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Register a new userVariational Average-Atom in Quantum Plasmas (VAAQP) - first numerical results
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R. Piron CEA
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The work on a new fully variational model of average-atom in quantum plasmas using a numerical code called VAAQP is reported. A brief description of the code is given. Application to aluminium at solid density and temperatures between 0.05 and 12 eV is presented. Comparisons to results obtained using other approaches are also shown and discussed. The results prove the feasibility of the variational model in the warm dense matter regime. Effects of the variational treatment can lead in this region to significant differences with respect to existing models.
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A new code called VAAQP (Variational Average-Atom in Quantum Plasmas) is reported. The model as well as main results of previous studies are briefly recalled. The code is based on a new fully variational model of dense plasmas at equilibrium with quantum treatment of all electrons. The code can calculate the Average Atom structure and the mean ionization from the variational equations respecting the virial theorem and without imposing the neutrality of the Wigner-Seitz sphere. The formula obtained for the electronic pressure is simple and does not require any numerical differentiation. A description of the principal features of the code is given. The thermodynamic consistency of the results obtained with VAAQP is shown by a comparison with another approach on the example of the aluminium 10 eV isotherm EOS curve. A first comparison to an INFERNO-type model is also presented.
In the present paper, we propose a variational average-atom model of electron-ion plasma performing a quantum treatment of bound electrons and accounting for correlations (VAAQBEC). This model addresses the correlation functions in a weakly-coupled plasma, while also accounting self-consistently for the ion average shell structure. This is done at the price of treating the free electrons classically, whereas bound electrons are treated quantum-mechanically. When ions are approximated by point-like particles, the present approach yields the usual Debye-H{u}ckel corrections to the orbital energies and chemical potential. If one disregards the interactions of continuum electrons, the present approach yields ion-ion correlation corrections through a self-consistent one-component-classical-plasma contribution. Comparisons are presented with the broadly-used continuum-lowering approach of Stewart and Pyatt and with the dense-plasma average-atom models INFERNO and VAAQP, on warm silicon and hot iron cases.
The frequency-dependent linear response of a plasma is studied in the finite-temperature Thomas-Fermi approximation, with electron dynamics described using Bloch hydrodynamics. The variational framework of average-atoms in a plasma is used. Extinction cross-sections are calculated for several plasma conditions. Comparisons with a previously studied Thomas-Fermi Impurity in Jellium model are presented. An Ehrenfest-type sum rule, originally proposed in a full quantum approach is derived in the present formalism and checked numerically. This sum rule is used to define Bremsstrahlung and collective contributions to the extinction cross-section. It is shown that none of these is negligible. Each can constitute the main contribution to the cross-section, depending on the frequency region and plasma conditions. This result obtained in the Thomas-Fermi-Bloch case stresses the importance of the self consistent approach to the linear response in general. Some of the methods used in this study can be extended to the linear response in the quantum case.
The average-atom model is applied to study Thomson scattering of x-rays from warm-dense matter with emphasis on scattering by bound electrons. Parameters needed to evaluate the dynamic structure function (chemical potential, average ionic charge, free electron density, bound and continuum wave-functions and occupation numbers) are obtained from the average-atom model. The resulting analysis provides a relatively simple diagnostic for use in connection with x-ray scattering measurements. Applications are given to dense hydrogen, beryllium, aluminum and titanium plasmas. In the case of titanium, bound states are predicted to modify the spectrum significantly.
We photoionize laser-cooled atoms with a laser beam possessing spatially periodic intensity modulations to create ultracold neutral plasmas with controlled density perturbations. Laser-induced fluorescence imaging reveals that the density perturbations oscillate in space and time, and the dispersion relation of the oscillations matches that of ion acoustic waves, which are long-wavelength, electrostatic, density waves.
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