Microbunching Instability in FEL Linear Accelerators Zhirong Huang - PowerPoint PPT Presentation

Microbunching Instability in FEL Linear Accelerators Zhirong Huang (SLAC) October 20, 2005 presented at

Outline Outline Outline � Introduction � Microbunching instability driven by CSR and LSC � LCLS analysis and cures � DUV-FEL beam modulation studies � Conclusions

Microbunch structures observed after compression structures observed after compression Microbunch Microbunch structures observed after compression � JLab (Piot et al., EPAC 2000) � Similar longitudinal structures at TTF and DUV-FEL y (Graves et al. PAC 2001) x (energy and time)

LCLS Distribution After BC2 Chicane LCLS Distribution After BC2 Chicane ε / ε 0 = 2.969; ε c / ε 0 = 2.650 Energy distribution ( σ E / E 0 =0.736%) σ E σ × 10 3 × 6 incoherent 10 − − 6 E / / E E 0 0 = 0.736 % = 0.736 % incoherent 3 1 1 energy spread energy spread Δ E / E 0 [%] Δ E / E 0 [%] 0 0 −1 −1 ← bunch head ← bunch head −2 −2 −0.04 −0.02 0 0.02 0.04 0 1 2 s /mm N 4 x 10 Longitudinal distribution ( σ s =24.8 µ m) CSR−induced Energy Gradient 100 0.1 σ s μ m σ = 24.8 μ m s = 24.8 E 0 = 4.54 GeV E 0 = 4.54 GeV ( Δ E / E 0 ) CSR [%] f ( s ) [1/mm] 0 50 −0.1 −0.2 0 −0.04 −0.02 0 0.02 0.04 −0.04 −0.02 0 0.02 0.04 s /mm s /mm M. Borland et al, PAC 2001, ELEGANT tracking

Introduction Introduction Introduction � FEL interaction in the undulator requires very bright electron beams (high current, small emittance and energy spread) � Such a bright beam interacting with self-fields in the accelerator may be subject to undesirable instabilities � Bunch compressors designed to increase the peak current can give rise to a microbunching instability that may degrade the beam quality significantly � This talk discusses physics of this instability, how to suppress it for short-wavelength FELs, and some experimental evidence relevant to the instabitily

Bunch compression Bunch compression Δ Ε/Ε Ε/Ε Δ Ε/Ε Ε/Ε Δ Ε/Ε Ε/Ε Δ Δ Δ Under- - Under 2 σ σ z 2 compression compression z 0 0 z z z z z z tail head 2 σ 2 σ z = 2 2 σ σ z0 56 ) ) ( 1+hR 1+hR 56 z0 ( z = sin( ω ω z Δ z Δ 56 Δ Δ Ε/Ε Ε/Ε z ) V = = V V 0 ) z = = R R 56 V 0 sin( RF Accelerating RF Accelerating RF Accelerating Voltage Voltage Voltage Path Length- Path Length -Energy Energy linear “chirp” Path Length-Energy Dependent Beamline Dependent Beamline Dependent Beamline

Instability mechanism Instability mechanism • Initial density modulation induces energy modulation through longitudinal impedance Z(k), converted to more density modulation by a compressor ( Saldin, Schneidmiller, Yurkov, NIMA, 2002 ) Current Gain=10 10% 1% λ z Impedance Energy R 56 λ z � growth of slice energy spread (and emittance)

CSR wake and impedance CSR wake and impedance CSR wake and impedance • Powerful radiation generated for λ ~ bunch length or bunch micro-structure lengths z’ z • Radiation from bunch tail s catch up the head, increase ρ: bending radius energy spread and emittance • Steady-state, line-charge CSR energy loss CSR “wake”, stronger at smaller scale • Longitudinal CSR impedance Z(k) (k =2 π / λ) Derbenev et al., 1995 Murphy et al., PAC 1995

CSR Microbunching Microbunching Movie Movie CSR f(s) f(s) Δ E / E 0 Δ E / E 0 γε x γε x courtesy P. Emma

Emittance damping to CSR damping to CSR microbunching microbunching Emittance Emittance damping to CSR microbunching • Consider a microbunched beam moving in a dipole σ x L d Microbunching normal direction θ ρ Longitudinal CSR force direction θ= L d /ρ • Characterize density modulation by a bunching factor • Smearing of microbunching when projected to longitudinal z direction in the bend

Integral equation and approx. solution Integral equation and approx. solution Integral equation and approx. solution • Linear evolution of b(k;s) governed by an integral equation ∫ s = + τ τ τ τ b ( k ( s ); s ) b ( k ( s ); s ) d K ( , s ) b ( k ( ); ) 0 0 τ I ( ) τ = τ → τ × ε σ kernel K ( , s ) ik ( s ) R ( s ) Z ( k ( )) exp(... , ...) � � � � � � δ � γ 56 I A Landau damping • Iterative solution for a 3-dipole chicane • Heifets, Stupakov, Krinsky PRST, 2002; ∫ s = + ( ; ) ( ; ) ' ( ' , ) ( ' ; ' ) b k s b k s ds K s s b k s 0 0 � � � � � � � � � 0 • Huang, Kim, PRST, 2002 one - stage amplificat ion � � � � � � � � � � � → + → I ( 1 3 ) I ( 2 3 ) f f ∫ s ∫ s ' + ' ( ' , ) ' ' ( ' ' , ' ) ( ' ' ; ' ' ) ds K s s ds K s s b k s 0 � � � � � � � � � � � � � � � 0 0 two - stage amplificat ion � � � � � � � � � � � 2 → → I ( 1 2 3 ) f

