How a physical definition of overmodedness can explain local statistical non-compliancy

Current understanding of reverberation chambers is firmly funded upon their being operated as overmoded cavities. A proper definition of this condition has been lacking for a long time, while being regarded as automatically satisfied as soon as a large (and unspecified) number of normal modes are set to resonate at the frequency of operation of the chamber. In a recent work, we have introduced in a formal way a proper definition of the overmoded condition, showing how, from a strict mathematical viewpoint, it is not related to any threshold frequency, but rather requires a statistical framework. In this paper we revisit the most important results from our analysis, and show how our theory can straightforwardly explain the local non-compliancies sometimes observed for field statistics in what are deemed to be overmoded cavities. Partial overlapping between the normal modes of the cavity are shown to lead to an alternative and more physically-based explanation for this phenomenon, without invoking the concept of an ineffective stirring technique, nor the presence of unstirred components. The proposed theory is finally applied for the assessment of the relationship existing between the actual confidence margin based on the ideal properties of a reverberation chamber and those predicted by our model, showing how there is a non-negligible probability of having a large number of samples outside the original confidence margin, i.e., a potentially erroneous estimate of the true variability of a field-related quantity.