Generals 2002 II 2A

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[edit] Part a

The ion saturation current is at about -1.3 mA. The electron saturation current is about 12 mA.

[edit] Part b

The floating potential is at about 2 V. The space potential is at about 40 V.

[edit] Part c

We know:

V_{sp}-V_{f}=\left(3.3+\ln\mu\right)T


So, for hydrogen μ = 1, and so T\approx40/3.3\approx12\,\mathrm{eV}.

[edit] Part d

We use the ion saturation current:

Isi = − 0.6neCsA


The sound speed is:

C_{s}=9.79\times10^{5}\mu^{-1/2}T_{i}^{1/2}\mathrm{cm/s}\approx3\times10^{6}\mathrm{cm/s}


The area is:

A=\pi\left(.1\,\mathrm{cm}\right)\left(.5\,\mathrm{mm}\right)=.15\,\mathrm{cm}^{2}


So:

n_{e}\approx\frac{.0013\mathrm{A}}{0.6\cdot\left(.15\,\mathrm{cm}^{2}\right)\left(3\times10^{6}\mathrm{cm/s}\right)e}\approx3\times10^{10}\mathrm{cm}^{-3}


Sheath expansion effects could affect the accuracy of the density estimate, since it varies like the inverse of the sheath area.

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