Limit distributions for imperfect electromagnetic reverberation

We investigate departures from ideal circular Gauss normality for the statistical distribution of complex fields in undermoded mode-tuned or mode-stirred reverberation chambers. A physical nonlinear model is developed, in which the energy density of the interior field is expressed as a functional of energy densities for equivalent boundary sources associated with a partitioning of the cavity surface. This results in Meijer G and Bessel K limit distributions which extend the well-known Gauss normal, chi and chi-squared asymptotic distributions for ideal reverberation fields, their magnitude and energy density, respectively. The additional distribution parameter permits graduation of the distribution, allowing one to incorporate chamber imperfections and operating at lower frequencies. The role of entropy, mode migrations, mode mutations, and the link with doubly stochastic random walks and cavity ensembles are outlined. In an alternative model based on cavity feedback, a powered gamma distribution is obtained for the field magnitude and energy density, exhibiting one further distribution parameter. Theoretical results are illustrated with measured and numerically simulated data, and include results on eigenfrequency dynamics.