l2 and l3 were 10 meter 1.5mm2
So I made L4 20m 0.75mm2

coil has a larger diameter. more windings more inductance, but also more capacity

so resonant frequency of L4 now is much lower. should tune L1 to this?
make a new L1? with more windings?

or keep L1 fast as the parametric excitation is happening in L3.

also windering about putting a diode between C3 and ground.
as earth is pumped and energy needs to be cummulated into the system from the ground

just like a valve in a hand water pump. pumping water out of the ground.

instead of tuning the impulse of L1 to L4, I will tune the impulse to L3.
for this I will remove the cap of L3, and see If I can match the impulse half wave to the L3 self resonant frequency.
I also will connect the new L4 with double the wire length of L3

I removed L4 and C3 and C1.
only leaving 45nF series tuning on L2.

I can now produce a decent impulse by giving 2x23.2 V input.
in yellow L2 in orange L3. (voltages) whereby L3 is ringing.
I zoomed in on the impulse duration.

L1 impulse is around 410nS
L3 half wave is 183.2nS longer in duration (593.2nS)

so this works. now I can tune the impulse to L3.  but first, I'll connect L4 in series and see how that looks.

OK I already expected this. without a c3 tuning cap parallel to L3  (and series to L4) and with L4 series connected to L3, the frequency now is much lower, as their harmonics couple. so I can't tune L1 impulse to L3 this way. I need to do it without L4 series connected.

I measured again, without L4 and c3.
first without c1 parallel to L1.
then I added 10x68pF in parallel to L1 (c1)
and this is the second measurement. it already almost matches L3 in frequency, but it needs a bit more.
I could make L1 bigger (more inductance) to match L2 and L3 better. I prefer having more inductance and less capacitance, as this will give a higher voltage impulse (using less power).

but for now it will do. as the L1 L2 and L3 are already cast in epoxy.

So I will add more capacity to L1.

edit: WHY is L3 changing in frequency when I tune L1? let's take a look at that again

L3 in orange with and without C1 parallel cap over L1.
measuring 4 peaks both have the same frequency of 4 x 305kc/s  (1220kc/s) so, the difference is due to to the impulse, so I need to measure and compare the impulse, after the impulse has passed over L3. (further in time)

4 periods= 3.28uS
1 period=820nS
 but lets take a closer look and zoom in to L3 half wave again.

yellow L1 impulse half wave =438.4ns (no C1 cap used)
orange L3 full wave (after impulse)=816ns           half wave =408ns

Wow did't expect that! L3 already is closely matched to L1, without even using a tuning cap. that's perfect!
L1 is even a tiny bit to slow (22ns)

very interesting. now lets tune L3 to a subharmonic by adding a parallel capacitor.
L3=1225.49kc/s
2nd   612.7
3rd    408.5kc/s
4th    306.4
5th    245.1
6th  204.2
7th  175.1
8th   153.2
9th   136.2
10th  122.5
11th  111.4 kc/s

I will leave C1 out of L1

impulse is measured over L2, should measure at the source of the mosfet, but error will be small

this method can also be used, to set the right distance between L2 and L3. L3 should ring at its maximum amplitude at the right distance.

tuned L3 to f=110.9kc/s by adding 21nf in parallel (c3) [scr31]
L4 and c1 still removed.
L2 c2 series cap made very big, 117nF, to get single impulse with no ripple (allows smaller c3)
power input was 1.35A 2x 32.3V
impulse =-2500V
L3 current (green)=18.82 A pp  (20mV/A current probe setting)

I measured current on L2 [green on scr32] and came to the conclusion, L2 also is parametrically excited by the impulse, and should also be tuned.
so now lets do that first.
impulse of L1 should already match L2. but let's take a look at that also, as l1 is close coupled to L2 but how? I can't let L2 ring by removing C2, as it is parallel fed by the mosfet...

or... is this bump on the current of l2 (green scr32)  just a measurement error, due to the impulse flowing through the L2?

