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Re: [TCML] spark models

On 5/30/11 6:23 AM, Bert Hickman wrote:

Hi Steve,

Doesn't look like Jim responded as yet. I'm also interested in his
thoughts.


been busy, but I'll respond later today..



Steve Ward wrote:

Jim,

I have great interest in this topic, but so far all I've managed to do is
come up with more questions. Some current questions are:

1) What impact does resonant frequency play?I think this must relate to
some basic principles about spark growth and basically the resonant
frequency plays a role in how often the leader gets a new "kick" which i
would suspect plays a big role (well, because my testing says so). Id
guess
that there's probably an issue with displacement current through the
streamer's capacitance, my guess would be that higher frequency could be
more beneficial in that it would keep more current circulating through
the
spark channel and keep it hot. I'd be curious to hear your thoughts.


The resonant frequency only plays an indirect role by helping to
maintain an already existing channel's conductance via displacement
current _at the fundamental frequency_ and reducing voltage ring-up time
for a given coupling coefficient. However, actual spark growth occurs
when the terminal voltage reaches a higher peak voltage than previous
peaks, so spark growth is more a function of the RF envelope. Sparks
grow only during a rising envelope. And, as Jim mentioned, growth occurs
in a series of quick jumps, each of the order of nanoseconds or tens of
nanoseconds. The detailed mechanism is significantly different depending
on the polarity of the terminal voltage.
I'd jump out on a limb here and postulate that the spark only advances on one polarity of RF halfcycle, and during the other one, the charge flows back into the top load, incidentally keeping the channel hot.
So what we'd have is a sort of burst of short jumps (nanosecond scale), with a pause, then another set of short jumps when the polarity is correct again, then a pause. 

Superimposed on that will be the longer scale "break rate" growth.








2) What is the difference between spark growth behavior on a "transient"
coil vs something like my quasi-CW system (which in my opinion is much
easier to do studies on)? Pics can be found at:
http://www.flickr.com/photos/kickermagnet/


You are directly controlling the key parameter - the shape of the RF
envelope. And, tighter coupling causes the secondary's output to more
closely track the primary drive waveform, unlike a classical coil where
you're sloshing a decreasing amount of energy between P and S.



It seems that any good streamer model would also factor in things that
effect the conductivity of the air, that is, how long ago was it recently
ionized or heated up, and how long does it take for the ions to
recombine or
for the temperature to come down.


Good ionic and thermodynamic models do exist, but they are quite
complex.
Now there is an understatement.. But I think we can use a fairly simple model that simplifies a lot of stuff. On the microsecond time scale (RF cycles) the heat loss by conduction is going to be "small", but the heat loss by radiation is going to be "high" (that T^4 term from 7000K). 


A leader is an arc, and like any free arc in air, it decays

with a time constant measured in hundreds of milliseconds. An RF arc has
a virtually constant dynamic resistance (which, in turn, is an inverse
function of peak channel current),
I agree that on the RF time scale, the channel is fairly stable in properties (although extending... sort of like a collapsible whip antenna)
Goncz says V = k*sqrt(I), as I recall. Something along the lines of the spark channel tends to have constant temperature/resistivity and grows in diameter to keep the current density such that it's right on the "fully conductive plasma" edge. The current flow tends to push to the outside (skin effect) but that's less conductive being cooler, so it has higher IR drop which gets it hotter, etc. 



 even though the channel is

continually being reignited after each zero current crossing. The
thermal lag of the arc channel is comparatively long, and the higher the
current (larger the channel) the larger the channel diameter, the hotter
the core temperature, and longer the thermal lag. For typical TC
leaders, the previous channel has fully decayed after 100 msec or so,
and the path taken by the NEXT leader is pretty much independent of the
previous one.



Im considering how i might be able to rig up a cheap(er) USB oscilloscope
(or some other data acquisition) to the topload of the coil so that i can
measure current between toroid and secondary, and current out of the
breakout point. Looked into USB-fiber optic converters, they are
pricey...
hoping i might be able to make my own if i can get fast enough
fiber-optic
parts.


Sounds like a great approach. A small, low bandwidth digital scope to
capture and store a single discharge event may also work.
The problem I see is that the phenomena of interest are in the tens-hundreds of ns scale. You'd want to see the current in the spark vs the top load voltage vs the current going from secondary into topload. Since it's all happening during basically 1/4 RF cycle, and we're looking at 100-200 kHz, that's a few microseconds.
Greg Leyh took some measurements on Electrum, which I need to go back and look at again He had a reasonably fast scope and a low RF frequency. 




High bandwidth is only needed if you're trying to capture the nanosecond
growth spurt currents. At this stage, even being able to accurately
capture the secondary-to-toroid and toroid-to-spark current envelopes
would be very useful in developing a macroscopic model lumped model.
Yes.. A 10 MSPS capture is probably good enough. 1 MHz seems a bit low bandwidth, except maybe on a HUGE coil. 




Bert


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