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

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

Outline Outline Outline

(Graves et al. PAC 2001)

x (energy and time) y JLab (Piot et al., EPAC 2000)

Microbunch structures observed after compression Microbunch Microbunch structures observed after compression structures observed after compression

Similar longitudinal structures at TTF and DUV-FEL

−0.04 −0.02 0.02 0.04 −2 −1 1 s /mm ΔE/E0 [%] ε/ε0= 2.969; εc/ε0= 2.650 1 2 x 10

4

−2 −1 1 ΔE/E0 [%] N

Energy distribution (σE/E0=0.736%)

−0.04 −0.02 0.02 0.04 50 100 s /mm f(s) [1/mm]

Longitudinal distribution (σs=24.8 µm)

−0.04 −0.02 0.02 0.04 −0.2 −0.1 0.1 s /mm (ΔE/E0)CSR [%]

CSR−induced Energy Gradient

LCLS Distribution After BC2 Chicane LCLS Distribution After BC2 Chicane

σ σs

s = 24.8

= 24.8 μ μm m σ σE

E/

/E E0

0 = 0.736 %

= 0.736 %

← ← bunch head bunch head

3 3× ×10 10−

−6 6 incoherent

incoherent energy spread energy spread

E E0

0 = 4.54 GeV

= 4.54 GeV

• M. Borland et al, PAC 2001, ELEGANT tracking

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

Introduction Introduction Introduction

Δ ΔΕ/Ε Ε/Ε z z Δ ΔΕ/Ε Ε/Ε z z Δ ΔΕ/Ε Ε/Ε z z V V = = V V0

0sin(

sin(ω ωz z) ) 2 2σ σz

z0

Δ Δz z = = R R56

56 Δ

ΔΕ/Ε Ε/Ε

Under Under-

• compression

compression

RF Accelerating Voltage RF Accelerating RF Accelerating Voltage Voltage Path Length-Energy Dependent Beamline Path Length Path Length-

• Energy

Energy Dependent Beamline Dependent Beamline

Bunch compression Bunch compression

linear “chirp”

2 2σ σz

z=

= 2 2σ σz0

z0 (

(1+hR 1+hR56

56)

) head tail

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) λ

z

Current

1% 10%

λ

z

Energy

Impedance Gain=10 R56

growth of slice energy spread (and emittance)

CSR wake and impedance CSR wake and impedance CSR wake and impedance

Derbenev et al., 1995 Murphy et al., PAC 1995

• Steady-state, line-charge CSR energy loss
• Radiation from bunch tail

catch up the head, increase energy spread and emittance z’ z s

• Powerful radiation generated for λ~ bunch length or bunch

micro-structure lengths

• Longitudinal CSR impedance Z(k) (k =2π/λ)

CSR “wake”, stronger at smaller scale ρ: bending radius

CSR CSR Microbunching Microbunching Movie Movie

ΔE/E0 ΔE/E0 f(s) f(s) γεx γεx

courtesy P. Emma

Emittance damping to CSR microbunching Emittance Emittance damping to CSR damping to CSR microbunching microbunching

• Consider a microbunched beam moving in a dipole

Longitudinal CSR force direction Microbunching normal direction Ld ρ θ=Ld/ρ θ σx

• Smearing of microbunching when projected to longitudinal z

direction in the bend

• Characterize density modulation by a bunching factor

Integral equation and approx. solution Integral equation and approx. solution Integral equation and approx. solution

• damping

Landau ...) , exp(... )) ( ( ) ( ) ( ) ( ) , ( kernel ) ); ( ( ) , ( ) ); ( ( ) ); ( (

56 δ

σ ε τ γ τ τ τ τ τ τ τ × → = + =

∫

k Z I I s R s ik s K k b s K d s s k b s s k b

A s

• Linear evolution of b(k;s) governed by an integral equation
• )

3 2 1 ( 2 ion amplificat stage

• two

) ' ' ; ' ' ( ) ' , ' ' ( ' ' ) , ' ( ' ) 3 2 ( ) 3 1 ( ion amplificat stage

• ne

) ' ; ' ( ) , ' ( ' ) ; ( ) ; (

'

