XFEL Impedance Effects and Mitigationaccelconf.web.cern.ch/ipac2018/talks/tuxgbf1_talk.pdfchange the compression (in BC2) by varying phase and amplitude of L2 → variation of wakes

XFEL Impedance Effects and Mitigation

M. Dohlus

IPAC 2018

May 01

The European XFEL

About FELs and Wakes

A Measurement

The European XFEL

500 m

main linac, Ltot = 1179 m

Lact = 640 × 1.038 m = 664 m

SASE1 Ltot = 225 m

Lact = 35 × 5 m = 175 m

Gun

accelerator L1

accelerator L2

main linacL3

injector linac

SASE1laserheater

dogleg collimator

BC2BC1BC0

bunch compressors

SASE1

SASE2

SASE3

Gun

SASE1

laserheater

dogleg

BC0

Compression Scenario

250 pC

→ BC0 →

¬ 14 A

¬ 48 A

¬ 2 keV

Gun

4 accelerator modules

BC1BC0

→ BC1 →

¬ 210 A

¬ 48 A

Gun

12 accelerator modules

BC2BC1

→ BC2 →

¬ 210 A

¬ 5 kA

¬ 1.9 MeV

BC1 → SASE1 → SASE3 → dump

¬ 5 kA

¬ 1.9 MeV

SASE2

SASE1SASE3

Impedance Budged before Undulatoraccelerator wakes for Q = 1nC

19%

42%4%

2%1%1%1%

10%

14% 2%4%

COL CAV TDS

BPMA OTRA BPMR

TORAO KICK PIP20

PUMCL FLANG

cavities

losscollimators“warm” pipe

about 2000 components

824 cavities (including TDS)

500 flanges

220 BPMs (5 types)

78 pumps

20 OTR screens

7 collimators

5 BAMs

3 kickers

warm pipe

…

total energy loss ≈ 35.3 MeV

total energy spread ≈ 15.4 MeV

intersection

SASE1:

Ltot = 225 m

Lact = 35 × 5 m = 175 m

SASE3: 21 segments

In the Undulator Chamber

Intersection

absorber bellows

pump

BPM

quadrupole

undulator chamber

energy spread

81/412

274 /412

numbers for Q = 1nC, Ipeak = 5 kA

elliptical pipe

surface effects

total energy spread (per section) ≈ 412 keV

elliptical pipe → 274 keV (pure surface effects)

surface effects → 331 keV

geometric effects → 81 keV

geometric effects

Impedance Budged for one Undulator Section

SASE1 has 35 sections

SASE3 with 21 sections

Surface Effects

15

8.8elliptical pipe

undulator chamber

• shape: large cross-section (mirror currents & pumping) + small gap (undulator)

→ elliptical pipe

• material: frequency dependent conductivity + anomalous skin effect

→ aluminum profile

• more surface effects: roughness + oxide layer

→ very tight tolerances 300 nm + 5 nm in undulators

1000 nm + 5 nm in BC chambers

3.5 nm, oxide layerroughness

absorber pump flange connections

(pinned)

bellows (pipe with gaps) beam position monitor

Geometric Effects

cu

optimize geometric effects

0.4 0.5 0.6 0.70

50

100

150

200

250loss [V/pC]

R [cm]

AR RE

Total

elliptical 15×8.8 mm2

AR

RE

EA

absorber

round pipe, R = ?

L = 4.6 m

About FELs and Wakes

resonance condition ( )( )22

2

20 22

12

yxK uul ′+′+

+

+=

λδγγ

λλ

overlap electron – photon beam lrr ,σσ ≈

πλσ lrlr L≈,

rg LL ≈

diffraction

power gain length ( ) ( )( )

1 32

5 6

2 3peak

12

1.18 1 ,n wAg

l JJ

KILI KA γ

ε λδ σ

λ

+

= + ⋯

(assuming optimal beta function)

beam properties energy, energy deviation

emittance, optics

bunch charge, peak current

wakes

compression

Some Dimensions ≈ European XFEL

undulator (SASE1) 24 10 muλ −≈ ×

cooperation length m10 8−µlL

bunch length m 10 5−µbL

power gain length 5 mgL ≈

Rayleigh length gR LL ≈(overlap electron-beam EM wave)

saturation length 10 .. 20s g gL L L≈

photon wavelength m10 10−µlλ 2γλuµ

bunch width m10 5−µµ glw Lλσ (overlap electron-beam EM wave)

transverse oscillation m10ˆ 6−µx (undulator trajectory)

linear operation 8 gz L<

typical beam properties energy ≈ 14 GeV (.. 17.5 GeV)

bunch charge ≈ 250 pC (.. 1 nC)

peak current ≈ 3 kA

linear operation

(exponential gain)

saturation

(whitewater rafting)

