Re: spark gap/arc resistance (fwd)

---------- Forwarded message ----------
Date: Mon, 20 Jul 1998 12:33:49 -0700
From: Jim Lux <James.P.Lux-at-jpl.nasa.gov>
To: Tesla List <tesla-at-pupman-dot-com>
Subject: Re: spark gap/arc resistance  (fwd)

Tesla List wrote:
> ---------- Forwarded message ----------
> Date: Sun, 19 Jul 1998 21:36:49 -0600 (MDT)
> From: Chip Atkinson <chip-at-pupman-dot-com>
> To: tesla-at-pupman-dot-com
> Subject: spark gap/arc resistance
> Greetings,
> Is there a rule of thumb type calculation for the resistance of a spark
> gap (that's firing :-)) such as 1 ohm /inch for example?  I checked my web
> site and list archives and didn't find anything such as this and don't
> remember any actual values, despite the fact that the topic is often
> discussed.
Check the EG&G web site for discharge characteristics of high pressure
xenon arcs.

Otherwise, for air at 10 kA, 1kV/meter. or 0.1 ohm/meter.
for 200 A, 2.5V/cm (250 V/m, 1.25 Ohm/meter )
for 10A, 20V/cm (2kV/m, 200 Ohm/meter)

Here are some summarized equations from Bazelyan and Raizer (p38-42)
where they make an analysis of an equilibrium arc.
(-> means are approximately equal)

Tm -> const/ (const - ln(i/R)		max Temp of arc
sigma max -> i/R*(const-ln(i/R))/const)		max conductivity
Power/length -> const/(const-ln(i/R))^2	
voltage = 8 *pi*k* Tm^2/ (I * i) -> same form as power/length
r0  = R *sqrt(sigma max/b) 	channel radius

R is the tube radius
i is the current
I is the ionization voltage

channel radius is roughly proportional to sqrt(current)
current density is rougly proportional to temperature which is roughly
proportional to current/(channelradius^2)

 It varies a lot, but a voltage drop goes as sqrt of current, so, for a
current of 100 A, 1 ohm/meter, etc.