DC glow discharge is hard to ignite in very low pressure of 0.001 mabar. For small systems (30 cm dia) the electron ionization mean free path routinely exceeds the system dimension for such a low pressure.
However for discharge ignited (breakdown) at higher pressure may be sustained in very low pressure in certain cases. Can any one suggest some reference papers or any other material which describes the DC glow discharge in very low pressure.
One example is DC Magnetron Sputtering discharge, but this uses special arrangement of magnets and confines plasma mainly near the cathode.
Igniting a real glow discharge, just consisting of an cathode, an anode and a low pressure gas in between at a pressure of 0.001 mbar is very hard to achieve, except you have a really large vacuum vessel as the ionisation mean free path is very long (as you stated correctly).
However, if you manage to create free electrons by some means (for example a hot filament, etc...) you can get a DC plasma at lower pressures as the mean free path is inversely proportional to the electron impact ionisation cross section and this goes up for very fast electrons (i.e. high voltages on your electrodes). This again makes the ionisation mean free path smaller and you have a kind of work around.
This is also the reason why you can sustain a burning glow discharge (which you ignite at higher pressure), when the pressure drops --> there are still free electrons around.
If you have no free electrons in the first place you will have a hard time because in such a case you can only rely on field ionisation and this is a very inefficient ionisation process, so you need very large fields.
That's why I guess there won't be many papers for glow discharges in such low pressure range (I did a quick google check, but I didn't find anything usefull on the first glance).
I hope that helps a little bit, anyway.
You have to think of discharge mechanism more using the breakdown voltage (Vb):
Let lm be the mean free path for collisions, i.e. the distance traversed by an electron between
two collisions. Then find the probability P, that a collision will lead to ionization. P can be expressed as exp[– II/Wc], where II is the ionization energy of the gas and Wc is the energy gained by the electron between two collisions. If EB is the electric field acting on the electrons due to the applied dc voltage, then one has Wc = e lm EB, where e is the electron charge. Cab deduce the relation in a more conventional form as
vb= Apd/(ln(pd) + const)
Here vb= EB.d
Again, as you know the mean free path lm to be inversely proportional to the gas pressure p.
Depending on your pd product you can generate a Paschen curve.
Consider Ar plasma, as your p is very small, now find d from pd ~ 1 (torr.cm) (near Paschen minimum) and operate near about that voltage to get a discharge. Initially, you have to apply high voltage and after ignition of plasma you can reduce the voltage.
You may consider/refer Paschen curve for this. (Typical magnetron plasma is about 2-3 mTorr).
Best wishes.
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