Analysis of the radial and longitudinal effect in a double TE104 and a single TE102 rectangular cavity

The response of the cavity to the rotation of a pointlike sample in the hor izontal y-z plane passing through the center of the Bruker double TE104 and single TE102 rectangular cavities in concentric circles of radii rho = 0, 1, 2, 3, 4, and 5 mm from the cavity center (radial effect) has been analyz ed. The experimentally observed dependencies of the EPR signal intensity, I -pp, showed the following: (i) for rho = 0 mm (a sample position in the cav ity 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 o val; (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 expe rimental observations are in very good agreement with the theoretical calcu lations, in which the response is modeled using modified Cassinian curves, K(rho, phi). Similar trends were observed for any position of the horizonta l y-z plane at which the sample is situated along the vertical x axis of th e cavity; however, the amplitude of the signal decreases with increase in t he absolute value of the x coordinate, /x/ The variation in the signal ampl itude along the cavity x axis (longitudinal effect) can be calculated theor etically using a modified sine-squared curve, G(x). In general, the respons e of the cavity to a pointlike sample situated at any position, P(rho, phi, x), can be represented as a product of the mentioned Cassinian curve, K(rh o, phi), and sine-squared curve, G(x), giving for the signal intensity I-pp (rho, phi, x) proportional to K(rho, phi)G(x). The response to a large cyli ndrical sample which is concentrically situated on the cavity x axis can th en 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 sourc e of systematic error in quantitative EPR spectroscopy and shows that accur ate and precise positioning of the sample in the microwave cavity is essent ial. (C) 2000 academic press.