Transcript Optics for Soft X-ray FEL Seeding

Compact Grating Monochromator Design
for LCLS Soft X-ray Self-Seeding
Y. Feng, J. Wu, M. Rowen, P. Heimann,
J. Krzywinski, J. Hastings
5/25/2011
1
FEL Seeding Benefits
Will produce (nearly) temporally fully coherent pulses
Enabling more precise characterization of FEL (distribution of) peak
intensity, which of great importance to the users, especially those in Xray nonlinear physics
Enabling more precise measurement of pulse duration using spectral
methods, which can then be used to calibrate the absolute fluence (w/
spot size information)
Enabling better control of FEL fluence on samples to help users achieve
greater measurement efficiency in damage-sensitive experiments
Will stabilize the FEL central wavelength
Enabling greater experimental efficiency when a monochromator is
required as in most spectroscopic/resonant excitation measurements
Will stabilize the FEL pulse intensity
2
3
Seeding Scheme
Originally proposed at DESY*
Conceptually straightforward
But requiring elaborate optics
Quiz:
Is there a mistake conceptually in
the schematic? if so, what is it?
chicane
1st undulator
2nd undulator
grazing
mirrors
FEL
slit
SASE FEL
electron
Seeded FEL
grating
GOAL: To fit in single undulator space
*J. Feldhaus, E.L. Saldin, J.R. Schneider, E.A. Schneidmiller, M.V. Yurkov,
Opt. Comm., V.140, p.341 (1997)
Electron
dump
Physics Requirements
Goal: produce a viable mono design that would
Be compact enough to fit in one undulator segment
Be ready to be built if funding permissible
To demonstrate soft X-ray seeding on LCLS-I
Critical performance parameters
Continuously tunable in energy range of
200 – 1000 eV
Sufficient resolving power to produce transform-limited seed for pulses
durations greater than (in low to medium low charge mode)
200 eV: 8.5 fs rms*, R = 1700 (flat-top)
1000 eV: 5.2 fs rms*, R = 5000 (flat-top)
Sufficient seed power w/o bringing the 1st FEL to saturation
200 eV: peak power ~ 10 kW
1000 eV: peak power ~ 15 kW
Optical delay that matches that of the e-beam magnetic chicane
3.3 ps +/- 10%
4
Soft X-Ray Monochromator/Mirrors and Chicane*
3.2 m
2.25 m
0.4 m
20 mm
2.07
32 mm
16 mm
16 mm
B = 12 kG
0.5 m
PLAN VIEW
10 mm
ELEVATION VIEW
0.89 m
0.21 m
E = 200 – 1000 eV
* Courtesy of P. Emma
1.15 m
Dtmono ~ 3.3 ps
6
Why Grating Monochromator?
Grating Equation (spacing s)
s  cosq cosq '  n
Since q and q ’ are both arbitrary, special conditions relating q and q ’ can be
imposed for special modes of operation
Constant incidence angle mode
q  const.
Grating  Angular dispersion
Focusing  Spatial dispersion
for obtaining resolving power
Constant included angle mode
Focusing
element
    const.
Constant focal-point mode (for current design)
cos  1
  const.
cos 
cos r '
M
cos  r
s
sL
HG
a
c
b
q’
q
Slit
element
Zeroth order
No dispersion!
d
Grating
element
Why Focusing
=> Resolving Power
7
Focusing requirements
Image angular size < grating angular dispersion
w0'  D
r'
r’~1m
Image angular size > 1.890 mrad
w0’ > 1.890 mm
+D
w0’
w0

r
source
r’
Focusing element
(VLS)
Possible solutions
Focusing pre-mirror + plane fixed line spacing grating
Spherical grating (fixed line spacing)
Plane variable line spacing (VLS) grating (current design)
Spherical +VLS grating (complex)
exit slit
8
Compact Soft X-ray Mono Design
Optical components (assuming dispersion in vertical plane)
(horizontal) Cylindrical focusing M1
Focusing at re-entrant point
(vertical) Planar pre-mirror M2
Varying incident angle to grating G
(vertical) Planar variable-line-spacing grating G
Focusing at exit slit
Adjustable/translatable exit slit S
(vertical) Spherical collimation mirror M3
Re-collimate at re-entrant point
x/2
1st undulator
source
point
M1
M3
g’/2
M2
h/2
2nd undulator
re-entrant
point
S
G
Variable Line Spacing Grating
VLS focusing
Focusing condition
Linear coefficient
Ds s 2  cos2 cos2  
 

r
r ' 
Dx  
r, r ’ are positive
If operate in fixed focal-point mode
Ds/Dx weakly energy dependent
Can only have a fixed linear coeff.
Required for exact fixed focal-point
for entire tuning range
Defocusing effect (to be discussed)
No impact on resolving power
Big impact on transverse profile
small angle (high energy) limit
w0
w0’
r’
 (D)

r

D
 (D)
D
s
s+Ds
x
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10
Mode of Operation
Fixed focal-point mode
s  sin  sin    n
cos  1
  5.7 1
cos 
s = 0.8 mm (1250 l/mm)
n=1
“Fixed” focal-point
Image, thus exit slit at “fixed” location
Included angle (+ ) variable
Tuning requires
Rotation of pre-mirror
Rotation of grating
Use outside order
Smaller q for larger footprint
Critical angles for
Si, B4C, and Be
*Exit angle q’
Incident angle q
Higher resolving power
+1 order

