Thin foil expansion into a vacuum

Plasma expansion into a vacuum is an old problem which has been renewed recently in various contexts: expansion of ultra-cold plasmas, cluster expansion, of dust grains, expansion of thin foils. In this presentation I will first discuss the physics of the expansion of a thin foil irradiated by an ultra-short ultra-intense laser pulse. The expansion results in the formation of high energy ions. For an infinitely steep plasma-vacuum interface the fastest ions are located in the outer part of the expansion and their velocity is given by νmax∼ 2 Cs (In ωpit) where cs(ZkBTe/mi)''1/2 is the ion-acoustic velocity ωpi=(ne0Ze''2/mie0)''1/2 is the ion plasma frequency, ne0 is the electron density in the unperturbed plasma, Z is the ion charge number. In the above expression, t is either the pulse duration or the effective acceleration time (in particular t∼L/2cs, where L is the width of the foil, when the electron cooling is taken into account). A salient characteristic of the expansion is the occurrence of a double layer structure and a peak of the accelerating electric field at the ion front. I will explain the origin of the peak and predict its temporal behavior. This peak has been diagnosed in recent experiments. I will also discuss the effect of a 2-temperatures electron distribution function on the expansion, showing the dominant role of the hot electron component. Finally I will discuss the occurrence of ion spikes in the expansion when the initial density profile is smooth. The ion spike is due to a wave breaking which cannot be handled in a satisfactory way by a fluid code and requires a kinetic description. A. simple collisionless particle code has been used to treat the evolution of the spike after the wave breaking and the results will be shown. (Author)