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Multipolar modes in a cylindrical, axially magnetized, cold, collisionless plasma that propagate near the cyclotron frequency are studied quantitatively. Examination of electromagnetic field patterns shows that in addition to the well-known spectrum of cyclotron modes there exists at positive azimuthal eigenvalues (n>0 in expjnφ) a mode that is distinguished by a different type of field pattern. The electric field of this mode is predominantly solenoidal, in contrast with the cyclotron modes, where a substantial part of the electric field is lamellar. This mode may be of importance in thick-beam parametric amplifiers at microwave frequencies (X-band) and in beam—plasma interaction near cyclotron frequency.

Electromagnetic-wave propagation for axisymmetric and dipolar modes in a circularly cylindrical waveguide containing a plasma column in an infinite axial magnetic field is studied. The plasma column is assumed to be cold, collisionless, and of uniform density, with a diameter one-half the diameter of the waveguide. Numerical solutions of the dispersion equation for typical cases at various values of the plasma density are presented. The electric field and power-flow density distribution are examined quantitatively for representative modes with reference to the existence of surface waves. It is shown that for an infinite magnetic field the high-frequency field distribution within the plasma can be a modified Bessel function of the first kind only for the superluminous phase velocities and only at plasma frequencies that exceed the lowest vacuum waveguide cutoff frequency. For slow waves of very short wavelength, ω/c≪2π/λg, the electromagnetic field and the power-flow density distribution are found to be confined to the plasma column with practically no field existing in the vacuum between the plasma and the waveguide wall.

The power flow of two types of cyclotron modes propagating in a waveguide filled with a cold collisionless axially magnetized plasma is studied as a function of the location of the point of operation on the Brillouin (ω-β) diagram. Dynamic analysis is used throughout. Partition of the total power flow corresponding to E, H, and EH power is examined and compared with results obtained by the quasistatic approximation in the domain of its presumed validity. The inadequacy of the quasistatic approximation for the analysis of the power flow, and hence the field patterns, is shown. New properties of cyclotron and plasmaguide modes obtained from the analysis are presented. A possible explanation is offered for the lack of published experimental observation of cyclotron modes in the superluminous phase velocity region.