Re: Impedance of Corona or Arcs vs Voltage (fwd)

---------- Forwarded message ----------
Date: Mon, 13 Jul 1998 14:56:58 -0700
From: Jim Lux <James.P.Lux-at-jpl.nasa.gov>
To: Tesla List <tesla-at-pupman-dot-com>
Subject: Re: Impedance of Corona or Arcs vs Voltage (fwd)

The impedance of a "free burning" arc is fairly well known and measured,
but may not be applicable to output from a tesla coil, which is more of
a "spark" phenomenon (i.e. the TC is a transient, the FB arc is steady
state).  That said, here is some data I have summarized from Bazelyan
and Raizer, "Spark Discharge", as well as from Uman, "Lightning".

Consider the arc as a conductive column. For a current of 10 kA, the
voltage drop along the column is roughly 1 kV/meter (this is lightning). 
The conductivity of plasma is quite low until it gets above about 5000K,
and then it rises sharply. So, most people model the temperature profile
(and hence the conductivity) across the arc channel as a rectangular
step. You can then do a heat balance comparing the amount of power
dissipated in the arc and calculate how big a column of air can be kept
hot enough to conduct. As the current goes up, the column gets bigger,
with the surface area through which the heat is lost going up linearly
with radius, but the area carrying the current going up as the square.

The volume resistivity is roughly constant, once you are hot enough to
get everything ionized (i.e. around 6000 K). The resistance along the
length is then inversely proportional to the square of the radius. 

The power required to keep the arc burning goes as the surface area,
which goes linearly as the radius.

So, as a rough order of magnitude, the radius goes as the 2/3 power of
the current.  Continuing in this vein, the voltage (per unit length)
then goes as the inverse of the current squared..