Eddy currents are neglegible in a ir cores because voltage isn't induced in a non-magnetic core. Magnetisim is induced in an iron core when voltage is applied to it, magnetizing the core in one direction. Additional power is needed to reverse the magnetic field, and the reversal may not be instantaneous, again resulting in distortion. Therefore, air cores have substantially reduced hystereses distortion due to the fact that they have no magnetic core. It should be noted that hystereses becomes greater at higher frequencies since the frequency changes much more rapidly , up to 20,000 times per second.
Induction becomes less as more power is applied.
The reason for this is when all the magnetic lines of induction become full, or saturated, only a small additional amount of induction can be produced which leads to distortion. Ir on cores often become saturated 2 or 3 times as fast as air core inductors. It seems that with all these reasons not to use iron cores that only air cores should be used. The main reason to use iron cores is cost. Iron cores use a smaller diameter wire and about 10 times less wire than the air core counterparts.