NMI3 meeting, ISIS, September 26-29, 2005
Contents:
• Overview of new capabilities of the RESTRAX software
• Numerical optimizations of TAS parameters
• Virtual TAS experiments - simulations with selected sample kernels
Recent developments of RESTRAX Optimization of neutron optics and virtual triple-axis
experiments
Jan Šaroun1, Jiří Kulda2, Vasyl Ryukhtin1
1Nuclear Physics Institute, Řež2Institute Laue-Langevin, Grenoble
RESTRAX homepage::http://omega.ujf.cas.cz/restrax/
SIMRES
Version for instrument optimizations
- more detailed simulation of TAS components - mapping neutron beam in phase-space- tools for numerical optimization
NMI3 meeting, ISIS, September 26-29, 2005
SIMRES - virtual triple axis spectrometer
collimator segments
source
sample
crystals
detector
+ setups that can be mapped onto a classical TAS layout (powder and strain diffratometers)
multi-purpose components:
source: 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 describing:Sollers, curved guides or benders, elliptic or parabolic guides, lobster-eye devices
multiplexing: flat-cone multianalyzer and multidetector systems
NMI3 meeting, ISIS, September 26-29, 2005
Ray-tracing & numerical optimizations
Fixed setup fast ray-tracing code, 103 -104 counts/sec
ray-tracing results are used to find extremum of fm numerically.
figure of merit, fm(a1, a2, ...):I ... incident intensityE ... energy spreadI / E, I / E2 ... inelastic scatteringI / , I /2 ... diffraction
free parameters, a1, a2, ... an
crystal curvature, mosaicity, cutting angle,guide dimensions, curvature, divergence, ...
Speed problem: number of simulations / iteration = 1+2n2 n 4 acceptable (CPU time < 1 hour)
NMI3 meeting, ISIS, September 26-29, 2005
Lobster-eye device & focusing monochromator
)sin( BX Rf
spatial focusing
Rl
B
monochromatic beam + spatial focusing
0 B
?
Simultaneous optimization of the crystal curvatures and guide parameters – mutual correlations– ray-tracing: realistic model of the instrument components
)sin(2 BE Rf
monochromatic focusing
0 B
NMI3 meeting, ISIS, September 26-29, 2005
Lobster-eye device & focusing monochromator
50 cm30 cm
50 cm
8 cm
12.5
Lobster-eye device• 20 (hor.) or 30 (ver.) blades• thickness 0.5 mm• m=3 supermirror (concave sides)• elliptic & parabolic profiles• optimization: entry & exit width
TAS - IN14 setup• cold source• straight 58Ni guide, 6x12 cm2
• monochromator: PG 002, doubly focusing, =4.05 Å
• target (sample) area: 3x3 mm2
• optimization: crystal curvatures
NMI3 meeting, ISIS, September 26-29, 2005
Parabolic guide
Focusing on small samples
400 200 0 200 400
40
20
0
20
40
55
55
fp
mm
550LS
mm
z
mm
ttz
mm
LL
mm
+ perfect focusing of a parallel beam
- large reflection angle at the entry
NMI3 meeting, ISIS, September 26-29, 2005
Focusing on small samples
400 200 0 200 400
50
0
5055
55
fp
mm
550LS
mm
z
mm
ttz
mm
LL
mm
Elliptic guide
- parallel beam does not focus to a point
+ lamellae are parallel at the entry
NMI3 meeting, ISIS, September 26-29, 2005
Lobster-eye device & focusing monochromator
Optimization in 2 dimensionsx
Mapping the parameter space
horizontal:1) monochromator: 1/RH
2) guide: exit width
vertical:1) monochromator: 1/RV
2) guide: exit height
adjustable parameters:
Resolution 32x32 pixels 1024 simulations
Number of blades is fixed adjusting focal distance
NMI3 meeting, ISIS, September 26-29, 2005
Mapping of parameter space
Elliptic bladesOptimization route in 2 dimensions
-0.2 0.0 0.2 0.440
50
60
70
80
90
H [m-1]
exit
wid
th [m
m]
0.0 0.2 0.4 0.670
80
90
100
110
120
V [m-1]
exit
heig
ht [m
m]
Intensity/E Intensity
horizontal vertical
NMI3 meeting, ISIS, September 26-29, 2005
Mapping of parameter space
-0.2 0.0 0.2 0.440
50
60
70
80
90
H [m-1]
exit
wid
th [m
m]
0.0 0.2 0.4 0.670
80
90
100
110
120
V [m-1]
exit
heig
ht [m
m]
Parabolic bladesOptimization route in 2 dimensions
Intensity/E Intensity
horizontal vertical
NMI3 meeting, ISIS, September 26-29, 2005
Lobster-eye device & focusing monochromator
Optimization in 3 dimensions
