Re: sparks

["John S. Denker" <jsd@MONMOUTH.COM>]

At 02:23 AM 2/18/01 -0800, Bernard G. Cleyet was skeptical of my guestimate
of the breakdown field:
> > It's about 3 megavolts per meter.  You can guestimate this answer based on
> > the previously-described model:  an ion needs to pick up enough energy
> > between collisions to have a fair chance of ionizing whatever it
> > hits.  That requires a field strength on the order of a fraction of a volt
> > per mean-free-path.

This guestimate is derived using one piece of physics that I should have
mentioned:

The mean free path is only a _mean_, namely an expectation
value.  Sometimes the path is longer, sometimes shorter.  There is one
chance in e^12 that the particle will miss 12 consecutive "expected"
collisions and pick up 12 times more energy than a simple "field * MFP"
calculation would suggest.

Meanwhile, the mean free time is quite short, so we are expecting millions
of collisions per millisecond.  Even the rare event of a 12x-too-long path
will happen dozens of times per millisecond per ion.  And if each of these
events creates a new ion pair, and each member of the pair has children in
an exponentiating family tree, then you very quickly wind up with _plenty_
of ions.

BTW: Another factor is that we get to subtract the electron affinity from
the ionization energy (although the e.a. is small enough that this is only
a minor correction).

============

Even taking these factors into account is not enough to derive an exact
value of the breakdown voltage from first principles.  The argument was
only offered as a ballpark guestimate.

Quite a lot is known about this general area;  a fellow named Geiger had
something to say about it.