Q2 is turned on through J22.
C4 discharges through Q2 and D4, Q1 sees between 0V and -0.7V at its base.
L1 sees 3V and its current increases linearly, later it may even saturate and its current jump to the sky.
When L1 current is too high for Q2 to sink, Q2 collector voltage starts to increase.
C4 charges up; the charging current can't flow through D4 so it flows through Q1.
Q1 shuts down Q2, Q2 collector voltage raises even faster, Q1 is turned on harder.
L1 dumps its current through D5 into C5, a high voltage is developed.
C4 negative pole is now at several volts, R2 slowly pulls current through C4 and charges it up, Q1 is kept active.
L1 energy is discharged, voltage drops down, C4 drops down and turns off Q1.
The cycle restarts.