A radio wave with propagates in an unmagnetised

PHYSICS · Subjective · Fermi University Physics · Plasma Physics · Waves in plasmas · Waves in plasmas

Plasma Physics, Ch Plasma oscillations and light in an unmagnetised plasma

Problem

A radio wave with ω=1.5 ωpe\omega = 1.5\,\omega_{pe} propagates in an unmagnetised, collisionless plasma. Someone argues: "The refractive index is n=(1−ωpe2/ω2)1/2=(1−1/1.52)1/2=0.745n = (1-\omega_{pe}^2/\omega^2)^{1/2} = (1-1/1.5^2)^{1/2} = 0.745, so the phase velocity is vp=c/n=1.34cv_p = c/n = 1.34c, which is faster than light. Since electromagnetic disturbances cannot outrun light, this plasma dispersion relation is unphysical, and if it were somehow allowed a pulse sent through a slab of this plasma would arrive earlier than an identical pulse sent the same distance through vacuum." Find the error in this reasoning, and state what actually happens to a pulse's arrival time relative to the same path in vacuum.

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