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Simulation of Edge and Diffraction Radiation
Propagation in the LCLS Bunch
Length Monitor
Radiation sources
Simulation of radiation propagation
Bunch length sensitivity of detector signals
10 April 2006
BIG Meeting
Henrik Loos
[email protected]
Layout
Diagnostics
Focusing
DR
Bend
200mm
10mm
ER
SR
Mirror
Focusing
f = 200mm
200mm
10 April 2006
BIG Meeting
Henrik Loos
[email protected]
38mm
Bunch Form Factor
Form Factor
Bunch length
determined by
low frequencies
Expansion of FF
f(k) = 1 – k2 σrms2
λ » 2πσrms
BC1: 1cm – 1mm
BC2: 1mm - .1mm
10 April 2006
BIG Meeting
BC1 FF
BC2 FF
BC1 Exp
BC2 Exp
1
0.8
0.6
0.4
0.2
0 -1
10
10
0
1
10
Wave Number (cm-1)
10
2
Henrik Loos
[email protected]
10
3
BC1 Radiation Distribution
10 April 2006
BIG Meeting
0
y (mm)
1
2
3
4
5
-5
Horizontal Pol.
0
5
10
15
x (mm)
20
25
30
20
25
30
0
1
y (mm)
Wavelength 1mm
200mm downstream of
BC1
Near field integration of
“acceleration field”
Edge length « λγ²
Mainly ER from both bend
edges, 4x larger than SR
Radiation from Entrance
edge hits vacuum chamber
2
3
4
5
-5
Vertical Pol.
0
5
10
15
x (mm)
Henrik Loos
[email protected]
Radiation Simulation
Intensity
Treat ER as TR
Take virtual quanta
transverse distribution and
propagate radiating part
through optical system.
E(r) = K1(kr/γ)
Radiating part
at γ→∞:
E(r) = (1-J0(kr))/kr
Max intensity at r = λ
Intensity falls off at r = γλ
10 April 2006
BIG Meeting
10
10
10
10
10
2
λ = 1mm
γ = 500
0
-2
-4
-6
10
-2
10
-1
10
0
10
1
r (mm)
Henrik Loos
[email protected]
10
2
10
3
Propagation with Gauss-Laguerre Modes
10 April 2006
BIG Meeting
Horizontal polarization
at magnet edge
-20
λ = 1cm
γ = 500
-10
y (mm)
Use Gauss-Laguerre
modes with radial
mode number 1 for
field of each
polarization
Needs γ/2 transverse
modes to get correct
far field distribution
0
10
20
-20
-10
0
x (mm)
Henrik Loos
[email protected]
10
20
BLM11 Layout
Detector
10mm
Lenses, f = 300mm
Window
100mm
BX14
e-Beam
38mm
15mm
200mm
10 April 2006
BIG Meeting
Henrik Loos
[email protected]
CER Transmission Through Optics
40
7
20
at detector
6
10
0
0
Beam Radius (mm)
3 cm-1
15 cm-1
30
200
80
400
600
Position (mm)
800
3 cm-1
15 cm-1
60
Transmission (%)
Transmission (%)
For one polarization, normalized to total 2π emission
5
4
3
2
40
1
20
0
0
10 April 2006
BIG Meeting
200
400
600
Position (mm)
800
0
0
20
40
60
80
-1
Wavenumber (cm )
Henrik Loos
[email protected]
100
Transverse Profile Through Optics
Radius (mm)
50
3 cm-1
40
30
20
10
0
100
200
300
400
Dist (mm)
500
600
700
800
500
600
700
800
Radius (mm)
50
15 cm-1
40
30
20
10
0
10 April 2006
BIG Meeting
100
200
300
400
Dist (mm)
Henrik Loos
[email protected]
Interference of CER and CDR
10 April 2006
BIG Meeting
10
Transmission (%)
Get field at detector for
CER and CDR
CDR is not focused on
detector
Wave front curvature
differs from CER
Intensity at detector shows
narrow fringe pattern
Fringes much faster than
changes in formfactor
CDR can be ignored
8
6
4
CER
CDR
CER+CDR
2
0
10
12
14
16
18
-1
Wavenumber (cm )
Henrik Loos
[email protected]
20
Spectral Efficiency and Bunch Form Factor
1
Pyro
Fused Silica
CER
Quartz
Transmission
0.8
0.6
0.4
0.2
0
0
10
20
30
40
50
60
Wavenumber (cm-1)
70
80
90
100
1
26 um
54 um
82 um
111 um
141 um
170 um
200 um
Form factor
0.8
0.6
0.4
0.2
0
0
10 April 2006
BIG Meeting
10
20
30
40
50
60
Wavenumber (cm-1)
70
80
90
100
Henrik Loos
[email protected]
Bunch Length Sensitivity of Detector Signal
Introduce high and low pass filters at 10cm-1 and 20cm-1.
Low signal for long bunches
More transmission of radiation below 10cm-1 needed
4
26 um
54 um
82 um
111 um
141 um
170 um
200 um
Efficiency (%)
5
4
3
2
Detector Signal
6
no
hp10
hp20
lp10
lp20
3
2
1
1
0
0
10
10 April 2006
BIG Meeting
20
30
40
Wavenumber (cm-1)
50
60
0
0
50
100
150
Bunch Length (m)
Henrik Loos
[email protected]
200
Summary
Study of proposed bunch length monitor after BC1
Main radiation source is edge radiation
Simulation of radiation transmission from dipole
edge to detector
Hole in out-coupling mirror is acceptable
Small apertures in optical system cut radiation
below 10 cm-1
Monotonic dependence of detector signal to bunch
length
Good sensitivity for shorter bunches at 200pC but
could be problematic for longer bunches at 1nC
10 April 2006
BIG Meeting
Henrik Loos
[email protected]
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