Theoretical and experimental advances on Coherent Synchrotron Radiation and Microbunching Instability at FERMI

Transcription

1 Theoretical and eperimental advances on Coherent Synchrotron Radiation and Microbunching Instability at FERMI S. Di Mitri, on behalf of the FERMI Commissioning Team Elettra Sincrotrone Trieste SIF 04, Pisa -Sezione VIIa

2 Outlook Motivations: Linac-driven FELs CSR instability: Transverse projected emittance growth Eperiments in bunch compressor and transfer line LSC instability: Laser Heater Phase Miing Final Remarks SIF 04, Pisa - Sezione VIIa simone.dimitri@elettra.eu

3 Linac-driven FELs Why VUV and X-ray FELs? o FEL is coherent radiation emission in the undulator N e, thus surpasses the undulator spontaneous peak brilliance in synchrotrons by a factor N e 0 9. Why Linac-driven FELs? o Single- (or few) pass accelerators overcome the e-beam equilibrium properties in synchrotrons: 6-D peak brightness is 0 4 higher (at same beam energy). e-beam Features for FELs (more in net slide):. Small transverse normalized emittances < µm are generated in the PC RF Gun. Challenge: preserve it until the undulator.. Peak current is increased in BCs to ka. Challenge: provide and maintain current uniformity. 3. Relative energy spread is made small 0-3 by adiabatic damping (acceleration). Challenge: keep it small all along the bunch. SIF 04, Pisa - Sezione VIIa simone.dimitri@elettra.eu 3

4 Requirements on e-beam e-beam peak current = Undulator parameter / Pierce parameter.the jack of all trades of D FEL theory. Typically 0 e-beam energy Transverse e-beam rms beam size ()= " # $% Radiation power grows eponentially along the undulator (typical behavior for instability-driven processes) until saturation. %&' ~ ) Radiation power at saturation is proportional to and e-beam power: ) =* ) +/. - %&' ~. # FEL power saturation length. This sets the scale for the undulator length. To have a large ρ (for a given lasing wavelength), we need a beam in the undulator with high peak current, small transverse emittance, small energy spread. All these parameters typically refer to the slice property of the bunch. However SIF 04, Pisa - Sezione VIIa simone.dimitri@elettra.eu 4

5 Disruption of transverse emittance Correlations in the slices transverse coordinates affect FEL intensity and bandiwidth: [Tanaka et al., NIMA 58 (004); G. Andonian et al., PRL 95 (005)]: e-bunch in FEL line 3.6nm (simul.) parasitic SASE FEL from optics mismatch and off-ais motion slice microbunching wavefront VISA IB, SASE How may these correlations happen? [Y. Derbenev et al., TESLA-FEL-05, 995] Photon emission/absorption, = β + η = 0 z z Initial betatron oscillation, β Newbetatron amplitude, β,phot = ηδ phot s Newdispersive trajectory, η,phot = η + ηδ phot Initial reference (dispersive) trajectory, η Bunch head gains energy Bunch tail is not affected SIF 04, Pisa - Sezione VIIa simone.dimitri@elettra.eu 5 head Bunch core loses energy tail

6 CSR Instability tail head Radiation catches up with electrons ahead /0() dipole ENERGY CHANGE ALONG BUNCH, per METER: = : < / Coherent emission (λ σ z ) dominates over incoherent, factor N e. Closed-form epression eists for electric field along direction of motion: two particles on same trajectory path, uniform circular motion (steady-state), use epressions for retarded-fields :( < ) : Current spikes or fast rises enhance the z-csr field. RELATIVE ENERGY SPREAD of GAUSSIAN bunch, per DIPOLE: =6.BC E 4 7 G 8 / F / high charge low beam energy short bunch length large bending angle D models accounting for transient effects are implemented in tracking codes. Codes with D effects (CSR transverse force) eist; 3D effects are in progress. The most notable effect of CSR is on the transverse dynamics. SIF 04, Pisa - Sezione VIIa simone.dimitri@elettra.eu 6

7 CSR-induced emittance growth H H [ η + ( βη'+ αη) ] β Different bunch slices feel different CSR kicks, thus move on different β-trajectories. If the slice ellipses are not concentric, the projected emittance is larger, although individual slices may have the same slice emittance. β β = η ε 0β + η σ δ, CSR ε 0α + ηη' σ δ, CSR H ε det α = ε 0 + σ + ε 0α ηη' σ δ, CSR ε 0 η' σ δ, CSR ε β NIM A 735, 60 (04) H = takes care of the coupled betatron and dispersive motion. Consider a 4-dipole magnetic compressor, θ<< and beam waist at the chicane end: σ z shorter in the 4 th dipole; H-function larger at the entrance of the 4 th dipole, and H βθ. δ, CSR Use the beam matri to compute the CSR effect (single-kick approimation, average effect): in MAGN.COMPRESSOR: ( βθ σ ε 0 + ε 0 δ, CSR PR 539, (04) SIF 04, Pisa - Sezione VIIa simone.dimitri@elettra.eu 7 /, dip 4

