Possible Loss of Mechanical Stability by Degenerate Charged Fermi Gases in Intense Magnetic Fields

The exact equations of state of a nonrelativistic degnerate ideal electron gas in an intense magnetic field are considered, and it is shown that its adiabatic index Gamma oscillates between 0 and a value just over 5/3 as a function of a given variable. Gamma reaches the critical points 0 when the variable = integer, corresponding to the filling of a Landau level. It is thus analogous to the de Haas-van Alphen effect, the normal quantized Hall effect, and magnetic domain formation. Corrections for a real gas, which could lead to Gamma less than 0 and mechanical stability breakdown, are considered qualitatively. In particular, an average index, valid in stars due to nonnegligible Newtonian self-gravition, suggest the possibility of observing this effect in astrophysical objects dominated by degenerate electrons in intense enough magnetic fields.