ScientificCoordination Session on NonIdeal Plasma Physics Dielectric properties

Scientific-Coordination Session on "Non-Ideal Plasma Physics" Dielectric properties of Warm Dense Matter (WDM) Saitov I. M. 02. 12. 2014 Joint Institute for High Temperatures of RAS

Dielectric function DFT Kohn. Sham Dielectric function Reflectivity Absorbtion Trasmission Plasma frequency Effective free electron density Conductivity …… Electronic density of states

Outline 1. Calculation method. 2. Reflectivity. 3. Plasma frequency. 4. Conclusions.

1. Calculation method

Dielectric function Longitudinal expression for the imaginary part of dielectric function:

Transversal expression Velocity operator Longitudinal expression

Transversal expression Velocity operator Non-Local potentials Kubo-Greenwood formula M. Gajdoš, K. Hummer, G. Kresse, J. Furthműller, F. Bechstedt, Phys. Rev. B 73, 045112 (2006).

Kramers-Kronig transformation for the imaginary part of the dielectric function: The convergence in the upper limit of the integral is checked Density functional theory is used for calculation of ψ and E

Pseudopotentional approach in DFT 46 e – «core» 8 e - valent

Reflectivity and conductivity

2. Reflectivity

Calculation parameters 0. 51 30050 0. 97 29570 1. 46 30260 1. 98 29810 2. 7 29250 3. 84 28810

Dependence of reflectivity on density Collisionless plasma Drude model [2] DFT this work DFT [3] Experiment [1] DFT with band gap corrections[3] [1] V. B. Mintsev, Yu. B. Zaporogets, Contrib. Plasma Phys. 29, 493 (1989). [2] H. Reinholz, G. Röpke, A. Wierling, V. Mintsev, V. Gryaznov, Contrib. Plasma Phys. 43, 3 (2003) [3] M. P. Desjarlais, Contrib. Plasma Phys. 45, 300 (2005).

3. Plasma frequency

Dependence of static conductivity of shocked xenon on density

DFT Drude

Method II. Sum rule. Xe, 3 e. V

Method III. Consideration of electrons with energies (E > Ef) as free particles

Dependence of plasma frequency in xenon on density

Effective free electron density

Dependence of plasma frequency on density for H

Dependence of plasma frequency on density for Se

Conclusions Method of estimation of plasma frequency and effective free electron number density is proposed, based on using sum rule. DFT is applied. The dependence of plasma frequency on density is obtained for warm dense Xe and H 2 and liquid Se.

Convergence (summary) in number of k-points in the Brillouin zone in number of particles in the supercell in frequency range in number of ionic configurations Relative error is ~ 5% - 30% depending on density

Dependence of reflectivity of shocked xenon on density

Dependence of reflectivity of shocked xenon on density

Dependence of reflectivity of shocked xenon on density

Calculation parameters 0. 51 30050 0. 53 32900 0. 97 29570 1. 1 33100 1. 46 30260 1. 6 33120 1. 98 29810 2. 2 32090 2. 7 29250 2. 8 32020 3. 84 28810 3. 4 31040

Longitudinal expression Kubo-Greenwood formula (transverse expression) M. Gajdoš, K. Hummer, G. Kresse, J. Furthműller, F. Bechstedt, Phys. Rev. B 73, 045112 (2006).

Plasma frequency of liquid selenium at ρ=5 g/cm 3

Dependence of plasma frequency on density in the liquid selenium

Dependence of charge density in plasma of shocked xenon on concentration of neutral atoms

эксперимент V. B. Mintsev, Yu. B. Zaporogets, Contrib. Plasma Phys. 29, 493 (1989). данная работа DFT/QMD with «band gap» corrections M. P. Desjarlais, Contrib. Plasma Phys. 45, 300 (2005)

Диэлектрические свойства разогретого Саитов И. М. плотного вещества (Warm Dense Matter) DFT Kohn. Sham Dielectric function Reflectivity Absorbtion Trasmission Plasma frequency Effective free electron density Conductivity …… Electronic density of states