Transverse Emittance Preserving Arc Compressor: Sensitivity to Beam Optics, Charge and Energy

Transcription

1 Transverse Emittance Preserving Arc ompressor: Sensitivity to Beam Optics, harge and Energy S. Di Mitri Elettra Sincrotrone Trieste ERL'5, Stony Broo Univ., NY

2 Where I come from... FERMI

3 is a nonprofit shareholder company of national interest, established in Trieste, Italy in 987 to construct and manage synchrotron light sources as international facilities.

4 Outline Prologue Motivations and hallenges Arc ompressors in Literature Optics Balance in a Transfer Line () -D SR model & Eperimental Proof Periodic Arc ompressor (45) Optics onsiderations Analysis and Simulations: Emittance vs. Bunch harge, Energy and Optics onclusions & Outloo ERL'5, Stony Broo Univ., NY simone.dimitri@elettra.eu 4

5 Motivations & hallenges Why magnetic bunch length compression? FELs: P out I Linear olliders: ε,y (w ) I - What are the challenges of σ z -compression? SR: ε (σ z,sr ) -8/ z z Why an arc compressor? ERLs: TURNAROUND FEL Recirculation AND ompression ERL'5, Stony Broo Univ., NY simone.dimitri@elettra.eu 5 B FEL Single-Pass: AR OMPRESSOR

6 Arc ompressors in (Recent) Literature Past ERLs design studies: BNL (00), KEK (007), ANL (008), JLAB (0), ornell (0). E >0.6 GeV Q p <0 (77p,.0GeV) ε n 0. µm Minimize the SR-dispersion function. [R. Hajima, 58 (004) 5]. SR primarily suppressed with a low charge. Our proposal: E >0.5 GeV Q p 45 (500p,.4GeV) ε n 0. µm Optics balance to cancel successive SR ics [Di Mitri, ornacchia, Spampinati, PRL (0)]. etended to a varying bunch length. [Di Mitri, ornacchia, EPL 09 (05) 600]. Bacground: D.Douglas, JLAB-TN-98-0 (998); Y.Jiao et al., PRTSAB 7, (04). ERL'5, Stony Broo Univ., NY simone.dimitri@elettra.eu 6

7 SR Picture tail head Radiation catches up with electrons ahead dipole RELATIVE ENERGY SPREAD of GAUSSIAN bunch, per DIPOLE: onsider -D steady-state SR emission, and linear optics. Transient SR effects and nonlinear dynamics will be included in the simulations.,. / / For a SINGLE PARTILE: For a BUNH: Photon emission/absorption, η 0 New betatron amplitude,,phot ηδ phot Bunch head gains energy z Bunch tail is not affected Initial betatron oscillation, New dispersive trajectory, η,phot η ηδ phot Initial reference (dispersive) trajectory, η head Bunch core loses energy tail Note: distortion is both in and ERL'5, Stony Broo Univ., NY simone.dimitri@elettra.eu 7

8 Projected Emittance Growth, σ z const. Multiple and identical SR ics (this applies to an isochronous transfer line): A. Use the ourant-snyder formalism for the particle coordinates, linear transport matrices, M 0, and J(0)0. B. When traversing a dipole, add the SR induced η-terms. This leads to an increase of the particle s -S invariant:. Repeat until the end of the line. All ics are identical in module, and we can write J f J f (J ). After averaging we find: Final SR induced -S invariant is zero (cancellation). ( η, η' ) J µ, π γ ' ' ( γ η αηη η ) δsr Hδ #5 α w' ' α ' # ' SR ( σ ) X (, α ) ε ε ε J δ, µ, f,0,0, SR ( η, η' ) 0 µ π, µ, π µ, 4 π µ, π ( η, η' ) # #7 w µ, 4 π ( η, η' ) ERL'5, Stony Broo Univ., NY simone.dimitri@elettra.eu 8

9 Eperimental Proof at FERMI Quadrupoles Dipole Quadrupole for scan ε measurement PRL 09, 0480 (0) Phys. Reports 59, (04) Quadrupoles ensure π-phase advance between dipoles and proper values of, α to cancel the SR-emittance. Horiz. energy dispersion, η y DBA DBA One quadrupole s strength is scanned to vary the phase advance between the DBAs. Results: Minimum ε n, for nominal optics (πphase advance and optimum Twiss parameters). Larger ε n, for shorter beam. ERL'5, Stony Broo Univ., NY 500p, 0.4 ps rms 0. ps rms simone.dimitri@elettra.eu 9

10 Periodic Arc ompressor H has to be small at the dipoles and small R 56 has to large enough to cumulate a >0 not too small Suitable, α, µ along the line for SR cancellation many quadrupoles We want to linearize the longitudinal phase during compression setupoles Possibly simple, robust and compact lattice 6 DBA cells (Elettra-lie lattice, EG). 80 o, 5 m long at.4 GeV R 56 5 mm per cell Due to symmetry and short bends, µ π. DBA cell ERL'5, Stony Broo Univ., NY simone.dimitri@elettra.eu 0

