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Re: Corona and Sphere - Puzzle -addition
Malcolm, Boris, and all,
Aha - I now understand your very interesting question! Spark breakdown
is ultimately a statistical process, even when you have a uniform
E-field around a very smooth electrode. A preconditioned uniformly
stressed electrode may see multiple sites of initial breakdown - this
property is used to advantage to obtain multiple conducting channels in
very high energy multichannel spark gaps. Once a streamer begins to
form, it takes significant energy to heat the breakdown channel and
further improve its conductivity. Once breakdown begins, energy will be
very rapidly transferred from the terminal into the advancing streamer
(in the order of nanoseconds or tens of nanoseconds). But if you have
multiple areas on the threshold of breaking down, one streamer still
seems to win out - Why? For this we need to change the timescale from
milliseconds to nanoseconds at the point on the output just as breakdown
occurs...
At the streamer's early formative stage, the forming conductive channel
is actually exchanging charge from the terminal into the space charge
surrounding the terminal as a partial discharge. However, the
instantaneous current flow (dq/dt) through the root of the forming
streamer is orders of magnitude larger than corona leakage currents
which immediately preceed it. And, the streamer root actually has a VI
characteristic that is similar to the negative resistance seen in an
arc. As long as the voltage on the terminal can be maintained, or can be
made to increase, the streamer will tend to propagate. However, this is
not the case for our Tesla Coil topload. The initial pulse of current
which feeds the growth of the newly-formed streamer comes from the
transfer of charge from the topload capacitance, and the sudden charge
transfer causes a corresponding decrease in the output terminal's
voltage.
In the nanosecond regime, virtually all of the instantaneous energy
necessary to propagate the streamer can ONLY come from the electrostatic
energy stored in the topload capacitance and the surrounding
space-charge. Now while a larger topload C will support heavier
instantaneous current flow into the new streamer and reduce the
magnitude of the terminal voltage drop, it will NOT totally eliminate
this initial voltage drop. The reduction in terminal voltage tends to
"starve" the propagation of any other streamers that may have also begun
to form. Once the terminal voltage recovers (via replenishment from the
relatively high impedance resonator winding hundreds of nanoseconds or
microseconds later), a hot channel has already been formed in the first
streamer, and the propagation process begins anew, preferentially
extending the length of the "winning" streamer.
-- Bert --
Tesla List wrote:
>
> Original Poster: boris petkovic <petkovic7-at-yahoo-dot-com>
>
<SNIP>
> ----------
> Hi List,
> Firstly ,thanks to Malcolm for formulating the
> problem.The formulation is a good one.I would add the
> same formulation of mine as I had formulated it to
> Malcolm (2 months ago).
> Think that question may be put the way is the strenght
> of local electrical field ,at the surface of smooth
> sphere,the only thing which determines breakdown of
> air at the other point parts of sphere after first
> streamer somewhere already issued (standard
> atmospheric conditions assumed) ?I'm affraid that
> there are cases in praxis offering negative answer to
> this question.
> Now ,a one more formulation of the problem :
>
> Let us consider behavior of smooth sphere excited by
> TC h.f wave form.Let sharp point be added at one side
> of sphere to allow issuing of spark.Let be considered
> only single pulse mode.Let diameter of sphere be
> 10".When voltage on sphere reaches 300-350 KV sphere
> should discharge in all directions in air,not only
> through already formed sharp point path judging by
> experiments of the same sphere without sharp point
> added.However,it proceeds to discharge through sharp
> point path despite voltages of 400 KV or more.At last
> when voltage in the order of 500 KV is reached ,sphere
> would start to form another streamer paths from its
> surface but even then those new streamers are not
> reaching so far distances as very first one ..In all
> the books can be found data the most responsible
> factor for breaking down of air is strenght of local
> electrical field (which is ~30 KV/cm for DC ,low
> frequency range or even somewhat lower for TC h.f
> range).But before forming new streamers el.field
> reaches 40 KV/cm in described case!
> I got as the same explanations like some of yours as
> I got from some physicist and HV engineers:Well ,you
> see the sphere electrode already discharges through
> adjanced sharp point path..or formed streamer offers
> less impedance than rest of surrounding air.."But when
> I formulated the problem like follows:
> Half of sphere with adjanced wire point is situated in
> black box (so you cannot seen if discharging occurs
> there or not),another half of smooth sphere is exposed
> and can be seen .When powered by TC you can measure
> strenght of el.field >40 KV/cm and nothing
> (caracheristic visible corona doesn't appear).The
> question :How do charges at exposed side "know" that
> discharging already occurs in the black box and follow
> that path instead of forming new streamers despite
> more than sufficient el.fields reached?What mechanism
> determines and allow such behavior (I know it is
> powerful streamer in the black box but what
> exactly?).After that some of them start scraping their
> heads...The problem is not as simply as someone may
> think.Anyway thanks for thoughts/tries.
>
> Regards,
> Boris
>
> =====
>
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