We have magnetic induction, and dielectric induction from L2 to L3.
so lets tune L2 so it gives high current. That would mean, a big capacitor.

AHHHHrrg. So parametric excitation of L3 now is clear.
but... Now for L2... how does that work? How to tune that?

no(in reaction to previous post ending) I assume L2 has the same frequency as L3, so it should automatically be tuned to the impulse.

The balance of the C2 and C3 cap, can probably only be seen by using the VNA.
but clearly C2 needs to be bigger than C3.
if C3 becomes to small, then its voltages become to high for the tuning caps. (2kV limit)

Now I will look into coupling between L2 and L3.
for this I will use 3 equal size coils. of 0,75mm2 wire.
L1 will be parallel shorted out, for a fast impulse.

L3 will be let ring free, without tuning cap, and distance will be adjusted, for max amplitude.
Will I first need to do coupling or first, tune the impulse to L3?

still not connected the new L4

I replaced the epoxied coils, with 4 equal size 0.75mm2 coils. these will be used for coupling tests, I placed L3 and L4 on the acrylic distance holder.

L1 was parallel shorted, to get high impulse speeds. but, since all coils now are equal and symmetric coupled, it is to fast. I could add capacitance to L1 to tune down the frequency of the impulse, but...
I will simply make L1 series tesla bifilar again. it should then have almost the same frequency of L3.

L4 is not twice the wire length, but will stay coupled but unconnected to L3.

This way, the impulse should be matched to L3, and I can test for coupling distance and see what happens.

this first test was at 145.2 kc/s
with 45nF on L2, no capp on L1 and L3, and L4 unconnected close coupled on top of L3.

L1 impulse now is 340.4ns (scr33) (measured at source, note it is half of L3, while parallel shorted)
while L3 halfwave is 694.4ns (scr34)
distance L2 L3=20mm

I made L1 bifilar, to bring the duration of the impulse up to the L3 coil speed.
I must check the connections... did someting wrong. L1 speed went up. duration of impulse now only is 276ns!
while L3 still is 673ns (was 694ns)
coil distance was the same, only to get the L2 ripple out of the picture, I needed to tune a lot higher to 240kc/s this is where the L3 rripple was max.

will tune down, and check L1 connections to see why it is faster

edit: checked at lower 145kc/s, gave almost the same results. Coil is bifilar. but!
it is reverse connected. inside rim is now grounded, and outside rim is connected to source.
Did not expect it to give this big a differnce. but I will reverse the L1 coil connections and measure again.
very nice to see the inside rim has a different speed (slowr) than the outside rim (faster)

ok, outside rim of L1 is now grounded, L1 is bifilar
scr39 shows orange ringing of L3  scr41 is zoomed in to show half wave duration of 688nS (still the same)
scr40 shows impulse duration which now is 1078ns much longer than expected. (expected it to match L3)
the yellow impulse of L1 is measured at source (as are all other tests)
as can see, there now is barely any overshoot, and the last part of the impulse traveling up is prolonged.
This can be explained, by having the resonant side of L1 close coupled to L2.
while L3 has its resonant side facing loose coupled L2, instead of close coupled (but ungrounded) L4.

So I will check, which side is resonant at L1 and L3
edit, I checked, and both L1 and L3 resonant inside rims are facing air. So in theory should be the same.
L3 is faster.  L3 might be faster due to LMD resonant mode.
I tuned to 90.8kc/s where ther ideal resonant mode was, without ripple.
note that with the faster impulse I needed to tune much higher to get rid of the ripple.
It seems the faster impulse creates a stronger shockwave ripple?

anyway... impulse now is to slow for L3. will need to revert to parallel shorted L1 (unifilar) and slow it down to L3 speed, by adding capacity parallel to L1. I could also loosen L3 from L2 to slow it down, but... the difference between the impulse and L3 is to much to solve it with coupling (frequency splitting)

maybe R is now to big, for a high Q impulse, since in series mode the wire is twice as long, and twice the R, with 0.75mm2 it might be "fatal" for proper impulse generation.

