September 27, 2011
Cheiron School 2011

X-ray Beamline Design 1- X-ray Monochromator Shunji Goto
SPring-8/JASRI
1

Outline
1.
2.
3.

4.
5.

Introduction
Light source
Monochromator
Fundamental of Bragg reflection
DuMond diagram ~ extraction of x-rays from SR
Double crystal monochromator
Crystal cooling
Example of beamlines at SPring-8
Summary2

Process of beamline construction
Scientific proposal
by user & facility

New beamline
Review & approval
by IAC,..

1. conceptual design
2. detailed design
3. construction

Support of budget& other resources
by government,..

4. utilization w/ output
5. upgrade or,...
Review

Beamline design is first step and crucial for success of the beamline !
Æ Fundamental of X-ray beamline; light source, monochromator, mirror,...
3

Beamline structure
Beamline = “Bridge” between light source & experimental station

Front-end

Light source
BendingmagnetExperimental
stationInsertion
deviceShielding
hutch

SR

Ring tunnel

Exp. hallÆ Transport and processing of photons
photon energy, energy resolution,
beam size, beam divergence, polarization,..
Optics & transportÆ Vacuumprotection of ring vacuum and beamline vacuum Monochromator, mirror
shutter, slit
Æ Radiation safety
4

Shielding and interlock

pump,..

Light sources & X-ray optics
Check points to be considered for your application:- White or monochromatic- Energy range- Energy resolution- Flux & flux density- Beam size at sample (micro beam?,...)- Beam divergence/convergence at sample (Resolution in k-space)- Higher order elimination w/ mirror- Polarization conversion- Spatial coherency....

Æ Light source, monochromator, mirror,
and other optical devices and components

5BL classification (energy region)
Photon energy (eV) ÆIR

Visible ~ UV~
100

Bendingmagnet

101

SX
102

103

HX
104

105

SAXS

Earth,..
HP/HT

XAFS

IR

Powder XRD
PX

Wiggler

Inelastic
SAXS

Undulator

PEEM
SX-PESSX-MCD

Inelastic
HX-PES

HP/HT
XRD
NRS
6

BL classification (energy resolution)
Energy resolution (ΔE/E) Æ
10-7

10-5

10-3

White

SAXS

XAFS

Single crystal
XRD

Earth,..
HP/HT

PX

BendingmagnetPowder XRD

Topograph

Imaging
Topograph
Inelastic

Wiggler
XAFS
Inelastic

Surface ・interface

XRF

Microbeam, imaging

Undulator

XMCD
NRS
HX-PES

SAXS
PX
HP/HT
XRD

7

Light sources (1)Bending magnet:
for wide energy range, continuous spectrum
for wide beam application for large samples

Undulator (major part of 3GLS beamline):for high-brilliance beam
for micro-/ nano-focusing beam

Wiggler:for higher energy X-rays > 100 keV.
Power, brilliance, flux density, partial flux,..
can be calculated using code.
e.g. “SPECTRA” by T. Tanaka & H. Kitamura

Brilliance (ph/s/mm2/mrad2/0.1% B.W.)

Bending magnet or insertion devices ?
1022
1020
1018
1016
1014
1012
100

101

102
103
104
Photon energy (eV)105

Brilliance for SPring-8 case8106

Light sources (2)Angular divergence and band widthÆ Core part we need
Bending magnet
σ r ′ ≈ 0.597

1

γ

λ
λc

Undulator
1 1+ K 2 2λn=σ r′ ≈
2 Nλu 2γ
nN

ΔE
1
≈
E
nN

SPring-8 in-vacuum undulator

9Light sources (3)SR power Æ mostly eliminated before/by monochromator
Bending magnet

Undulator

Power distribution

ψv ≈1 γψ v ≈1 γψ h ≈ constψ h ≈ K γ
K: deflection parameter(K= 0.5~2.5)

Total power

L Arc [m]Ptot [kW ] = 1.27 E 2 [GeV]B 2 [T]R[m]φ[rad]I [A]
E= 8 GeV, I= 0.1 A, B= 0.68 T, R= 39.3 m
Æ Ptot= 0.15 kW/mrad

B0 sin 2 (2πz λu )1 2
Ptot [kW] = 1.27 E 2 [GeV] B0 [T]L[m]I [A]2
B0= 0.87 T, L= 4.5 m
10
Æ Ptot= 14 kW
2

Monochromator
Key issues from experimental request:
White or monochromatic ? Æ monochromatic
Energy region Å Bragg’s law
Energy resolution Å Source divergence, Darwin width,..
Flux (throughput) Å related to energy resolution

Double-crystal monochromator for fixed-exit
Single-bounce monochromator is for limited caseHeat load Å depending on light source11Bragg reflection
Laue condition (Kinematical)
in reciprocal space

Bragg’s law in real space

Q = Ks − K0 = h1) Phase matching on the single net
plane by mirror-reflection condition.
2) Phase matching between net planes.