8 Projected emittance Lower energy particles Higher energy particles path length difference (bunch shortening) particles energy difference QUADRUPOLES SCREEN ) Vary compression ) Re-match optics through BC region 3) Measure ε From injector: 00pC, 6ps fwhm. before H-tuning, ε n, = 0.4 CF=5. 3. B A B A C after H-tuning, ε n, < 0. CF=5 PRST-AB 5, 080 (0) PRST-AB 5, 0070 (0) SIF 04, Pisa - Sezione VIIa simone.dimitri@elettra.eu 8

9 Slice analysis RF DEFLECTOR + QUADRUPOLES SCREEN ) Fi compression ) Tune H -function (β -min.) in BC 3) Measure ε and (t,) From injector: 800pC, 0ps fwhm ε n, =. µm ε n, =.9 µm ε n, =.3 µm t 0.3 mm 0.3 mm 0. mm QUAD BC DEFL. SCREEN mm.4 mm 0.5 mm SIF 04, Pisa - Sezione VIIa simone.dimitri@elettra.eu 9 Measurements by L.Fröhlich, L. Giannessi et al.

10 CSR effect for constant bunch length Problem. CSR-induced emittance growth in a bunch compressor can be minimized through optics manipulation in the very last bend magnet. What if the bunch length is constant all along a multi-bend line, so that we cannot recognize the «most damaging point» of CSR emission? Idea. Adjust the optics in the line so that successive CSR kicks cancel each other. A note by D.Douglas (JLAB-TN-98) proposes a perfect optics symmetry and π phase advance between identical CSR emission points. Real case. In real life, spatial and other optics constraints make hard to achieve such a symmetry. We propose to balance the CSR kicks in the presence of optics asymmetry. From LINAC to FEL Double bend achromatic lines are often used in FELs to bring the e-beam from the linac end to the undulator. Optics design may include: achromaticity, isochronicity, matching section, diagnostics, collimation... SIF 04, Pisa - Sezione VIIa simone.dimitri@elettra.eu 0

11 Optics balance & Courant-Snyder invariant A. Use the Courant-Snyder formalism for the particle coordinates. Initial invariant is zero. B. While traversing a dipole, add the CSR induced η-terms. This leads to an increase of the particle C-S invariant: C. Repeat until the end of the line. Each new invariant after a CSR kick in a dipole, can be defined in terms of J and of the local Twiss functions. After the last dipole we find: Final CSR induced C-S invariant is zero (cancellation). µ = π, µ, 3 = π µ 3, 4 = π 7 7 ' ( η, η' ) µ, = π = ηδ = η' δ = ' = J β cos µ J β µ = 0 J Hδ CSR γε µ, 3 = π ' ' = γ + α J + β = ( α cos µ + sin µ ) = β 5 β H Jβ σ δ, CSR 7 + β7 X 7 Jβ = γε J α + β #5 ( η, + η' ) #3 ε β 5 β7 β w' µ = 0 = α J β α S 34 < 0.µ m J α β7 α β + ' β β ( C α S ) +... = β # #7 ( +η, + η' ) w = µ 3, 4 = π β β ( +η, η' ) SIF 04, Pisa - Sezione VIIa simone.dimitri@elettra.eu

12 Eperimental results Quadrupoles Horiz. energy dispersion, η β y Dipole PRL 09 (03); PR 539, (04) Quadrupole for scan Many quadrupoles ensure π- phase advance between dipoles and proper values of β, α to cancel the final emittance growth. One quadrupole s strength is varied in the eperiment to scan the phase advance between the two achromats. β ε n, is measured at the line end as function of the quadrupole strength: minimum ε n, for nominal optics (πphase advance) Larger ε n, growth for shorter beam 500pC, 0.4 and 0. ps rms SIF 04, Pisa -Sezione VIIa simone.dimitri@elettra.eu

13 Disruption of longitudinal emittance Correlations in the slices longitudinal coordinates affect FEL wavelength and bandwidth [E. Allaria et al., MB workshop 007]: SPECTRUM 800 A beam for FERMI FEL- (CDR) POWER Zoom-in: 0 fs period modulation How may these correlations happen? [Z. Huang, MBW 007, Saldin et al., NIMA 490, 00] Current Energy λ λ % Longitudinal Space Charge force GAIN = 0 R 56 0% SIF 04, Pisa - Sezione VIIa simone.dimitri@elettra.eu 3 z z The local (slice) energy spread is now much larger Current modulation enhances the instability in the rest of the linac

