Re: [TCML] Re: Re: Spark models, revisited

["Udo Lenz" <udo_lenz@xxxxxxxxxxxxxx>]

First, I want to thank you all for the interesting contributions
to this thread.

Jim Lux wrote:

> It's really like that.. inductance is weakly dependent on diameter of the
> conductor.  The original work in the area was done by E.B. Rosa at NBS.
> The book/report is online (I can't recall where.. but hunting for it will
> find it)

I agree, it's a slow logarithmic effect. Going down to, say, 0.2 mm
diameter will make some difference, though, if a higher accuracy is desired.

Steve Ward wrote:
> The max straight spark length for the QCW gun is about 56".  The peak
> inverter power is 350VDC*100Apk*.707 = 25kW at an operating frequency
> of around 330khz with the biggest sparks.

That makes me wonder, why my 20 kW sparks are just half as long.
They aren't straight and do branch. Maybe that is the reason.

> I found that tuning makes a considerable difference in inverter power,
> but im not sure how to explain it.  It looks like good tuning maybe
> provided a significant efficiency increase...
(Lots of interesting tuning info snipped)

My guess is, that in the case of bad tuning you burn up most of the input
power in your primary tank. I've written about that some time ago in
http://4hv.org/e107_plugins/forum/forum_viewtopic.php?128985

> > The arc length grows with the square of Vinp. I believe Steve Ward
> > has seen a rather sudden growth of spark length with voltage
> > and my own observations confirm this.

> My tests make it look more like a linear thing with a big offset.  It
> took about 56kV to produce a 6" spark, and then fairly linearly the
> voltage climbs to 65kV with a 50" spark.  Maybe im still at the base
> of the curve so my crude numbers look linear?  i seem to recall 66"
> sparks needing ~72-76kV, so it had looked to me like sparks were
> actually going to require even more voltage to grow bigger.

My assumption, that the arc resistance is proportional to 1/P^2 very likely
holds only for a certain range of P. (P being the power dissipation of
the arc per unit length). A 1/P dependence would make the length
grow linearly with V. I've tried to find theoretical justifications for
various dependencies of this kind, but the issues are complex.

> Another observation is that splitting of sparks greatly reduces their
> length.  As expected, making 2 sparks instead of 1, makes them shorter
> with a given amount of power input.  When i "over-voltage" the coil by
> ramping the inverter voltage to maximum early on in the spark
> formation, it can only achieve about 36" sparks (same 25kW as before),
> but it produces usually 3 main arc channels each with several little
> branches.  Its only with a very slow and controlled increase in
> inverter voltage over a 15mS period that i can make straight long
> sparks.  This, i believe, is due to keeping the spark voltage low
> enough that branching is not promoted, and only enough voltage is
> supplied to overcome the existing channel resistance and keep the tip
> propagation going.

Nice observation and I believe your conclusions are correct.

Bert Hickman wrote:

> Although a lossless transmission line model of a leader would have a wave
> velocity of c, real-world (i.e., lossy) leader channels actually have a
> measured velocity of about 0.1*c, implying that Sqrt(LC) for long leaders
> is approximately equal to 10 instead of 1.
> See Raizer (GDP, section 12.10).

I haven't gotten the Raizer book yet. 0.1*c seems extremely fast. Is that
for DC arcs? I've left out the inductance in Jim Lux's model along the arc,
because it doesn't seem to play a big role compared to the resistance.
> From my data (100kOhm/m at breakout point, 15pF/m, 220kHz), using
a R-C arc model I get a phase velocity of around 1400km/s and group
velocity being double the value.

> It also looks like Raizer agrees with you regarding the effect of the space
> charges surrounding the leader. Per Raizer in GDP, section 12.9.4, the
> higher capacitance is due to the, "thick "sheath" surrounding the
> high-conductivity thin leader channel; the sheath is formed of weakly
> conducting plasma and the space charge injected into it by streamers". In
> the case of an RF leader, charge is being repetitively injected and removed
> by the oscillating driving voltage - the source of the "displacement
> current" being sourced by the HV terminal.

In the case of Wards non branching arcs, I tend to believe more in
non ionizing charge drift, since sideways streamers aren't visible. For
branching arcs, I'd agree with him. I have a problem with the drift of
ions, though. They seem much too slow for this effect (< 1mm/us). Electrons
are much faster (>100mm/us).

> The velocity of a _propagating_ leader is a function of the electrical
> field at its tip. Since growth involves forming a propagating front of
> countless avalanches, streamers, and multiple streamer-to-leader
> transitions as the leader grows, leaders propagate considerably slower
> than the wave velocity within an existing leader. The higher the tip
> E-field, the higher the leader velocity. Laboratory leaders typically
> propagate at between 10E6 - 10E7 cm/s. This can reach 10E7 cm/s
> for lightning.

I think that it also is important to consider the time it takes to get
enough heat into the leader to make it conductive. Only then it can
transport sufficient charge to fill up the capacitors along the way.

Udo


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