MC workshop, PSI Villigen, October 2-4, 2005 Contents: • Overview of RESTRAX features • Example of TAS simulations with flat-cone multianalyzer • Overview of SIMRES features • Example: multichannel supermirror guides Introduction to RESTRAX Jan Šaroun 1 , Jiří Kulda 2 , Jiří Svoboda 1 , Vasyl Ryukhtin 1 1 Nuclear Physics Institute, Řež 2 Institute Laue-Langevin, Grenoble RESTRAX homepage::http://omega.ujf.cas.cz/restrax/
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Introduction to RESTRAXlns00.psi.ch/mcworkshop/papers/RESTRAX_introduction.pdfModel describing phonons in diamond lattice (Si, Ge, α-Sn, Eigenvalues & eigenvectors are calculated
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MC workshop, PSI Villigen, October 2-4, 2005
Contents:
• Overview of RESTRAX features• Example of TAS simulations with flat-cone multianalyzer
• Overview of SIMRES features
• Example: multichannel supermirror guides
Introduction to RESTRAX
Jan Šaroun1, Jiří Kulda2, Jiří Svoboda1, Vasyl Ryukhtin1
1Nuclear Physics Institute, Řež2Institute Laue-Langevin, Grenoble
What is RESTRAX?Virtual three-axis neutron spectrometer– Modeling of TAS resolution functions using both analytical (matrix) and
Monte Carlo ray-tracing methods.– 4D convolution with an “arbitrary” scattering kernel – S(q,ω) function– data analysis (non-linear χ2 fitting)
What is SIMRES?Ray-tracing simulation program for instruments with “TAS-like” layout (e.g. powder diffractometer) – More detailed simulation of some components (benders, crystals)– Absolute neutron fluxes and beam profiles in r, k, t space.– Tools for instrument design – mapping intensity/resolution in the space of
instrument parameters + numerical optimization
Win32 and Linux versions available at http://omega.ujf.cas.cz/restrax
MC workshop, PSI Villigen, October 2-4, 2005
RESTRAX
Resolution function ray-tracing + analytical calculations
S1(q,ω)
S2(q,ω)
S3(q,ω)
4D convolution
data fitting
dynamically loaded scattering models
5 collimator/guide segments
sample
focusing crystal assemblies
Source
detector
MC workshop, PSI Villigen, October 2-4, 2005
MC workshop, PSI Villigen, October 2-4, 2005
Resolution function: R(Q,ω)
∫ −−= ωωωωπ
σω ddRSkk
NIi
f QQQQQ ),(),(4
),( 0000
Defined as convolution ...
∫ Φ= fififiFI dddPWIFI
kkrkrkrkkkk kk ),(),(),(),(
… or neutron transport
Scattering probability
Flux distribution at the sample
Detection probability
MC workshop, PSI Villigen, October 2-4, 2005
Resolution function obtained by ray-tracing
Resolution function is represented by a cloud of points
weighted by event probability, αp
Em i f0
22 2
2≡ − ( ), ,k kα α
Q k kα α α≡ −f i, ,
A “specimen” scattering to all kf with equal probability:
( ),..., ααα EQX ≡
MC workshop, PSI Villigen, October 2-4, 2005
Monte Carlo convolution with S(Q,E)
step
Inte
nsity
scan step (∆Q, ∆E)
Event histogram∑ ∆+∆+=
αααα ),( EjEjSpI j QQ
All events are counted at each step:
Diffuse S(Q,ω)
MC workshop, PSI Villigen, October 2-4, 2005
Monte Carlo convolution with S(Q,E)
scan E=const.
QX
QY
Ener
gy
scan Q=const.Zero-width dispersion:
Events are sorted according to their distance from the dispersion branch
MC workshop, PSI Villigen, October 2-4, 2005
TAS: conventional arrangement
monochromator
sample
analyzer
detector
MC workshop, PSI Villigen, October 2-4, 2005
TAS: flat-cone analyzer
monochromator
sample
analyzer
detector
MC workshop, PSI Villigen, October 2-4, 2005
TAS: flat-cone multianalyzer
monochromator
sample
analyzer
detector
MC workshop, PSI Villigen, October 2-4, 2005
Mapping reciprocal space
New flat-cone analyzer for ILL TAS instruments, 32 channelsIN20: monochromator Si, ki=3 A-1
0 1 2 3-2
-1
0
1
2
3
ξ
[0 1
0]
E=0 meV
0 1 2 3
E=4 meV
ξ [1 0 0]0 1 2 3
E=12 meV
non-linear scans in rec. lattice
a3
a4
MC workshop, PSI Villigen, October 2-4, 2005
Example 1: Incommensurate satellites
Incommensurate satellites: ∆E →∞
210
010
200
210000
010110
E
raw data10 20 30 40 50 60 70 80
-40
-20
0
20
40
E=4 meV
a4 [deg]
a3 [d
eg]
M.C. ray-tracing & convolution with S(Q,E)
MC workshop, PSI Villigen, October 2-4, 2005
Example 1: Incommensurate satellites
0 1 2 3-2
-1
0
1
2
3
ξ [0
1 0
]
E=0 meV
0 1 2 3
E=4 meV
ξ [1 0 0]0 1 2 3
E=12 meV
... and transformed to rec. lattice space
MC workshop, PSI Villigen, October 2-4, 2005
Example 2: bond charge model (BCM)
Model describing phonons in diamond lattice (Si, Ge, α-Sn, ...)Eigenvalues & eigenvectors are calculated using coulombic potential of bond charges for each of Q,E points representing simulated TAS resolution functionW. Weber, Phys. Rev. B 15 (1977) 4789.
