Self-similar motion of laser half-space plasmas. I. Deflagration regime

The one-dimensional self-similar motion of an initially cold, half-space plasma of electron density n0, produced by the (anomalous) absorption of a laser pulse of irradiation φ =φ0t/τ (0<t⩽τ) at the critical density nc(nc/n0≡ε≪1), is considered. The analysis allows for electron heat conduction and ion-electron energy exchange and retains three dimensionless numbers: ε, Zi (ion charge number), and α= (9k/4mi) (τk2n20/φ0K̄e)2/3, where k, mi are Boltzmann’s constant and the ion mass, and K̄e × (electron temperature)5/2 = heat conductivity. If α ≫ε−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 α≪ε−5/3(α≫ε−5/3). The compression to expansion ratio for both energy and thickness is O (ε1/2). For Zi large, a deflagration exists even if α∼ε−4/3. Condition α≫ε−4/3 may be applied to pulses that are not linear.