A long theta pinch confines a plasma column of pressure inside an external axial field

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

Plasma Physics, Ch Holding a plasma still: pinches, flux surfaces and the Grad-Shafranov equation

Problem

A long theta pinch confines a plasma column of pressure

p = 8.0\times10^5\,\mathrm{Pa}

inside an external axial field

B_0 = 2.0\,\mathrm{T}

. Idealise the column as straight, uniform along its length, and in one-dimensional pressure balance,

p + \frac{B_{\rm in}^2}{2\mu_0} = \frac{B_0^2}{2\mu_0}.

((a)) Find the plasma beta

\beta = 2\mu_0p/B_0^2

. ((b)) Find the field

B_{\rm in}

inside the plasma.

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