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https://en.wikipedia.org/wiki/Townsend_discharge

Townsend discharge only occurs when an initial ionization event (e.g. from a cosmic ray) creates a single free electron which causes an 'avalanche' of further ionization events.

I'm a bit suprised that there's effectively zero chance of a single free electron existing in the gas without the cosmic ray. Aren't there roughly about 10^20 atoms in a small tube of low-pressure gas? Surely there is one free electron somewhere. The wikipedia article for glow discharge states that there are free electrons from cosmic rays AND thermal collisons! So I don't know what's going on here.

I'm wondering if there is a way to see intuitively that there cannot be a free electron any other way than an ionization event.

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  • $\begingroup$ Is it just a M-B distribution calculation for particles with energy more than the ionization energy? (something like 13eV)? $\endgroup$
    – Matt
    Aug 17, 2021 at 21:08
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    $\begingroup$ Yes :) using a typical temperature of 300 K. The other factor is that free electrons don't cascade and cause discharge unless they have enough energy. Otherwise they will just recombine. $\endgroup$
    – Alwin
    Aug 17, 2021 at 21:16
  • $\begingroup$ @Alwin appreciate it. And I guess cosmic ray energy is just so far off the charts that you're never gonna see something like it in a tube of thermal gas, it'd cascade ionize thousands or millions of gas particles just from the single ray, even ignoring an external field. $\endgroup$
    – Matt
    Aug 17, 2021 at 21:24
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    $\begingroup$ Yes! Speed of a typical particle in air, 300 m/s. Speed of a cosmic ray, 300,000,000 m/s. $\endgroup$
    – Alwin
    Aug 17, 2021 at 21:27
  • $\begingroup$ Just writing this again since I understood and then forgot: SOME particles MIGHT be ionized thermally (do the calculation), but we define Townsend discharge to be the discharge that happens BEFORE you can expect thermal electrons to avalanche. -- and there's a population of energetic particles just as background which end up producing millions of free electrons from a single event, so it turns out these produce the activity. When thermal electrons avalanche, that's defined as glow discharge. $\endgroup$
    – Matt
    Aug 18, 2021 at 22:19

1 Answer 1

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The problem isn't the lack of free electrons, the problem is how quickly a free electron loses energy in air.

For Townsend discharge, there needs to be an electric field strong enough for each new free electron to have enough energy to knock at least >1 new electron free on average.

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