Re: [TCML] Voltage Question

[Paul Nicholson <tcml88@xxxxxxxxxxx>]

I wrote:
> To produce long streamers, really the coil just needs to
> develop enough voltage to start the breakout, and then be
> able to back that up with plenty of charge (ie a big toroid)
> and enough power to keep the streamers hot and low resistance.
> Therefore you're more likely to find a simple relationship
> from input power * efficiency to arc length.

I wish I could justify this with some data, but measurements
have not yet been performed (as far as I know) on a TC.

Udo Lenz wrote:
> ... it seems a bit extreme.  I can't imagine an endlessly
> growing streamer given infinte power but just a certain
> voltage.

There'll be a voltage drop along the arc and at some point
the arc will reach sufficient length for the tip not to have
a local field strength high enough to make further extension.

Arc voltage drop would depend on streamer current which
in turn depends on operating frequency, duty cycle, etc.
How much, I don't know but maybe in the range 100V/cm to 1kV/cm.
For example a coil might break out at 200kV and need another
25kV to support a 50cm arc.  These are just guesses.

If you turned the voltage up to compensate, the topload will
start to issue more streamers rather than extend a single one
beyond max length.   The extreme example of this would be a
brush discharge in which the voltage tries to go way above the
breakout voltage of the electrode (considering the radius of
curvature) so a vast number of short arcs are produced.

And the streamer would collapse as the beat envelope takes the
secondary voltage back down, so it has only a few RF cycle
peaks in which to do all this.   If break rate is high enough
(and there's not too much wind) the next break might follow
the still-warm channel of the previous arc.

I suppose the challenge for the coiler is to tailor the voltage,
envelope, break rate, charge (topload size) and power so that
everything goes into producing a small number of the longest
possible streamers.   The challenge for the experimenter is to
measure all this happening and the theoretical challenge is to
develop the design rules to achieve an optimum operation.

There are a few coils which have been measured and modeled,

 http://abelian.org/tssp/cmod/

Take the first one: mm3p by Marc Metlicka - this had a large
bang energy, enough to send the top voltage to over 1MV based
on energy conservation (the MCTV value - max conceivable
top volts).  But at 1200kV the toroid surface field would be
around 60kV/cm which is over twice the breakout field strength.
The coil probably broke out at around 500kV and the excess
charge went into producing the multiple streamers.  The voltage
is trying to push too high for this toroid.   Probably a wider
(major diameter) toroid on this coil would have done better -
reduced MCTV but same breakout field strength (toroid minor
diameter) would have produced fewer but longer arcs for the
same coil and bang energy.

Contrast this with the 3rd coil - jftt42b by John Freau. Bang
energy wants to produce 571kV but breakout would occur around
380kV (surface field reaches 26kV/cm).  There is only one
streamer with this system, the voltage isn't able to go high
enough above the breakout level to launch more.

We can try a metric here: the MCTV (ignoring efficiency for now)
compared with the calculated breakout voltage (derived from
toroid radius of curvature and using 26kV/cm as the breakdown
field strength for air at TC frequencies).

Define a breakout ratio BR = MCTV / breakout_voltage

 coil           BR               Streamers
 -----------------------------------------
 mm3p     1156kV/500kV = 2.3     multiple
 jftt42a   769kV/260kV = 3.0      2 or 3
 jftt42b   571kV/382kV = 1.5      1
 mw1       437kV/464kV = 0.94     no breakout
 ba0       907kV/591kV = 1.5      1 or 2

A few more points in this table would help, and taking account
of other factors such as efficiency might tighten things up.

What can we suggest? -

 - BR < 1 naturally produces no breakout;
 - BR ~= 1.5 to produce one or 2 streamers;
 - BR > 2 to produce 2 or more streamers;
 - BR >> 1 to produce brush type discharges;

BR can easily be increased - add a breakout point.

If we are more realistic and assume a 50% efficiency from
bang to peak secondary envelope, then all the MCTVs are
multiplied by 1/sqrt(2) and the BR for 1 or 2 streamers is
about 1.1.

I invite measurements to add a few more entries to this table.
We'd expect all coils with BR < 1 to need a breakout point.

There's not much more to say about top voltages without
measurements.  We don't know how much higher the voltage
actually pushes above the breakout threshold.   We can set
reliable limits - easily calculated breakout voltage for the
lower limit, and MCTV for the upper limit. It's reasonable to
expect some voltage clamping effect from the dynamic load of
the arcs but we don't know how stiff that is.

--
Paul Nicholson
--

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