A cylindrical pinch has a uniform density and a temperature that falls from to

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

Plasma Physics, Ch From particles to fluids: the distribution function, its moments and the two-fluid model

Problem

A cylindrical pinch has a uniform density n=3×1019 m−3n = 3\times10^{19}\,\mathrm{m^{-3}} and a temperature that falls from T(r=2 cm)=12 eVT(r=2\,\mathrm{cm}) = 12\,\mathrm{eV} to T(r=3 cm)=8 eVT(r=3\,\mathrm{cm}) = 8\,\mathrm{eV}. The axial field is uniform, B=0.6 TB = 0.6\,\mathrm{T}. ((a)) Find the pressure p=nTp = nT at each of the two radii. ((b)) Estimate the radial pressure gradient ∣∇p∣|\nabla p| between them by finite difference. ((c)) Estimate the magnitude of the diamagnetic current density j∗=∣∇p∣/Bj_* = |\nabla p|/B there.

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