q
<
0th order
q’
*Exit angle above qc  low efficiency
Multilayer could help but limited tuning
11
Resolving Power
Contributions
Quadrature addition of all terms
# of grating grooves
Entrance slit
Slit-less, defined by incident beam
Adjustable exit slit size per design
Image size
Slit setting
Slope error
Input Pulse Length
90
Effective resolving power
80
70
60
DTFWHM(fs)
Size of incident beam
Footprint @ incident angle q
50
Transform-limited pulse for
required pulse length
40
30
In comparison
Current SXR grating
Resolving power 5000 @ 1.0 keV
20
10
0
200
400
600
Energy (eV)
800
1000
12
Dispersion Plane
Optical components
Deflecting mirror
Pre-mirror
VLS Grating
Collimation mirror
2.25 m
ELEVATION VIEW
1.90 m
0.89 m
0.21 m
1.15 m
1.82 m
L1
LM1M2
rM2G
r’G
rM3
r’M3
DLRe-entrant
rtotal
200 eV
1.900
1.082
0.019
0.992
0.160
3.446
-1.626
5.973
1000 eV
1.900
0.891
0.206
0.992
0.160
3.357
-1.537
5.973
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Beam Size in Dispersion Plane
Beam size evolution
Grating
w0
w0’
object
image
zR
zR’
dr’()
r’()
r
Ray-optics
source
r’non-coherent
Collimation mirror
w0
w0’
Re-entrant
point
image
object
zR’
zR
r’()
r
r’non-coherent
dr’()
Ray-optics
location
Re-entrant
point
14
Time Delay
Optical delay
Variable when tuning energy
~ 3.3 - 3.5 ps
Variation Minimized by optimize P
M3
M1
x
M2
g’
H’
P
h
G
H
15
Sagittal Plane
Optical components
(Sagittally) Focusing mirror
Deflecting pre-mirror
Deflecting VLS Grating
Deflecting collimation mirror
2.25 m
ELEVATION VIEW
1.90 m
0.89 m
0.21 m
1.15 m
1.82 m
4.07 m
L1
r’M1
DrRe-entrant
rtotal
200 eV
1.900
2.644
1.430
5.973
1000 eV
1.900
2.352
1.721
5.973
16
Beam Size in Sagittal Plane
Beam size evolution
Focusing mirror
object
image
w0
zR’
Re-entrant
point
Ray-optics
location
w0’
zR
r’()
dr’()
at designed location
(ray-optics)
r
source
r’non-coherent
re-entrant
point
17
Grating Efficiency
Overall throughput
M1 ~ 100%
M2 ~ 100%
G ~ R·h·b ~ 0.42% - 0.20%
Reflectivity R
Estimated grating efficiency h
Bandwidth factor b
Beam size mismatch (very small)
reflectivity
Reflectivity x grating efficiency
M3 ~ 100%
More rigorous calculations
To be done by J.Krzywinski*
grating efficiency
overall throughput
including bandwidth factor
*Derived by solving Helmholtz equation in inhomogeneous media, in paraxial approximation
18
Seeding Power
Output power
poutput ~ pinput·R·h·b
Estimates indicate goal is met
Simple amplitude grating estimate
J.K. rigorous calculation
input power
output power
design goal
Summary
Design meets all requirements
Grating Monochromator
Fixed-focus operation excellent choice
Only single grating needed
Capable of tuning entire energy range
Defocusing effects understood
Efficiency sufficient for seeding
Estimate and rigorous calculation indicate enough output power after mono
Delay is variable
but only weakly energy dependent
Mirrors
Pre-mirror
Enables fixed-focus operation
Vertical collimation mirror
Re-collimates mono beam at entrance point
Has a short focal length, defocus effect is evident, but could be compensated
Horizontal focusing mirror
Focuses input beam at entrance point
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Optics Specs
Grating specifications
Parameter
symbol
value
unit
Line spacing
s
0.80
mm
Linear coeff
Ds/Dx
-1.881x10-6
Groove height
h
11.35
Grating profile
nm
Lamella/Steps
Incident angle
q
8.45 – 18.77
mrad
Exit angle
q’
46.2 – 103.4
mrad
Included angle
2q
176.87 – 173
degree
Object distance
Lobj
~4
m
Image distance
Limg
~ 1.333
m
Exit slit
s
3.3 – 10
mm
22
Optics Specs
Mirror specifications
Parameter
symbol
value
unit
Cylindrical mirror Radius
R1
0.1380
m
focal length
f1
5.1113
m
Incident angle
x/2
13.50
mrad
Incident angle
g ’/2
3.99 – 37.7
mrad
Spherical Mirror Radius
R3
38.775
m
focal length
f3
0.1905
m
Incident angle
h/2
9.825
mrad
Offset-1
H
0.030
m
Offset-2
H’
~ 0.0284
m
Offset-3
P
~ 1.4
mm
Planar mirror
23
Optics Specs
Performance
Parameter
symbol
value
unit
Energy range
e
200 – 1000
eV
Pulse length (rms)
t
8.5 – 5.2
fs
Pulse energy
E
1.2 – 1.5
mJ
Peak Power
Pinput
10 - 33
MW
E-beam size (rms)
s
50 -18.4
mm
Resolving power
R
4300 - 4800
Throughput
htotal
0.42 – 0.20
%
Output peak Power
Poutput
43 - 67
kW
Time delay
DT
2.5 +/- 10%
ps