Re: Maximum Secondary Voltage...

Tesla List wrote:
> >
> > My understanding is that for each shot, the secondary rings up as the
> > primary rings down until Cp is empty. There is then a finite amount
> > of energy available to charge the terminal capacitance. How can the
> > terminal reach a voltage higher than that allowed by conservation of
> > energy? I have grappled with this one for a long time now. The Corums
> > (oft quoted as an authority in this area) make no mention of this
> > fundamental limitation in a cap discharge system (at least in the
> > notes I've read), but appear to treat the secondary/extra coil as
> > though it is fed from a voltage source (which a capacitor most
> > definitely is not).
> >     In fact the situation is even worse when one takes the awful gap
> > losses into account.
> >
> > Malcolm
> Malcolm,
> I like the thinkers in this group and you are certainly one of them.  The
> conservation law is always in full effect here.  The Corums and myself
> treat the system in a more idealized fashion, as you say.  It is as if
> the base of the resonator is voltage fed.  It is obviously this way in a
> magnifier system.  But, it is also this way in a two coil system!!!  Yep!
>  No matter what sized counterpoise you use, the base of the resonator in
> a two coil system has a nice hefty voltage on it.  It may not be much,
> but what it lacks in EMF it more than makes up for in Ultra-Low impedance
> drive!!!  This means current!  Current and its rate of delivery interact
> with the resonator's inductance to create 100% of the resonant rise in
> any Tesla system.
>   A maggey uses, hopefully, a moderately low impedance drive source and a
> fairly high base voltage. (trade offs).  The energy is coupled into the
> resonator in a two coil system magnetically and directly in a magnifier.
>  Needless to say the maggey system gives more bang for the buck where
> resonator coupling from the driver top turn is always 100%.
> The terminal can reach ANY POTENTIAL UP TO INFINITY based on even a 10
> watt input!!  Conservation of energy will still hold! With 10 RMS watts
> in to the system and with only 50% efficiency,  5 RMS watts makes it to
> the toroid.  If we choose to have 1 pico-ampere in an arc, we would
> expect a voltage out of 5 TRILLION volts!!  Thus the law is satisfied!
> (using crude in phase RMS values!)  Even a microamp arc off the toroid
> (exactly 1 million times hotter) would make a 5 million volt output from
> 5 watts in the toroid.
> The above is a bit out of context (but notheless valid) and just not
> doable, but you see the conservation of energy law is not a good point to
> argue some sort of voltage limitation rule from!  Forget energy
> conservation!!  It is "auto-adjusting" in this universe! (thank god)
> Look at it as a sort of automatic level or gain control  (ALC - AGC)
> imposed by God.  We can't fiddle with it beyond trying to engineer for
> max transfer 100% ideal, unatainable, ever!  In theory, and by the
> conservation rule.... any voltage all the way to infinity is possible
> with any coil at any wattage.
> In reality, a two coil system is great at 10% efficiency. (wall outlet to
> arc).  A maggey might double this!
> Richard Hull, TCBOR

Interesting Discussion!! Some thoughts....

Richard is definately correct regarding the high current and moderate 
voltage at the base of a 2-coil system. I've got three 10 foot ground 
rods tied to the base of my 10" coil, and it has NO problem pulsing these 
with over 600 volt RF peaks. Even though the duty cycle is relatively 
low, the average current is still high enough to easily "pop" the 
filaments of 60 Watt light bulbs connected in series with the base lead. 
I also once had a poor connection once between the RF ground and the 
secondary coil base - a VERY hot white arc closed this small gap with  
evidence of mucho power!

However, I also think that Malcolm has the right idea by invoking 
Conservation of Energy. In well quenched disruptively excited systems 
each discharge event will be independent of the previous one. Most of the 
energy stored in the primary cap will be discharged via all of the losses 
in the system (hopefully much of it in nice secondary sparks!). There is 
little argument that in a two-coil system the maximum energy transfer 
occurs during the first half of the first "beat" of energy transfer from 
the primary to secondary, and rapidly declines due to various gap, 
discharge, resistive, and radiative losses. For the moment ignoring 
these losses, the maximum energy available for each event is proportional 
to the tank capacitance (Cp) and square of the capacitor voltage just 
prior to when the gap fired (Vg). This should hold for a disruptively 
excited three-coil system as well.

Once the gap fires, no more energy is available to the primary:secondary 
system. Any residual energy stored in the secondary from the previous 
discharge event will have already "rung down". Although the secondary 
energy loss occurs more slowly once the secondary voltage drops to the 
point where the toroid discharge is extinguished, virtually all of the 
energy from the previous event has dissipated long before the gap fires 
for the current event.

If we assume that ALL of the available energy in the primary circuit is 
transferred to the secondary, and that secondary breakout is inhibited 
through the use of a very large toroid, then up to (1/2)*Cp*Vg^2 Joules 
of energy could be transferred to the secondary. Assuming an "effective" 
secondary capacitance of Cs, consisting of (at a minimum) the sum of the 
effective isotropic capacitance of the secondary and the top discharge 
terminal, it would seem that the maximum secondary energy should never 
exceed (1/2)*Cs*Vs^2. I don't think that "Resonate voltage rise", helical 
resonator theory, transmission line theory, or having infinate VSWR's 
will violate this, since it would imply "over unity" operation. 
Hopefully, most of the "over unity" crowd is on another list...

If we say these energies are equal: (1/2)*Cs*Vs^2 = (1/2)*Cp*Vg^2 and 
solve for Vs, the maximum secondary voltage is limited by 
Vs=Vg*SQRT(Cp/Cs). This assumes no secondary discharge is present. If we 
have a secondary discharge, the maximum voltage can only be less than 
this, since we are removing energy from the system. Any added capacitance 
from an ion cloud around the toroid will also tend to reduce this voltage 
since Cs will tend to increase. I'm not aware of any ways to 
significantly reduce Cs while maintaining capability of preventing 
premature breakout and energy loss. Indeed, this was the battle that 
Tesla fought (and never won) while trying to reduce inter-turn 
capacitance for high inductance windings. 

A Note on Richard's example: 
If we assume a reasonable minimum value of Cs (say 1-10 pF), charged to 5 
trillion volts, this represents 0.5e+12 to 0.5e+13 Joules of 
electrostatic energy. With a lossless system it would be possible, in 
theory, to transfer to charge Cs from a 5 trillion volt 10 Watt power 
source (sort of like the world's BIGGEST photoflash unit) if we could 
wait a LONG time. If we are transferring 10 watts of energy from the 
primary to a secondary in a 2-coil system, it's not clear how we could 
achieve even million volt levels...  

Another thought:
Suppose we were somehow able to send the next slug of energy into the 
secondary before the first one was dissipated, and we used a BIG toroid 
to prevent premature breakout. We should be able to break the 
Vg*SQRT(CP/Cs) voltage limitation in this case. Proactically 
speaking, this would require being able to appropriately phase primary 
"shots" so that they would only add to the energy stored in the secondary 
BEFORE it had a chance to "ring down". We would also need to block 
any transfer of energy back into the primary circuit. A vacuum tube or 
FET coil, run in high power pulsed mode from a very "stiff" DC source 
just might be able to do this! Shezaam - a trillion volt Tube Coil!!

Hopefully this will spark some discussion :^)

-- Bert --