Contribution of wave chaos theory to the study and the optimisation of reverberation chambers – CAOREV

The criteria used to characterize the chaotic behavior of the cavity and the ones related to the well-operating of a reverberation chamber have been compared, in particular through statistical studies and simulation results.
Using simulations, three cavities have been studied and their statistical properties have compared: an empty parrallelepipedic cavity and then by loading it with one or two hemispheres on their walls.
Some first measurements have been performed in a small 3D cavity.

The criteria issued in the study of chaotic cavities have proven their efficiency in the comparison of the three studied cavities. New criteria have been proposed.
The insertion of hemispheres leads to a clear improvement of the field properties. Above a minimal frequency, all the modes are ergodic.
An acceptable precision has been obtained for the field measurements within the 3D cavity obtained with a probe or through a perturbative approach.

In the new proposed reverberation cavity, the stirring process will be provided by the displacement of the hemisphere. The modification of the field will be studied through simulations. In this case, the criteria classically used for reverberation chambers will be suited, but the knowledge issued from the wave chaos theory will also be used.

The influence of the losses on the field properties will also be studied at theoretical and numerical levels.

• K. Selemani, E. Richalot, O. Legrand, F. Mortessagne, « Study of a reverberation chamber shape inspired from chaotic cavities », Advanced Electromagnetics Symposium, AES2012, 16-19 April 2012, Paris, France.
• K. Selemani, E. Richalot, O. Legrand, F. Mortessagne, “Etude d’une géométrie de chamber réverbérante inpirée par le chaos ondulatoire”, Colloque International sur la Compatibilité Electromagnétique, CEM2012, Rouen, 24-27 avril 2012.

Reverberation chambers (RC) constitute a performing tool for radiated emissions and immunity measurements, and arouse increasing interest in academic and industrial domains. They are electrically large metallic cavities equipped with a stirrer that modifies the field within the chamber while moving. Above a specific frequency, this mechanical stirring results in an average homogeneous and isotropic field on the equipment under test. Several parameters have to be taken into account to design an RC: the frequency, the shape of the cavity and of the stirrer, and the losses. By widening the resonance peaks, the losses introduce modes overlap.
ESYCOM laboratory studies reverberation chambers since 12 years. Using numerical simulations, it studies the statistical properties of the fields, the criteria to evaluate the chamber working, the modes perturbation by the stirrer rotation, the losses modelling, and the expansion of the field on plane waves.

Because of the analogy between the Schrödinger and Helmholz equations, quantum chaos theory has been extended to wave chaos with the study of electromagnetic cavities. The main advantage of this transposition is that experimentation is easier in the electromagnetic domain. The first experiments aimed to validate the predictions of the random matrix theory (RMT). In RMT the cavity modes are described in terms of universal spectral or spatial statistical properties depending on the system global symmetries, but not on its geometrical details. One important result was to understand the behavior of 2D cavities and to give prominence to two types of system depending of the cavity shape: integrable and chaotic. Within a chaotic cavity, the spatial field distribution is statistically isotropic and homogeneous, as required in an RC.
LPMC laboratory works on the subject of wave chaos since 16 years for various systems as optic fibers, vibrating plates or RF cavities. A 2D electromagnetic cavity has been built. As its geometry is reconfigurable, measurements have been performed to study the ray propagation chaoticity as well as in disordered configurations leading to Anderson localization. Measurements are performed with a minimal field perturbation and the results obtained are in accordance with simulations and some RMT predictions. The studies on electromagnetic fields in presence of scatterers have led to conclusions whose validation would be interesting in the case of a 3D RC loaded by an object.

Using the complementarity between the two research teams, we will adopt an original approach consisting of applying the wave chaos theory to the study of reverberation chambers.

The practical contributions of this project could be:
- The optimization of the RC geometrical parameters, using wave chaos theory
- The decrease of the lower useable frequency of the RC
- The definition of better criteria for the RC utilization
- A more precise measurement technique
- A better control of the RC working in the presence of an object.

The theoretical aspects that will be investigated are:
- Extension of the results on the chaotic properties of a 2D cavity to a 3D cavity.
- Description of the statistical properties of the fields in the presence of losses. Non-hermitian random matrices will be used.
- Spectral statistics of a cavity with parametric variations (that correspond to the stirrer rotation).