High precision measurements of LINAC coupled cells

For an assembled structure (module, tank) of a linac, the single cells, when coupled, loose their individuality and in cooperation contribute to the generation of the structure modes (resonant frequencies) F_m. On the other end these modes are the only measurable quantities. The system of the coupled cells can be modelled, in a narrow frequency band, as a lumped constant circuit. The modes are solution of an equation obtained equating to zero the determinant relevant to the lumped circuit representation. This is an algebraic equation of the same order as the number N of cells. A plausible question can be posed: is it possible from a manipulation of the measurable quantities (F_m) to draw the lumped circuit parameters, namely coupling constants and single cell resonant frequencies? The answer is positive if a certain degree of symmetry is satisfied. The coefficients of above mentioned equation can be easily related to the measured modes F_m. By varying, by means of tuners, the tune of a single cell of a small unknown amount, any couple of equation coefficient moves on a straight line. Therefore, we have N(N-1)/2 known straight line coefficients which may give the unknowns with extremely high accuracy.