SASE

JradE

mz

Amplifier Model (linear operation)

only one eigenvector is amplified

=

XEM wave

beam, density modulation

beam, energy modulation

( ) ( ) ( )2 1ω ω ω=X U X

010

white noise1XU 2XU nXU⋯

( ) ( ) ( ) ( )e eα ω ω ω ω=X U X

( ) ( )( ) ( )nn eω α ω ω→ X X∼

� �� 0

� �� 0

�

( )0 ωω ω σ−

SASE

spectrum

( ) ( )0n nα ω α ω δω≈ −

Amplifier Model (linear operation)

( )2

2 12 2u

ln

Kn λλγ

= +

energy loss per stage 0n nγ γ δγ= −

shifted resonance condition

�� ��� 0� �� �

�� 0

( )0 ωω ω σ−amplification at ω0

SASE

spectrum

Amplifier Model (linear operation)

0

0.0005ωσω

≈our parameters: after 9 power gain length

wake:

ISR:

CSR: exponentially increasing but smaller

than wake + ISR

0

9 0.00045gLωω

′≈ for Gaussian bunch with 250 pC, 5 kA

( )18 MeV 100 m≈ −

( )5.7 MeV 100 m≈ −

with undulator intersections

( )0 ωω ω σ−

SASE

spectrum

saturation

SASE in Non-Linear Regime

JradE

mz

for our parameters (SASE1, 0.1nm, 250pC, 5kA):

linear operation

linear regime:

beyond linear regime:

wakes + ISR > CSR (SASE)

mild shift of resonance condition

CSR > wakes + ISR

energy loss → further shift of resonance

complicated interaction of kinetic- and field-energy

and micro-bunching

Tapered Undulator (Mitigation)

JradE

mz

( )( )( )2

2 122

ul

K S

Sλλ

γ

= +

systematic energy loss γ(S) can be compensated by tapering K(S)

keep resonance condition:

optimal tapering is more than compensation of resonance condition, it also

considers the dynamics of the bunching process

the optimal taper is non-linear in the range of saturation, it is usually adjusted

empirically

Energy Profile before Undulator

the taper compensates wake effects in the undulator, but different parts of

the bunch (~ cooperation length ≈ 10 nm) radiate on wavelengths defined

by the energy before the undulator (+ some frequency shift)

idealized longitudinal phase space

≈ 37 MeV

Gaussian bunch with 250pC, 5kA

the initial energy width causes an

additional broadening of the SASE3

spectrum

0.0026γγ

∆≈

0.0053ωω

∆≈

⇓

chirp

compensates

wake

A Measurement

L2

B2

CL T4T4D

operation: 14 GeV, 250 pC, no SASE

change the compression (in BC2) by varying phase and amplitude of L2

→ variation of wakes due to different bunch length

measure energy loss (B2, CL, T4 and T4D) and keep BCM signal

repeat measurement for few phase settings and measure rms bunch length

with transverse deflecting structure

SASE2

SASE1SASE3

B2

CL T4

strong compression

-60 -50 -40 -30 -20 -10 0

/deg

-80

-70

-60

-50

-40

-30

-20

-10

0

Energy(0+ ) - Energy(

0-60deg), t=114146

B2

CL

T4

T4D

change of Energy

normalization

TDS measurement:

inverse bunch length

SASE2

SASE1SASE3

T4D

T4

comparison with simulated compression (vs rms bunch length)

SASE2

SASE1SASE3

T4D

Summary/Conclusion

European XFEL

FELs and Wakes

Measurement

impedance data base with about 2000 components

before SASE1: major sources of wakes are cavities, collimators, warm pipes

(L3 to undulator) and fast kickers

SASE1 and 3: optimized geometry (cross section, flanges, pumps, diagnostics, …)

consider surface effects (material, roughness, oxide layers)

wake before undulator causes broadening of SASE spectrum

mitigation: energy losses in undulator can be compensated by tapering

compensation of energy variation before undulator (wake

versus chirp)

wake before SASE1 is small

SASE1 wake causes energy variation before SASE3

measurements of energy losses (due to variation of bunch length) are in

reasonable agreement with simulation based on impedance data base