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What We've Done:

This page describes some examples of our work

Efficient Software :

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Monte Carlo Simulations:

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Some comments on MC ray tracing simulations as a design methodology

The major MC ray tracing simulation packages, especially McStas and VITESS, represent an enormous investment in time, talent and funding over many years. They are now benchmarked against real instruments and against each other and can be viewed as accurate and reliable (although occasionally a bug still surfaces and is usually quickly fixed). They are excellent tools to model the performance of full or partial neutron scattering instruments, beam elements or delivery systems.

It is common to underestimate the difficulty of producing accurate and meaningful results. A simulation usually needs many input parameters and great care is needed to avoid mistakes in input and layout. Often, the only way to know if it is correct is to check the output against some result which is independently known. Many studies remain incomplete or over simplified.

Simulations can be used to compare different models of neutron scattering delivery systems and instruments in a cost effective way. In principle, by running repeated simulations with slightly altered parameters, observing closely and keeping good records one can build up experience of the effect of different parameters.

These programs have in effect become the primary design tool used in studies to improve instrument and component design. We have not yet seen their full potential. If using the simulations to improve a design, it becomes clear that the programs offer no guidance as to which of the infinite number of possible models should be tried. In the absence of a quantitative quality factor, comparing results is far from simple.

More recently, these programs have been used as the kernel of multivariate optimisation routines in the hope that this approach may allow full optimisation of instrument designs. Parameters often have correlated effects. The large number of variables and the correlations make a numerical optimisation inherently difficult. Again, in the absence of a quantitative figure of merit one must ask what is being optimised.

Because calculations in the full 10 dimensional spatial-wavevector-time-polarisation space which describes neutron scattering instruments are not really practical, such computer simulations are the only way to avoid the approximations necessary in analytic calculations of instrument resolution and transmission. However, it is important to appreciate that the code underlying the simulations also contains significant approximations. Of course, as is confirmed by the vast number of successful neutron scattering measurements, the approximations applied do not usually create any real problem.

In summary then, MC programs can accurately show the effect of a given change to an instrument but they can offer no guidance as to which changes are likely to be beneficial.

Cussen Consulting’s seemingly unique approach to design combines Analytic, Graphical (Acceptance Diagram) and Monte Carlo methods and rapidly identifies beneficial lines to follow. Contracting out simulation studies to an experienced firm can reduce the time needed for effective simulations. The contract process itself means the work must be delivered to an agreed specification, schedule and budget with records and documentation. Any errors or misunderstandings must be corrected. The process is probably faster in many cases and hence, cheaper – a crucial point in tightly scheduled and budgeted projects. CC can do the work using either McStas or VITESS – each of which has strengths – or use both to provide a cross check. Cussen Consulting has an unrivalled track record in design optimisation and proven creativity in novel beam elements, instrument design and resolution visualisation methods. Add 25 years of experience for a powerful combination.

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Technical Writing:

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Shielding Design:


IFE Report on shielding material choices

It is accepted that modern shielding design must be completed using a Monte Carlo simulation approach with coupled neutron-gamma ray calculations. However, the initial choice of materials and dimensions is best guided not by a random search or numerical optimisation but a solid knowledge base and calculations including such things as separating source radiation load into fast neutron, thermal neutron and gamma rays and then calculating transmissions and gamma ray build up factors. For fission reactor shielding, the main cheap and suitable materials are iron, hydrogen (in the form of wax or plastic and boron). Just as important is a consciousness of materials to avoid due to activation or prompt gamma risks - especially those which appear as trace quantities in otherwise sound materials (eg cobalt impurities in iron).

MTF Transfer Technology GMBH Collaboration on shielding materials choice.

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Instrument Design

The "micro-TAS" In collaboration with Peter Willendrup at Risoe for ESS and recognising that beam angular divergence rather than spatial size determines instrument performance especially on guide sources, we tested the performance capabilities of a very small three-axis spectrometer. Typical modern TAS samples are 5 mm x 10 mm cylinders and for such samples, a very small instrument can deliver equal or better count rates than a typical large modern machine. Such small TAS offer better efficiency in using available beams and could be constructed using cheap mass produced optical components. One could multiplex such small machines in a guide hall and at modest cost provide vastly increased user beam time.

