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