Little mistake here, I was talking about R2, R1 is set to 1k.
Anyway, since the beginning as my resonnant frequency was pretty low (220kHz) I didn't put a capacitor on the top of my tesla coil. But I tried to add one "just too see" and... it works much MUCH better. I think the even lower resonnant frequency makes the phase between the current transformer and the driver circuit even lower.
Also I need to add a DC blocking capacitor to avoid excess heating from my IGBTs. I apparently need a MKP capacitor that would act as a dead short at the resonnant frequency. I found the one in the picture. Will this one do the trick ?

About the time the signal amplitude ramps up faster than it ramps down, I have no idea as well, I'm still using a 4069 for now, I don't know if it can explain this.
Anyway, if I replace R2 by a potentiometer, maybe I can adjust the phase shift at high power to get optimal results, right ? and them replace it with normal resistors, I think it won't survive for long. Or should I keep R2=1k and change the capacitor value ?

I tried to use a feedback transformer. I only did about 32 turns on a about 800 Al core because the wire I was using is too short. Anyway, it somehow works, but it's not consistent, again. If I inject a tone signal on the enable pin of the drivers the sound coming from the top of the tesla is quite low and full of noise (lot of clipping sound), seems like the transformer keeps loosing the signal. And if I bring a piece of metal on the top of the tesla to trigger an electric arc the tesla will stop working as soon as the electric arc apprears.
However it works fine with a 555 instead of the antenna (very loud and clear buzzing sound, once it's tuned correctly).
By removing R1 from your schematic it's a little bit better.
I also tried inverting the tesla coil primary wires.
I tried to make 2 or 3 turns at the primary of the feedback transformer, but it won't change anything.
Tried with both 4069 and 74hc14.

I found some BYW80-150, BYW81PT-200 and BXT08PT-400 (don't know if it's PI or PT). The last one seems to be able to hold 400V reverse voltage and 8A of current. But I don't know how fast should my freewheeling diodes have to be.
I'll try more experimentations with 74HC14 chip.

i read the datasheet again and indeed there is something weird  . Anyway, I'll try to add those capacitors ant try to seek for any parasitic oscillations.
Hope this will fix all my problems  .
I have another little problem, concerning the feedback antenna. Well, when I use a 74hc14 hex inverter with Schmitt-trigger inputs, it doesn't work. The tesla coil won't work at all. I tried different cables for the antenna, no luck. But... with an old 4069 it actually works, and pretty good, but the antenna has to be close to the tesla coil, or it will stop working.
Or is there a better way to make a consistant working antenna than an inverter chip ?

Oh, first, thanks you soo much for helping me everybody  .
Then, according to the GDT troubleshoot web site i'm in the "Massively overdamped gate drive waveform" case. Before using 47 Ohm resistors I tried with 10 Ohm resistors and I got something similar to "The perfect gate drive waveform!" with a very little overshoot, but with a even lower peak voltage and my drivers where heating even more.
The core i'm using has an Al of about 4700. I might have some ferrite core laying around, the anti parasitic ones (grey, looks like carbon). Should I use one of them ?
Yes, I'm using quite long cables to connect my IGBTs to my transformer.
What do you mean by "not coated"  GDT ? The leakage inductance is quite low (about 0.8 µH, I shorted all the secondaries and plugged the primary in a (quite accurate) RLC meter).
So for my circuit I should try to make all my connections as short as possible ?
Oh, and I'm not using any DC Blocking Capacitor in serie with my tesla coil. I'll add one later.

Ok, thanks you for all those information. I'm using 47 Ohm gate resistors, but discharge time is way too high (and charge time too). But if I lower them to, let say, 10-15 Ohm like everybody does, will my drivers heat even more ?
And why full bridge SSTC shematics aren't that commmon ? Primary voltage amplitude is twice as high than with a half bridge right ? Or maybe it's too hard to drive, and lead to problems like mines.

Hello,
I'm creating my first SSTC for some school project. However, I have some troubles :
I want to use a full H-bridge. I got some IXGH40N60A IGBTs.
I also got some UCC27321 and UCC27322 to drive them (isn't that the most used driver ?)
For the tests I use a 555 timer that creates a 220kHz square signal with 50% duty cycle (that's about the resonant frequency of my tesla coil), that will be replaced by an antenna later. The 555 timer is powered by a 7805 regulator, and the drivers are powered by a 7812 regulator, pluged on a variable power supply.
Everything is plugged like this schematic found on instructables : https://www.instructables.com/id/Building-a-solid-state-tesla-coil/
Except i'm not using a 555 to modulate my tesla coil, I plug the pin 3 of my drivers to +5V (for now).
When I scope between the 2 outputs of my drivers I got a nice square wave signal, going from +12V to -12V, 50% duty cycle, at 220kHz, so everything is OK, working fine for now.
Time to make a gate driving tranformer. 1 primary coil for 4 secondary coils. ratio 1:1.
My transformer core is kinda big, but it has an Al=4700 approximately.
When I plug the primary of my transformer to the output of my drivers (with a 100nF capacitor in serie, like the schematic) and scope one of the secondary, I still have my nice square wave signal, from +12V to -12V. But when I plug all my IGBTs... the signal voltage at the primary of my transformer drops from +12V/-12V to barely +7V/-7V as you can see on the first picture, and my drivers starts heating (there is some ringing as well, but it's due to my oscilloscope, didn't had them with a numeric one with a different probe).
I'm using 47 ohm gate resistors. On the 2nd picture i'm probing Vge of my IGBTs... again, barely +7V/-7V "square" wave, probably because of too high gate resistors value.
I tried to reduce the amount of turns in my transformer, with no luck.
What should I do ? It will end up killing my drivers, they are heating quite a bit.
BUT... the tesla coil actually works, I can replace the 555 by an antenna, I can get some nice electric arcs (also works with the 555 timer but it's not tuned correctly). But, why are my UCC27321/UCC27322 heating that much ? Why is the voltage droping that much ? Can those drivers handle a full H-bridge ?