A wave crossing an evanescent gap between a cutoff and a nearby resonance is…

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

Plasma Physics, Ch Waves in a non-uniform plasma: rays, reflection, mode conversion and radiofrequency heating

Problem

A wave crossing an evanescent gap between a cutoff and a nearby resonance is described by the Budden problem with parameter η=0.15\eta = 0.15. ((a)) Calculate the transmitted fraction T=e−πη\mathcal{T} = e^{-\pi\eta}, the reflected fraction R=(1−T)2\mathcal{R} = (1-\mathcal{T})^2 and the converted fraction C=T(1−T)\mathcal{C} = \mathcal{T}(1-\mathcal{T}). ((b)) Verify that T+R+C=1\mathcal{T} + \mathcal{R} + \mathcal{C} = 1 and compare C\mathcal{C} with the largest conversion any single Budden layer can produce.

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