Question

A Faraday probe is a planar disk that measure ion current density. It has a collector area of 5 cm2 and the probe surface is biased 25 V below plasma potential (the sheath has a potential drop of 25 V). The plasma has Te = 2 eV. Assume Maxwellian energy distributions and singly charged xenon ions.
a. If the probe collects 2 mA of current from the disk, estimate the plasma number density in the bulk plasma. Assume all electrons are repelled and the 2 mA is purely ion current that enter the sheath and thus is collected by the disk.
b. Now assume not all electrons are repelled. For the 2 eV plasma, how much electron current reaches the collector through the repelling sheath?

Answer 1

As per the given question,

Collector area $(A)=5 cm^2$

Plasma potential = 25V

energy of plasma (Te)=2 eV

We know that Q= ne

b)

Collector current on probe (i)=2mA

So, $i = IAe^{\dfrac{e}{KT}}$

$i=2\times 10^{-3}\times e^{\dfrac{2\times 1.6\times 10^{-19}}{273.15\times 1.372\times 10^{-16}}}$

$i=2\times 10^{-3}\times e^{0.0085\times 10^{-3}}$

$i=2\times 10^{-3}\times e^{8.5\times 10^{-6}}$ A

a)

From the option b, we can conclude that,

$n'=\dfrac{i}{e}=\dfrac{2\times 10^{-3}\times e^{8.5\times 10^{-19}}}{1.6\times 10^{-19}}$

$n'=1.25\times 10^{16}\times e^{8.5\times 10^{-19}}$