The one-dimensional self-similar motion of an initially cold, half-space plasma of electron density « 0 , produced by the (anomalous) absorption of a laser pulse of irradiation = (j> 0 f/T(0< (< T) at the critical density n c (« c /« 0 =eoK e ) 213 , where k, m, are Boltzmann's constant and the ion mass, and K e X (electron temperature) 5 ' 2 = heat conductivity. If a >e -4 ' 3 , a deflagration wave separates an isentropic compression with a shock bounding the undisturbed plasma, and an isentropic expansion flow to the vacuum. The structures of these three regions are completely determined; in particular, the Chapman-Jouguet condition is proved and the density behind the deflagration is found. The deflagration-compression thickness ratio is large (small) for a^e -5 ' 3 (a>e -5 ' 3 ). The compression to expansion ratio for both energy and thickness is 0(e" 2 ). For Z,-large, a deflagration exists even if a~e~4 13 . Condition a>e~4' 3 may be applied to pulses that are not linear.