A Langmuir wave with propagates in a Maxwellian plasma with .

PHYSICS · Multi-part · Fermi University Physics · Plasma Physics · Kinetic theory, collisions and transport · Kinetic theory, collisions and transport

Plasma Physics, Ch The Vlasov equation and Landau damping

Problem

A Langmuir wave with

k\lambda_{De} = 0.4

propagates in a Maxwellian plasma with

\omega_{pe} = 5.00\times10^{10}\ \mathrm{rad\ s^{-1}}

. ((a)) Using the weak-damping formula of the plasma dispersion function, find the damping rate

\gamma

and the time for the wave amplitude to fall by a factor of

e

. ((b)) The exact Maxwellian root at this

k\lambda_{De}

gives

\gamma = -6.61\times10^{-2}\,\omega_{pe}

. Find the

e

-folding time from it, and say whether the formula can be trusted here.

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