Equation of state of a strongly magnetized hydrogen plasma

Abstract

The influence of a constant uniform magnetic field on the thermodynamic properties of a partially ionized hydrogen plasma is studied. Using the method of Green' s function various interaction contributions to the thermodynamic functions are calculated. The equation of state of a quantum magnetized plasma is presented within the framework of a low density expansion up to the order e^4 n^2 and, additionally, including ladder type contributions via the bound states in the case of strong magnetic fields (2.35*10^{5} T << B << 2.35*10^{9} T). We show that for high densities (n=10^{27-30} m^{-3}) and temperatures T=10^5 - 10^6 K typical for the surface of neutron stars nonideality effects as, e.g., Debye screening must be taken into account.Comment: 12 pages, 2 Postscript figures. uses revtex, to appear in Phys. Rev.

Partially ionized hydrogen plasma in strong magnetic fields

“…Recently, Steinberg et al [21] calculated the second virial coefficient of the proton-electron plasma in arbitrary magnetic field and constructed an EOS at low densities. The bound states were included using the Planck-Larkin partition function.…”

“…However, the Planck-Larkin formalism fails at higher densities, where one has to resort to the chemical picture of the plasma, as discussed in detail, e.g., by Däppen et al [23]. In addition, atomic binding energies were calculated in [21] using approximations [19] which have very restricted applicability as shown in [24].…”

Ionization Equilibrium and Equation of State of Hydrogen Plasmas in Strong Magnetic Fields

“…These effects have been studied only in the low-temperature or low-density regimes (e.g., ref. [10] and references therein). Here we use a scaling (r eff s = sr s ) of the density parameter r s = (4πn e a 3 0 /3) −1/3 at a fixed Coulomb parameter Γ = βe 2 /(a 0 r s ) in the formulae of ref.…”

“…For the contribution of electron-electron and electron-ion interactions in F ex , the scaling factors are s ee = (1 + θ m /θ 0 )/ 1 + (θ m /θ 0 ) exp(−θ −1 m )f 1 and s ie = 1/f 2 2 , where θ 0 = 2 (9π/4) −2/3 r s /Γ and θ m = 8 γ 2 r 5 s /(9π 2 Γ) are the non-magnetic and magnetic degeneracy parameters, respectively, and the factors f 1 and f 2 (depending on β ω c ) are given in ref. [10].…”

“…The same approximation was used in ref. [10], devoted to the low-density equation of state. Here we employ new fitting formulae to atomic energies and sizes [11] based on the previous study [8], valid for any state of atomic motion.…”