A patch of the Earth's ionospheric F-region has singly-charged oxygen ions ( ) and…

PHYSICS · Multi-part · Fermi University Physics · Plasma Physics · Fluid and magnetohydrodynamic description · Fluid and magnetohydrodynamic description

Plasma Physics, Ch Magnetohydrodynamics: Ohm's law for a moving plasma, frozen flux and magnetic pressure

Problem

A patch of the Earth's ionospheric F-region has singly-charged oxygen ions (mi=16mpm_i = 16m_p) and electrons of density n=1×1012 m−3n = 1\times10^{12}\,\mathrm{m^{-3}}, sits in a field B=5×10−5 TB = 5\times10^{-5}\,\mathrm{T}, and is driven by a neutral wind at U=100 m s−1U = 100\,\mathrm{m\,s^{-1}} over a scale height L=1×105 mL = 1\times10^{5}\,\mathrm{m}. Its resistivity, quoted from the Spitzer formula scaled to Te=0.2 eVT_e = 0.2\,\mathrm{eV}, is η=1×10−2 Ω m\eta = 1\times10^{-2}\,\Omega\,\mathrm{m}, and Ti=Te=0.2 eVT_i = T_e = 0.2\,\mathrm{eV}. ((a)) Estimate the Hall term relative to U×B\mathbf{U}\times\mathbf{B} in the generalised Ohm's law. ((b)) Calculate the resistive diffusion time τR=μ0L2/η\tau_R = \mu_0L^2/\eta. ((c)) Calculate vAv_A and the Lundquist number S=μ0LvA/ηS = \mu_0Lv_A/\eta. ((d)) Compare B2/2μ0B^2/2\mu_0 with n(Ti+Te)n(T_i+T_e).

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