I didn't want to give up on this project, so I continued the research and found various Tesla coils I can buy on eBay.

The first was NPN transitor based and made little plasma discharge.

but the second one was just what I needed. It has a nice two inch plasma flame that I wanted.After careful examination I found that this Tesla coil had the same schematic like the one I saw on 'Youtube Plasma Candle' but with different frequency and different MOSFET. After being extremely optimistic I found out that this device didn't give me much insight. Although I know which MOSFET is used (IRFP250N) and coil values for the device, connecting scope to this device actually paralyzed it.

Although it was functional once scope disconnected, I had no idea how it worked in real time. Plus my scope at the time 'Hantek BE6022' made strange reading, that when I started to suspect that my problem was not in devices but my tools!