Looks to me like you're using the scope just fine The only thing that's not clear to me is the amplitude of the pulses. I see that it's set for 5V/div but the graticule (division lines) isn't visible. Can you tell if the pulse amplitude is about 5 volts? I'm thinking it probably is but would like to be sure.
The frequency looks okay but the duty cycle looks wrong: too much on time, which would tend to make things get hot. I'm going to change my mind here and blame the inductor regardless of what the LCR tester said. It looks like the Arduino is trying hard to pull up the high voltage, by applying max duty cycle to the MOSFET gate, but the voltage isn't coming up.
Hopefully Ian will look at this thread today and let us know if he thinks we are on the right track. It is, after all, his circuit,
Look into it later when the dust is clearing off the crater.
my scope is probably a museum piece
As I also own an analog scope, which is probably even older and was even less usefull now.
I will try to find an inductor with 150uH to replace it.
Do you know what specs I need, because there are so many different sorts of them.
I have found an 150uH inductor, I could not find the same model for quick delivery, so I don't know if this one should also work. See attached pictures.
I have tested it with the new inductor and a new mosfet. The bulbs go on and display the numbers, but after about 20 seconds, the mosfet begins to smoke, and it will die. It has also burned 2 inductors and killed an arduino.
I have tried 640,740 and 840 mosfets.
The frequency from the arduino was the same as last time. The 170V pin was about 173Volt.