Variation of the values of the adiabatic invariant in near-critical conditions in the short-wave range

The possibility of significant variations of the adiabatic invariant is examined for the propagation of radio waves in an irregular earth-ionosphere waveguide with a parabolic dependence of permittivity on height. Numerical and analytical results indicate that nonexponential deviations of the adiabatic invariant can occur not only when the characteristic size of horizontal irregularity decreases (e.g., during resonant beam excitation) but also in quasi-critical conditions and for smoothly irregular waveguides.