undulator gap error tolerances for wakefield compensation in xfel
DESCRIPTION
Undulator gap error tolerances for wakefield compensation in XFEL. Igor Zagorodnov BDGM, DESY 08.05.06. SASE 2 parameters. Steady-state. SASE. The maximum power dependence on tapering (left) and the radiation power along the undulator (right). Optimal taper. Steady-state. - PowerPoint PPT PresentationTRANSCRIPT
Undulator gap error tolerances for wakefield compensation in XFEL
Igor Zagorodnov
BDGM, DESY
08.05.06
Parameter symbol unit Value
radiation wavelength nm 0.1
Energy E GeV 17.5
energy spread E MeV 1
undulator parameter rmsK 1.97
Emmitance n mm*mrad 0.7
peak current I kA 5
average beta function m 17.25
undulator section length sectL m 5
intersection length intersL m 1.1
total length totalL m 260
undulator period u m 0.048
SASE 2 parameters
47.1 10
0 0.005 0.01 0.0150
2
4
6x 10
10
max [ ]P W
rmsK 0 50 100 150 200 250
10-6
10-5
10-4
10-3
10-2
[ ]radE J
[ ]z m
with wakeno wake
wake taper
0 0.005 0.01 0.0150
2
4
6x 10
10
max [ ]P W
rmsK 0 50 100 150 200 250
10-6
10-5
10-4
10-3
10-2
[ ]radE J
[ ]z m
with wakeno wake
wake taper
The maximum power dependence on tapering (left) and the radiation power along the undulator (right)
3 11800[ ]lnb
sh
c c
WW W
N N
Steady-state SASE
|| 150 / /W kV nC m
Optimal taper
2
3.694exp 5.068 1.52uu u
g gB
2
5.068 3.04rms
rms u u
K g g g
K g
93.4 2rms u uK B
0.0124 rms rmsg K K
2
3.694exp 5.068 1.52uu u
g gB
2
5.068 3.04rms
rms u u
K g g g
K g
93.4 2rms u uK B
0.0124 rms rmsg K K
60.0124 60 10 [ ]rms rmsg K K m
max[ ]P GW
[ ]g m
P
P
max[ ]P GW
[ ]g m
P
P
Impact of statistical errors of undulator gap on power gain.
2
2
1( ) exp
22 gg
gf g
0
0
100% 20%P P
P
0
0
3100% 20%
pP P
P
10gfor m
2gfor m
Steady-state
60 80 100 1200
1
2
3
4x 10
-3
[ ]z m
[ ]radE J
0 5 10 15 200
0.2
0.4
0.6
0.8
1
[ ]g m
max
0max
gP
P
Steady-state vs. SASE
(150 )
SASE
seeds
(150 )
meanenergy
with errors
seeds
without errors
60 80 100 1200
2
4
6
8x 10
10
60 80 100 1200
1
2
3
4
5
[ ]z m
[ ]radE J
[ ]z m
[ ]z m[ ]z m
[ ]radP W
PE
Steady-state SASE
0 50 1000
10
20
30
40
0 50 1000
10
20
30
40
0 0.5 1 1.5 20
0.5
1
1.5
2
Energy distribution at 42.24m
E/<E>
p(E
)
0 0.5 1 1.5 20
0.5
1
Energy distribution at 88.32m
E/<E>
p(E
)
0 0.5 1 1.5 20
0.5
1
1.5
2
Energy distribution at 134.4m
E/<E>
p(E
)
0 0.5 1 1.5 20
2
4
6
Energy distribution at 42.24m
E/<E>
p(E
)
0 0.5 1 1.5 20
0.5
1
1.5
Energy distribution at 88.32m
E/<E>
p(E
)
0 0.5 1 1.5 20
1
2
3
Energy distribution at 134.4m
E/<E>
p(E
)
Steady-state
SASE
1
1( ) exp
( )
MMM E E
p E MM E E E
17% 33%
9.3M
25%
6% 20% 14%
0 2 4 6
x 1010
0
10
20
30
40Fluctuations of the power in the radiation slice
P [W]
sigm
a [%
]
0 1 2 30
10
20
30
40Fluctuations of the energy in the radiation pulse
E [mJ]
sigm
a [%
]
0 50 100 1500
10
20
30
40
[ ]z m
E
0 50 100 1500
10
20
30
40
[ ]z m
P
Steady-state SASE
For 5 mkm gap error at position z=130m
max
0max
0.91gP
P
max
0max
0.88EE
E
0.22P 0.16E
0 5 10 15 200
0.2
0.4
0.6
0.8
1
[ ]g m
max
0max
gP
P
Steady-state vs. SASE
(150 )
SASE
seeds
0 0.5 10
10
20
30
40Fluctuations of the energy in the radiation pulse
E/Emax
sigm
a [%
]SASE
Steady state
Steady-state SASE
The gap error results• in decrease of the expected radiation
energy by 10%• in RMS deviation of the radiated
energy by 16%
5g m