A laboratory deuterium ( ) linear pinch has ion (and electron) density

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

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

Problem

A laboratory deuterium (

m_i = 2m_p

) linear pinch has ion (and electron) density

n = 1\times10^{21}\,\mathrm{m^{-3}}

, magnetic field

B = 0.4\,\mathrm{T}

, scale length

L = 0.2\,\mathrm{m}

and a flow speed

U = 2\times10^{4}\,\mathrm{m\,s^{-1}}

. Its resistivity, quoted from the Spitzer formula at

T_e = 50\,\mathrm{eV}

, is

\eta = 2\times10^{-6}\,\Omega\,\mathrm{m}

, and

T_i = T_e = 50\,\mathrm{eV}

. ((a)) Estimate the size of the Hall term relative to

\mathbf{U}\times\mathbf{B}

in the generalised Ohm's law, using

j \sim B/\mu_0L

. ((b)) Calculate the resistive diffusion time

\tau_R = \mu_0L^2/\eta

. ((c)) Calculate the Alfven speed

v_A

and the Lundquist number

S = \mu_0Lv_A/\eta

. ((d)) Compare the magnetic pressure

B^2/2\mu_0

with the plasma pressure

n(T_i+T_e)

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