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Typical Langmuir probe I-V characteristics.

Evaluation of the I-V trace obtained with a Langmuir probe can be performed using the following recipe:

1. Make a straight-line fit to the ion saturation current and subtract the ion current from the total current toobtain just the electron current.
   
   
2. Plot the natural logarithm of the electron current vs voltage.
   
   
3. Make a straight-line fit to the electron retardation and saturation currents. Note that in a discharge plasma there is a hotter "tail" population of discharge electrons.
   
   
4. Determine the plasma potential and electron saturation current from the intersection of the two straight-line fits.
   
   
5. Evaluate the electron temperature of the colder secondary electrons. Note that a change of one in lnI corresponds to a voltage change of kT_e.
   
   
6. From the electron saturation current and electron temperature calculate the electron density, given by n_e = I_e,sat / [A_probee {kT_e/2(pi)m_e}^1/2].

Evaluation of I-V Characteristic via method outlined in text.

The sample trace is replotted by taking the natural logarithm of the current in arbitrary units (100 mm = 4 mA, ln(100) = 4.605).

The straight-line fits yield an intersection at V_plasma = 2.82 V and ln(I_e,sat) ~ 4.36, i.e.,

The electron temperature is the voltage difference for a change in ln(I) of one, i.e., kT_e~ 1.47 eV.

The probe is a disk of 1/4" diameter. It's area is

Note that the tail electron population has been ignored in this analysis. How does this affect the result? The tail temperature is about 2.5 eV. This is what a double probe would yield.

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