Explaining high voltage inverter principle (KIKUSUI COS5020 oscilloscope)
This is a positive feedback oscillator with inverted polarity current
injected in to the base. The transformer inductance and Cap C654
determine the resonant frequency.
The 18V supply current is limited if Q651 fails with a short circuit
by R657 and is filtered by L650 and C635.
The failure suggests an excessive load current condition caused C635
to fail open with excess ripple current heat loss and thermal rise
and Q651 to fail in short cct mode.


Ensure a low ESR cap is used to replace C654.

check U651 output is not low (&lt;1V) causing CR651 to conduct and suppress the feedback.  
This Op Amp uses the scaled output HV by R divider in a DC loop to regulate the HVDC out.  (TP = estimate -2kV to -3kV)
even though it appears to be a +ve feedback loop, the +ve diode clamp voltage doubler produces a -ve DC out thus making the loop negative feedback.