Re: What it takes to get big sparks?

At 12:20 PM 12/31/98 -0800, you wrote:
>I have been contemplating the whole issue of what factors most influence
>the length and size of the sparks from a tesla coil and have some ideas
>which I'm going to throw out for discussion.
>Starting with some assumptions:
>1) The actual spark develops very quickly if there is a suitable low
>impedance source. The leader moves very very fast, essentially running its
>entire length in a microsecond or thereabouts.

My last paper shows that the spark starts as soon as the voltage of the
terminal gets high enough to breakout.  Usually, within 10-20 uS (for the
voltage to develop).  Once the arc is started, current is being supplied to
the arc for about 100 more uS without interruption until the secondary
voltage drops way down.

>2) The charge for the spark comes almost exclusively from the top load. The
>inductive impedance of the secondary coil is so high (when considered in a
>time frame of a microsecond) that any sort of stored energy in the coil
>isn't going to get there in time (except of course, for the current already
>flowing from the inductor into the capacitor as the top load voltage is

I think the top terminal is able to supply the capacitive energy stored in
the space around the top of the coil and under the toroid.  As the toroid
size increases it is effectively using more of the space around the coil to
store energy.  This energy can be supplied to and arc very quickly.  I also
have found that the coil is oscillating during the arc and the streamer is
a source of loss to the system (but not a giant loss really).  See my
latest paper...

>3) As the spark develops, it is essentially a capacitor that has increasing
>capacitance (because it is getting bigger) and is charging at the same
>time, as well as heating the air up.  This means that current is flowing
>through this "spark capacitor".

The capacitance is around 1 or 2 pF per foot of spark.  There also seems to
be about 220K of resistance in the path that is fairly constant.  The loss
in this resistance is probably why the arc is really hot and dissipating
heat energy.

>I asked myself, where is the other connection of this capacitor?

A charged body in free space doesn't really need a ground to store a
capacitive charge.  However, in our case, the surrounding objects do
provide a ground path and tend to increase the secondary capacitance.

>I think it is the ground (and the surroundings, etc.).
>And, because we are talking fast time scales here (microseconds, again),
>the inductance of any sort of wire connection from the bottom of the coil
>to the "ground" means that the coil can't really supply any appreciable
>current while the spark is forming.

My paper shows that the arc is being supplied with about 1 amp of current.
The paper doesn't show it but there is about 3 amps entering the terminal
from the secondary during this time.  So the arc is eating about 30% of the
current entering the terminal.  The rest is returned to the coil as the
oscillation continues.

>So then, what we have is an inductor (the secondary) which charges a
>capacitor (the top load working against the ground). That capacitor then
>breaks down (i.e. a leader forms) and discharges into the spark. The actual
>spark formation is almost independent of the secondary inductor because the
>current required to develop the spark is much higher than that coming from
>the inductor to the capacitor.

The current from the inductor seems to be supplying the arc once it gets
started.  The initial current seems to be a spike but then the current goes
way down to a rather low level for the rest on the 100uS time it is

>This is why big top loads help make big sparks. And it is also why good
>grounds make big sparks.  Interestingly, though, the nature of the ground
>is important. Of course, it has to be low impedance at the coil's basic
>operating frequency (otherwise, the secondary can't charge the top
>load/ground capacitor fast enough). Given the high inductance of most
>secondaries (milliHenries) compared to the inductance of even thin wires
>that are several feet long (microhenries), from this standpoint, it doesn't
>matter how you connect the base of the coil to the "ground".

I think if the ground had a poor RF connection performance would suffer
because there would be more resistance and loss.  Of course, the high
voltage could probably arc through any poor connections and such.

>However, once that "capacitor" is charged, and it starts to discharge (into
>the spark), you want the capacitor to be low inductance. The top load is
>pretty low inductance (it is physically small) and resistance (it is
>metal), but what about that ground? How low impedance is that ground?
>Remember, at this time, what we are really looking at is one capacitor
>charging another through a resistance and inductance.

Good question!  It would be interesting to plot the impedance of the ground
connection over the range of 10kHz to 1MHz.  A good DC ground may fall far
short at RF frequencies.  An experiment to be preformed...

>  So, I think what you want is a suitably conductive sheet to operate your
>coil on top of. It doesn't have to be solid, but it does have to have low
>resistance per square, and, also important, low inductance per square (i.e.
>I don't think one long wire running around would really do it). It can be
>insulated because it is part of a capacitor with mostly air dielectric, and
>adding a thin layer of anything won't make any difference. It should be big
>enough that it can supply enough charge to keep the spark going... I would
>suggest that it should be big enough so that increasing its size by some
>increment doesn't increase the capacitance to the top load by more than
>5-10%. This probably isn't all that big.  For a big sheet which has low
>inductance, the propagation velocity of the charge is going to be a
>significant fraction of c (1 ft/nSec), and assuming you want your capacitor
>to be able to discharge in something on the order of 10-100 nSec, making it
>bigger than 20-30 ft isn't going to buy you much.

Greg Leyh's Electrum's arc discharge lasts over a period of about 150uS!
That's 1000 times longer than you suggest.  His scope photos show this.  My
coil discharges in around 100us as my last paper shows.  So Greg and I
perhaps could use a terminal in the 100000 foot range! :-))  In the very
first stage of the arc, the fast response of the terminal capacitance
probably helps things get going.

>Thinking about how the field from the top load is distributed, in fact, I'd
>hazard a guess that you should work against a disk of radius equal to the
>height of the top load above the disk, or maybe, twice that.

I am trying to develope a program that shows such things...

>Comments, thoughts, etc.....

An interesting subject.  The paper I referred to is at:


It shows all the voltages and currents in my coil.  (except the coil to
terminal current that I forgot...).