In the edge of a fusion device the electrons and ions of a hydrogen plasma are not in…

PHYSICS · Multi-part · Fermi University Physics · Plasma Physics · The plasma state and single-particle motion · 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

In the edge of a fusion device the electrons and ions of a hydrogen plasma are not in thermal equilibrium with each other:

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

T_e = 20\,\mathrm{eV}

and

T_i = 100\,\mathrm{eV}

, with the ions singly charged (

Z=1

). Assume the shielding cloud is quasistatic: each species has had time to settle into a Boltzmann density at its own stated temperature around the test charge, while collisions between the species have not yet brought the two temperatures together. Assume also that

e\phi \ll T_e, T_i

everywhere the linearisation is used. ((a)) Starting from Poisson's equation for a test charge with a linearised Boltzmann density for each species, electrons responding through

\exp(e\phi/T_e)

and ions through

\exp(-e\phi/T_i)

, show that the combined shielding length obeys

\frac{1}{\lambda_D^2} = \frac{1}{\lambda_{De}^2} + \frac{1}{\lambda_{Di}^2}, \qquad \lambda_{Ds} = \left(\frac{\epsilon_0T_s}{n_se^2}\right)^{1/2},

where

\lambda_{Ds}

is the Debye length that species

s

alone would give. ((b)) Evaluate

\lambda_{De}

\lambda_{Di}

and the combined

\lambda_D

for the stated plasma, and say which species dominates the shielding.

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