The application of the Kramers-Kronig relations to the calculation of the dielectric loss tangent of high grade insulators

The use of high grade insulators in fusion reactors is discussed and the effects of radiation on their a.c. electrical properties is described. The equations describing radio frequency power loss are derived in terms of the complex relative permittivity, epsilonsub(r) = epsilon ' -jepsilon ''. Epsilon '' and epsilon ' are shown to be related via the pair of integral transforms known as the Kramers-Kronig relations. The possibility of totally characterising a dielectric material by making only capacitance measurements is assessed. It is concluded that for high grade insulators, measurement of the real part of the permittivity cannot be made with sufficient precision in the radio frequency range (1MHz - 1GHz) to permit the radiation induced conductivity to be calculated in this way. (author)