Reciprocal lattice vector h- Normal to net plane- Length = 1/d2d sin θ B = mλθScattering vector Q

θ
d

dsinθ

dsinθ

Incident wave
K0
θ

Reciprocal lattice vectorhScattering waveKsθnet plane(spacing d)
12

Miller indices and d-spacing for silicond=
Top viewah2 + k 2 + l 2

a = 5.431Å[001]

d-spacing(400) : 1.3578 Ǻ
(111) : 3.1356 Ǻ(311) : 1.6375 Ǻ

[010]

a

(511) : 1.0452 ǺSide view
a

(400)
(111)

(311)

(511)

[100]

[011]

13

Crystal structure factor for diamond structure
Structure facrtor Î Sum of atomic scattering with phase shift in the unit cell
F (h ) = ∑ f j (h, E ) exp(2πih ⋅ r j )6j

Atomic scattering factor

5

F (h ) = ∑ f j (h, E ) exp{2πi (hx j + ky j + lz j )} z

7

2
1

(xj, yj, zj) =84jFor diamond structure

Position of atoms in the unit
cell for diamond structurey 3
xh, k , l Mixture of odd and even numbers
F =0(0, 0, 0)1, (1/4, 1/4, 1/4)2,(1/2, 1/2, 0)3, (3/4, 3/4, 1/4)4,(0, 1/2, 1/2)5, (1/4, 3/4, 3/4)6,(1/2, 0, 1/2)7, (3/4, 1/4, 3/4)8h, k , l All odd, or, all even numbers, and m: integer,h + k + l = 4m

F =8f

Å 8 atoms in phaseh + k + l = 4m ± 1

F = 4(1 ± i ) f

Å Half contribute with phase shift ±π /2

h + k + l = 4m ± 2

F =0

Å Half cancel with π
14

Crystal structure factor for diamond structure(111), (311),...
Half contribute with phase shift ±π /2(400), (220),...
All in phaseÎ F = 4(1 ± i ) f

Î F =8f
a

(400)
(111)

(311)

(511)

(200)
[100]

[011]

(011)

(011), (200),...
Half cancel with πÎ Forbidden reflection

F =0
15

X-ray monochromator using perfect crystal
Æ Perfect single crystal: silicon, diamond,..
120- Crystal & lattice plane- Bragg angle range

Photon energy (keV)

Photon energy range:100
Si 511 refl.

80

Si 311 refl.

60
40
20

Si 111 refl.
0

0

5

10
15
20
Bragg angle (deg)2530e.g. for SPring-8 standard DCM
Bragg angle: 3~27°
16

Reflectivity (dynamical theory)
Darwin curve (intrinsic reflection curve for monochromatic plane wave)
for Bragg case, no absorption, and thick crystal:(

R = W + W −1
R =1

(

2

)

2

(−1 ≤ W ≤ 1)

R = W − W −1
2)

2

(W < −1)
Å Total reflection region(W > 1)

W: deviation parameter for s-polarization, symmetrical Bragg case

ΔE
⎛
⎞ 1
+ χ0 ⎟
W = ⎜ Δθ sin 2θ B + 2 sin 2 θ BE⎝⎠ χhAngulardeviation

χh: Fourier component of polarizabilityÆproportional to the structure factor

re λ2
F (h, E )
χh = −
πvc

Energydeviation
Refraction

Geometry forsymmetrical
Bragg case

K0

Kh

θB

θB

vc: unit cell volume

Surface
net planeθ B + Δθ

θ B + Δθ17

Darwin curve
For Bragg case, no absorption, and thick crystal:
1.2

Reflectivity

1
0.8
0.6
0.4
0.2
0
-5

-4

-3

-2

-1

0

1

2

3

4

5

W
18

Reflectivity with absorption
Fourier component of polarizability for diamond structureχ h = χ h′ + χ h′′
h + k + l = 4mrλ
χ h′ = − e 8( f 0 + f ′)e − M
πvc
2

re λ2
χ h′′ = −8 f ′′e − M
πvc

h + k + l = 4m ± 1
re λ2
χ h′ = −4(1 + i )( f 0 + f ′)e − M
πvc
re λ2
4(1 + i ) f ′′e − Mχ h′′ = −πvc

h=k =l =0re λ28(Z + f ′)
χ 0′ = −πvc
re λ2
8 f ′′
χ 0′′ = −πvc

Reflectivity- symmetrical Bragg case,- s-polarization,- thick crystal
R = L − L2 − 1⎧W 2 + g 2 +⎨L= ⎩(W − g − 1 + κ ) + 4(gW − κ ) ⎫⎬
2