→ → + → + → + =

∫ ∫ ∫

f I s k b s s K ds s s K ds f I f I s k b s s K ds s k b s k b

s s s

• Iterative solution for a 3-dipole chicane
• Heifets, Stupakov, Krinsky

PRST, 2002;

• Huang, Kim, PRST, 2002

• 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

Numerical example: Berlin Benchmark Numerical example: Berlin Benchmark Numerical example: Berlin Benchmark

• More about CSR, see http://www.desy.de/csr/

20 40 60 80 100 λ HµmL 2 4 6 8 Gain CSR_calc elegant Theory

σδ=2×10-6, γεx=1 μm

Borland Emma

LSC Impedance LSC Impedance LSC Impedance

• Free-space longitudinal space charge impedance
• 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)

rb

λ 1/γ

• CSR impedance much stronger than LSC, but LSC instability is

not subject to emittance damping (chicane is achromat)

• At low energy in the injector region, space charge oscillation

dynamics (typically requires careful SC simulations)

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)

local energy spread λ

z

Energy

R56

• All beams have finite incoherent (uncorrelated) energy

spread, smearing of microbunching occurs if

E-spread

• No emittance damping!

Uncorrelated energy spread of PC RF gun Uncorrelated energy spread of PC RF gun

Parmela at 1 nC Δ ΔE E/ /E E

3 keV 3 keV

Δ Δt t (sec) (sec)

• 3

3 keV keV ( (rms rms), accelerated to 14 GeV, & compressed ), accelerated to 14 GeV, & compressed × ×32 32 ⇒ ⇒ 3 3× ×10 10-

• 6

6 ×

×32/14 < 1 32/14 < 1× ×10 10-

• 5

5 relative energy spread

relative energy spread

• “Intrinsic” energy spread mostly generated from r-

dependent LSC force in the gun (Huang et al., PAC 2005) TTF measurement at 4 nC

• M. H
• M. Hü

üning, ning, H. Schlarb,

• H. Schlarb, PAC

PAC’ ’03. 03.

simulation simulation measured measured

Heating within FEL tolerance Heating within FEL tolerance

• LCLS FEL parameter ρ ~ 5×10-4, not sensitive to

energy spread until σδ ~ 1×10-4

• 10

10−

−5 5 “intrinsic” energy spread too small and cannot be used in

too small and cannot be used in LCLS LCLS undulator undulator due to QE (no effect on FEL gain when < due to QE (no effect on FEL gain when <10 10-

• 4

4)

)

• M. Xie’s fitting formula

γε = 1.2 μm Ip = 3.4 kA β = 20 m

1 2 3 4 ΣΔf104 4 5 6 FEL Power Gain Length

quantum diffusion

can increase σδ by a factor of 10 without FEL degradation in order to suppress microbunching instability FEL limit

LCLS accelerator systems LCLS accelerator systems

• Two bunch compressors to control jitters and wakefield effect
• Impedance sources: LSC, CSR, and linac wakefields

Linac 1 BC1 (X4) BC2 (X8) DL2 DL1 photoinjector Linac 2 Linac 3 14 GeV SC wiggler at 4.5 GeV a SC wiggler before BC2 to suppress CSR microbunching Laser heater at 135 MeV

• r a laser heater for LSC instability (suggested by Saldin et al.)
• Two Landau damping options (to increase E-spread 10X)

• High BC1 gain significant energy modulation in Linac-2

temporally smearing in BC2 to become effective slice energy spread ( SC wiggler too late)

Growth of slice energy spread Growth of slice energy spread

Need ~0.1% initial density modulation at injector end

• r suppress BC1 gain effectively

wiggler wiggler on

• n

0.1% 0.1%

Final long. phase space at 14 GeV for initial 15-μm 1% modulation at 135 MeV Final long. phase space at 14 GeV for Final long. phase space at 14 GeV for initial 15 initial 15-

• μ

μm 1% modulation at 135 m 1% modulation at 135 MeV MeV

20 30 40 50 60 Λ0 Μm 5 10 15 ΣΔf104 FEL limit Elegant Theory

• Undulator radiation
• FEL interaction: energy exchange between e- and field

(v•E=vxEx) can be sustained due to the resonant condition

• Some e- loss energy, others gain energy modulation

with a relative amplitude ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ + = 2 1 2

