start-to-end simulations for the european xfel · sc r pipe k iz k z k r ... method1 method2 bunch...

● description of European XFEL beam line● technical aspects of simulation

matching / codes / tools● gun● µ-bunch “instability”

laser heater / technical aspects of simulation● European XFEL – segmentation (for simulation)● method 1 (fast)● method 2 (reference)● method 3 (efficient & accurate) – to be done

Start-To-End Simulations for the European XFELMartin Dohlus, Igor Zagorodnov

European XFEL, description, s2e home page

s2e simulation: technical aspects

rf settings: phase and amplitude settings are very sensitivewakes & space charge effects change longitudinalprofile significantly!→ iterative optimization

matching: realartificial

steering

bunch: 1nC, ~50A (initial)

simulation: s2e particles (ASTRA-generator & gun simulation)Ns2e ≈ 200000try to track these particles; avoid conversions toother distributions (if possible);

simulation tools

ASTRA: on-axis-tracking, rz-space charge, rf, magnets,no wakes

CSRtrack: non-linear motion effects,1d CSR model, sub-bunch models

GENESIS: time dependent 3d FEL code

ELEGANT: rf, magnets, wakes,no space charge, 1d CSR model

utility programs

format conversion: ASTRA / CSRtrack / sdds

some simple manipulations of longitudinal phase space:add cavity wakes (based on point particle wakes,

asymptotic fit to ECHO calculations),add space charge wakes (semi analytic model)

some simple manipulations of transverse phase space:(transport matrices)

drift,transport as defined by linear optics (design),matching

ASTRA: rz space charge model

3d: slices & centroids ASTRA rz-model for s.c. calculation

charge density is underestimated

1) extract centroid offsets

2) ASTRA tracking of particles withextracted centroid offsets

3) transport centroid offsets (matrix)4) restore new particle coordinates

(add centroid offset)

remark: 3d space charge models create more noise (or need more particles)

CSRtrack

projected or 1d-CSR model:

sub-bunch model:1) create distribution of ‘generating’ 3d-sub-bunches

Ng ≈ 100000; (x, x’, y=0, y’=0, z, pz, q)2) combine s2e-particles and ‘generating’ bunches3) set charges of s2e-particles in combined

distribution to zero4) CSRtrack: self consistent tracking

~101h on linux cluster with 20 cpu-s (64bit)5) extract coordinates of s2e particles

z

x′

s2e particlescenter of ‘generating’sub-bunchesprojected vs. sub-bunch:

1d model sufficient for centroid motion & projected emittance;XFEL: slice effects are weak;

uncorr. energy spread dominated by laser heater

particles distribution → smooth 1d current → 1d longitud. field → particle energylow numerical effort

semi analytic space charge model

steady state space charge impedance:

( ) ⎟⎟⎠

⎞⎜⎜⎝

⎛≈′

rpipersc k

kiZRkZσγ

πγγσ ln

2,,, 2

0e.g. free space, kσr/γ << 1:

( ) ( ) ( )( )∫b

apiperscsc dzzRzkZbakZ γσ ,,,, ′=→

( ) ( ) ( )∫( )∫ dxdyyx

dxdyyxRkyxRkZ piperzpipersc ,

,,,,,,,,,

ψψγσ

γσEu ⋅

=′

( ) ( ) ( )ikzRkyxkzyx piper −⋅= exp,,,,,,,, γσEE

ψ(x, y) = transverse profile (round, rms width σr)

Rpipe = radius of beam pipeσr = rms width of round gaussian beamγ = Lorentz factor

with:

( ) ( ) ( )zz

z nr twissβ

γεσ =

εn = normalized design emittance

( ) ( ) ( )2

22

twiss

zzz yx ββ

β+

≈

βx, βy = beta function

gun

ASTRA simulation“black box”(ASTRA input from K.Flöttmann)

1nC, 200000 particles

energy-offset correlation after gun

energy-offset correlation1m after cathode

energy-offset correlation

1m after cathode

after module 1

µ-bunch “instability”

picture fromZ. Huang, J.Wu: Microbunching instability due to bunch compressionhttp://icfa-usa.jlab.org/archive/newsletter/icfa_bd_nl_38.pdf

impedances (steady state):

( )γσ ,,, pipersc RkZ ′ ⎟⎟⎠

⎞⎜⎜⎝

⎛≈

rkkiZ

σγ

πγln

2 20 (free space, kσr/γ << 1)

( ) ( )3 20 32

32,curv

curvCSR iRkZRkZ

πΓ≈′

“SC-instability”

“CSR-instability”

wavelength before bc1 / mm

gain

keV10entrancerms, =Eδ

after BC1 after BC2

aftercollimator

keV10entrancerms, =Eδ

after BC1 after BC2

aftercollimator

gainafter

collimator

keV/entrancerms,Eδ5

10

15

2025

keV/entrancerms,Eδ5

10

15

2025

wavelength before bc1 / mm

contributions of the sub-sections of the linac for an uncorrelated energy spread of 10 keV

overall gain for different uncorrelatedenergy spreads

gain curves of µ-bunch “instability”

