# Properties of magnetized Coulomb crystals of ions with polarizable electron background

## TL;DR

This paper investigates phonon and thermodynamic properties of magnetized Coulomb crystals of ions with a weakly polarized electron background, emphasizing the conditions under which electron polarization significantly affects these properties.

## Contribution

The study applies the Thomas-Fermi formalism to analyze phonon and thermodynamic properties of magnetized Coulomb crystals, highlighting the impact of electron background polarization.

## Key findings

- Electron background polarization affects properties only at certain parameters.
- Thomas-Fermi approximation closely matches RPA for phonon moments.
- Polarization effects are significant at specific temperature and screening conditions.

## Abstract

We have studied phonon and thermodynamic properties of a body-centered cubic (bcc) Coulomb crystal of ions with weakly polarized electron background in a uniform magnetic field ${\bf B}$. At $B=0$ the difference between phonon moments calculated using the Thomas-Fermi (TF) and random phase (RPA) approximations is always less than one percent and for description of phonon properties of a crystal TF formalism was used. This formalism was successfully applied to investigate thermodynamic properties of magnetized Coulomb crystals. It was shown that the influence of the polarization of the electron background is significant only at $\kappa_{\rm TF}a > 0.1$ and $T \ll T_{\rm p}(1+h^2)^{-1/2}$, where $\kappa_{\rm TF}$ is the Thomas-Fermi wavenumber, $a$ is the ion sphere radius, $T_{\rm p}\equiv\hbar \omega_{\rm p}$ is the ion plasma temperature, $h\equiv \omega_B/\omega_{\rm p}$, $\omega_B$ is the ion cyclotron frequency and $\omega_{\rm p}$ is the ion plasma frequency.