PEARL... In 2010 Cussen Consulting prepared a conceptual design for the new PEARL powder diffractometer at TU-Delft. The design used the then best practice numerical optimisation (restricted to Soller collimators and flat monochromators). The instrument was completed in late 2015 at a total cost far lower than that of comparable machines elsewhere. Tests conducted during commissioning show that despite the very modest 2MW reactor source at TU-Delft, this machine is much faster than equivalent machines at much more powerful sources.
Watch this space!

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An Introduction to Acceptance Diagrams

It seems that human brains are more than 50% devoted to processing visual images. If a problem can be expressed graphically, its solution is often more readily found or more sophisticated solutions can be envisaged.

Discussing neutron instrument resolution, transmission, design or optimisation usually involves complicated equations.

With such diagrams, one is usually interested in a close up view of a small segment of the whole space. Then a DuMond Diagram can be seen to be a variant of a 2D wave-vector space diagram. Reciprocal space acceptance diagrams (ADs) are also very useful for describing beams from primary spectrometers or even over whole instruments. Then the angular variation becomes proportional to the transverse wavevector variation and the fractional wavelength variation just proportional to the longitudinal wavevector variation. In particular they can describe the performance of novel beam elements for neutron scattering instruments outside the usual Gaussian approximation.

The AD description turns out to be much clearer and more direct than conventional analytic methods; so much so that they make it possible to optimise instruments completely. They clarify the relationship between individual beam elements and the beam produced making it possible to select beam elements to produce the beam required. Acceptance Diagrams cannot themselves identify the beam character needed – but the pictures do give strong indications.

Cussen Consulting's work applies ADs to neutron scattering instruments, but the approach is equally applicable to any diffraction instruments including those for X-ray and electron scattering. While the techniques are still being developed, there are already several interesting results. These include

ADs are a valuable adjunct to traditional calculation methods or Monte Carlo simulation programs. If old important problems cannot be solved using existing approaches, a new approach may prove successful.

Primary Spectrometer Acceptance Diagrams
The picture illustrates an Acceptance Diagram (AD) view of the beam at the sample position produced by a conventional primary spectrometer. The plot is of transmission in a 2D (in-plane) wave-vector space. The total transmission (d) is the product of three component ADs due to the collimator before the monochromator (a), the monochromator mosaic (b) and the collimator preceding the sample (c).

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Novel Ballistic Guide Design

This work was conducted at HZB and formed part of an international collaboration of about 100 scientists working on neutron delivery systems for the ESS. The key problems confronting the group were how to avoid line of sight to the source in a ballistic guide, how to get good transmission through elliptic profile guides (simulations showed irregular divergence transmission), how to site beam choppers in the very wide elliptic guides and how best to arrange simultaneous viewing of the cold and thermal sources (bispectral extraction).

A neutron guide is constructed as an evacuated tube with very flat walls which are coated with neutron mirrors which reflect neutrons only at very small glancing angles. The mirrors are often just nickel metal which give almost perfect reflectivity of 99% up to a critical glancing angle which is just 0.1 degrees multiplied by the wavelength in Angstrom. Increasing the critical angle requires “supermirrors”, usually multilayers of nickel and titanium, but then the reflectivity decreases as the glancing angle increases.

The ESS needs extremely long guides and with many reflections over such long distances the lower supermirror reflectivity gives no effective advantage. A brilliant solution to this problem was the development of the “ballistic” guide where the guide tapers out from the source (increasing beam area and decreasing divergence) and tapers in to the target (restoring the original area and divergence).

It is well known that a parabolic mirror converts a divergent beam from a point source like a car headlight and produces a larger parallel beam. In such a situation the product of the beam divergence and area cannot be less than that at the source itself. It was believed that if a ballistic guide had an elliptic profile, with the source at one focus and the target at the other, then all neutrons would reach the target after only one bounce thus giving near perfect transmission. Monte Carlo simulations showed that while the transmission was higher than for a straight guide, it was not as high as expected and the divergence distribution at the target was irregular and so not very useful. Careful tests confirmed this.

Calculations showed that the guide curvature needed to be a very nearly perfect ellipse rather than the approximation from long straight segments usually used (or the segment lengths near the guide ends had to be very small indeed). Using short guide segments alone did not fix the problems. The image in an elliptic mirror is not the same as the source – angular divergences are inverted in the transmission – but this also could not explain the uneven divergence distributions. Tests of two ellipses in series to undo this angle inversion improved the beam character but did not solve the problems.