‘laser heater’ System (LCLS layout)

µ-bunch “instability”, numerical aspects

1) µ-bunch-gain calculations are not subject of full s2e simulations

2) → separate investigationsCSR: integral equation method (limited applicability)

projected method: modulated beam, 1- and 2-stage compressionSC: impedance + r56

3) s2e simulations:avoid artificial instabilityNs2e << number of electrons → use smoothing techniques

1d methods: adaptive filtering techniques

ASTRA: resolution of longitudinal mesh for calculation ofspace charge field

CSRtrack sub-bunch-method: use of ‘generating’ sub-bunches

European XFEL, segmentation

gun → 1nC ~50A ~7MeV1 x module → 130MeVdogleg4 x module + 2 x module-3rd → 500MeVbc1 → ~1kA12 x module → 2GeVbc2 → ~5kAmain linac → 17.5GeVcollimatorbeam distribution … undulators …

European XFEL, segmentation

gun acc0+ … dogleg heater &

linac 1 bc1 linac 2 bc2

cathodecavitysolenoid

modulequad

dipolesquads

modules(1st & 3rd)quads

dipoles modulesquads

dipoles

modulesquads

dipolesquads

undulator(with quads)

mainlinac

colli-mator … SASE1 …

130 MeV 500 MeV 2 GeV

17.5 GeV

rf, dispersion

method 1 - fast

gun acc0+ … dogleg heater &

linac 1 bc1 linac 2 bc2

cathodecavitysolenoid

modulequad

dipolesquads

modules(1st & 3rd)quads

dipoles modulesquads

dipoles

modulesquads

dipolesquads

undulator(with quads)

mainlinac

colli-mator … SASE1 …

130 MeV 500 MeV 2 GeV

17.5 GeV

ASTRA CSRtrack‘projected’ transport GENESISrf-field

cavity wake & s.c. field

10 keV by laser heater

1.3GHz: 442.85 MV 1.42 deg3.9GHz: 90.63 MV 143.35 deg

method 1

before BC1

after BC1

after BC2

≈50A

≈1kA

≈5kA

current long. phase space rms energy spread

method 1

after BC2

≈5kA

after collimator

current long. phase space

rms energy spread

norm. emittance

horvert

0 50 100-2

0

2

4

6 x 1010

130 [ ]mP W

[ ]s mμ

with wake

wake taper+

no wake

bunch

the radiation power at z=130m

6070

4050

2030

80

10P[GW]

6070

4050

2030

80

10P[GW]0 100 0 100 0 100

no wake with wake wake+taper[ ]z m

[ ]s mμ [ ]s mμ [ ]s mμ

0 50 100 150 200 25010-6

10-5

10-4

10-3

10-2

[ ]radE J

[ ]z m

with wakeno wake

wake taper+

method 1 – GENESIS

TESLA-FEL Report 2005-10: Impact of Undulator Wake-Fields and Tapering on the European X-Ray FEL Performance

method 2 - reference

gun acc0+ … dogleg heater &

linac 1 bc1 linac 2 bc2

cathodecavitysolenoid

modulequad

dipolesquads

modules(1st & 3rd)quads

dipoles modulesquads

dipoles

modulesquads

dipolesquads

undulator(with quads)

mainlinac

colli-mator … SASE1 …

130 MeV 500 MeV 2 GeV

17.5 GeV

ASTRA CSRtracksub-bunch GENESISrf-field

cavity wake & s.c. fieldELEGANT

more investigations

method 2

method 1 method 2

xε

yε

current & slice emittance

method 1 method 2

long. phase space

method 1 method 2

(self-miss-match)

slice miss-match parameter with respect to the slice with the peak current

50 100 150 200 25010-6

10-5

10-4

10-3

10-2

the radiation power along the bunchat z=130m

the radiation energy along the undulator

[ ]radE J

[ ]z m

method 2

method1

40 60 80 100

-2

-1

0

1

2

3x 1010 130 [ ]mP W

[ ]s mμ

method 2method1

bunch shapes

GENESIS: method 1 vs. method 2

method 3 – accurate&effcient (to be done)

gun acc0+ … dogleg heater &

linac 1 bc1 linac 2 bc2

cathodecavitysolenoid

modulequad

dipolesquads

modules(1st & 3rd)quads

dipoles modulesquads

dipoles

modulesquads

dipolesquads

undulator(with quads)

mainlinac

colli-mator … SASE1 …

130 MeV 500 MeV 2 GeV

17.5 GeV

ASTRA CSRtrack‘projected’ GENESISrf-field

cavity wake & s.c. fieldELEGANTCSRtracksub-bunch

ASTRA (method 2) vs. ELEGANT (method 3)linac before bc1

ASTRA ASTRA without s.c. ELEGANT

6.0m 29

2.2m 47

====

y

y

x

x

αβαβ

6.0m 45

9.1m 30

====

y

y

x

x

αβαβ

6.0m 45

0.2m 30

====

y

y

x

x

αβαβ