1. Investigating multiple scattering with McStas
James Tricker
Mantid Vacation Student
Been investigating multiple scattering in Mantid and whether it may be possible to incorporate McStas into a solution to multiple scattering for general samples and geometries

2. Multiple scattering
Can minimise MS in experiments by using a sample that is:
Small in comparison with its mean free path.
Strongly absorbing
When we do have MS we would like perform corrections on our data so it appears to contain only single scattering event and the neutrons have undergone no absorption
It is not always possible or desirable to make our sample small or strongly absorbing because this will either reduce the number of singly scattered neutrons as well or reduce the intensity of our beam which is an inefficient use our the full intensity of our beam

3. Integrating over a sample:
dV1
dV2
l12 l2
The neutron intensity undergoes exponential decay as it passes through a sample
Trying to do this rapidly becomes intensive
Successive terms converge to zero
Can simplify the calculation in some cases
Calculating the attenuation involves an integration of all the possible paths through the three-dimensional volume and for successive orders of scattering we require successively more integrations and so the attenuation and multiple scattering contributions are intertwined due to the increased path length when neutrons scatter back and forth through a sample.
Obviously we don’t need to go on forever since eventually the contribution is so negligible.
This brings us to what Mantid is capable of doing with MS

4. What can Mantid do currently?
Mayers Sample Correction
Multiple Scattering Cylinder Absorption (MSCA)
Muscat
First two assume the sample is a cylinder and that scattering is elastic and isotropic - essentially restricted just to vanadium
Muscat is quite dated and not widely used but in principle a good general method
Mayers performs the integration for attenuation of a single scattered neutron and then simulates a load of second scattering events to produce a ratio between second and first order scattering which is then assumed constant between orders
MSCA uses power series approximations for both corrections
Only noticed Muscat this week, not had much time to look at it. Written in FORTRAN. Will mention this again in relation to McStas

5. Cylinder absorption
Since both separate the correction into two factors, absorption and multiple scattering, decided to test the absorption correction first. Preexisting analytic algorithm cylinder absorption (CA) well trusted by Mantid, been tested in other cases and been tested against similar Monte Carlo algorithms. Mayers quite grainy especially zoomed in. Could increase integration steps. MSCA slanted. Assumes out of plane scattering.

6. Full comparison
Simply divided the two algorithms. Apart from scaling factor and slight slope due to cylinder absorption correction differences the algorithms seem to agree which is reassuring considering they use different methods to calculate the correction.

7. A general tool for simulating neutron scattering instruments and experiments
Great for multiple scattering investigation. Can track how many times individual neutrons have scattered before detection.
Possible to simulate scattering inside complicated geometries and between the sample and surrounding environment

8. Suggested approach utilising McStas
Generate a scattering function S = S(Q) or S(Q, omega) from the data in question using Mantid
Making the assumption that multiple scattering for S does not contain multiple scattering and is good first order approximation of the true S of the sample
Insert this S into a McStas component and do a McStas simulation where the output of this simulation is separated into single and multiple scattered neutrons
The single workspace then represents a simulated approximation of what the experiment would have looked like in the absence of unwanted multiple scattering. A scattering function can then be derived and the process iterated several times. Interestingly the Muscat algorithm mentioned earlier appears to follow this exact approach although Spencer will know more about this. The main point is that McStas has the potential to be a powerful engine in the Monte Carlo simulation part of the calculation

9. Mantid and McStas
From the McStas instrument file generate the IDF file for Mantid.
Compile the McStas c code. (Remember to link correctly to NeXus libraries)
Run McStas simulation with the NeXus flag on to produce event data for Mantid.
This can already by somewhat automated
Research being done to bring OFF to Mantid
Always improving interoperability
So how does McStas currently fit into Mantid?

10. Investigation with McStas
Disclaimer: Some potential flaws in this analysis. See full report for a discussion of this or ask at the end
Ran a simulation with a cylindrical sample of vanadium and split the output into a single and all workspace. Applied the corrections to the All workspace and also did a cylinder absorption correction on the single workspace to get rid of any attenuation effects to give us a comparison workspace called Ideal.

11. Investigation with McStas
A lot going on here but essentially the top two lines are simply there to verify that the algorithms are actually doing something to the original workspace called All. When the bottom two lines are the ratios of the corrected workspaces versus what we would expect to see. Pleasingly they sit closer to one and the slope in them has been reduced.

12. Further Information McStas
McStas Union components for simulating multiple scattering
Slides and full report

13. Questions?

14. Why might the investigation be flawed?