Its interesting though, if the turns stay the same, and the required back EMF stays the same, the flux must be the same too. It just takes a massive amount of current to do it when you remove the core.
In a purely ac circuit, the flux will always be symmetrical around zero.
So the peak to peak flux will remain the same to generate the same flux linkages per turn, which is what produces the EMF.
Its all vastly different to a choke that has a large amount of dc bias in one direction.
Resonant tanks are characterized for its high efficiency. Using iron cores may increase losses on the inductor. I strongly recommend you to employ ferrite cores. Due to the high value current, saturation will occur. Gapped ferrite planar/ E cores are able to handle high currents with reduced gaps avoiding saturation.
Supposing average current value on the inductor is close to zero, inductor losses can be easily calculated using the empirical Steinmetz equation. You can check all the cores losses and contrast them.
Remember: more gap-> more reluctance-> less flux. more core material/volume-> less flux density . Excesive gaps (more than half the length of the "arm") are not recommended.