2 2

2

1+ κ

2

⎭

2

ΔE
⎛
⎞ 1
+ χ 0′ ⎟W = ⎜ Δθ sin 2θ B + 2 sin 2 θ B
E⎝⎠ χ h′

χh′′
χ 0′′
, κ=
g=
′
χh
χ h′

19

Reflectivity curve for silicon
Examples for symmetrical Bragg case, with absorption,s-polarization and thick crystal:
Si 111 refl., 10 keV

1

χ 0′ = −9.78 ×10−6′ = −3.66 ×10 (1 + i )χ111−6′′ = −7.30 ×10 −8 (1 + i )χ111

Si 333 refl., 30 keV
χ 0′ = −1.07 ×10−6
χ 0′′ = −1.75 ×10−9′ = −2.24 ×10 −7 (1 + i )χ 333′′ = −7.87 ×10 −10 (1 + i )χ 333

Si 111 refl.
10 keV

回折幅
Reflectivity

χ 0′′ = −1.48 ×10

0.8

−7

Si 333 refl.
30 keV

0.6
0.4
0.2
0
-100

-50

0
Δθ (µrad)50

100

・Width of 0.1～100 µrad
・Peak ~1 with small absorption20

DuMond (angle-energy) diagram
The diagram helps to understand how we can extract x-rays from SR source.
Angular width(Darwin width)
Energy resolution
Effective band widthΔθ Darwin =2 χ h′
sin 2θ B

Í ΔW= 2ΔE
2= cot θ B Ω 2 + Δθ Darwin
EÍ Gaussian approximation for bothlight source and reflection curve

χ h′
ΔE
≈
E sin 2 θ B

Relative energy

ΔE E
W = −1 W = 1∝ F (h )Relative energy

ΔE E

Light source

Darwin width
Shift by refraction
Slope: − cot θ B

Effective
band width

Energyresolution

Kinematical
Bragg condition

θB

Incident angle θIncident angle θLight source divergence φ21

Source divergence and diffraction width
Natural divergence103- Bending magnet

FWHM (µrad)102

σ r ′ ≈ 0.597

Bending magnet
Undulator

101

1

γ

λ
1
∝
λc
hω

- Undulator
Si 111 refl.

σ r′ ≈

Si 311 refl.

100

λ
1
∝
2 Nλu
hω

Si 511 refl.

For SPring-8 case:

10-1
0

20

40

60

Photon energy (keV)

80

100

- Bending magnet
σ r ′ ≈ 60 μrad

- Undulator (N= 140)
σ r′ ≈ 5 μrad

Divergence of undulator radiation ~ diffraction width

22

Energy resolution
ΔE= cot θ B Ω 2 + ω 2
E

Ω: source divergence,
ω: diffraction widthφ
10-2

BM & Si 311 refl.

Light source
distribution

10-3

Acceptanceby crystal

Resolution

Angle ÆAngle-energy diagram(DuMond diagram)

ΔE/E

Photon energy Æ

BM & Si 111 refl.

BM & Si 511 refl.
Undulator & Si 111 refl.

10-4

10-5
0

20

40

60

80

100

Photon energy (keV)

For usual beamline : ΔE/E=10-5～10-3

23

DuMond diagram: undulator & DCM
φSPring-8 standard undulator(λu= 32 mm, N= 140, K= 1.34, E1st= 10 keV)
+ DCM (Si 111 refl.)

200

600

10 keV (1st)1000

30 keV (3rd)

50 keV (5th)0

ΔE (eV)ΔE (eV)ΔE (eV)

Intensity
distribution ofundulator
00

DE/E= 2x10-4

Acceptanceby crystal
-200

-600
-50

0
φ (μrad)

50

-1000
-50

0
φ (μrad)

50

-50

0
φ (μrad)

50 μradWider slit increases unused photons (power) on the monochromator !

