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Re: theory(?) for long sparks
From: Bert Hickman[SMTP:bert.hickman-at-aquila-dot-com]
Reply To: bert.hickman-at-aquila-dot-com
Sent: Friday, November 28, 1997 1:13 PM
To: Tesla List
Subject: Re: theory(?) for long sparks
Tesla List wrote:
>
> From: Benson_Barry%PAX5-at-mr.nawcad.navy.mil[SMTP:Benson_Barry%PAX5-at-mr.nawcad.navy.mil]
> Sent: Wednesday, November 26, 1997 4:02 PM
> To: tesla-at-pupman-dot-com
> Subject: RE: theory(?) for long sparks
>
> Hi Jim, All,
> When I finished designing and building the 2 Megavolt Marx generator at
> the Lightning Laboratory I did some voltage and current comparison
> measurements. The voltage rose, leveled off like a square wave, and then
> collapsed at which time the current started to rise. This took only about 2
> microseconds for a 10 foot point plane arc (2.2 MV) with a current peak of
> about 14 kiloAmperes. The erected Marx capacitance was around 3 nanoFarads.
> The terminal capacitance of a Tesla coil is several orders of magnitude
> less than this. Is it possible that the source charge feeding the streamer
> effects the propagation velocity?
>
> Barry
>
> ----------
> From: "tesla"-at-pupman-dot-com-at-PMDF-at-PAXMB1
> To: Benson Barry; "tesla"-at-poodle.pupman-dot-com-at-PMDF-at-PAXMB1
> Subject: theory(?) for long sparks
> Date: Tuesday, November 25, 1997 11:49PM
>
> <<File Attachment: 00000000.TXT>>
>
> From: Jim Lux[SMTP:jimlux-at-earthlink-dot-net]
> Sent: Tuesday, November 25, 1997 8:27 AM
> To: Tesla List
> Subject: theory(?) for long sparks
>
> I have just gotten my copy of "spark discharge" by Bazelyan and Raizer (CRC
> press). I have been inspired by the picture of the 100 meter+ spark
> produced by only 5 MV, and have given some thought to what it takes to make
> long sparks.
>
> It appears that a spark propagates at around 2-3 cm per microsecond. If the
> voltage pulse producing the spark only lasts 10 microseconds, the maximum
> spark length that can be developed will be in the area of 20-30 cm.
>
> What is necessary for the spark to start is that the field at the starting
> point be greater than the breakdown for air (i.e. around 30 kV/cm). Then,
> for the spark to propagate, the voltage has to increase enough to cover the
> drop along the spark, and, the source has to supply sufficent current to
> "fill" the spark channel with charge. (I am doing horrible injustice to the
> pretty complex physics here, sorry).
>
> So, then, if you want to produce a 100 meter spark, (i.e. 1E4 cm), the
> voltage has to be there for at least 5000 microseconds, and probably
> longer. Further, the voltage has to be high enough to overcome the drop in
> a 100 meter long spark channel, i.e. several MV.
>
> A tesla coil running at 100 kHz (for example), has a half period of only 5
> microseconds, well short of the desirable 5 milliseconds. It is possible
> that the fine structure (i.e. the 100 kHz carrier) isn't the significant
> thing, but rather the overall envelope (i.e. the time til the first
> "notch"), which would be more consistent with the observed 1-3 meter length
> sparks from a medium sized tesla coil.
>
> Ideas anyone?
>
> ¿
Barry, Jim and all,
Geeze Barry, some guys get to have all the fun, and get paid for it to
boot! :^)
Very interesting discussion! Jim is right - the physics is quite complex
and certainly not fully understood, but his high-level explanation
sounded pretty close to the mark for streamer growth. Unfortunately long
RF sparks is an area where little hard experimental work appears to have
been done by the scientific community.
Most available long-spark research has been done using rod-plane gaps,
triggered by (usually unipolar) impulse generators. This research, and
similar work done with lightning, shows that long sparks tend to
propagate in a series of "jumps", similar to stepped leaders in
lightning.
The length of each jump, and the time between jumps, is a function of
the "stiffness" of the external voltage supply - the degree to which it
can deliver slugs of charge (current) to a propagating streamer without
collapsing the supply voltage.
Long-spark research also appears to support Barry's supposition that the
average propagation velocity IS, indeed, proportional to leader
current. The lower the external driving source impedance, the greater
its capability to deliver relatively large spikes of current. These
current peaks are typically in the 0.1 - 10 ampere range. The greater
the available surge current, the longer each "jump" can be. If the
voltage comes from from a relatively high impedance source, the source
voltage will collapse, terminating further streamer growth until the
supply voltage can recover (if it can..). A voltage source having a low
enough impedance may bridge the gap in a single, high velocity, jump.
Even though the initial E-field necessary to start the corona/streamer
process is of the order of 26 - 30 kV/cm, once breakdown has been
initiated, the voltage breakdown voltage for a long spark gap declines
significantly, particulrly for non-uniform E-field gaps. Barry's Marx
generator, for example, breaks down 10 feet of air with 2.2 MV, or about
7.2 kV/cm (average). However, generating a 100 meter spark with only a 5
MV source would imply an average of about 500 Volts/cm (ave.) which
sounds much too low(!).
Long-spark RF appears to be a little different story! For example, the
maximum voltage a given Tesla coil can produce can be fairly easily
estimated once a few of it's parameters are known (Vgap, Cp, Cself,
Ctoroid). Using these parameters from my coil, I estimate the peak
output voltage to be of the order of 400 kV or less. Under "single shot"
firing conditions, maximum spark length is more like 20" (7.2 kV/cm).
However, when running at 360-420 Breaks/Second, the measured maximum
point-point discharge length is 63", implying an "average" breakdown
voltage of only 2.5 kV/cm.
The difference between 20" and 63" discharges for the same peak voltage
is due to the relatively short time between successive bangs (about 2.5
milliseconds), which permits a streamer from the present "bang" to build
upon the thermal and ionic remnants of the spark channel blasted by its
predecessors. This growth can be clearly seen in successive video-tape
frames of streamers. Large top C and lower Zo for larger coils appears
to also improve spark length and "heat", probably because of the greater
current delivery capability during streamer propagation and the fact
that thermally-generated ions remain longer in hotter channels during
the time between breaks.
Hopefully, we'll know a bit more about streamer propagation and the
associated current structures when Greg Leyh takes some actual
measurements of streamer currents coming off his 130 KVA monster coil...
from _inside_ his toroid! :^)
BTW, Greg, how's your big coil coming along?
Safe sparkin' to you!
-- Bert --