The Sun's convection zone extends from the photosphere down to about depth

PHYSICS · Multi-part · Fermi University Physics · Electricity, Magnetism & Electromagnetism · Plasma Physics · Fluid and magnetohydrodynamic description

The Solid Earth, Ch The geomagnetic field: potential, spectrum, induction and the palaeomagnetic record

Problem

The Sun's convection zone extends from the photosphere down to about L=2×105 kmL = 2\times10^5\,\mathrm{km} depth. Large-scale convective flows there have a characteristic speed of order v=10 m s−1v = 10\,\mathrm{m\,s^{-1}}, and the magnetic diffusivity set by the electrical conductivity of the plasma near the base of the convection zone is ηm≈1 m2 s−1\eta_m \approx 1\,\mathrm{m^2\,s^{-1}} (quoted from solar physics). ((a)) Using the same definition of the magnetic Reynolds number as for the core, Rm=vL/ηmR_m = vL/\eta_m, estimate RmR_m for the solar convection zone. ((b)) State, with reference to the induction equation, what this value of RmR_m implies for whether a solar dynamo can be self-sustaining.

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