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More’s QEOS • The pressure is equal to zero at the solid density and the experimental bulk modulus is reproduced. • The cold pressure at the density less than the solid density should be negative (tensile force). • The Fermi pressure of electron is reproduced to be a dominant term at high density in the limit of eF >> Te, wheneFis the Fermi energy of electron. • The ideal gas EOS should be reproduced at high temperature Te >> eF . • The effective charge Z* is determined not only by the thermal ionization, but also by the pressure ionization.
Formula of Equation of State Applicable to Wide Range of T and n Total Free Energy Thermodynamic Consistency
Ion Equation of State (Cowan Model by More) • 0 < Ti < D (low-temperature solid phase) • D< Ti < Tm (high-temperature solid phase) • Tm < Ti (fluid phase)
Melting Temperature (eV)
Electron Equation of State based on Thomas-Fermi Model
Thomas Fermi Model Takabe-Takami model,
Bonding Correction where Pb0 = eb0brs/3, rs the solid density, R/Rs = (rs / r)1/3. The parameters eb0 and b are determined so that the total pressure is equal to zero at r = rs and Te = 0 and the bulk modulus defined by
Image of Atoms in Hot-Dense Plasmas(Pressure Ionization) 10.2 Atomic Physics of Hot Dense Plasam
Average Atom Model Screened Hydrogen Model rn =a0n2 / Zn
photo excitation cross-section sm,m' ∫fm,m'ndn = 1 xn = Pn / gn