm S 1.43 µm Courtey of A. Novokatki CSRtrack-1D -D CSR field modifie the beam energy ditribution. Energy pread i correlated both along z and. CSRtrack-3D P 4.95 µm S 1.85 µm CBB Workhop at UoC, 7-8/10 017, Chicago, IL 10

11 S. Bettoni et al., PRAB 19, Slice Emittance Slice emittance growth become noticeable in ultra-low emittance beam. 3-D effect are weakened in pencil beam but charge denity i higher pace charge force? Slice linear optic mimatch CSRTrack-1D CSRTrack-3D Chromatic aberration 0. GeV, 0. nc, < 0. ka 3D + Beam Optic Mimatch CBB Workhop at UoC, 7-8/10 017, Chicago, IL 11

12 Shielding D. Sagan et al. 009 Shielding of CSR field would require pipe gap a mall a < mm or o. J. Eberg et al. for CERN 015 V. Yakimenko et ATF 01 Model Ep. CBB Workhop at UoC, 7-8/10 017, Chicago, IL 1

13 C.-Y. Tai et al., PRAB 0, CSR-Microbunching: Theory CSR amplifie microbunching gain typically driven by longitudinal pace charge force. In a multidipole line, CSR can even dominate the intability gain. Theoretical precription on beam optic were found for minimizing both the CSR-induced emittance growth and microbunching gain local iochronicity, π-phae advance, mall beta, ecc.. MERIT FUNCTION Bunching i proportional to thi parameter when CSR only i conidered. CALCULATE DESIGN & SIMULATE CBB Workhop at UoC, 7-8/10 017, Chicago, IL 13

14 Final Remark 1-D teady-tate analytical formula guide to the deign of e-beam line chicane, tranfer line, arc. σ 0.1%, ε 0.1 µm accuracy of prediction for E > 300 MeV, σ > 10 µm, Q < 0.5 nc I < ka δ n, z Control of CSR-induced emittance growth through beam optic i well-etablihed Prediction get wore at lower beam energie, and with multiple bend in long beam line 1-D approimation eem to be ok for a relaed Derbenev criterion even 3-D effect are epected to raie at full compreion Picture i unclear to me yet Propoal of reearch line: Sytematic invetigation of 1-D v. 3-D effect code benchmarking, eperimental accuracy Validation of the CSR-driven microbunching gain v. beam optic Direct characterization of CSR-induced ditortion in z,e, z, and z, phae pace. CBB Workhop at UoC, 7-8/10 017, Chicago, IL 14

15 Thank you for Your attention CBB Workhop at UoC, 7-8/10 017, Chicago, IL 1