Coulomb crystals in the magnetic field

TL;DR

This study analyzes how strong magnetic fields influence Coulomb crystal properties, revealing significant changes in phonon spectra, thermodynamic quantities, and ion displacements, with implications for astrophysical and plasma systems.

Contribution

It provides a comprehensive calculation of phonon spectra and thermodynamic properties of Coulomb crystals under strong magnetic fields, highlighting new anisotropic effects and their astrophysical relevance.

Findings

Magnetic fields drastically increase phonon specific heat.

Ion displacements become highly anisotropic under strong magnetic fields.

Magnetic fields can suppress nuclear reaction rates in neutron star crusts.

Abstract

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 $B \gtrsim 10^{14}$ 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.