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2003 II 1B

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Once one obtains an I-V trace for the probe, one could use the ion saturation current:

I s i = - n e e A p C s e - 1 / 2

The ratio gives:

$\frac{I_{si1}}{I_{si2}}\propto\sqrt{\frac{m_{i2}}{m_{i1}}}$

So whichever has a larger ion saturation current would have a larger mass. Since the box is grounded, $V f = 0$ , then taking $V p$ from heating the probe into strong emission, we can use:

$V_{p}=\frac{T_{e}}{2e}\left[\ln\left(2\pi\frac{m_{i}}{m_{e}}\right)+1\right]$

To find:

$V_{p1}-V_{p2}=\frac{T_{e}}{2e}\ln\left(\frac{m_{i1}}{m_{i2}}\right)$

Thus the box with the highest value of $V p$ will have the larger mass.

It is still possible to use the ion saturation current measurements to determine the mass of the ion, as this does not depend on the electron temperature. If we use the plasma potential, we find:

$\frac{m_{i1}}{m_{i2}}=\exp\left[\frac{2e}{T_{e}}\left(V_{p1}-V_{p2}\right)\right]$

If there is error in $T e$ :

$\frac{m_{i1}}{m_{i2}}=\exp\left[\frac{2e}{T_{e}}\left(V_{p1}-V_{p2}\right)\right]\pm\frac{2e\delta T_{e}}{T_{e}^{2}}\left(V_{p1}-V_{p2}\right)\exp\left[\frac{2e}{T_{e}}\left(V_{p1}-V_{p2}\right)\right]$

So that the error as a fraction of the correct value is:

$\Delta=\frac{2e\delta T_{e}}{T_{e}^{2}}\left(V_{p1}-V_{p2}\right)$

Plugging in for $V p 1 - V p 2$ :

$\Delta=\frac{\delta T_{e}}{T_{e}}\ln\left(\frac{m_{i1}}{m_{i2}}\right)$

In order to tell the difference between two species:

Failed to parse (syntax error): 1>\frac{m_{i1}}{m_{i2}}\left(1-\Delta\right)

So that we can only tell the difference if:

Failed to parse (syntax error): 1<\frac{m_{i2}}{m_{i1}}+\frac{\delta T_{e}}{T_{e}}\ln\left(\frac{m_{i1}}{m_{i2}}\right)=\frac{1}{4}+\frac{1}{2}\ln\left(4\right)

Which is not satisfied. Therefore, we will not be able to determine the difference between Hydrogen and Helium. If we plug in for U-238, though, the condition is satisfied, and so we will be able to identify the ionic species in those boxes.

One way to measure the ion temperature in plasmas is CHERS. This works by charge-exchange between neutral beam atoms and plasma ions. When an electron is traded between the two, it is emitted by the ion at a specific frequency. The doppler broadening of this frequency gives the ion temperature.

The ion temperature can also be measured by fast neutrals. A well-collimated detector outside of the plasma can take neutrals from the plasma. Once the neutral is outside of the magnetic field, it can be ionized and put into a mass/energy analyzer. Some ions in the core will spontaneously combine with an electron and become neutral. It is then not confined, so can move outside.

A last measurement method is by X-ray measurement. High-Z ions in the core may still keep helium-like electron configurations. These then emit by bound-bound transition, and the doppler broadening can be measured. The required resolution, though, is very high, and the impurity temperature may not be the same as the ion temperature.

This page was recovered in October 2009 from the Plasmagicians page on Generals_2003_II_1B dated 01:09, 7 May 2007.

Retrieved from "https://qed.princeton.edu/main/PlasmaWiki/Generals/2003_II_1B"

Category: Plasma Physics Generals