50

24

Acceptanceby crystal

Resolution

Slit width

Photon energy ÆLight source
distribution

Resolution

Angle ÆAngle Æ(A) Collimation using slit(B) Collimation using pre-optics
w/ collimation mirror, CRL,..
Photon energy Æ

Photon energy Æ

Photon energy Æ

Improvement of energy resolution

Resolution

Angle Æ(C) Additional crystal
w/ (+,+) setting

Resolution

Angle Æ(D) HR monochromator of
π/2 reflection (~meV)(B)~(D): restriction on photon energy

25

Photon flux after monochromator
Photon flux (throughput) after monochromator can be
estimated using effective band width:
Photon flux (ph/s) =Photon flux from light source (ph/s/0.1%bw)
x 1000

Photon energy Æ

x Effective band width of monochromator

Light source
distribution
Acceptanceby crystal

Effective
band width

Angle ÆThroughput is estimated by overlapped area.
Note difference from energy resolution.

26

Effective band widthStarting with Darwin width in the energy axis

χ h′
ΔE
≈
E sin 2 θ B

1χ h′ ∝ λ2 { f 0 (d hkl ) + f ′(λ )}χ h′ ∝ λ2 f 0 (d hkl )
χ h′
ΔE
Δλ
=−
≈
E
λ sin 2 θ B= 4d hkl

2

χ h′
λ2

ΔE
Δλ
2
=−
∝ d hkl f 0 (d hkl )E
λIndependent of photon energy

0.8

Reflectivity2

Neglecting anomalous scattering factor f’

10 keV
30 keV

0.6
1.4x10-4
0.4
0.2
0
-5

-4

-3

-2

-1

0

ΔE/E

1

2

3

4

5

(x10-4)e.g. for Si 111 refl. DCM case
Note relative energy width is constant.
27

Effective band width (Integrated intensity)

For double-crystal monochromator

χ h′
ΔE
2
=
R
W
dW
(
)
2
∫
E
2 sin θ B

Effective band width(x10-5)14
Si 111 refl.

12
10
8
6
4

Si 311 refl.

2

= ~2

0

Si 511 refl., Si 333 refl.
0

20

40
60
Photon energy (keV)

80

100

Effective band-width is obtainedby integration of reflection curve.

When you need flux Æ Lower order (Si 111 refl.,..)
When you need resolution Æ Higher order (Si 311, Si 511 refl,..)28

Photon flux at undulator beamline

Photon flux (ph/s/100 mA)

1016(a) total flux

1015(a) Total flux @ 0.1% b.w.
(b) After frontend slit
1×1 mm2 @30 m(c) Si 111 refl. @10 keV
Effective b.w. = 1.3x10-4(d) 3rd harmonics @30 keV
Effective b.w. = 8.0x10-6

(c)

1014
1013
1012

(d)

1011

(b) partial flux

1010
0

10

20

30

40

50

Photon energy (keV)

Higher harmonics elimination more Æ mirror or detuning of DCM
We can obtain photon flux of 1013～1014 ph/s/100 mA/mm2
using standard undulator sources and Si 111 reflections at
SPring-8 beamlines.

29

Double-crystal monochromator¾

Fixed-exit operation for usability at experimental station.

¾

Choose suitable mechanism for energy range(Bragg angle range).

¾Precision, stability, rigidity,...

30θ1 + translation + θ2 computer link
2nd crystal

θ -stage

1st crystal

θ -stagehyTranslation stage

SPring-8 BL15XU
SPring-8 information Vol. 5, No.1 (2000)

h= 100 mm, θB= 5.7~72°(for lower energy range)
Large offset, long-stroke translation
Difficulty of adjustment between 1st and 2nd crystal31θ + two translation (KEK-PF)

1st crystal

2nd crystal
O
Exit beam
θB
θB B

A
z

y

OffsethθBh= 25 mm, θB= 5~70°
Two cams for two translation-stages
PF BL-4C..
Matsushita et al., NIM A246 (1986)

Rotation center at 2nd crystal
32

SPring-8 standard DCM

Offset h= 30 mm

θB =3~27º for higher energy range

High-precision adjustment stages
for undulator beamline DCM

Yabashi et al., Proc. SPIE 3773, 2 (1999)

Sub-µm & sub-µrad control

33

Crystal cooling
Why crystal cooling？
Qin (Heat load by SR) = Qout (Cooling + Radiation,..)Æ with temperature rise ΔT
Æ αΔT = Δd (d-spacing change)
α: thermal expansion coefficientor Æ Δθ (bump of lattice due to heat load)
Miss-matching between 1st and 2nd crystals occurs:Æ Thermal drift, Loss of intensity, Broadening of beam, loss of brightness
Æ Melting or limit of thermal strain Æ Broken !
Qin

