Mean field theory of the nonlinear response of an interacting dipolar system with rotational diffusion to an oscillating field

A mean field theory of dipolar relaxation in a system of interacting dipoles is developed on the basis of a local field picture. The distribution of orientations of a selected dipole is assumed to satisfy a rotational diffusion equation of Smoluchowski type with time-dependent potential determined self-consistently from the mean dipole moment. The response to an oscillating Maxwell field acting in a volume element is studied for arbitrary. amplitude and frequency of the field. For weak field the theory is similar to that developed by Debye, who used the Lorentz local field factor, and derived an expression for the frequency-dependent susceptibility of Clausius-Mossotti form. In the present theory the local field factor is found from the static linear response in thermal equilibrium. The same local field factor is used for strong field. Then the mean dipole moment oscillates anharmonically, and the maximum absorption shifts to higher frequency.