The solar corona is a fully ionised plasma of free electron number density

PHYSICS · Multi-part · Fermi University Physics · Plasma Physics · Waves in plasmas · Waves in plasmas

Modes, Packets and Media, Ch Transmission lines and electromagnetic waves in matter, plasmas and guides

Problem

The solar corona is a fully ionised plasma of free electron number density ne=1.0×1014 m−3n_e=1.0\times10^{14}\,\mathrm{m^{-3}}. Treat the electrons as free (unbound) charges of mass mem_{\rm e} and charge −e-e, responding to a radio wave's electric field E(x,t)=Re[E~0ei(ωt−kx)]E(x,t)=\mathrm{Re}\big[\tilde E_0e^{i(\omega t-kx)}\big], using the time factor e+iωte^{+i\omega t} throughout; a result quoted with the opposite convention e−iωte^{-i\omega t} is related to this one by complex conjugation. ((a)) Starting from the electron's equation of motion, derive the relative permittivity εr(ω)=1−ωp2/ω2\varepsilon_r(\omega)=1-\omega_{\rm p}^2/\omega^2, defining ωp\omega_{\rm p}, and state briefly why the choice of sign convention for the time factor does not affect this result. ((b)) Substitute into the wave equation to obtain ω2=ωp2+c2k2\omega^2=\omega_{\rm p}^2+c^2k^2. ((c)) Evaluate the plasma frequency fpf_{\rm p} of the corona in megahertz. ((d)) A radio burst at 60 MHz60\,\mathrm{MHz} is generated deep in the corona. Say, with a one-line reason, whether it can propagate outward through this layer of the corona.

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