Magnetic-field dependence of the ultrasonic attentuation in metals

A self-consistent, semiclassical treatment is given for the attenuation of a sound wave by a free-electron gas in a positive background which supports the sound wave. Emphasis is placed upon the kinds of magnetic-field dependence which can be found under a wide range of values for the magnetic field, frequency, and mean free path. Applications of the general formalism include propagation parallel and perpendicular to the magnetic field. The special phenomena studied include geometric resonances, cyclotron resonances, and magneto-plasma resonance. A qualitative physical interpretation of the various effects found in the detailed calculations is also presented.