phonons in Si
MC workshop, PSI Villigen, October 2-4, 2005
E=20 meV
Phonons in Si
MC simulation for IN20kf=3A-1, E=20meV64 channels, ∆a4=1.25o
91 steps, ∆a3=0.75o
convolution with flat-cone resolutionsimulated by ray-tracingCPU time: 4 hours
MC workshop, PSI Villigen, October 2-4, 2005
SIMRESsource: arbitrary energy, spatial and angular distributions via look-up tables
crystals: focusing arrays of elastically bent or mosaic crystals (incl. simulated extinction effects, absorption, etc...)
collimators: universal components• coarse and Soller collimators• curved guides or benders• elliptic or parabolic guides
(multilamellar)
tools for• simulation of absolute neutron flux• Resolution and intensities for
inelastic scattering and powder diffraction
• numerical optimization for any of ~ 280 instrument parameters
7 collimator segments
sample
crystal assemblies
source
detector
M11M10
M9
M8M7
M6M5M4M3
M2
M1
M0
MC workshop, PSI Villigen, October 2-4, 2005
Source definition: lookup tables
Resampling TRIPOLI data for H53:
-0.15 -0.10 -0.05 0.00 0.05 0.10 0.15-60
-50
-40
-30
-20
-10
0
10
20
30
40
50
60
β [rad]
Y [m
m]
-0.15 -0.10 -0.05 0.00 0.05 0.10 0.15-30
-20
-10
0
10
20
30
α [rad]X
[mm
]
horizontal vertical
in the middle stream
)(4 λφλ
φπΩ∂∂
∂
0.1 1 100.01
0.1
1
10
100
H53 entry, middle stream, TRIPOLI HCS, by P. Ageron (1989)
dφ/d
λ [1
012 n
/s/c
m2 /A
]
λ [A]
used as look-up tables in RESTRAX ⇒
MC workshop, PSI Villigen, October 2-4, 2005
Mosaic and gradient crystals
• Random-walk model for secondary extinction
( ) ( )
⋅−⋅−∆=∆ −
segkin
PQ
graderferfgrad
t ξθθθ
η 1log1
( ) ( )θξ ∆⋅−−=∆ gQPt kinseg1log
( )θ∆g
mosaic
mosaic & gradientTilted segments of mosaic crystalsMigration between segmentsOptional uniform lattice gradient - theoretical
model by Hu H.-C., J. Appl. Cryst.26, 1993, 251-257.
Absorption - capture, TDS, incoherent scattering by Freund A. K., Nucl. Instr. Meth.A 213, 1983, 495-501.
• Random walk steps: ∆t
• Sampling procedure
Mosaic distribution:
where Pseg is the total scattering probability for 1 segment
MC workshop, PSI Villigen, October 2-4, 2005
Multichannel parabolic & elliptic guides
Test: point to point focusing:guides: 21x21 slots, space 1.8 mm, lam. thickness 0.2 mm, m=3 source: 1x1 mm2, λ=4.5 A
30 cm
300 cm
30 cm
-20 -10 0 10 20
-20
-10
0
10
20
X [mm]
Y [m
m]
spatial distribution
-0.04 -0.02 0.00 0.02 0.04
-0.04
-0.02
0.00
0.02
0.04
kY/k [rad]
k Y/k
[rad
]
angular distribution
MC workshop, PSI Villigen, October 2-4, 2005
Multichannel parabolic & elliptic guides
Test: point to point focusing:guides: 21x21 slots, space 1.8 mm, lam. thickness 0.2 mm, m=3 source: 1x1 mm2, λ=4.5 A
30 cm
300 cm
30 cm
-20 -10 0 10 20
-20
-10
0
10
20
X [mm]
Y [m
m]
spatial distribution
-0.04 -0.02 0.00 0.02 0.04
-0.04
-0.02
0.00
0.02
0.04
kY/k [rad]
k Y/k
[rad
]
angular distribution
MC workshop, PSI Villigen, October 2-4, 2005
Multichannel parabolic & elliptic guides
Test: point to point focusing:guides: 21x21 slots, space 1.8 mm, lam. thickness 0.2 mm, m=3 source: 1x1 mm2, λ=4.5 A