14 LSC Instability Model the beam as a point charge: Beam Q I J Test-particle Energy change eperienced by test electron over a distance L: /=K* L -= M 6N 0 P I J Q LSC is typically important for electrons beam energies lower than 0s MeV. LSC can become relatively large (and dominant) at higher energies, either for very short bunches or on short length scales. Model the beam as a beer-can: λ /γ r b * L R,S UVW : X Y : Space-charge suppression at high energy log ]^ + ] a _ ] a ] _ U] a _ Field is proportional to local derivative of current profile. High frequency sinusoidal perturbation with wavenumber b = /.. Density wave induces energy modulation Δc=Δ*/de over a distance -: f = 6 Q g M b with D LSC- Dγ ghi(b) ( ) ln, >> M impedance /m: 6 Dγ r b r SIF 04, Pisa - Sezione VIIa simone.dimitri@elettra.eu 4 Z k i + Dγ b

15 Landau damping: «Laser Heater» Current λ Courtesy of Z. Huang Energy λ Uncorrelated energy spread smears out microbunching at λ R 56 σ δ,uncorr t E-spread Courtesy of M. Venturini Laser pulse Gaussian mode co-propagating with e-beam) dipole Short-undulator dipole t E.Saldin et al., NIM A 538 (004) Z. Huang et al., PRST-AB 3, (00) E (MeV) e-beam dipole < =+8 B H+8 B H < +8 Bj > 8 B dipole H< Q / z(mm) SIF 04, Pisa - Sezione VIIa simone.dimitri@elettra.eu 5

16 Eperimental results () Optical transition radiation: Measurements by S. Spampinati et al. Submitted to PRST-AB, 04 Phase Space: Calibration σ E,LH vs. P L : Current profile: OFF σ ε L U = 0 σr ( ) σ + σ ( ) r PL K mc 0 P γ σ ( ) 0 0 r [ JJ] ds, 5keV 5keV SIF 04, Pisa - Sezione VIIa simone.dimitri@elettra.eu 6

17 Eperimental results () Simulations by M.Venturini At large heating, longitudinal Landau damping wins and final energy spread LH-induced energy spread (Liouville theorem for the longitudinal emittance) FERMI works here Measurements by S. Spampinati et al. Submitted to PRST-AB At low heating, the instability wins and final energy spread remains large PRL, 480 (03) Laser heater may enhance the FEL intensity by a factor 3, and narrow the FEL bandwidth 3.5 nm SIF 04, Pisa - Sezione VIIa simone.dimitri@elettra.eu 7

18 Phase miing Idea: control and possibly minimize the micro-bunching (in the high gain regime of the instability) with a magnetic device (e.g., a 4-dipoles chicane). How to: i) leave the MBI growing along the linac to collect some energy modulation (typically after one bunch compressor); ii) remove any macroscopic z-e correlation at the entrance of «miing» chicane, e.g. with RF off-crest phasing. iii) «Mi up» and verify MBI suppression through COTR/IOTR signal. Gun BC Miing Chicane Proc. EPAC 008 PRST-AB 3, 0070 (00) σ 30µm, σ y 80µm z R 56 σ δ SIF 04, Pisa - Sezione VIIa simone.dimitri@elettra.eu 8

19 Eperimental results (). Gain red-shifts and enhances COTR MBI lmhi f n/ n f h / h (). Peak gain is moved to longer λ 6 M 6 G@ 8 Bj 8 Bj > G(λ) for varying miing strength (R 56 ) INCOHERENT LEVEL pc, CF = in BC E BC = 0.65 GeV E f =.3 GeV LH ON 50 kev RMS (3). Gain suppression by phase miing is the same as with a laser heater SIF 04, Pisa - Sezione VIIa simone.dimitri@elettra.eu 9

20 Conclusions CSR and LSC are serious concerns for VUV and -ray FELs. They mainly affect the transverse emittance (CSR instability) and the local energy spread (MBI). Optics manipulation in a magnetic compressor may minimize the CSRinduced projected emittance growth. Almost full compensation of CSR kicks is allowed by optics balance in a line at constant bunch length. Linear theory of MBI can be used for a quick evaluation of the overall gain of the system, aid numerical studies and eperiments. Beams from PC RF gun are too cold in energy spread. A laser heater warms up the beam within FEL tolerance (~0X) to control the MBI while not degrading (or improving) FEL performance. COTR can be used to diagnose the behavior of the MBI gain. Particle magnetic phase miing turns out to act like a mild heating. The scheme might be used for diagnostics and/or FEL operation purposes. It naturally fits in nowadays linac layouts. SIF 04, Pisa - Sezione VIIa simone.dimitri@elettra.eu 0

21 Team E. ALLARIA D.CASTRONOVO M.CORNACCHIA P.CRAIEVICH M. DANAILOV A.DEMIDOVICH M.DAL FORNO G.DE NINNO S. DI MITRI B. DIVIACCO W. FAWLEY E. FERRARI L.FRÖHLICH L. GIANNESSI A. LUTMAN S. MILTON G. PENCO S.SPAMPINATI M. TROVO M. VERONESE Thank you for Your attention SIF 04, Pisa - Sezione VIIa simone.dimitri@elettra.eu