Dispersion relation for cyclotron waves as a spatial condition for minimum collisionless damping

It is shown that the dispersion relation for cyclotron waves of the extraordinary type (ECW) propagating in a metal with a cylindrical Fermi surface may be found in a simple way from the zero's of certain Bessel functions. This follows as a consequence of a requirement of minimum damping of the waves by direct collisionless interaction between the electrons and the waves. A detailed comparison with calculations based on a realistic silver Fermi surface and a spherical Fermi surface, in both cases for a finite value of ωτ, is performed. The behavior of the dispersion relation in the limit of vanishing magnetic field is considered in some detail and a number of interesting features are pointed out.