Trying to understand the working principle of a weird transformer driver / oscillator

I'm trying to fix the high-voltage power supply of an old scope. The HV transformer is burnt, and I'm trying to replace it with a similar one (EPC19 core), but I'm failing.

I already know how to wind and drive this same transformer with a half-bridge, but the driving circuit in this particular scope is something I can't understand.

This is the scope's HV section schematics (I did the annotations in red, annotations in blue may be original from the schematics, or may have been made later by someone else):

The HV transformer is T1001. HV circuitry is inside the red line. T1001 has a feedback winding on the primary, and in the scope schematics, it seems to be changing TR1003 base constantly, making the thing oscillate at a given frequency.

In the original burnt transformer, 1-2 are 8 turns and 3-4 are 2 turns, both AWG 28, but they are strongly coupled: both windings are completely stacked on top of each other. There are no side turns. The bobbin has been made specially for that, the primary/feedback section is a deep slot for only one AWG 28 wire to fit. In my replacement bobbin, this is not possible without modifications. So, my first question: is this coupling critical to make this oscillator work?

I tried making a similar transformer using a core about the same size, (without the strong coupling between primary and feedback, with turns laying side by side) but the circuitry shows only marginal oscillation (2Vpp), with a DC level of 19V approximately. I was expecting something like the blue waveform, annotated on the schematics. Any ideas on what may be wrong?

Another question is: if I only make primary and feedback windings (1-2 and 3-4), should the circuit oscillate? Or oscillation depends on the secondary also? If only primary and feedback are needed, it's much easier to test (no need to wind hundreds of turns on secondary).

And the last, and most important question: How this circuit really works, and which features this transformer must have to properly work with this particular topology?

EDIT:

• The transistor gets very hot in my tests. It's seems the oscillator is constantly on, making the transistor draw heavy current.

• The original core is formed by EI ferrites. Central part is circular. Replacement core (EPC19) has no gap, formed by two E parts. Central part is kind of oval, but with quite similar section area when compared to the original.

• Close coupling may be important. You might try twisting 5 wires together and winding 2 turns of that. Use one for the FB winding and series the other four.
– user16324
Commented Jul 11, 2016 at 14:11
• This is another one of those circuits that relies on transformer core saturation to work. When the transistor first turns on, the feedback winding provides positive feedback, but when the core saturates, the feedback signal inverts, shutting off the transistor. If the B-H curve of your replacement core is not similar enough to the original, you may have trouble making it work right. Is there any way you can reuse the original core? Commented Jul 11, 2016 at 14:28
• @DaveTweed, the core broke when I dismantled the transformer, but it's fixable, at least visually speaking. It broke in 3 parts. Do you think it's magnetic properties will be preserved if I glue it back? Thanks! Commented Jul 11, 2016 at 14:43
• Yes, I would think so, as long as you can keep the glue layer as thin as possible to get a good fit between the pieces. Commented Jul 11, 2016 at 14:53
• Yes, that sounds right. It would be interesting to observe the base voltage on the transistor to see whether it ever goes into full cutoff -- i.e., how close it gets to 0.65 V. Commented Jul 11, 2016 at 15:43