A continuous-wave source at one end of a long

PHYSICS · Subjective · Fermi University Physics · Plasma Physics · Waves in plasmas · Kinetic theory, collisions and transport

Plasma Physics, Ch The Vlasov equation and Landau damping

Problem

A continuous-wave source at one end of a long, uniform, collisionless plasma column launches a Langmuir wave at fixed real frequency. The electron density is ne=1.0×1018 m−3n_e=1.0\times10^{18}\,\mathrm{m^{-3}} and the electron temperature is Te=10 eVT_e=10\,\mathrm{eV}, and the source is tuned so that the excited wave has kλDe=0.3k\lambda_{De}=0.3. Estimate the spatial damping length LL over which the wave amplitude falls by a factor 1/e1/e, using the exact Maxwellian Landau rate at this kλDek\lambda_{De}, γ=−1.26×10−2 ωpe\gamma=-1.26\times10^{-2}\,\omega_{pe}, and the Bohm-Gross group velocity vg=dω/dk≈3kvte2/ωpev_g=\mathrm{d}\omega/\mathrm{d}k\approx 3kv_{te}^2/\omega_{pe}, treating the damping as slow enough that a wave packet travels at vgv_g while decaying at the temporal rate ∣γ∣|\gamma| (so L=vg/∣γ∣L=v_g/|\gamma|).

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