  In this research the transverse hydrostatic stability of a gravitating
Fermi-Dirac plasma under a quantizing field is explored. It is revealed that
such plasma is magnetically unstable due to the Landau electron spin-orbit
quantization in all magnetic levels which might explain the gravitational
compactification in the case of magnetic compact-stars. It is also revealed
that the Coulomb interaction plays a fundamental role in the magnetic
instability when a critical field is reached for a given plasma composition. It
is remarked that, the Coulomb interaction, on specific condition depending on
the field-strength and plasma composition, can suddenly destroy the transverse
stability of the relativistically degenerate Fermi-Dirac plasma. The
consequences of such instability on mass-limit of magnetic compact-stars and
the neutron star crust with possible relation to gamma-ray bursts is
numerically examined.
