Finite Temperature Densities via the S-Function Method with Application to Electron Screening in Plasmas

Details Finite Temperature Densities via the S-Function Method with Application to Electron Screening in Plasmas Finite Temperature Densities via the S-Function Method with Application to Electron Screening in Plasmas

Dec 1997

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1997phdt.........3w&link_type=abstract

Thesis (PHD). UNIVERSITY OF WASHINGTON , Source DAI-B 58/06, p. 3093, Dec 1997, 113 pages.

Computer Science

1

Scientific paper

A new approach to the Green's-function method for the calculation of equilibrium densities within the finite temperature, Kohn-Sham formulation of density functional theory is presented, which extends the method to all temperatures. The contour of integration in the complex energy plane is chosen such that the density is given by a sum of Green's function differences evaluated at the Matsubara frequencies, rather than by the calculation and summation of Kohn-Sham single-particle wave functions. The Green's functions are written in terms of their spectral representation and are calculated as the solutions of their defining differential equations. These differential equations are boundary value problems as opposed to the standard eigenvalue problems. For large values of the complex energy, the differential equations are further simplified from second to first-order by writing the Green's functions in terms of logarithmic derivatives. An asymptotic expression for the Green's functions is derived, which allows the sum over Matsubara poles to be approximated. The method is applied to the screening of nuclei by electrons in finite temperature plasmas. To demonstrate the method's utility, and to illustrate its advantages, the results of previous wave function type calculations for protons and neon nuclei are reproduced. The method is also used to formulate a new screening model for fusion reactions in the solar core, and the predicted reaction rate enhancements factors are compared with existing models.

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