On the theory of electromagnetic waves in metals in a magnetic field

Theoretically investigated in the paper is the possibility of the propagation in metals, of electromagnetic waves whose wavelength is small compared to the diameter of the electron orbits in a magnetic field. The dissipative conductivity due to the Cerenkov absorption of the wave by electrons fluctuates with the change in the relationship between the wavelength and the diameter of the electron orbits ("geometric resonance"). The Cerenkov absorption may vanish at the minimums of these oscillations in metals with a simply-connected Fermi surface. The non-dissipative conductivity hence turns out to be greater than the dissipative conductivity due to electron scattering. Consequently, electromagnetic waves with a discrete wave vector and frequency spectrum may be propagated in a metal. The spectrum, damping and polarization of these waves are investigated. It is shown that their frequencies may be both greater and less than the reciprocal of the electron relaxation time. As the magnetic field changes, the surface impedance of the metal experiences resonant oscillations due to the coincidence of the proper frequencies ${\mathrm{\omega }}_n$ and the external wave frequency $\mathrm{\omega }$.