Ignition of a combustible stagnant gas layer by a circular hot-spot

The influence of a circular hot-spot on the thermal stability of a thin layer of exothermically reacting gas is considered. A hot-spot of this kind would be produced by a laser beam emerging from an optical fibre and impinging on a solid bounding surface from the gas side. The temperature of the hot-spot is not constant across a diameter but decreases radially. The effect of such radial variation on the critical conditions for ignition has been evaluated.