  Aims: We perform an advanced study of the fast magnetoacoustic sausage
oscillations of coronal loops in the context of MHD coronal seismology to
establish the dependence of the sausage mode period and cut-off wavenumber on
the plasma-beta of the loop-filling plasma. A parametric study of the ratios
for different harmonics of the mode is also carried out.
  Methods: Full magnetohydrodynamic numerical simulations were performed using
Lare2d, simulating hot, dense loops in a magnetic slab environment. The
symmetric Epstein profile and a simple step-function profile were both used to
model the density structure of the simulated loops. Analytical expressions for
the cut-off wavenumber and the harmonic ratio between the second longitudinal
harmonic and the fundamental were also examined.
  Results: It was established that the period of the global sausage mode is
only very weakly dependent on the value of the plasma-beta inside a coronal
loop, which justifies the application of this model to hot flaring loops. The
cut-off wavenumber kc for the global mode was found to be dependent on both
internal and external values of the plasma-beta, again only weakly. By far the
most important factor in this case was the value of the density contrast ratio
between the loop and the surroundings. Finally, the deviation of the harmonic
ratio P1/2P2 from the ideal non-dispersive case was shown to be considerable at
low k, again strongly dependent on plasma density. Quantifying the behaviour of
the cut-off wavenumber and the harmonic ratio has significant applications to
the field of coronal seismology.
