All Problems

Dispersion and Absorption of Light

Problem 5.201

An electromagnetic wave of frequency \(\omega\) propagates in dilute plasma. The free electron concentration in plasma is equal to \(n_{0}\). Neglecting the interaction of the wave and plasma ions, find: (a) the frequency dependence of plasma permittivity; (b) how the phase velocity of the electromagnetic wave depends on its wavelength \(\lambda\) in plasma.

Reveal Answer
 (a) ε=1−n0e2/ε0mω2,v=c1+(n0e2/4π2ε0mc2)λ2\text { (a) } \varepsilon=1-n_{0} e^{2} / \varepsilon_{0} m \omega^{2}, v=c \sqrt{1+\left(n_{0} e^{2} / 4 \pi^{2} \varepsilon_{0} m c^{2}\right) \lambda^{2}}
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