Muon Flux Budgets for Monitoring Blast Furnace Hearth Refractory Thickness

This paper computes the muon attenuation, exposure and resolution budget for imaging a blast furnace hearth with cosmic-ray muons. Sight lines through 4 metres of refractory and iron-bearing material at a density of 3.8 grams per cubic centimetre present an opacity of 1520 grams per square centimetre (15.2 metres of water equivalent), which sets a minimum muon energy of 3.048 GeV and a transmitted vertical intensity of 13.51 per square metre per second per steradian. For a detector of 0.5 square metres with the stated acceptance and efficiency, divided among 80 image elements, the stated feature produces a flux contrast of 0.4464 and reaches five standard deviations in 0.02123 days of counting, while the target precision of 0.04 per image element requires 0.1057 days. A deployment of 30 days delivers a per-element precision of 0.002375, corresponding to a thickness sensitivity of 0.009499 metres. The combined angular resolution is 39.09 milliradians, of which tracking contributes 2.828 milliradians and multiple scattering at the threshold momentum 38.99 milliradians. The budget is compared with published muography of the same class of target, for which muon measurements at operating blast furnaces have reported sensitivity to hearth refractory condition and to the density distribution of the burden and hearth contents. Every number is computed by the accompanying script from the stated inputs. Computed, not measured.