McStas and Scatter Logger driven calculations of prompt gamma shielding for neutron guides

2.1.Reflection with q>qcNi

In [6 ,7] capture probabilities in the multilayer coatings per incident neutron were calculated for multilayer compositions used in commercial production of supermirrors (m=1.6…6) at SwissNeutronics. When momentum transfer at reflection exceeds a critical value for total reflection from nickel, qcNi=0.0218 Å−1, the reflection occurs at bilayers following the outermost nickel layer of the coating. In this case, the probabilities of absorption in coating materials per incident neutron, fa, are conveniently described as functions of a ratio of neutron momentum transfer at reflection q⊥ to the critical value qcNi, μ=q⊥/qcNi. The functions have a parametric dependence on the coating m-value with two distinct regimes:

2.2.Low angle reflection, effect of waviness

At reflection with low momentum transfer neutrons typically don’t penetrate beyond the outermost nickel layer of the coating and the parametric dependencies given by (1) and (2) don’t hold [7]. For momentum transfer at reflection below critical value qcNi and a perfectly even layer surface, the reflection loss is typically below 0.01%. This is in contrast with an empirical value of 0.5÷1% (99÷99.5% low angle reflection probability) commonly accepted for describing neutron transport in the guides. Attributing the low-angle reflectivity loss fully to neutron interaction in the coating would thus overestimate neutron capture and would lead to way too conservative estimates and unnecessary overshielding of the guide.

The main reason for the low-angle reflectivity loss is however waviness of the reflecting surface which effectively increases beam divergence.11 When an angle of grazing incidence is considered with respect to the local normal to the surface, a certain fraction of neutrons falls beyond the coating cutoff and are not transported further. Typical values for the waviness22 of ≲10−4rad [10] translate to approximately 0.5·10−4rad variation of the grazing angle at the reflection point. At a wavelength λ=5Å this corresponds to a δk⊥≈6.3·10−5Å−1 variation of the normal momentum component which constitutes around 0.6% of the critical momentum for nickel, kcNi=0.5·qcNi=0.0109Å−1. With a uniform distribution of the grazing incidence angle from zero to cutoff (k⊥=0…kcNi), a fraction of transported neutrons around ∼δk⊥/kcNi will appear beyond the cutoff and will not be reflected. The number is consistent with 0.5–1% loss of the reflectivity at low angles which is commonly accepted for the neutron optics calculations.

Probability of capture per non-reflected neutron at low angles for an m=1 single layer coating hence can be evaluated as capture probability per incident neutron in the first reflection minimum beyond the critical momentum transfer. A calculation of this quantity was performed in [8] and the following conservative estimate was derived:

Correspondingly, for a multilayer coating with m>1 the probability per non-reflected neutron at low angles can be evaluated as capture probability per incident neutron at the reflection threshold (Eqs (1) and (2) with μ=m).

3.1.Recording neutron capture

A description of a neutron instrument within McStas ray-tracing Monte-Carlo package is written in a meta-language. It is composed of predefined or user-supplied components placed according to the real setup of the instrument under consideration in a text file. The original Scatter Logger bundle enables logging and processing details of neutron interactions within parts of the instrument contained between Scatter_Logger and Scatter_Logger_Stop components. A subsequent Scatter_Log_Iterator component iterates through the recorded states and propagates pseudo-neutrons with non-reflected weight and pre-collision momentum starting from the interaction point. Characteristics of non-reflected neutrons can then be explored and recorded by various McStas components of type Monitor.

Extending functionality of the Scatter Logger in order to address neutron capture in the coating materials includes several key steps. First, neutron capture probability at reflection depends on the m-value of the coating. Correspondingly, a number of McStas components which are commonly used in construction of the guide systems were customized in order to allow logging of the m-value at reflection point by assigning a value to a global variable at each neutron interaction. The corresponding modifications were made to the following key components: Guide, Guide_curved (be used instead of Bender component, was modified to have the same syntax for the input parameters), Elliptic_guide_gravity and Guide_chanelled.

Second, the original Scatter_Logger component was updated in order to include the m-value at the reflection point to the saved state (in addition to neutron states before and after the reflection as it was originally). A possibility to have more than one Scatter_Logger component in the instrument, that is record neutron states in different parts of the instrument independently was also implemented. To avoid confusion with original components, an updated component was named Shielding_Logger.

