I suppose Q1 turns ON through the startup resistor 15k.But once turned ON, the L2 will get a voltage induced on it in the same polarity as L1.This can send current into the base node aiding turning ON process to be faster. But how the transistor turns OFF.??
In the Graph Wave Forms -Legend from Top to Bottom
1.Inductor current
2.Vce
3.Vbe
4.Vout at capacitor
" Current through L1 builds.", so the voltage across L2 is a constant ( V = L X DI/DT). When the current STOPs increasing, i.e. DI/DT goes negative, the voltage across L2 changes polarity and switches the transistor off.
Frank