From a database encompassing 457 experimental and numerical data from 32 machines among solid-walled tokamaks, stellarators and linear plasma devices, we derive physics-informed multi-machine scaling laws predictive of fuel and impurity puffing rates sufficient to access edge plasma detachment. The validation of our laws against up to 40 diverse plasmas in low- and high-confinement mode featuring traditional and advanced configurations demonstrates accuracy within a factor 1.5 in up to 50% of the validation instances, and within a factor 2 on average. In the era of nuclear fusion reactor design, these results find immediate applicability in informing reactor fuel cycle and edge plasma modelling. More generally, our findings prove that physics-based laws able to relate detachment to the engineering actuators exist, and pave the way for analytical models bridging to the true inputs of experimental operation.
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