A warm ionised patch of the interstellar medium has proton density

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

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

Problem

A warm ionised patch of the interstellar medium has proton density n0=1×105 m−3n_0 = 1\times10^{5}\,\mathrm{m^{-3}}, field B0=5×10−10 TB_0 = 5\times10^{-10}\,\mathrm{T}, size L=1 pc=3.086×1016 mL = 1\,\mathrm{pc} = 3.086\times10^{16}\,\mathrm{m}, a turbulent flow speed U=1×104 m s−1U = 1\times10^{4}\,\mathrm{m\,s^{-1}} and a quoted resistivity η=1.571×10−3 Ω m\eta = 1.571\times10^{-3}\,\Omega\,\mathrm{m}. ((a)) Calculate the magnetic Reynolds number Rm=μ0UL/ηR_m = \mu_0UL/\eta and say which term of the induction equation dominates. ((b)) A passing shock squeezes a roughly spherical piece of the patch equally in all directions, halving its radius without losing any plasma. Treating the field as frozen in and roughly uniform through the piece, find the new field B1B_1 and density n1n_1. ((c)) Check B1B_1 with the local form of the theorem, using the fact that B/ρ\mathbf{B}/\rho changes as a fluid line element does.

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