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Back to Transport: Diffusion with Charge
We find that the diffusion coefficient is essentially that of the ions multiplied by the ratio of electron and ion temperatures. The diffusivity of the ions will be of similar magnitude to that of neutral molecules. Recall that at atmospheric pressure these values were typically around 0.1 cm2/sec, so at e.g. pressures of 1 Torr, diffusivity values of 75 cm2/sec are reasonable. For typical plasmas the electron temperature is around 35 eV and the ion temperature perhaps 0.050.1 eV, so the multiplier Te/Ti is about 50100. Thus reasonable values of ambipolar diffusivity are 3500 to 7500 cm2/sec at 1 Torr. Let's look at what this implies for the transport of electrons and ions in a fairly typical sort of plasma chamber: a cylinder 50 cm in diameter and 5 cm high, operating at 1 Torr, with a typical Da = 5000 cm2/sec. [As usual, we use the ideal gas law, and make the simplifying assumption that the gases are near enough to room temperature that we can ignore thermal expansion. If you're puzzled by the table, see the Introduction and the discussion of diffusion length in Transport. ] 
diffusivity 
5000 
cm2/sec 
diameter 
50 
cm 
radius 
25 
cm 
area 
1960 
cm 
height 
5 
cm 
volume 
9.8 
liters 
flow in 
1 
slpm 
volume in 
760 
liters/minute 

12.7 
liters/second 
residence time 
0.77 
seconds 
diffusion length 
124 
cm 
Peclet # (radius) 
0.04 

We see that the ambipolar diffusion length greatly exceeds the chamber size. Electrons and ions diffuse very rapidly, and at typical values of gas flow velocity convection is not important in determining where the charged species go. This is very convenient for analyzing what's going on in the reactor: we can treat the plasma behavior while ignoring any flow velocity of the gas, and then treat the transport of species with the plasma providing a mechanism for generating stuff in the gas phase, without trying to intimately couple them together. 
