ALARA and job planning
Inverse square, stay time against a dose budget, collective dose across tasks, and half- and tenth-value layers.
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Time, distance, shielding — in order of cost
The three controls are usually recited as equals. They are not. Distance is free and acts as the square: stepping from one metre to two cuts the dose rate to a quarter, and the same job can then be done in four times the time for the same dose. Time costs schedule but no money. Shielding costs money, weight, and the handling dose incurred putting it in place — which is why a lead blanket installed to save 50 µSv can cost more dose than it saves.
This ordering is why a planning calculation should start by asking how far back the work can be done, and only then how long it will take and what needs shielding.
Where inverse square stops working
The 1/d² law is a statement about a point source radiating into open space. It is an excellent approximation once you are several source dimensions away, and a poor one closer in. Near a line source — a contaminated pipe run, a loaded transfer line — the falloff is closer to 1/d. Near a large contaminated plane or a tank wall it is nearly flat, because moving back brings more of the surface into view at the same time as it increases the distance to each part of it. Backing away from a spill on the floor buys far less than the same step away from a sealed source.
The practical test is whether the distance you are moving to is large compared with the size of the source. If it is not, measure rather than calculate.
Stay time and its honest use
Stay time is the dose budget divided by the dose rate, and it is the simplest calculation in radiation protection. Its failure mode is not arithmetic but the assumption that the dose rate is constant. Rates change when a shield is opened, when a source is moved, when a worker leans in, or when the job goes differently than planned. A stay time computed from a single pre-job reading is a planning figure, not a control — the control is a dosimeter with an alarm.
Building in margin is normal practice: plan to a fraction of the budget so that an unexpected rate does not immediately consume it.
Collective dose, and what it hides
Collective dose sums the dose over everyone involved, in person-millisieverts. It is the right quantity for comparing two ways of doing the same job, and it is the quantity an ALARA programme is usually judged on. It also contains an incentive worth being aware of: because it adds people together, it can be reduced by using fewer workers for longer, which pushes individual doses up while the total falls.
Optimisation that only looks at the collective figure will drift in that direction. The correct practice is to check both — the collective total for comparing options, and the highest individual dose against the individual constraint. The per-worker figure alongside the total in this calculator is there for that reason.
Half- and tenth-value layers
A half-value layer halves the dose rate and therefore doubles the stay time; a tenth-value layer divides by ten. Both are quoted at a specific photon energy and depend strongly on it, and handbook values are broad-beam figures that already include scattered radiation. Narrow-beam values computed from attenuation coefficients alone are thinner and will underestimate the shielding a real installation needs.