Probability distribution of the quality factor of spacecraft structures modelled as undermoded reverberation chambers

In this paper, we discuss the electromagnetic modelling of a large spacecraft structure excited by relatively low frequencies. The intrinsic complexity of such a scenario allows for invoking an analogy with studies of mode-stirred cavities. We therefore derive a probability distribution of the quality factor of a reverberation chamber, operated at relatively long wavelengths compared to the characteristic dimensions of the cavity. In this regime, the cavity does not operate in overmoded regime, yet a statistical description of fields can be preserved provided a proper (physically based) limit distribution can be assumed. The method developed in our work is based on an instantaneous (sample), rather than an averaged (thermodynamic) value in the definition of the cavity quality factor. This factor is actually a random variable fluctuating over the stirring process, because of the changing geometry (mechanical sturring) and/or excitation frequency (electronic stirring). We find that the probability distribution in undermoded case deviates from the idealized one, as it exhibits stronger positive skewness.