Abstract
Extraordinary solutions of the weakly relativistic, electromagnetic dispersion relation are investigated for waves propagating perpendicular to a uniform magnetic field in a Maxwellian plasma. As in a companion paper, which treated ordinary modes, weakly relativistic effects are found to modify dramatically the dispersion predicted by strictly non-relativistic ‘classical’ theory in the neighbourhood of harmonics of the cyclotron frequency Ωe. The infinite families of classical Gross–Bernstein and Dnestrovskii–Kostomarov modes are truncated to include only harmonics s satisfying s ≲ (ω2p mc2/4kB TΩ2e)⅓ and s ≲(ωp/Ωe)⅔/8 respectively where ωp is the plasma frequency and T the temperature. All classical cut-offs and resonances are removed apart from the x– and z– mode cut-offs. The only coupling between large- and small-wave-vector modes is between the z mode and a Gross–Bernstein mode near the upper-hybrid frequency and between the x mode and the second Gross–Bernstein mode near 2Ωe. Dispersion of the weakly relativistic counterpart of the x mode departs only slightly from that predicted by cold plasma theory except near Ωe and 2Ωe.
Publisher
Cambridge University Press (CUP)
Cited by
24 articles.
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