Cherenkov radiation in biaxial crystals—I

The radiation emitted by a uniformly moving point charge in a biaxial crystal is studied by a new method. Fourier integrals for the field are set up for the general case without imposing any restriction on the dielectric and magnetic properties of the crystal or on the direction of motion of the charge. In the case of motion along a principal dielectric axis the integrals are evaluated exactly and closed expressions for the radiated energy are obtained. For radiation of either kind these expressions involve Heuman's Lambda function and the complete elliptic integral of the first kind.