In the ionospheric F2 layer

PHYSICS · Multi-part · Fermi University Physics · Plasma Physics · The plasma state and single-particle motion · The plasma state and single-particle motion

Plasma Physics, Ch What makes an ionised gas a plasma: shielding, the plasma parameter and the natural frequencies

Problem

In the ionospheric F2 layer, ne=1.0×1012 m−3n_e = 1.0\times10^{12}\ \mathrm{m^{-3}} and Te=0.10 eVT_e = 0.10\ \mathrm{eV}. A daytime electric-field patch maintains a potential difference ϕ=1.0 V\phi = 1.0\ \mathrm{V} across a horizontal distance L=100 mL = 100\ \mathrm{m}. Take the potential to vary roughly parabolically across the patch, so that the field itself changes by order ϕ/L\phi/L over LL. ((a)) Compute the electron Debye length λDe\lambda_{De} using λDe=7.43×103 (Te[eV]/ne[m−3])1/2 m\lambda_{De} = 7.43\times10^{3}\,(T_e[\mathrm{eV}]/n_e[\mathrm{m^{-3}}])^{1/2}\ \mathrm{m}. ((b)) Estimate the fractional charge imbalance δn/n\delta n/n that sustains this potential, using δn/n∼(λD/L)2 (eϕ/Te)\delta n/n \sim (\lambda_D/L)^2\,(e\phi/T_e).

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