11 ERL'5, Stony Broo Univ., NY Optimum Optics in a Single DBA: Optimum Optics in a Single DBA: Optimum Optics in a Single DBA: Optimum Optics in a Single DBA: ( ) ( ) ( ), / / / / ' ρ ρ δ ρ α ρ ρ ρ ρ S S S S S For a single DBA, at the eit of the nd dipole we have: ( ) ( ) i i i i z i S, e ) Q/(e 0.459r sin, cos γσ ( ) ( ) ( ) [ ] ( )( ) 6 6 / l l J b b α α ρ 0 0 α α d dj d dj Loo for the optimum Twiss parameters at the dipoles: ( ) ( ) ( ) ( ) 6 6,, l l b opt b opt α α ( ), 6,, b opt opt l α 0 J where as already in [Y. Jiao et al. PRTSAB 7, (04)]. SR ic scales with σ z

12 Optimum Optics along the Arc ompressor:. The local i depends on the upstream E-chirp, which varies along the arc:. The optimum,dip depends on i, thereby it varies along the arc. h i loc i tot j E 0 j i de dz i loc i i h i σ δ,0 R σ 56 z, i, i, j,...,6 Optimum,dip, i loc and J i, for α,dip 0: J i vs.,dip, for α,dip 0: too small Most of the SR dynamics is the very last cell ( tot 45) larger,i optimum ERL'5, Stony Broo Univ., NY simone.dimitri@elettra.eu

13 Final Emittance vs. harge and Optics E.4 GeV tot 45 σ z,0 mm ε n,0 0.8 µm h m -,dip is the same for all the dipoles (periodic solution). ε,sr minimum growth minimum growth Each step corresponds to a different,dip. hromatic aberrations ( ) are NOT corrected at each step. ERL'5, Stony Broo Univ., NY simone.dimitri@elettra.eu

14 Final Emittance vs. harge and Energy Ansatz: the emittance sums in quadrature after each DBA: ε, i ε, i ε, ij i j j, f ε,0 ε,0 J i J i ε,0 ε << Theory: J i as above. Steady: -D SR in Elegant. Total: Steady Edges Drifts. This is: sqrt[(ε n,f ) (ε n,0 ) ], and ε n,0 0.8 µm. I f,0.5.5 A I f,0..0 A I f, A We may achieve ε n 0. µm for, e.g.: 00p, E > 0.5 GeV 00p, E >.0 GeV 500p, E >.0 GeV ERL'5, Stony Broo Univ., NY simone.dimitri@elettra.eu 4

15 Full Particle Tracing (Elegant) Particle tracing now including: rd order transport matrices, ISR and SR transient effects, SR-induced microbunching from a quiet start and 5 M-particles Enlarged uncorrelated energy spread, as from a laser heater (0 ev rms) Two sets of beam parameters at.4 GeV, 45: Q 00 / 500 p I f. /. A σ δ,0 0. / 0.4 % ε n,0 0. / 0.8 µm rad Slice emittances and pea current EPL 09, 600 (05) ε,slie 0.05 µm ε,slie 0.05 µm 00p 500p ERL'5, Stony Broo Univ., NY simone.dimitri@elettra.eu 5

16 Nonlinear Dynamics EPL 09 (05) 600 Nonlinearities in the longitudinal phase space evolve during compression due to: Incoming RF curvature, T 566 of the DBA cells, Nonlinear SR-induced energy chirp. 4 setupole magnets linearize the compression. Strengths and positions optimized for minimizing chromatic aberrations (these are responsible for the emittance modulation along the line, see below). ε,proj. 0. µm SR rd ORDER ISR ε,proj. 0.5 µm 00p 500p ERL'5, Stony Broo Univ., NY simone.dimitri@elettra.eu 6

17 Microbunching Instability The effect of SR-induced microbunching (MB) is damped by the initial beam heating. The strength of MB dynamics sounds over-estimated because: E/I-modulations tend to smear as the # of particles increases from 0. to 5 M; filtering suppresses λ f µm, while MB appears at λ f > 0 µm; transverse emittance smearing effect not included. EPL 09 (05) 600 Accurate MB analysis is pending. See, e.g.,.-s. Tsai s tal (today, this session) 00p 500p ERL'5, Stony Broo Univ., NY simone.dimitri@elettra.eu 7

18 onclusions & Outloo The etension of SR-driven liner optics balance to the case of varying bunch length leads to a simple formula for a periodic system. The final emittance estimate is in reasonable agreement with -D tracing results (see also.hall s tal, this session). For a DBA-based 80 o arc compressor, we epect a gain 0 in Q / E, w.r.t. the eisting literature. Woring plan: more accurate microbunching instability analysis; massive numerical optimization of the emittance vs. linear and nonlinear dynamics; scaling to a (low energy) compact ERL, and to a (high energy) single-pass beamline. A proof-of-principle eperiment may be possible at the FERMI Main e-beam Dump line (two big dipoles and quads available at.5 GeV). ERL'5, Stony Broo Univ., NY simone.dimitri@elettra.eu 8

19 Acnowledgements A special than to my good friends, collaborators, and often co-authors, M. ornacchia and S. Spampinati: M.ORNAHIA S.SPAMPINATI Acnowledgements to Y. Jiao, X. ui, M. Venturini, D. Douglas, R. Li and.-s. Tsai for interesting and productive discussions. Thans to the FERMI Team for maing the machine available for physics studies, and to the FERMI Management for supporting this activity. Than You for Your attention ERL'5, Stony Broo Univ., NY simone.dimitri@elettra.eu 9