horizontal:1) monochromator: 1/RH
2) guide: entry width3) guide: exit width
vertical:1) monochromator: 1/RV
2) guide: entry height3) guide: exit height
adjustable parameters:
mapping in 3D is not feasible 32768 simulations/map …
Number of blades is fixed adjusting focal distance and spacing between blades
NMI3 meeting, ISIS, September 26-29, 2005
Lobster-eye device & focusing monochromator
Optimization in 3 dimensionsElliptic blades
-30 -20 -10 0 10 20 30-30
-20
-10
0
10
20
30
x [mm]
y [m
m]
-0.08 -0.04 0.00 0.04 0.08-0.08
-0.04
0.00
0.04
0.08
kx/k
k y/k
NMI3 meeting, ISIS, September 26-29, 2005
Lobster-eye device & focusing monochromator
Optimization in 3 dimensions
-30 -20 -10 0 10 20 30-30
-20
-10
0
10
20
30
x [mm]
y [m
m]
-0.08 -0.04 0.00 0.04 0.08-0.08
-0.04
0.00
0.04
0.08
kx/k
k y/k
Parabolic blades
NMI3 meeting, ISIS, September 26-29, 2005
Lobster-eye device & focusing monochromator
Optimization in 3 dimensionsFocusing monochromator only
-30 -20 -10 0 10 20 30-30
-20
-10
0
10
20
30
x [mm]
y [m
m]
-0.08 -0.04 0.00 0.04 0.08-0.08
-0.04
0.00
0.04
0.08
kx/k
k y/k
NMI3 meeting, ISIS, September 26-29, 2005
Lobster-eye device & focusing monochromator
Optimization in 3 dimensionsResults
Total intensity (whole beam) [109/s]:
parabolic 1.3elliptic 1.6no 3.4
RESTRAX
Version for TAS resolution simulations and data analysis
- simplified TAS setup with faster ray-tracing code - 4D resolution functions + convolution with S(Q,)- dynamically loaded modules with S(Q,) model- non-linear data fitting
NMI3 meeting, ISIS, September 26-29, 2005
Sample “exchanger” in RESTRAX
TAS ray-tracing, R(Q,)
4D convolution
• data simulation• data fitting
dynamically loaded modules, S(Q,)
• Damped harmonic oscillators • Damped harmonic oscillators, free
dispersion gradient• Bond charge model (phonons in Si, Ge, ...)• Incommensurate fluctuations (diffuse
satellites)• … others defined by users
NMI3 meeting, ISIS, September 26-29, 2005
TAS: conventional arrangement
monochromator
sample
analyzer
detector
NMI3 meeting, ISIS, September 26-29, 2005
TAS: flat-cone analyzer
monochromator
sample
analyzer
detector
NMI3 meeting, ISIS, September 26-29, 2005
TAS: flat-cone multianalyzer
monochromator
sample
analyzer
detector
NMI3 meeting, ISIS, September 26-29, 2005
Sweeping 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
[
0 1
0]
E=0 meV
0 1 2 3
E=4 meV
[1 0 0]0 1 2 3
E=12 meV
non-linear scans in rec. lattice
a3
a4
NMI3 meeting, ISIS, September 26-29, 2005
Example 1: Incommensurate sattelites
Incommensurate sattelites: 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)
NMI3 meeting, ISIS, September 26-29, 2005
Example 1: Incommensurate satellites
0 1 2 3-2
-1
0
1
2
3
[0
1 0]
E=0 meV
0 1 2 3
E=4 meV
[1 0 0]0 1 2 3
E=12 meV
... and transformed to rec. lattice space
NMI3 meeting, ISIS, September 26-29, 2005
Example 1: Incommensurate satellites
detail ...
NMI3 meeting, ISIS, September 26-29, 2005
Example 2: bond charge model (BCM)
Model describing phonons in diamond lattice (Si, Ge, -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
NMI3 meeting, ISIS, September 26-29, 2005
Phonons in Si
E=10 meV E=20 meV
NMI3 meeting, ISIS, September 26-29, 2005
Phonons in Si
E=30 meV E=40 meV
NMI3 meeting, ISIS, September 26-29, 2005
Phonons in Si
E=50 meV E=60 meV
NMI3 meeting, ISIS, September 26-29, 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
NMI3 meeting, ISIS, September 26-29, 2005
Summary
Numerical optimizations• using ray-tracing simulations in numerical optimization is feasible
• multiple correlated TAS parameters can be optimized with respect to different figures of merit
Lobster-eye guides• high flux at small samples, leaves space for sample environment
• vertical and horizontal focusing can be splitted in 2 guide sections
• alternative to focusing monochromators at quasiparallel beams
Dynamically loaded S(Q,) modules• data simulations and fitting with various sample kernels
• extensions provided by users
RESTRAX homepage::http://omega.ujf.cas.cz/restrax/