Dipole Modes and the One-Wave Approximation for Trapped Modes in Magnetoplasma Cylinders

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Abstract
An analysis of trapped mode wave propagation is given for a cold, uniform magnetoplasma cylinder embedded in free space. The full set of Maxwell's equations is used and an arbitrary magnetic field strength is allowed. New simplified forms are obtained for the dispersion relation and the fields. The simplified expressions are used to study the dipole modes in detail. Computer solutions are given for the dispersion relation and for the longitudinal fields when the cyclotron frequency is above and below the plasma frequency and for two different column diameters. The fields solutions are sums of terms with two different propagation constants. For the circularly symmetric and dipole modes, it is found that one wave dominates. This has led to a new approximation, the ``one‐wave'' approximation, which gives dispersion curves accurate to within 1% except for the lowest‐order dipole mode.