Consider a laboratory plasma with electron density and immobile

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

Plasma Physics, Ch Plasma oscillations and light in an unmagnetised plasma

Problem

Consider a laboratory plasma with electron density ne=2.5×1016 m−3n_e = 2.5\times10^{16}\,\mathrm{m^{-3}} and immobile, uniform ions providing a neutralising background. ((a)) Starting from the linearised cold electron continuity equation, the linearised cold electron momentum equation with no pressure term, and Poisson's equation, derive the dispersion relation for small-amplitude electron density oscillations. Take all perturbed quantities to vary as ei(kx−ωt)e^{i(kx-\omega t)} along one direction xx. ((b)) Evaluate the oscillation frequency in hertz for the given density, and state the group velocity of this disturbance.

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