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Re: Reflections in Power Transfer

Subject:      Re: Reflections in Power Transfer
       Date:  Fri, 16 May 1997 10:17:13 -0700
       From:  Bert Hickman <bert.hickman-at-aquila-dot-com>
Organization: Stoneridge Engineering
         To:  Tesla List <tesla-at-pupman-dot-com>
 References:  1


Tesla List wrote:
> 
> Subject:       Re: Reflections in Power Transfer
>        Date:   Fri, 16 May 1997 07:40:40 +1200
>        From:   "Malcolm Watts" <MALCOLM-at-directorate.wnp.ac.nz>
> Organization:  Wellington Polytechnic, NZ
>          To:   tesla-at-pupman-dot-com
> 
> Hi Greg,
> 
> > Do you think that the streamer impedance can change as fast as
> > the current in the sinusoidal waveform?
> 
> Yes.  (To be investigated :)
> 
> Malcolm

Greg, Malcolm and all,

There's very strong evidence that the [non-arcing] streamers coming off
our coils are actually repetitive partial-discharge breakdowns of the
air. Accompanying each "punch" of energy required to further extend a
streamer is a transfer of charge from the toroid to the streamer - and a
corresponding rapid change in the effective streamer impedance "seen" by
the top of the coil. 

Some indirect support for this speculation comes from some of the
laboratory work done by Allibone and Schonland, extended by Meek,
looking a long spark propagation using streak cameras. Meek, for example
describes the growth of stepped leaders during studies of a 100 cm gap,
a 100 pF capacitor also connected across the gap, and a series resistor
going to this setup from an impulse generator (p 187-189, "Electrical
Breakdown of Gases", J. M. Meek a,d J. D. Craggs, Oxford University
Press, 1953). 

"The first leader exhibits branching and travels relatively slowly. The
subsequent leader strokes travel rapidly without branching over the
previously ionized track, and then more slowly with branching as they
extend the track. Where the stepped leaders extend the track their
velocity is comparable with that of the initial leader but there is a
gradual increase as the discharge process grows across the gap. The
total time between the initiation of the first leader stroke and the
occurence of the main stroke, and the number of stepped streamers
recorded, both vary appreciably even under the same conditions. For
example, in two successive discharges across a 135 cm gap, one has a
time of 94 uS between the first leader and the main stroke, and exhibits
no stepped leaders, while the second has a time of 180 uSec and exhibits
four stepped leaders". 

While there's lots of differing explanations of the mechanisms of
avalanche-to-streamer transition, theres ample work by Rogowski and
later researchers that significant current "streamer pulses" ar
associated with charge transfer to filamentary partial discharges,
typically 1000x greater than the coronal ("glow" discharge) current.
Today, these spikey partial-breakdown currents are looked for during
high voltage stress testing of high voltage equipment to warn of the
potential for impending failure.

If the driving point impedance is comparatively high (i.e., a relatively
low Ctop and high secondary Zo), the capability to supply these high
current peaks is limited. Adding to total Ctop, either by having a coil
with high self-C, or by adding a larger lumped C via a large toroid, 
would provide an additional "reserve" of charge to support longer
streamer growth/propagation. Hence the observation that a larger toroid
(for high Zo coils at least) improves the character of the streamers.

In short, the answer to your question is absolutely yes - streamer
impedance can and does change VERY rapidly, in the order of tens or
hundreds of nanoseconds during growth of partial discharges - certainly
much more rapidly than the oscillating current rate of the secondary
coil itself. Once the full streamer has formed (or re-formed along part
of the path blazed during a previous "bang"), the effective impedance
should then be more a matter of transfer efficiency between the
secondary:toroid and the energy lost in the partial discharge (heat,
light, ionization). At this stage, it would be governed more by the
coil's power level and Zo. The negative resistance characteristic should
still apply, however - the more power we dump in, the lower the
effective streamer impedance should be. At this stage, however, I'd also
agree with Ed's view that the behavior is probably more "arc-like", with
slower resonse to rapidly changing RF voltages/currents. Also, if we
develop an arc to ground, the instantaeous impedance would also drop
dramatically (and very quickly!).


-- Bert H --