Numerical example: Berlin Benchmark Numerical example: Berlin Benchmark Numerical example: Berlin Benchmark • Elegant and CSR_calc (matlab based) codes used • a few million particles are loaded with 6D quiet start • CSR algorithm based on analytical wake models σ δ =2×10 -6 , γε x =1 μ m 8 Theory Borland elegant 6 Emma Gain CSR_calc 4 2 20 40 60 80 100 λ H µ m L • More about CSR, see http://www.desy.de/csr/

LSC Impedance LSC Impedance LSC Impedance • Free-space longitudinal space charge impedance λ r b 1/γ • At low energy in the injector region, space charge oscillation dynamics (typically requires careful SC simulations) • At higher linac energy, beam density modulation freezes and energy modulation accumulates due to LSC, can dominate microbunching gain at very high frequencies (Saldin, Schneidmiller, Yurkov, NIMA, 2004) • CSR impedance much stronger than LSC, but LSC instability is not subject to emittance damping (chicane is achromat)

LSC instability gain and Landau damping LSC instability gain and Landau damping LSC instability gain and Landau damping • Gain due to upstream impedances (LSC, linac wake) • No emittance damping! local energy spread Energy R 56 λ E-spread z • All beams have finite incoherent (uncorrelated) energy spread, smearing of microbunching occurs if

Uncorrelated energy spread of PC RF gun Uncorrelated energy spread of PC RF gun Parmela at 1 nC TTF measurement at 4 nC ning, H. Schlarb, H. Schlarb, PAC PAC’ ’03. 03. M. Hü üning, M. H E / E E / Δ E Δ 3 keV 3 keV simulation simulation measured measured Δ t Δ t (sec) (sec) • “Intrinsic” energy spread mostly generated from r- dependent LSC force in the gun ( Huang et al., PAC 2005 ) × 32 ), accelerated to 14 GeV, & compressed × • 3 3 keV keV ( (rms rms), accelerated to 14 GeV, & compressed 32 • ⇒ 3 × 10 × 32/14 < 1 × 10 ⇒ 3 × 6 × 32/14 < 1 × -6 -5 5 relative energy spread 10 - 10 - relative energy spread

Heating within FEL tolerance Heating within FEL tolerance • LCLS FEL parameter ρ ~ 5×10 -4 , not sensitive to energy spread until σ δ ~ 1×10 -4 FEL Power Gain Length 6 FEL limit M. Xie’s fitting formula γε = 1.2 μ m 5 I p = 3.4 kA quantum β = 20 m diffusion 4 0 1 2 3 4 Σ Δ f � 10 4 • 10 10 − 5 “intrinsic” energy spread too small and cannot be used in −5 too small and cannot be used in -4 4 ) LCLS undulator undulator due to QE (no effect on FEL gain when < due to QE (no effect on FEL gain when <10 10 - ) LCLS � can increase σ δ by a factor of 10 without FEL degradation in order to suppress microbunching instability

LCLS accelerator systems LCLS accelerator systems SC wiggler at 4.5 GeV photoinjector DL1 DL2 Laser heater Linac 3 14 GeV Linac 1 Linac 2 at 135 MeV BC1 (X4) BC2 (X8) • Two bunch compressors to control jitters and wakefield effect • Impedance sources: LSC, CSR, and linac wakefields • Two Landau damping options (to increase E-spread 10X) a SC wiggler before BC2 to suppress CSR microbunching or a laser heater for LSC instability (suggested by Saldin et al.)

Growth of slice energy spread Growth of slice energy spread • High BC1 gain � significant energy modulation in Linac-2 � temporally smearing in BC2 to become effective slice energy spread ( � SC wiggler too late) Final long. phase space at 14 GeV for Final long. phase space at 14 GeV for Final long. phase space at 14 GeV for μ m 1% modulation at 135 - μ initial 15- initial 15- μ m 1% modulation at 135 MeV m 1% modulation at 135 MeV MeV initial 15 15 wiggler on on wiggler Theory Elegant Σ Δ f � � 10 4 � 10 FEL limit 5 0.1% 0.1% 20 30 40 50 60 Λ 0 � Μ m � Need ~0.1% initial density modulation at injector end or suppress BC1 gain effectively

Beam-radiation interaction in an undulator Beam-radiation interaction in an undulator • Undulator radiation ⎛ + ⎞ λ 2 K x λ = ⎜ ⎟ u 1 γ 2 ⎝ ⎠ 2 2 θ =K/ γ λ u z • FEL interaction: energy exchange between e- and field ( v • E =v x E x ) can be sustained due to the resonant condition • Some e- loss energy, others gain � energy modulation with a relative amplitude laser peak power 8.7 GW laser rms spot size