Analysis of the radial and longitudinal effect in a double TE(104) and a single TE(102) rectangular cavity

The response of the cavity to the rotation of a point-like sample in the horizontal (y-z) plane passing through the center of the Bruker double TE(104) and single TE(102) rectangular cavities in concentric circles of radii rho = 0, 1, 2, 3, 4, and 5 mm from the cavity center (radial effect) has been analyzed. The experimentally observed dependencies of the EPR signal intensity, I(pp), showed the following: (i) for rho = 0 mm (a sample position in the cavity center), I(pp) is independent of the angle of rotation; (ii) for rho = 1, 2, and 3 mm, the I(pp) dependence progressively changes from circular to oval; (iii) when the radius is further increased to rho = 4 and 5 mm, the I(pp) dependence changes dramatically, giving a figure eight shape. These experimental observations are in very good agreement with the theoretical calculations, in which the response is modeled using modified Cassinian curves, K(rho, phi). Similar trends were observed for any position of the horizontal (y-z) plane at which the sample is situated along the vertical x axis of the cavity; however, the amplitude of the signal decreases with increase in the absolute value of the x coordinate, ||x ||. The variation in the signal amplitude along the cavity x axis (longitudinal effect) can be calculated theoretically using a modified sine-squared curve, G(x). In general, the response of the cavity to a point-like sample situated at any position, P(rho, phi, x), can be represented as a product of the mentioned Cassinian curve, K(rho, phi), and sine-squared curve, G(x), giving for the signal intensity I(pp)(rho, phi, x) approximately K(rho, phi)G(x). The response to a large cylindrical sample which is concentrically situated on the cavity x axis can then be obtained by integrating the above product, K(rho, phi)G(x), over the sample volume. The nonlinear radial effect may give rise to a serious source of systematic error in quantitative EPR spectroscopy and shows that accurate and precise positioning of the sample in the microwave cavity is essential.