Radiation & convection
T1
Heat conduction in crystal

CrystalT0

熱伝達

Coolant/holder

Heat transfer
to coolant/holder
34

Solution for crystal cooling
We must consider:
Thermal expansion of crystal: α,Thermal conductivity in crystal: κ,
Heat transfer to coolant and crystal holder.
Solutions:(S-1) κ/α Æ Larger(S-2) Large contact area between crystal and coolant/holderÆ larger(S-3) Irradiation area Æ Larger, and power density Æ smaller

35

Figure of merit
SiliconSiliconDiamond

300 K

80 K

300 K

κ (W/m/K) 150

1000

2000

α (1/K)-5x10-7

1x10-62000

2000

2.5x10-6

κ / α x106 60

Figure of merit of cooling:
Good for silicon (80 k) and diamond (300 K)
36

For SPring-8 case
Bending magnet beamline
Power and density : ~100 W, ~1 W/mm2 @40 m
Method:Æ Direct cooling with fin crystal

Å S-2

Undulator beamline(Linear undulator, N= 140, λu= 32 mm)
Power and density : ~500 W , ~500 W/mm2 @40 m
Methods:
Æ Direct cooling of silicon pin-post crystal+ Rotated inclined geometry (Æ10 W/mm2)
Æ or Cryogenic cooling using LN2 circulation
Æ or Indirect cooling of IIa diamond crystal

Å S-2
Å S-3
Å S-1
Å S-1
37

Crystal monochromator at SPring-8
X-rays<Bending magnet beamline>
Power & power density:~100 W, ~1 W/mm2

O-ringFin crystal direct-cooling - (S2)Water flow

Si-Au-Sibondingb) Silicon cryogenic cooling - (S1)

<Undulator beamline>
Linear undulator, N= 140, λu= 32 mm
Power & power density: 300~500 W ,300~500 W/mm2a) Direct cooling of silicon pin-postc) IIa diamond withcrystal – (S2) & (S3)indirect water cooling - (S1)
0.2 mm 0.6 mm
0.6 mm
0.5 mmWater flow

38

Example of x-ray beamline- SPring-8 case -39

XAFS & single crystal diffraction- Bending magnet- Collimator mirror,+ DCM,+ refocusing mirror(a)Double-crystal
Downstream
monochromator
shutterGamma
Collimator
stopper
Bellows
mirror

Refocusing
mirrorRoller
G1

J1

J2

G2

J4 G3 J5

J3

J6

Motor
Shaft

Link

G1-G3: Gear box

J1-J6: Jack

Ideal reflection axis
y

(b)

δ

(0, h)(x0, y0)h-y0xFixed point

Beamline center40Protein crystallography- Bending magnet- DCM + focusing mirror

Optics hutch with standard components

Double-crystal
Focusing mirror
monochromator (Vertical deflection)

Experimental hutch

Shielded tube

30 m

40 m

50 m
Distance from the source

41

High resolution inelastic scattering- Undulator- DCM + back-reflection monochromator & analyzer (w/ ~meV resolution)

Optics hutch

Experimental
hutch 1

Downstream
shutter 1

Double-crystal
monochromator

Experimental
hutch 2

Experimental hutch 3(Back scattering hutch)

Experimental hutch 4(Analyzer hutch)

Dual movableend-stopper

Focusing mirror
Downstream
shutter 3

Downstream shutter 2(Dual shutter)
Shielded beam duct

Sample position
Inclination stage

Si 111 double-crystal
beam displacer
Back scattering
monochromator

5

30 m

40 m

50 m

60 m

70 m

80 m
Distance from the source42200-m-long beamline- Bending magnet- DCM
Storage ring building

Roots pump with dry pump

Optics hutch with standard transport channel and optics
Experimental hutch 1
Dry pump

Front end
40 m

60 m

140 m

160 m

120 m

100 m

80 m

Dry pump

400-mm-diameter shielded beam duct

Arcade120 m

Beam monitor andgate valve

Biomedical imaging center
Experimental hutch 2 and 3

180 m

200 m

220 m
Distance from the source

300-mm-wide beam at end-station
43

Summary- Starting point of X-ray beamline design is shown here,
w/ light source and monochromator.

- It helps to figure out what we can do at the beamline.

- We will have to go into details of design refinement using;
FEA (ANSYS), ray-tracing (SHADOW,...).
- Ray-tracing Æ wave simulation for “diffraction limited source and optics”

44