Near the edge of a tokamak

PHYSICS · Multi-part · Fermi University Physics · Electricity, Magnetism & Electromagnetism · Plasma Physics · The plasma state and single-particle motion

Plasma Physics, Ch What makes an ionised gas a plasma: shielding, the plasma parameter and the natural frequencies

Problem

Near the edge of a tokamak,

n_e = 1.0\times10^{19}\ \mathrm{m^{-3}}

and

T_e = 50\ \mathrm{eV}

, and a radial potential

\phi = 300\ \mathrm{V}

develops across a scale length

L = 5.0\ \mathrm{cm}

, with the radial field itself changing by order

\phi/L

across that length. ((a)) Compute the electron Debye length

\lambda_{De}

using

\lambda_{De} = 7.43\times10^{3}\,(T_e[\mathrm{eV}]/n_e[\mathrm{m^{-3}}])^{1/2}\ \mathrm{m}

. ((b)) Estimate the fractional charge imbalance

\delta n/n

that sustains this potential, using

\delta n/n \sim (\lambda_D/L)^2\,(e\phi/T_e)

. ((c)) Treat the thin edge layer as locally planar, ignoring the curvature of the plasma's edge. Suppose instead that the same

300\ \mathrm{V}

fell exactly linearly across the same

5.0\ \mathrm{cm}

. What net charge density would the layer's interior then carry, and where would the charge that supports the field sit?

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