with the core inserted I now already measure 39mH with a Q of 79 at 100kc/s
that is way to high, I just calculated 18mH so... I will remove windings.
its not linear so I will take it easy

I removed the last 5 layers of windings, but those appeared to be a lot more.
measured again with the core inserted, and this time 35mH still to much

removed another 5 layers, now down to 25mH. coming close to the target.
My LCR meter acts weird. I gave it a new battery.
I need to not touch the clips or the 100kc/s measurement signal leaks away.

but also closing the ferrite core lowers the inductance? hmmm

I've decided not to go lower in windings. I appears this is the last 5 layers.
If needed I can always go lower in turns.

lets zee what this will do.

I will now give the primary  8 turns. meassure the primary inductance, and then calculate the capacitor to make it reasonant at 85kc/s
or... should I recalculate the freqeuncy from the 25mH I now have? hmmm
yes.

resonant around 74kc/s that's good

25.83mH  for the secondary @100kc/s
5.356 uH for the primary
the calculator says 863.64 nF for the primary. that looks ok.

I did the calculations twice, also on this one:
https://www.omnicalculator.com/physics/resonant-frequency-lc

YESSS!!!
finally it works.
I can smell ozone from the high voltage discharge.

My power supply gave 2.78A at 12.6V DC =35W
and the stepped up voltage became 5.1 kV pp

before I tested with 8.0 V and 2.00 A =16W which gave 3.7 kV pp

I want to push the voltage up to 16.6 V or even 26V but then the amps will run very high, and I need fans for my mosfets.

This is tuned with a 1uF on the primary, but I calculated it to be around 800 nF so I could improve it even more.
Still the frequency now is 74 kc/s which is a very good result.

Very happy that this method finally works.
Lets enjoy this succes, and then continue to refine! ( isolate the couplings so no ozone/voltage leaks away)

yellow is the primary between cap and coil.

orange is between the secondary and the high voltage coil.

I havent even measured at the other open end of the coil, often the voltage is even higher there

it makes sense to keep the 1uF in place, and tune the secondary coil to it, so it reaches maximum voltage.
the 1uF is a 100V dc cap. wima mkp2 poly propylene  63V ac

I now sit around 30V pp on the primary so I can go higher if needed
I just need to watch the temperatures, if needed I can get 10x 0.1 and place them in parallel to lower the ESR.

https://www.wima.de/wp-content/uploads/media/e_WIMA_MKP_2.pdf

Ideal:
Primary:
1uF with 4.503 uH gives 75kc/s which is 2.12199 Ohms reactance (inductive)

Secondary:
180pf at 75kc/s needs 25018 uF inductance. minus the HV coil (798.8) is 24219uH (24mH)

I now measure 25.3 mH so I say that it is close enough. I could remove a few windings but the gain would be very little.

WOW I did it. this was difficult. but my inutition helped me as it always does.

lets put some fans on the mosfets

I could double the capacitor on the primary to 2uF
which will bring the frequency to 53 kc/s

The secondary then would need 53 mH  which gives a lot more wire, plus, more resistance.
I already had 39mH before which is near that 53.  hmm..

it will be lower in freqeuncy but, that also means I will need to provide even higher currents from my PSU at lower voltages.

No I will stay here, this is good for this experiment. plenty of voltage. very nice.

ok. that means, the next phase. Tuning the parallel resonance to this frequency (75kc/s)
I will tune the coil with the parallel caps. now I need to connect them so they can handle the large currents.

I placed 2 fans on my 2 mosfets.
they are 12v, so I connected them in series, and dr8ve them from the 17V psu of the pcb

I also reconnected the coils again, to see if I can measure higher voltages at the open end.

after that, I can loose (capacitive) couple the probe and retune again and note the frequency.

1.64A 5.0V dc PSU 8.2W
f=60.9842 kc/s
1.9V pp

I connected the other side of the high voltage coil to the secondary coil.
And probed the open end.
apparently this gives more capacity as the frequency went down to 61kc/s

let's push the power, and see how much current and voltage appears

3.07A 10.0V =30.7W dc from the PSU
gave 3581.9 V pp  at 61kc/s

Amps run high, but I can go higher now I have active cooling.
lets see if I can hit 13V (full battery level)

driver cap is still around 45 V so it can handle it

3.8A at 13.0V =49.4W
gives 4.44 kV pp

That is a nice level. lets work with this.
now I need to decouple the probe, and loose capacitive coupled it and tune it again, to get the right frequency

Ok, I wished I could step up the amplitude much higher to 30kV,
but this is it for now.

I wondered about using another series resonant coil to step up the voltage further, but that makes no sense at all.

Instead I will continue with tuning the parallel resonant coil to this frequency.

after that I need to make the choke coil.

and, then start testing. I actually think I can get the voltage up higher to 30kV by the impulses of the current coil.

since the coil cap voltage field is pumped and a flow of cold current / voltage appears, I assume it will also step up the high voltage side of the coil capacitor.

fingers crossed. let's see if this can work

Measured with loose coupled probe
HV resonant frequency is 61.5kc/s

Measured the same as before 173 pf beteen HV coil, and the output+high current coil (shorted together).

I fail to understand why the resonant freqeuncy is so much lower no, but I accept it.

With the output coil shorted out, the high current coil measures 1.372uH
with the output coil open is measures 2.314 uH

Since a large load presents a low resistance (high current) I will calculate with the smallest number
at 61.1 kc/s this demands a capacity of 4.88uF

So for now I will use 5x1uF in parallel
this will make it resonant at 60.766 kc/s which is a close match.

I made a parallel capacitor of 5x 1uF 100v mkp2 wima caps, and it measures 4.78uF (@100kc/s)
perfect.

