Relaxation of polar cylinders in strong electric fields

The problem of rotational diffusion of a polar cylinder about its long axis in an electric field has been solved. The solutions apply to the high as well as the low field limits. The results are presented as a function of a reduced time and the variable κ, which is a measure of the ratio of mean electrical energy to thermal energy. Asymptotic expansions are obtained for the distribution function and the fractional polarization. The eigenvalues and even solution of a Whittaker–Hill–Ince differential equation have been calculated as functions of κ. Asymptotic expansions of the eigenvalue and solution of this equation are given.