The suspicion of multiple reflections arose (although “theoretically impossible”), was tested and was confirmed. More than 99% of rays bounced more than once! Those which bounced once all came from the minute centre of the source. This explanation did not suggest a solution.

The reason to use an ellipse or any ballistic design is to increase beam divergence at the target – a straight nickel guide transmits very well for small divergence. An examination of the paths of rays with large incident divergence showed that they had small exit divergence and vice versa. This angle inversion coupled with Liouville’s theorem thus explained the multiple reflections which occur predominantly near the guide exit. Calculations of where most rays bounced first within the guide showed that the interesting rays with large incident divergence bounce before the centre of the ellipse.

Thinking about large divergence rays in a double ellipse with second bounces near the joint between the ellipses suggested removing the middle section. Keeping the first ellipse entry, the second ellipse exit with a straight guide between produced a good output. The beam at the centre of the guide is symmetric – so an angled mirror placed at the centre can reflect the beam unchanged. With some adjustments following MC simulations this then solved the guide problems giving high transmission, no direct line of sight, suitable narrow guide points for siting chopper and good divergence profiles.


Crazy Guide
The last refinements were to add a parabolic or elliptic feeder to the guide entry and to test some ideas from Wolter optics to refine the beam profiles. It was found that one could refine the guide for short or long wavelengths by different choices of elliptic and parabolic profiles in different parts of the guide.

Suitable bispectral source performance was achieved using short angled parallel mirrors inserted at the entrance to the guide feeder. The guide design was a critical part of the ESSEX spectrometer design.

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Optimising Polarisation Analysis Measurements:


Dr. D.J. Goossens made significant contributions to much of this work.

A polarising transmission filter, such as 3He or magnetised Fe, exploits the difference between the scattering cross sections for the two possible neutron polarisations in the incident beam. The more strongly scattered polarisation is scattered from the beam leaving a beam with nett polarisation. The thicker the filter, the higher the polarisation, p, but the lower the transmission, t. Clearly there is some optimum filter thickness – not too thin and not too thick - for any given measurement which maximises the measurement quality. This work was first prompted by the need to choose the proper thickness for LONGPOL's iron filters but applies more interestingly to 3He filters.

In summary,


Filter thickness vs <sup>3</sup>He polarisation

The picture plots a typical variation of effective filter thickness as a function of 3He spin polarisation in a filter. The work is of course useful in designing neutron beam polarisers. More significantly perhaps, it illustrates that deducing a quantitative quality factor for a measurement permits rational decisions to be made about instrument design. This particular work is quite mathematically involved, as is usual for instrument optimisations. It was only possible after developing a number of new methods and tools. Being aware of the difficulties this would pose to anyone needing a result for some slight variant of measurement without access to the toolkit, we consciously decided to analyse as many variants as possible and publish the many quite complex papers on this topic.

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Optimising Constant Wavelength Neutron Powder Diffractometers:

Early work on the problem of optimising constant wavelength powder diffractometers (CW PDs) began in May 2003 with the numerical and then analytic proof that many primary spectrometer beam element combinations could produce the same beam at a sample. Coupled to many earlier insights from Acceptance Diagram modelling of primary spectrometers, this suggested a path to a complete numerical optimisation for CW PDs. However, the complete optimisation solution required many further novel steps and it was Dec 2010 before they were all found and later yet that they were assembled coherently. A numerical optimisation for CW PDs using Soller collimators and flat monochromators was completed by late 2003 and showed dramatic performance improvements. Extensive Monte Carlo simulation tests in 2008-2009 disclosed two errors in the original solution (incorrect numerical constants) and when the corrections needed were identified and implemented, the gain factors increased much more. Extensive studies using the software developed to do the optimisation showed poor convergence. The cause and cure were eventually tracked to a necessary change of variables. Recasting the resolution equations in terms of variables describing the beam character rather than the instrument beam elements showed the path to a full analytic optimisation. From having all the key ideas to assembling them, simplifying the tortuous path through the problem and writing the flow of ideas in a clear brief enough form took a great deal of time and it was only in April 2015 that the fully assembled optimisation was clearly expressed and tested. It took until December 2015 for the results to be verified.

