Damping of the Magnetoionic Z Mode

Abstract

The magnetoionic z mode has traditionally been of less interest (outside ionospheric physics) than the x and o modes because it cannot escape directly from a distant source. However recent work on the cyclotron maser instability has shown that when the electron plasma frequency, ω_p, is smaller than the electron gyrofrequency, Ω, under plausible conditions most of the free energy available to the instability may be transferred to the z mode rather than the x or ο modes (Hewitt et al, 1983; Omidi et al, 1984; White, 1984). The condition ω_p < Ω is thought to be satisfied in solar magnetic flux tubes which are the sites of flares and microwave emission. The possibility that a large fraction of the energy released by a flare may be radiated as z-mode waves leads us to consider the fate of such waves. The conclusions are important for understanding the energy balance in solar flaring regions and, by analogy, in stellar radio sources also. In particular, we wish to know if a high z-mode energy density leads to observable radiation. We consider two effects here: damping of the z-mode waves as they propagate through the ambient coronal plasma, and coalescence of z-mode waves to produce second-harmonic radiation.

Exact calculations of the damping of the z mode have been carried out for a plasma with a Maxwellian distribution corresponding to a typical coronal temperature of 2 million K, using the full relat-ivistic gyroresonance condition. In a plasma with ω_p < Ω, the properties of the damping rate are as follows: (a)the damping rate is very large over a broad bandwidth of frequencies near ω = Ω, except for angles θ between the wavevector and the magnetic field direction which are close to 90°; (b)damping is small for θ ≃ 90° at frequencies ω < Ω; (c)there can be no resonance between the z-mode waves and particles near θ = 90° for frequencies luing between Ω and the z-mode cutoff frequency, ω₊ (θ) = (Ω² + ω² _psin²θ)^1/2, and so damping is exactly zero in this range; (d)damping exactly at ω = Ω is small at all angles Θ; (e)there is a narrow band of very strong damping at θ ≃ 90° at a frequency ω just below the gyrofrequency. The z-mode waves are likely to be generated with ω < Ω and θ ≃ 90°, in a region of low damping. As they propagate the ratio ω/Ω and the angle θ may change due to gradients in the plasma parameters. Damping near ω = Ω will prevent such waves from reaching regions in which ω/Ω > 1. It is concluded that the z-mode waves are likely to be damped at the ω = Ω layer, and thereby cause heating of the coronal plasma outside the flaring flux tube (cf. Melrose and Dulk, 1984).

If the z mode is the dominant emission then the brightness temperature of the z-mode waves in the source will be high. Coalescence of two z-mode waves to produce x- and o-mode waves with ω ≃ 2Ω will then be an efficient process which could act as a sink for the energy in the z-mode radiation. For this second-harmonic radiation to be observable, it must pass through the absorption layer in the corona at ω = 2Ω. This is not likely to be possible (Melrose and Dulk, 1984). The second harmonic causes heating of the corona in essentially the same layer as does the z-mode damping. One requires some effect other than coalescence of two z-mode waves in order to produce observable radiation.