RE: Gap Question

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

Original poster: "Luke" <Bluu-at-cox-dot-net> 

If the current goes up and the channel widens would that give the
channel less resistance because it now has a larger cross section to
travel through?

Like a piece of 28Awg wire having a higher resistance than a piece of
10Awg wire.  The larger cross sectional area decreases its resistance.

Thanx


Luke Galyan
Bluu-at-cox-dot-net
http://members.cox-dot-net/bluu

-----Original Message-----
From: Tesla list [mailto:tesla-at-pupman-dot-com]
Sent: Monday, February 23, 2004 5:01 PM
To: tesla-at-pupman-dot-com
Subject: RE: Gap Question

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>