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Re: The worlds Largest Coil

At some point, the rate at which you put pulses of power into the system
(i.e. break rate for spark gaps) will be higher than the resonant frequency
of the system.  This isn't any problem.

Let's say, for example, that your monster coil is resonant at 1 kHz and it
has a Q of 10 (which is fairly high, I agree)...

Further, let's assume that your topload is big enough so that it doesn't
break down to air until 10 Megavolts..

We start out with no power in the coil.

We put 1 power pulse in (by inductively coupling it to the bottom of the
secondary).  The coil begins it's first oscillation.  A quarter cycle later
(0.25 mSec), the voltage on the secondary has peaked (say at 1 MV, for
grins).  Another quarter cycle, the voltage has dropped to zero, but the
current in the secondary is peaked (opposite in sign to the original
current), and another quarter cycle, the voltage peaks (opposite sign),
then, finally a millisecond after our first pulse, we are ready for another
pulse... we add another chunk of energy.

Now the energy in the system is 1.9 times the single pulse energy (Q of 10
implies that 10% of the energy is lost each cycle).  The electrode voltage
is now 1.4 MV..

Next cycle, we kick it again, and the energy in the system is 2.71.....

and so it goes, ... at pulse 10, we're up to an energy of about 6.8 times
the pulse energy, or a voltage of 2.6 MV..

Eventually, we converge to where we lose exactly one pulses energy per
cycle, when the energy in the system is 10 times the pulse energy (Aha, that
Q of 10...)..  And we are at sqrt(10) = 3.16 MV...


you can get there a bit faster, and get more voltage, by pulsing it every
half cycle, but alternating the polarity of the pulses... Now, we get twice
the energy in the system before it is losing it at the same rate we are
putting it in..


What you are essentially doing is building a giant class C amplifier...

So.. start computing.. How much Q can you get (mostly due to IR losses, and
some corona).  How much energy do you want to store?

Why not use lightning as a model?
(http://home.earthlink-dot-net/~jimlux/lfacts.htm )...  100 kJ/meter of bolt.
Your hundred foot tower would work out to about 30 MJ of stored energy.
The stored energy is limited by your top load, really, at 114 pF per meter
radius and 3MV max per meter radius.  So max energy is .5*CV^2 = 0.5*  114*r
* (3 * r)^2 Joules (rewriting it, and rounding a bit... .. 500 * r^3., or
radius = cuberoot( 2*energy in kJ))

For 1 kJ.. 1.25 m radius.
For 10 kJ, 2.7 m radius
for 100 kJ, 4.6 m radius (now we're getting to interesting power levels)
for 10 MJ, 27 meter radius.... (100 foot radius???)

These will be within an order of magnitude.. The coil itself will have some
self C, the losses are inevitable, etc.

Go to it.. start calculating... Do some reasonableness checks on Q... Just
use the wire resistance as your R and Q = X/R, where X is the reactance of
the coil (or cap) at your frequency.



I note that these sorts of resonance problems cause HUGE problems for the
folks running long distance power lines, which are a resonant circuit (of
sorts), and have fairly high Q.  Switching transients of 4 or 5 times the
line voltage are not unheard of.