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For any appreciable radiation source, such as a nuclear reactor core or radiation physics accelerator, there will be the safety requirement to shield operators from the effects of the radiation from the source. Both the size and weight of the shield need to be minimised to reduce costs (and to increase the space available for the maintenance envelope on a plant). This needs to be balanced against legal radiation dose safety limits and the requirement to reduce the dose to operators As Low As Reasonably Practicable (ALARP). This paper describes a method that can be used, early in a shield design, to scope the design and provide a practical estimation of the size of the shield by optimising the shield internals. In particular, a theoretical model representative of a small reactor is used to demonstrate that the primary shielding radius, thickness of the primary shielding inner wall and the thicknesses of two steel inner walls, can be set using the Lagrange multiplier method with a constraint on the total flux on the outside of the shielding. The results from the optimisation are presented and an RZ finite element transport theory calculation is used to demonstrate that, using the optimised geometry, the constraint is achieved

Use of Lagrange Multipliers to Provide an Approximate Method for the Optimisation of a Shield Radius and Contents