We study the explosion dynamics of rare-gas clusters (Ar 55 , Ar 147 , Xe 55 , and Xe 147 ) in an intense, femtosecond laser pulse via Monte Carlo classical particle-dynamics simulations. Our method includes tunnel and impact ionization as well as ion-electron recombination, and allows us to follow the motion of both ions and free electrons during laser-cluster interaction. Our simulation results show that ionization proceeds mainly through tunnel ionization by the combined fields from ions, electrons, and laser while the contribution of electron-impact ionization is secondary. The ions are ejected in a stepwise manner from outer shells and accelerated mainly through their mutual Coulomb repulsion. Taking a spatial laser intensity profile into account, we show that the Coulomb explosion scenario leads to the same charge dependence of ion energy, i.e., quadratic for lower charge states and linear for higher ones, as that observed in experiments with larger clusters. This indicates that Coulomb explosion may be a dominant cluster explosion mechanism even in the case of large clusters. We also find that the ion energy is higher in the direction parallel to laser polarization than in the direction perpendicular to it. When ions are emitted along the direction of laser polarization, their charge changes in phase with the laser field, and this leads to an efficient acceleration.
In order to design extreme ultraviolet (EUV) sources for nanolithography, xenon EUV emission has been experimentally studied in a plasma generated by the interaction of a high-power laser with a droplet jet. A theoretical model assuming that the resulting plasma is optically thick allows one to find the distribution of the relevant ions and transitions involved in the emission process. Atomic physics computations are performed using the HULLAC code to give a detailed account of the transitions involved. The importance of 4p–4d, 4d–4f, and 4d–5p transitions is stressed, as well as the need for configuration-interaction treatment of the Δn=0 transitions. Comparisons of a modeled local thermodynamical equilibrium spectrum with experiment provides qualitative agreement and permits an estimate of the plasma temperature, density, and dimensions.
Models of screened ions in equilibrium plasmas with all quantum electrons are important in opacity and equation of state calculations. Although such models have to be derived from variational principles, up to now existing models have not been fully variational. In this paper a fully variational theory respecting virial theorem is proposed-all variables are variational except the parameters defining the equilibrium, i.e., the temperature T, the ion density ni and the atomic number Z. The theory is applied to the quasiclassical Thomas-Fermi (TF) atom, the quantum average atom (QAA), and the superconfigurations (SC) in plasmas. Both the self-consistent-field (SCF) equations for the electronic structure and the condition for the mean ionization Z* are found from minimization of a thermodynamic potential. This potential is constructed using the cluster expansion of the plasma free energy from which the zero and the first-order terms are retained. In the zero order the free energy per ion is that of the quantum homogeneous plasma of an unknown free-electron density n0 = Z* ni occupying the volume 1/ni. In the first order, ions submerged in this plasma are considered and local neutrality is assumed. These ions are considered in the infinite space without imposing the neutrality of the Wigner-Seitz (WS) cell. As in the Inferno model, a central cavity of a radius R is introduced, however, the value of R is unknown a priori. The charge density due to noncentral ions is zero inside the cavity and equals en0 outside. The first-order contribution to free energy per ion is the difference between the free energy of the system "central ion+infinite plasma" and the free energy of the system "infinite plasma." An important part of the approach is an "ionization model" (IM), which is a relation between the mean ionization charge Z* and the first-order structure variables. Both the IM and the local neutrality are respected in the minimization procedure. The correct IM in the TF case is found to be Z-Z*= integral d3 r[n(r)-n0], where n(r) is the first-order electron density. It is shown that in the QAA case the same IM has to be used and that other IMs lead to unphysical solutions. With this IM R becomes in both cases (TF and QAA) equal to the WS radius and the variational calculation leads to SCF equations in an infinite plasma while n0 (or equivalently Z*) is to be found from the condition integral d3r theta(r-R)Vel(r)=0, where theta denotes Heaviside function and Vel(r) is the SCF electrostatic potential. In the SC case results are similar except that averages over all superconfigurations appear. In the TF case the condition for n0 gives the neutrality of the WS sphere and one gets the classical TF ion-in-cell average atom. The situation is different in the QAA and in the SC cases in which the cavity is not neutral and the SCF potential Vel(r) is not zero outside the cavity. Due to the fully variational character of our approach the expression for the thermodynamic pressure in all cases does not require any numerical differentiat...
The numerical code VAAQP (variational average atom in quantum plasmas), which is based on a fully variational model of equilibrium dense plasmas, is applied to equation-of-state calculations for aluminum, iron, copper, and lead in the warm-dense-matter regime. VAAQP does not impose the neutrality of the Wigner-Seitz ion sphere; it provides the average-atom structure and the mean ionization self-consistently from the solution of the variational equations. The formula used for the electronic pressure is simple and does not require any numerical differentiation. In this paper, the virial theorem is derived in both nonrelativistic and relativistic versions of the model. This theorem allows one to express the electron pressure as a combination of the electron kinetic and interaction energies. It is shown that the model fulfills automatically the virial theorem in the case of local-density approximations to the exchange-correlation free-energy. Applications of the model to the equation-of-state and Hugoniot shock adiabat of aluminum, iron, copper, and lead in the warm-dense-matter regime are presented. Comparisons with other approaches, including the inferno model, and with available experimental data are given. This work allows one to understand the thermodynamic consistency issues in the existing average-atom models. Starting from the case of aluminum, a comparative study of the thermodynamic consistency of the models is proposed. A preliminary study of the validity domain of the inferno model is also included.
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