Monte-Carlo Modeling 

of Multiplexed Neutron 

Spectrometers

Samantha Isaac

Mentor: Leland Harriger
Standard Triple Axis Spectrometers

A1(θM): Angle of the Monochromator A2(2θM): Take-off angle from the Monochromator 

A3(θS): Angle of the Sample A4(2θS): Take-off angle from the Sample

A5(θA): Angle of the Analyzer Crystal Group A6(2θA): Take-off angle from the Analyzer Crystals
RITA-Style Multiplexed Triple Axis 

Spectrometers

• In order to cover a larger A4 range, multiple analyzer crystals are aligned along A5 in order 

to form an Analyzer Crystal Group

• Each crystal can then be individually rotated to scatter a different energy
Rowland Geometry

• Uses the Central Angle Theorem

• Bragg’s Law

• Waves are scattered from lattice planes whose interplanar distance is d. The 

angle necessary for this scattering process to take place is the Bragg angle (θB). 

The waves then scatter off at an angle of 2θB.

• nλ=2dsinθB

http://www.mathopenref.com/arccentralangletheorem.html

https://en.wikipedia.org/wiki/Bragg%27s_law#/media/File:BraggPlaneDiffraction.svg
Rowland Geometry

• Typically, this simple geometry is used 

throughout the world in triple axis 

spectrometers

• A wide A4 range created by the sample is 

compressed to produce a sample image at 

the position of a single detector

• The analyzer crystal group is placed tangent 

to the circle

• In fixed-Ef mode (our primary mode of 

interest), each analyzer crystal is individually 

rotated such that each reflect off the same 

energy

• This results in a relaxed Q-resolution due to 

the loss of the A4 information

Sample 

Image
Inverse Rowland Geometry

• This is a new geometry developed for RITA 

style multiplexed spectrometers by Leland 

Harriger and Igor Zaliznyak

• A sample image reproduced by the 

multiplexed analyzer is projected onto the 

Rowland circle and then viewed by a 

position sensitive detector (PSD) through a 

radial collimator. 

• This ability to use a radial collimator just 

before the PSD greatly increases the signalto-noise ratio.

Sample Image
Monte-Carlo Simulations

• All simulations were run using McStas, a neutron ray-trace 

simulation package.

• http://www.mcstas.org/

• I built a virtual triple axis spectrometer that mirrors SPINS in 

McStas where neutron ray paths were determined 

component by component using the Monte-Carlo method

• Monte-Carlo simulations use a repeated random sampling 

process rather than an analytical calculation to determine 

neutron ray paths

Focal Length at Sample Image

Sample Image

Focal Point
Focal Length at Sample Image

Sample Image

Focal Point
Focal Length at Sample Image

Sample Image

Focal Point
Calibration Results

• The elastic lines from a 

simulation of a 

spectrometer using 

Rowland defocusing is 

consistent with real data 

from SPINS

• The A4 scans are also 

very similar
Calibration Results

1

2

3

4

5

• All Monte-Carlo 

results were 

restructured to 

mimic real data 

files and DAVE was 

then used to run 

calibrations.

• The peak and 

width (A, b) are 

use to determine 

the sensitivity of 

each pixel.

• The center (x0) is 

used to determine 

the A4/Ef value 

sampled by each 

pixel.

A

b

x0
Calibration Results

• Fits were then run in DAVE using the 

previous calibrations to produce these 

plots

• Curved shape of the energy plot is a 

result of the crystals lying tangent to the 

Rowland circle

• Intensities are not uniform across the 

crystals for this same reason as seen in 

the sensitivity plot
Simulating a ‘Perfect’ Rowland 

Triple-Axis Spectrometer

• The analyzer crystal group is 

placed along the circle as 

opposed to tangent to it

• Each crystal is then rotated to 

produce the A5 value relative to 

their individual position on the 

circle. 
Results

• Uniform intensity 

across crystals is 

due to a reduction 

in beam depletion 

caused by being 

further and further 

away from the 

sample
Wide Angle Designs

IRIS (Inverse Rowland Inelastic Spectrometer)

• We can expand the multiplexing of analyzer crystals to a 150o

A4 coverage by closely packing the crystals

• The PSD is then converted into a large detector bank

LEAF (Low Energy Anti-Focusing Spectrometer)

• This design superimposes multiple Rowland circles with 

each encompassing its own reduced IRIS design

• Slightly reducing Q-space allows for sampling of 

multiple energies at once

LEAF IRIS
Conclusions

• Multiplexing a triple axis spectrometer increases 

throughput considerably.

• Rowland defocusing can be applied to triple axis 

spectrometers immediately 

• Monte-Carlo results agree very well with 

experimental results for a Rowland defocused triple 

axis spectrometer

• Monte-Carlo results for wide angle designs can now 

be carried out with a high level of confidence
Acknowledgments

• Leland Harriger

•Jeff Lynn

•Julie Borchers and the other SURF Directors

•NSF and CHRNS