Unperturbed moderator brightness in pulsed neutron sources

The unperturbed neutron brightness of a moderator can be defined from the number of neutrons leaving the surface of a moderator completely surrounded by a reflector. Without openings for beam extraction, it is the maximum brightness that can be theoretically achieved in a moderator. The unperturbed brightness of a cylindrical cold moderator filled with pure para-H2 was calculated using MCNPX; the moderator dimensions were optimised, for a fixed target and reflector geometry corresponding to the present concept for the ESS spallation source. This quantity does not depend on openings for beam extraction and therefore can be used for a first-round optimisation of a moderator, before effects due to beam openings are considered. We find that such an optimisation yields to a factor of 2 increase with respect to a conventional volume moderator, large enough to accommodate a viewed surface of 12×12 cm2: the unperturbed neutron brightness is maximum for a disc-shaped moderator of 15 cm diameter, 1.4 cm height. The reasons for this increase can be related to the properties of the scattering cross-section of para-H2, to the added reflector around the exit surface in the case of a compact moderator, and to a directionality effect. This large optimisation gain in the unperturbed brightness hints towards similar potentials for the perturbed neutron brightness, in particular in conjunction with advancing the optical quality of neutron delivery from the moderator to the sample, where by Liouville theorem the brightness is conserved over the beam trajectory, except for absorption and similar type losses