Finally, in addition to an original iterator component pair which processes the buffer of saved states and returns weight of the non-reflected neutrons, two new iterator components were written, Shielding_Log_Iterator_Ni and Shielding_Log_Iterator_Ti, which implement parameterizations Eqs (1)–(5) and propagate neutron weights corresponding to the capture in the correspondent materials of the coating. The same buffer of saved states is processed three times by the three iterators which are placed in the McStas instrument file one after another. This also required some minor modifications to the original Scatter_Log_Iterator component (when iterator is the last one in the line one must specify that explicitly to clean the memory) which after modification was renamed to Shielding_log_iterator_total. Neutron capture rate in particular materials along the guide can be addressed by the standard Monitor_ND McStas component which would write the output to a text file.

The syntax of the logger and iterator components is similar to the syntax of the original constituents of the Scatter Logger bundle and the relevant examples of use may be found in the McStas repository.

3.2.Dose rate and shielding parameters evaluation from a McStas simulation

In general, there are several contributions to the dose rate around the guide (e.g. high energy neutrons, slow neutron scattered from beam windows or escaping through the gaps between guide segments and others). However, in many cases, for example outside the line of sight to the neutron source, the prompt gammas coming from neutron capture in the guide coating dominate the dose rate. Capture rates of neutrons in the coating material and in the substrate along the guide calculated in McStas can be used to define a corresponding source term for a transport Monte-Carlo simulation. Equivalently, they can be used for a direct numerical evaluation of the prompt gamma contribution to the dose rate and assessment of guide shielding requirements.

For a mono-energetic photon source, the dose rate beyond lateral shielding H can be obtained as a product of uncollided source photon fluence rate, energy dependent fluence to effective dose conversion factor K(E) and a buildup factor B(E,x) [12,13]. The buildup factor accounts for a contribution to the effective dose from scattered radiation arriving at the detection point and depends on both the energy of primary photons and their optical path length. For a particular case of guide shielding, once the radiation energy spectrum and intensity along the neutron guide I(E,z) is known, the photon fluence rate is obtained via integrating I(E,z) along the guide with account of attenuation due to distance and traversed material thickness. The expression for the effective dose thus takes on the form (for notations see Fig. 1):

Fig. 1.

Geometry for the dose rate evaluation outside lateral guide shielding at the surface.

The energy dependent linear attenuation coefficient μ, dose buildup B(E,μd) and flux to dose conversion coefficient K(E) are table values available from the literature on radiation protection [13–16].

For the two newly written components in McStas performing dose rate calculations and evaluating shielding needs, it is assumed that the non-reflected neutrons which are not captured in the coating are captured in the borosilicate guide substrate. Although neutron capture in the borosilicate glass occurs presumably by boron atoms, a small fraction of neutrons transmitted to the substrate are captured by other elements, in particular silicon, with release of photons with energy of several MeV. The McStas components thus implement equation (7), interpolation of table values for μ(E), B(E,x), K(E) for some typical shielding materials and, finally, spectra of prompt gamma radiation per neutron capture in nickel, titanium and borosilicate glass. The spectra are calculated using cross sections of (n,γ) reactions from a Prompt Gamma Activation Analysis datafile available at [17].

The Dose_calculator component calculates dose rate outside lateral shielding of a specified material with fixed thickness at its surface along the neutron guide. The Shielding_calculator component evaluates shielding thickness required to reach given dose rate at a shielding surface outside as one moves along the guide. A user can choose from a few common shielding materials (lead, iron, light concrete) and the presence or absence of an inner iron shielding layer of a specified thickness. The components simply read the output of the Monitor_nD monitors placed within the three iterators as described in Section 3.1 (the names of output files for the monitors which must have identical binning have to be specified) and perform the requested calculations. The components may be run from a separate McStas file which doesn’t contain the description of an instrument. In this case, a user has to provide a path to the files which contain pre-calculated capture in Ni, Ti and overall loss along the guide.

The components were benchmarked to a measurement of a gamma dose rate along the PSI instruments (mostly m=2 guides) shielded with 120 mm steel and a good correspondence between the calculation and measurement was obtained [8].