CASIMIR FORCE BETWEEN TWO PARALLEL PLATES WITH SMALL DISTORTIONS OF DIFFERENT TYPES

Abstract

We investigate the corrections to the Casimir force between two parallel plates covered with distortions described by periodic functions of two variables. The periods of the distortions in both coordinates are suggested to be much smaller than the sizes of the plates. A general expression is obtained for the Casimir force in the form of a perturbation expansion with respect to the amplitude of the distortions divided by the distance between the plates. The coefficients of this expansion are expressed in terms of the Fourier coefficients of the distortion function up to fourth order. It is shown that the perturbative expansion starts from the second order and does not depend on the period of the distortions. Some characteristic examples are calculated for both longitudinal and hillock-type distortions. It is shown that the contribution of the distortions to the Casimir force may achieve some 10%. So it must be taken into account in precision Casimir force measurements.