2005 II 6

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In the absence of secondary electron emission, the condition that a probe or other particle collecting surface immersed in a plasma be at the floating potential (i.e. conduct no current to ground) is satisfied when the electron and ion currents are equal, or ji = je:

n_{e} \sqrt{ \frac{ kT_{e} }{ 2\pi m_{e} } } \exp \left( \frac{ -e \left( V_{sp}-V_{f} \right) }{kT_{e}} \right) = 0.6 n_{e} \sqrt{ \frac{kT_{e}}{m_{i}}}

Contents

Part a

What modification to the above relationship is introduced by a nonzero secondary electron emission coefficient?

To add nonzero secondary electron emission coefficient δ:

n_{e} \left( 1- \delta_e \right) \sqrt{ \frac{ kT_{e} }{ 2\pi m_{e} } } \exp \left( \frac{ -e \left( V_{sp}-V_{f} \right) }{kT_{e}} \right) = 0.6 n_{e} \sqrt{ \frac{kT_{e}}{m_{i}}}


Part b

What is the effect (qualitative) of a moderate secondary electron emission coefficient on the floating potential? Consider δe=0.5 as a quantitative example.

Taking the log of both sides:

V_{f}-V_{sp}=\frac{kT_{e}}{e}\log\left[0.6\left(1+\delta_e\right)\sqrt{\frac{2\pi m_{e}}{m_{i}}}\right]


If delta were to increase, the floating potential will increase.


Part c

For what secondary electron emission coefficient would the particle collecting surface (or probe) float at the space potential? If it develops that no material on earth has such a secondary electron emission coefficient, can you think of another approach with would allow a probe of some type to float at the space potential?

For Vf − Vsp = 0:

\left(1-\delta_e\right)=0.6\sqrt{\frac{2\pi m_{e}}{m_{i}}}


So, for hydrogen, δe = 0.96 will cause the probe to float at the space charge potential. If no material has this potential, the probe could be heated, so that it emits electrons on its own. This would add a term to the right of the current balance, increasing the allowed incident electron current.


Part d

If the particle collecting surface were a conducting limiter to which a voltage bias could be applied, what effect would biasing the limiter at the space potential have on the power flow to the limiter?

Biasing the limiter to the space potential would mean increasing the voltage (since it is usually at the floating potential), and so would increase the power flow to the limiter (since the electrons would no longer be repelled).


Part e

If the conducting limiter were replaced with an insulating limiter (obviously not biased in this case), would there be an effect on the power flow to the limiter? Compare to an unbiased limiter, and to the situation in (d) above.

There would be no difference between an insulating limiter and a conducting limiter, since the charge for the limiter comes from the plasma and so does not need to be brought in from ground. This means that there will be less power flow than part d.

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