A microwave beam is launched through a laboratory plasma column

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

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

Problem

105\,\mathrm{GHz}

microwave beam is launched through a laboratory plasma column. Near the point of interest the electron density has a gradient scale length

L_n = 0.50\,\mathrm{m}

, and the beam is far from any cutoff there. ((a)) Estimate the WKB validity parameter

|k'|/k^2 \approx \lambda/(2\pi L_n)

at this point, where

\lambda

is the vacuum wavelength. ((b)) State whether the WKB approximation is trustworthy here, and by roughly what factor.