VNA has arrived, will need to. install and calibrate first.

played a lot with tuning the impulse.
It can be tuned to L3, but also to. L4
L4 gave the ground currents

Now recording the process for L3, as that also applies for regular tesla coils.

I've installed and calibrated the VNA
usb audio drivers seemed to be random windows drivers, not the ones from the software installation package.

I need to check that.
but for now it works.

I misplaced my sma cable for connecting the coils, so I had to make a new one.
Luckily I had BNC connectors, and ordered a sma to BNC plug.

first measurements seemed off, but the start has been made.

I want to test how a secondary responds to a single impulse L1 coil as primary.

as this L1 is most efficient for creating almost free impulses.

I've done several tests without the L2 as primary, but using it direct as a secondary (without series resonance, without L3).
So L2 is earth grounded, untuned and open ended.

When close coupled to L1 the impulse is collapsed from the loading of L2 impedance

but when L1 L2 is 15mm appart, it works very efficient. I am able to get 6kV pp at 92 kc/s with 3kV impulses.
thos could even increase if I Precisely tuned the impulse to the secondary ringing.

But I still use around 0.63A 2x 32.3V to do this.
and L2 is loading L1.

So using L2 as a primary has benefits, when I tune it above the LMD series resonance.

When resonant it draws much power, but whem tuned above resonance the power draw is much less, while still producing this impulses that excite the secondary L3.

thus tuning L2 with a large capacitor, and above resonant frequency is a interesting option to excite the parallel series resonance of L3/L4.  as the magnetic field isn't loaded, since it is not there in L2 (not as big as when resonant).

And when L3 L4 is loaded, it whil thus not feedback into L2 L1 and the power supply, as it now is fully excited by dielectric induction.

the real power, should then come from the displacement og the earth currents into the system, that will be directed into a large capacitor bank, after being trapped in the parallel series tuning capacitor c3

excellent!
"Show me the m̶o̶n̶e̶y̶ VNA!"
~oft-repeated quote from the bad 1990's movie Jerry Maguire

putting a diode between ground and yhe c3 parallel series capacitor does not provide a dc offset for harvesting.
instead the capacitor is incapacitated

What I did notice is that I can still tune to lower harmonics and still get a single sine wave on L3 and L4.
L4 is rippling if it is not precisely tuned. but it is possible.

This is good because I need a bigger capacity to produce more power.
lower frequencies can also produce higher voltage impulses,
and my current probe has less phase shift error

when tuning to a lower harmonic around 125 kc/s I had around 4kV on L4.
I drew sparks with an isolated scissor and it amazed me how far I got. around 7mm.
it was a purple noiseless spark

if the primary uses its magnetic current sine wave to induce the L3 secondary transverse resonance

and the primary impulse dielectricly induces the extra coil (and amplifies the L3 secondary current) into the lmd resonance

so L3 secondary has conventional current
and L4 has displacement current, which explains why it can be phase shifted.

Is the impulse directly interacting with the earth of L3? I think not.

Tesla said the extra coil uses the series capacitor (connected to ground) to produce the ground currents.

A friend said, put a load on the ground connection to see if there is current there.

VNA is becoming clearer, need more playtime with it.

L3 L4 series connected, no cap.
S11 VNA measurement 

still not fully calibrated properly, but the combined coils have a low resonant frequency

second VNA measurement, this time with 3nF in parallel to L3 (and series with L4)
reduced band width and recalibrated.

frequency has dropped from 330kc to 157kc

ok I'm starting to "get" the VNA.
I can couple L3 and L4 to L2 and read where the resonant modes are, so I can tune down to the sub harmonics.

7 nF parallel series to L3 L4 brings it down to 110kc/s which is the third subharmonic of the coils without a cap (330kc/s)

so when this is coupled to L2, L2 could also be measured, being coupled.
but what about L1? couple it open ended? I guess so

finetuning should still be done with the coils running, but it gives good insight with the vna