A magnetic loop above a solar active region has length scale

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

Stars from the Inside, Ch The Sun as a test: calibration, sound, neutrinos and a magnetised atmosphere

Problem

A magnetic loop above a solar active region has length scale L=5×107 mL = 5\times10^{7}\,\mathrm{m}, a plasma flow speed v=2 km s−1v = 2\,\mathrm{km\,s^{-1}}, and magnetic diffusivity η=0.5 m2 s−1\eta = 0.5\,\mathrm{m^2\,s^{-1}} (the coronal value at 106 K10^{6}\,\mathrm{K}). ((a)) Compute the magnetic Reynolds number Rm=vL/ηR_m = vL/\eta. ((b)) Compute the ohmic diffusion time L2/ηL^2/\eta, in years. ((c)) The loop is observed to persist for a few hours. State whether the field can be treated as frozen into the plasma over that time, giving the reason.

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