Introduction

The construction of laser based particles (electrons, ions) and light sources (x-rays) require efficient coupling of laser energy with a target material. It is experimentally established that nano-meter size atomic clusters (hydrogenic and rage gas) can absorb laser light very efficiently. Compared to the size of a cluster, the wavelength ƛ of light is usually very large (typically ƛ ˜ 248−1064 nm). For this reason, on one hand, light can completely illuminate a cluster having solid-like atomic density, and on the other hand, the reflection of laser energy becomes negligible leading to more than 80% laser absorption[1]. Laser heated clusters were shown to produce (i) near MeV ions[1−8], (ii) keV electrons[9−13], (iii) harmonic radiation[14−18], and (iv) x-rays[19−22].

The laser energy absorption in clusters is commonly studied with a pump-probe experimental setup[24−26]. After the ionization by the pump, the charge density p(t) and the corresponding Mie-plasma frequency ωM(t) = ωp increases above the laser frequency ω (ωp is the plasma frequency, atomic units e = m = 4“0 = 1 are used unless mentioned explicitly). Due to the higher mobility of electrons than the massive ions, electrons first absorb laser energy. Their displacement from the quasi-static ion background leads to the formation of a space charge field which may exceed the applied laser field. The space charge field when added to the laser field may cause further ionization of ions, known as ionization ignition[27−32] which is not possible by the laser field alone. At a given laser intensity, this ionization ignition and ionization of atoms/ions (inner ionization) depend upon the number of electrons who have left the cluster completely. The complete removal of an electron from the cluster is called outer ionization. The outer ionization leaves behind a non-neutral ionic background which expands due to Coulomb repulsion between the ions. When the Mie-frequency of the expanding plasma meets the condition ωM(t) = ω at a later time, typically > 50 fs[24] for 800 nm laser, enhanced energy absorption takes place from the probe. This linear resonance (LR) was explained with a nano-plasma model[33] where the expanding cluster was assumed to be homogeneously charged. However, in reality, ions near the cluster boundary leave the cluster with higher kinetic energy much earlier than the relatively slower ions at the cluster core.