Here is a helpful link about air-gaps: 
http://info.ee.surrey.ac.uk/Workshop/advice/coils/gap/index.html

What isn't obvious is that an air-gap results in higher stored energy for a 
given core size (you can do the math from energy=0.5LI^2, and I=Vt/L) 
because current-squared is the dominant term, and lowering the inductance 
results in higher current (assuming voltage & time are fixed).

For a flyback converter, stored-energy is the name of the game.

Another, less-obvious, advantage to an air gap is that it reduces the 
variation of inductance due to variations in permeability of the core 
material.
This is very important for manufacturing/design quality control.

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