2 2

K

u

γ λ λ

θ=K/γ λu z x

Beam-radiation interaction in an undulator Beam-radiation interaction in an undulator

laser peak power 8.7 GW laser rms spot size

LCLS laser heater design LCLS laser heater design

• Laser-electron interaction in an undulator induces rapid

energy modulation (at 800 nm), to be used as effective energy spread before BC1 (3 keV 40 keV rms)

Ti:saph Ti:saph 800 nm 800 nm

Injector at 135 MeV Injector at 135 MeV

0.5 m

• Inside a weak chicane for easy laser access, time-

coordinate smearing (Emittance growth is negligible)

Huang et al., PRST-AB 7, 2004

P P0

0 = 37 MW

= 37 MW σ σr

r =

= 1.5 mm >> 1.5 mm >> σ σx

x, ,y y ≈

≈ 187 187 μ μm m Non-uniform heating

Large laser spot size

P P0

0 = 1.2 MW

= 1.2 MW σ σr

r = 175

= 175 μ μm m σ σx

x, ,y y ≈

≈ 187 187 μ μm m

Matched laser spot size

spread by laser transverse gradient

more uniform heating In Chicane After Chicane

50 50 Γ0mc2 keV 0.005 0.01 0.015 V keV1

large laser spot matched laser spot

Gain suppression depends on laser spot size Gain suppression depends on laser spot size

50 100 150 200 Λ0 Μm 5 10 15 BC1 Gain

Elegant matched laser spot Theory matched laser spot Elegant large laser spot Theory large laser spot

• Large laser spot generates “double-horn” energy distributioin,

ineffective at suppressing short wavelength microbunching

• Laser spot matched to e-beam size creates better heating

when when

• Injector space charge dynamics modeled by ASTRA,

Injector space charge dynamics modeled by ASTRA, Linac Linac by by ELEGANT with LSC/CSR/machine impedances ELEGANT with LSC/CSR/machine impedances

Start-to-end simulation Start-to-end simulation

Example: final long. phase space at 14 Example: final long. phase space at 14 GeV GeV for initial 8% for initial 8% uv uv laser intensity modulation at laser intensity modulation at λ λ=150 =150 μ μm m No Laser No Laser-

• Heater

Heater

t (sec) ΔE/E

2×10−3

Matched Laser Matched Laser-

• Heater

Heater

t (sec)

1×10−4

SDL zero-phasing experiment SDL zero-phasing experiment

E z E z E z z E z

65 MeV Energy spectrometer

X (E) profile

(Graves et al. PAC01)

• Small energy modulation gets projected to large horizontal

density modulation (enhanced by λrf/λm ~ 1000)

• Measurement can be used to reveal energy modulations
• rf zero phasing energy spectrum is very sensitive to beam

energy modulation

Zero phasing sensitive to energy modulation Zero phasing sensitive to energy modulation

Wavelengths correspond to calculated maximum energy modulation due to space charge dynamics

Modulation wavelength Modulation wavelength

Shaftan, Huang, PRST, 2004

Simulated energy modulation assuming 4% initial density modulation after chicane, which is comparable to drive laser modulation amplitude

Energy modulation amplitude Energy modulation amplitude

• Zero-phasing modulation can be used to extract energy

modulation amplitude (25 – 35 keV at 200 A or 2X10-4 at 177 MeV)

• Such energy modulations can be converted to large density

modulations if a downstream bunch compressor is used, and may hurt a short-wavelength FEL

Microbunching instability driven by LSC, CSR and other machine impedances is a serious concern for short-wavelength FELs

Summary Summary

Strong LSC-induced energy modulation (and maybe density modulation) is characterized in DUV-FEL A laser heater with a laser spot matched to the transverse e- beam size is most effective in suppressing microbunching and is designed for LCLS It also gives flexible and desirable control of slice energy spread to manipulate FEL signal Beams from PC RF gun are too “cold” in energy spread, “heating” within FEL tolerance (~10X) to control the instability

Thanks for your attention! Thank Lia and Alex for the invitation!