The leads are thin, so I need a solid connection for the high currents. I'll solder everything together, and add some thicker wire

I grounded the orange side of the current coil and probed the blue side, output coil was also grounded.
resonant frequency was barely changed, just slightly lowered to 60.6 kc/s

So I guess now it is ready to calculate the reactance of the choke coil and the inductance it needs turn it connected and so on

The Idea is clear.
I provide a positive dc voltage offset on the high current coil.
This is then very quicly discharged by the mosfet, which has a low duty cycle on.
The choke limits the dc current supply. It should give just enough current, to slowly charge it back up to max until the next discharge.
there is one discharge per period (with this setup, full H bridge is possible)
the 60.6kc/s has a period of 16.5 us 8% duty is then 1.32us which leaves 15.2us to charge the dc level back up.
Now... how much current do I need for that?
first of all... the voltage. I can use series batteries for voltage. so 12V 24V 36V and so on.
The quick mosfet I will use is the irf510
https://www.vishay.com/docs/91015/irf510.pdf
which has a maximum of 100V.
the coil can become resonant, with high current, but there also will be some voltage.
so lets stick to a maximum of 48V. which is 4 batteries in series.
but... I have dual power supply, so I could also use 32V. lets do that.
Now if the capacity is known, then The RC time constant is known.
Lets measure the capacity between the current coil and the high voltage coil again.
This should be lower than 175pF as it is a smaller surface area.

with the output coil grounded,
and the current coil shorted out, it measures 130pF which is still more then I expected, but lets work with this value.
the time constant is at a 63% but I want a higher voltage so I will use 4T
https://www.electronics-tutorials.ws/rc/rc_1.html
T=RC  R=C/t

t=15.2/4=3.8us
c=130pF 
so R should be 130p/3.8u= 0.34 m ohm? no that can't be right. way to low. with 32V that gives 941 amps... nope wrong

lets calculate differently.
32 volt 0.06A =533 ohm and this should be the reactance of the coil at 60.6 kc/s
gives an induction of 1.4mH ok this I can deal with.
It is just a rough estimate, but if needed I can always ajust the windings on the choke coil.
I will just have to monitor the voltage at the drain of the mosfet, and see how fast the voltage restores, and to what level.

lets just wind a torid and measure the inductance

Nice I still had a 1446 uH choke from another experiment

I have set the duty cycle to 7.7% on.
Now I need to connecte the 32 volt power supply to the choke connection on the PCB (where the large caps sit to buffer the voltage)
Then I need to measure the voltage on HV coil again, and set the phase. Shall I use positive max on negative max? I say negative.
Then the plate will discharge and the current will flow.
but... if I use positive max volts then the blabla.

this is something beyond my logic.
I will use negative max first, to tune it.

I can also measure the voltage change on the current coil without the high voltage coil.
This can give an indication of the charge slope of the dc voltage offset of the current coil.
Which probably will be different when the HV coil is at positive or negative max, due to the charge present in the field, which resists change, so I will nee more charge current.

So if the charge is fast without the hV coil, then it will charge slower with the high voltage.
lets see. enough to play with. and measure

my mind doesn't want to let go...

if the dc voltage offset of the current coil  is quickly discharged,
then a change in the high voltage field of the coil capacitor will setup a current.

this "cold" current should (quicly) charge the parallel capacitor of the current coil.
it should become positive voltage charged.

the dv dt is positive, so the radiant energy flows out of the conductor (current coil).

and the voltage of the parallel capacitor should become positive.

this effect is crucial.

now the question is, hVMax is positive or negative?

if we have a positive voltage maximum om the hv coil, then the discharge of the dc offset actualy is charging the coil capacitor.

but... there is no charge current since the choke prevents this. so the ambient medium supplies the energy.

If the high voltage coil has a negative maximum,
the discharge of the dc offset high current coil, will really discharge the coil capacitor.
then the mosfet will have to deal with large current from the discharge. not good.

hmm ok. so lets first tune to the positive maximum of the HV coil, and set the pulse to that point.
fascinating.

I have made a mistake that has been bothering me and needs to be resolved.

how can the parallel capacitor of the current coil charge by cold current, if both ends are connected to the same dc offset coil.

the current coil is switched to ground on one end. while its other end is at the choke.

so... how can that cap develop a voltage difference from the coil current?

should the choke leg of the cap, not be at the other side of the choke?

but then it would be charged from the dc offset supply, when the mosfet puts the other cap leg to ground.

although that would generate some parallel resonance, is it then still charged feom the cold current?

how does that work? hmm

the 8% duty cycle would not be enough to give the large cap a big charge.

another solution which is the best... is to wind another current coil, and connect it to the second mosfet switch which I already placed on the pcb.

winding the coil should be posible, but the output coil would loose wingings, So it would need thinner wires, to be able to give enough voltage.

the cap would then sit parallel over both coils.

connected to both the drains, while both coils connect to the same choke coil.
that os the best solution but asks for more work.

Why not use a resistor instead of a choke.
well the charging current of the dc offset must be low, so that the voltage change will be slow.
it just needs to reach maximum voltage at the resonant frequency of the coil or, half that period when 2 mosfets are used.

when the mosfet is discharging the dc offset to ground, then this is a much higher frequency quarter wave event. Thus the choke now has a much much higher resistance to flow (reactance / impedance)

for a capacitor this is inverted. when the frequency becomes higher the reactance goes down.

further more it depends on the amount of charge in the coil or capacitor.

when a capacitor is empty it has low reactance(resistance to flow) so it can handle large currents (cold or hot)

when a coil is empty (no magnetic field) it has a high reactance (resistance to flow) so only very small currents can flow.

when fully charged the reactance is again opposite. the capacitor will resist flow to charge higher and current deminishes

a coil once magnetised allows flow more so current is high and impedance/reactance resistance to flow is low.