  We report on a numerical study intended to examine the possibility that
magnetic oscillations persist in type II superconductors beyond the point where
the pairing self-energy exceeds the normal state Landau level separation. Our
work is based on the self-consistent numerical solution for model
superconductors of the Bogoliubov-deGennes equations for the vortex lattice
state. In the regime where the pairing self-energy is smaller than the
cyclotron energy, magnetic oscillations resulting from Landau level
quantization are suppressed by the broadening of quasiparticle Landau levels
due to the non-uniform order parameter of the vortex lattice state, and by
splittings of the quasiparticle bands. Plausible arguments that the latter
effect can lead to a sign change of the fundamental harmonic of the magnetic
oscillations when the pairing self-energy is comparable to the cyclotron energy
are shown to be flawed. Our calculations indicate that magnetic oscillations
are strongly suppressed once the pairing self-energy exceeds the Landau level
separation.
