Wave spectra of a strongly coupled magnetized one-component plasma: quasilocalized charge approximation versus harmonic lattice theory and molecular dynamics.

Two different approaches to the calculation of the wave spectra of magnetized strongly coupled liquid one-component plasmas are analzyed: the semianalytical quasilocalized charge approximation (QLCA) and the angle-averaged harmonic lattice (AAHL) theory. Both theories are benchmarked against the numerical evidence obtained from molecular dynamics simulations. It is found that not too far from the melting transition (Γ≳100), the AAHL theory is superior to the QLCA, while further away from the transition, the QLCA performs comparably to or better than the AAHL theory.

Coulomb crystals in the magnetic field.

The body-centered-cubic Coulomb crystal of ions in the presence of a uniform magnetic field is studied using the rigid electron background approximation. The phonon mode spectra are calculated for a wide range of magnetic-field strengths and for several orientations of the field in the crystal. The phonon spectra are used to calculate the phonon contribution to the crystal energy, entropy, specific heat, Debye-Waller factor of ions, and the rms ion displacements from the lattice nodes for a broad range of densities, temperatures, chemical compositions, and magnetic fields. Strong magnetic field dramatically alters the properties of quantum crystals. The phonon specific heat increases by many orders of magnitude. The ion displacements from their equilibrium positions become strongly anisotropic. The results can be relevant for dusty plasmas, ion plasmas in Penning traps, and especially for the crust of magnetars (neutron stars with superstrong magnetic fields B > or approximately equal 10(14) G ). The effect of the magnetic field on ion displacements in a strongly magnetized neutron star crust can suppress the nuclear reaction rates and make them extremely sensitive to the magnetic-field direction.

Effect of the electron gas polarizability on the specific heat of phonons in Coulomb crystals.

The effect of the background polarizability on the thermodynamic properties of a Coulomb crystal of ions is studied. The response of electrons is treated using the Thomas-Fermi (TF) and random phase approximations (RPA). For the case of ions fixed at their lattice sites, the energy of bcc and fcc crystals is calculated to first order in the screening parameter (kappa(TF)a)(2) (kappa(TF) is the TF wave number and a is the ion sphere radius). It is shown that in the RPA there exist domains of parameters (mass density rho and charge number Z) where energy of fcc crystal is lower than that of bcc. The effect of ion vibrations is studied using harmonic lattice approximation. It is shown that phonon modes are nearly identical in the RPA and in the TF approximation. The latter allows one to apply the Ewald technique to the construction of the dynamical matrix, which speeds up all calculations considerably. The main thermodynamic quantities of phonons are calculated as functions of the quantum parameter T(p)/T (where T(p) is the ion plasma temperature) and the screening parameter. The electron polarizability leads to a moderate increase of the phonon thermodynamic quantities as compared to the case of one-component plasma with rigid background (by approximately 30% at kappa(TF)a=0.8). Zero-point motion of ions modifies the aforementioned domains where fcc has lower energy than bcc for static ions. The effect is profound at small Z but leaves the domains unaltered at larger Z. The thermal vibrations of ions at T greater, similar T(p) eliminate completely the domains where fcc is thermodynamically preferable at T=0. The related model of Yukawa-Wigner solid is briefly studied. It is shown that neither bcc nor fcc crystal structures are stable in this model.

Thermodynamic functions of harmonic Coulomb crystals.

Phonon frequency moments and thermodynamic functions (electrostatic and vibrational parts of the free energy, internal energy, and heat capacity) are calculated for bcc and fcc Coulomb crystals in the harmonic approximation with a fractional accuracy < or equivalent to 10(-5). Temperature dependence of thermodynamic functions is fitted by analytical formulas with an accuracy of a few parts in 10(5). The static-lattice (Madelung) part of the free energy is calculated with an accuracy of approximately 10(-12). The Madelung constant and frequency moments of hcp crystals are also computed.