  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.
