RE: Gap Question

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

Original poster: Jim Lux <jimlux-at-earthlink-dot-net> 

At 07:28 AM 2/23/2004 -0700, you 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.


Hot gaps are different than cold gaps, but, any spark has a negative 
resistance characteristic, regardless of gap, electrode, material in the 
gap, etc.  All negative resistance means is that the voltage drop decreases 
as the current increases. (it has some incidental effects too.. like you 
can make oscillators and memory from negative resistance devices)



>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.


Actually, a better model is that the voltage drop falls as the square root 
of current. It doesn't really spiral.

And, the gap resistance (calculated as V/I) doesn't actually go negative in 
an absolute sense, it's just that the slope of the V/I curve is negative.

Set up a little spreadsheet. There are two parameters:
Cathode Drop (put this in, e.g. $C$4)
Proportionality constat (put this in, e.g. $C$5)

Set them both to 100.

Then make a table of currents from 1 to 20, and calculate the voltage as 
follows:
V = $C$4 + $C$5/sqrt(I)

For example, if the currents are in A9 through A28, cells B9 through B28 
would be filled with:
A9:  1  B9: =$C$4+ $C$5/sqrt(A9)
A10: 2 B10: =$C$4+ $C$5/sqrt(A10)
A11: 3 B11: =$C$4+ $C$5/sqrt(A11)

Now start plotting Voltage vs Current.






>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".

The "breakdown" behavior and the "during arc" behavior are separate and 
distinct, and can't really be connected.

Hot electrodes have lower breakdown voltages for a variety of reasons.

The V/I characteristic of the arc once struck is a combination of three things:
a) A fixed voltage drop (cathode drop) mostly determined by the materials 
of the electrodes (and some other things)
b) The resistance of the arc channel, which in turn is determined by:
         The current through the arc (which determines how many "volts per 
cm") the arc channel will have (in accordance with the general 1/sqrt(I) rule)
         The length of the channel.





>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... a shorter arc will always have lower voltage drop than a longer one, 
and, once you've taken out the fixed cathode drop, it's pretty linear.

This is why multiple gaps are higher loss than a single gap (but might have 
other advantages). The total arc length will be about the same, the 
current's the same, but the multi-gap has multiple cathode drops.






>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?

Heat makes the gap breakdown at a lower voltage, which changes the voltage 
available to support the arc (since you're breaking down from energy stored 
in a capacitor)






The entire thing is actually quite complex, but a bit of fiddling with some 
spreadsheets where you can play with voltages and currents will help.