BOUNDARY VALUE PROBLEM FOR EXCITING A ROTATING CYLINDRICAL WAVEGUIDE WITH IMPEDANCE WALLS
Abstract
The aim of the paper is to study the behavior of electromagnetic field excited in rotating waveguides. Solution of the problem of excitation of electromagnetic waves in rotating waveguides is important for interpreting the experiments with electromagnetic waves in rotating interferometers and gyroscopes. It can also be used for development of new methods of rotation rate measurement. Formulation and solution of such problems in rigorous way is complicated due to the fact that the rotating reference frames are non-inertial, and the presence of centrifugal forces and Coriolis forces make the space curved. In this paper, formulation and solution of the problem of excitation of electromagnetic field in a rotating cylindrical waveguide is presented in a rigorous form. The rigorous solution of the problems is derived with covariant Maxwell equations and take into account the effect of an equivalent gravitational field on the electromagnetic field in rotating reference frames. Influence of the rotation on the main characteristics of the waveguide is studied. Impedance boundary problem of excitation of an electromagnetic field in a rotating cylindrical waveguide with constant impedance walls is solved. Frequency responses of the rotating waveguide are calculated on the basis of the analytical solutions. It is shown that the parameters of the excited electromagnetic field depend on the waveguide rotation rate. It is shown, that the azimuthal harmonics, which propagate in the clockwise and counterclockwise directions in the waveguide have different wavelengths and propagation constants. Calculations confirm the effect of splitting of the waveguide cut-off frequency into two new cut-off frequencies due to rotation. The new cutoff frequencies are equal to the difference between the cut-off frequency of the waveguide at rest and the rotation rate of the waveguide multiplied by the order of the mode, which is excited in it. The dependence of the electromagnetic field parameters on the rotation rate can be used for rotation rate measurement. The solution derived can be used for setting up and analysis of the results of scientific experiments with rotating waveguides.
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