Here, optimising a CW-PD means maximising the instrument transmission from source to detector at constant peak resolution. The problem constraints required are a value for transmission (which sets the intensity-resolution trade-off) and a measurement range defined in terms of the sample dS range of interest. In practice, the optimisation requires matching the resolution contributions from beam divergence in and out of the scattering plane before and after the sample and matching those contributions to that due to wavelength spread. Lastly, the choice of scattering angle at which resolution is best must be made using the monochromators Bragg angle and curvature. Expressed in this way, the CW-PD optimisation is effectively the same as the small angle scattering diffractometer optimisation. Since any measurement is over some range in scattering angle and since resolution varies with scattering angle, these matching conditions must be averaged in some way over the measurement range. To make the optimisation analytic requires using an RMS average in a Gaussian approximation. The wavelength should be almost as long as is allowed by the dS range needed in the measurement. The resulting instrument configuration is fully scalable giving great flexibility.

This analytic description has the advantage of showing why the optimum parameters take the values they do, of being simpler to verify and of inspiring more confidence in the process. Two surprising benefits were the discovery that one could simply generate rectangular profile transmissions as a function of angular spread without using special beam elements and the suggestion of a novel primary spectrometer design which offers full flexibility in choosing the instrument’s resolution character.

Over a 12 year period, this project represented over 5.5 years of full time work. Do the results justify the effort? MC simulations of the new designs show 2.5 – 3.5 orders of magnitude performance improvements are possible over current best practice with simpler, cheaper and more flexible machines. What new science will this permit?


CW PDs performance

The figure illustrates McStas simulated data from four powder diffractometer configurations using a NAC sample. Two form a reference being current best practice machines. The bottom two figures show predicted performance from an optimised machine using the same ILL beam tube and monochromator position. The new machine is very flexible in choosing resolution configurations and should be cheap to build.

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Novel Neutron Beam Collimators:

Since their first use in the 1950's Soller slit collimators for neutron beams have become the usual approach used to define beam angular divergence. A conventional Soller slit is a set of parallel absorbing sheets separated by air channels. The air channel width and length determines the allowed divergence. The absorbers are usually vertical and set parallel to the beam axis and the device thus defines the beam angular divergence in the plane. The blades may be thin aluminium or mylar sheets usually coated with paint loaded with absorbing gadolinium oxide. Typically the collimators are quite bulky (~ 20x20x7 cm2) and the absorbed thickness (~80mm) reduces the transmission.

Slit pairs can also be used to defne beam angular spread and offer higher peak transmission but tend to greatly limit achievable beam widths and also tend to be inefficient at reducing noise in the beam. From the beginning, reflections from Soller collimator blades were seen as a way to enhance transmission but implementation proved very difficult despite many attempts. Using highly perfect single crystal silicon wafers as the transmission channels (an idea first explored in the early 1980's for supermirror neutron polarisers by Trevor Hicks' group at Monash University) now makes such devices possible.

In 1989, a first crude silicon wafer collimator was made by spray painting the wafers with Gd doped paint. That 2cm long prototype collimator was routinely used in experiments at the HIFAR reactor in Australia until 2005. Since the early 1990's several groups including workers at NIST, HMI and ILL showed interest in these devices. Prototype tests were conducted at VUT and ANSTO in 1994 and an article describing the design was published in 1998. Prototypes were tested at HMI by Mezei and Krist and at ILL in 2000. The ILL prototype tests showed near perfect performance from these extremely compact collimators.
Picture of reflecting collimator Rocking curve from reflecting collimator Rock of two reflecting collimators
It was not until 2003 that the full effect of reflecting collimators on neutron beams was correctly analysed and understood. If there is no correlation between wavevector and angular variance in the incident beam, the transmitted beam simply has a rectangular profile of transmission as a function of angular divergence, as expected. On the other hand, if there are angle-wavevector correlations in the beam (as is the case following a diffracting element like a monochromator), then the reflections within the collimator disrupt these correlations. The analysis is simplest using 2D Acceptance Diagrams. The devices can usually give intensity gains over an instrument of a factor of 2 with no resolution cost but on an instrument, the change from triangular to the more efficient rectangular transmission profiles applies to the beam wavelength spread as well as the angular spread and gains may be a factor of 3 (on powder diffractometers) or even 5 (on three axis spectrometers). These devices have other significant advantages over conventional collimators which also apply to silicon wafer based collimators with non reflecting coatings.

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