RE: Gap Question

["Tesla list" <tesla-at-pupman-dot-com>]

Original poster: "Malcolm Watts" <m.j.watts-at-massey.ac.nz> 

Hi Luke,
         Nice try:

On 23 Feb 2004, at 7:28, Tesla list wrote:

 > Original poster: "Luke" <Bluu-at-cox-dot-net>
 >
 > Bart:
 > I thought about what you said with the negative resistance thing. May
 > I lay something out that does not use real values but values
 > arbitrarily picked out to make the example simple.  I may be way off
 > base but would like some in put.  I think the idea has merit.
 >
 > I was thinking it may appear to be negative resistance but may not
 > really be.  Maybe it is like having a gap that has different
 > dimensions when it heats up.
 >
 > Let me try to explain.  And before anyone starts quoting some actual
 > values try to look past that for about 30 seconds just to get the idea
 > I am getting at.  Then fire away with all the real value stuff.
 >
 > Let's pretend for the example that:
 > 1:	The breakdown voltage of air is 100 volts per inch. And
 > 2:	That an arc has a certain amount of resistance per length.
 >  But that resistance follows a logarithmic curve or spiral.
 >  What I mean by this is like that of a logarithmic spiral.
 >  Where the curvature gets tighter and tighter as the spiral
 >  Curves inward.
 >  Now draw a line from the center outward.  Measure the distance
 >  from center to where the line intersects each turn of the
 > spiral.
 >  So say 0.5=3, 1=6, 1.5=12, 2=24, 2.5=48, 3=96, 3.5=192 etc.
 >
 >
 > Imagine only the spark gap the primary coil and the capacitor.
 > And all this is at the time of break down for the gap.
 >
 > Ok say we have a gap of 3" that would give 300 volts for break down
 > and
 >  >From the curve above the resistance of that arc would be 96 ohms.
 > Using plain old ohms law you would get a current of 3.125 amps.
 >
 > Now let's say the electrodes get hot.  Instead of just looking at it
 > like The voltage breakdown got lower, lets assume it acted as though
 > it made the distance between the electrodes closer, which would have a
 > lower breakdown voltage.  I think of it like the hot air/ions whatever
 > might act as an extension of the electrodes making them have a larger
 > diameter and therefore be closer together.
 >
 > So lets say that the heat involved made the gap ACT as though the
 > distance was 2.5" even though the measured distance might actually be
 > 3".
 >
 > This would give a break down voltage of 250 volts and a resistance of
 > 48 ohms.  So the current would be 5.2 amps.  So the voltage the cap
 > charged to was 50 volts lower but the current went up.  Not because of
 > negative res. but because the electrodes in a way are now closer.
 >
 > So is it that the gap has a negative resistance?
 > Or is it that the heat makes the gap act as though it has,
 > different dimensions (a closer spacing)?
 > so the gap acts different?
 >
 > I know this might be reaching a little but I think there is some logic
 > in it I would like some opinions on.
 >
 > If what I am saying had some truth to it then if one did not take into
 > account the gap acted as if the distance were closer it would seem
 > that there was indeed negative resistance.
 >
 > Any thoughts?  And keep in mind I am no math whiz.  Just laying out a
 > concept and hoping to get some qualified people thinking / talking so
 > I can hear bout it.

What really happens is that as gap current goes up, the width of the
arc increases. A spark tries to keep to as narrow a channel as
possible at "normal" atmospheric pressure. The width of the channel
at a particular current is defined by the number of ions (current
carriers) that can be formed in the channel cross-sectional area, the
molecular density of air being the arbiter. In effect, the arc
behaves in a saturable manner, extending no wider than it has to. If
the available current goes up, the channel widens to boost the cross-
sectional area. So it is the fact that the channel is able to widen
without limit that gives an arc the negative-resistance
characteristic. In an inductor analogy, it is as though the inductor
core increased in cross-sectional area as the applied magnetizing
force tried to take it beyond saturation. In a camera flashtube
however, the ability of the arc to widen is restricted by the
diameter of the flashtube (ions that can be formed per unit area) so
after initially exhibiting a negative resistance, the tube truly
saturates and stays there meaning that beyond a certain current, the
arc reverts to a positive or normal characteristic, highly desirable
since you don't want the storage capacitor seeing voltage reversals.

      The short distances involved in Tesla spark gaps don't have a
huge influence on the gap dissipation.

Malcolm
<snip>