Hi Kanofski,

Although aluminium is classified as paramagnetic and it has a magnetic permeability of 1.000022 and this should increase your coil inductance a very little, the eddy current effect of its good electrical conductivity greatly 'overwhelms' this effect (the more alu volume you fill up the coil's inside volume with, the less inductance you get).  Try to insert a certain sized Alu kitchen foil and see the change, it will be less dramatic (material thickness strongly influences eddy currents),  for instance if you glue a piece of paper to fully cover one side of the Alu foil (electrical insulation) and then you roll up this paper-Alu layer into a cylinder shape (so that the paper layer should be included between two adjacent Alu layer) and insert it into the coil, then you might see a very small increase in inductance as the Alu's tiny bit higher than 1 permeability would forecast.

(In the 1960s and 70s car radios were designed by moving Alu cylindrical slugs for tuning the antenna and oscillator coils in the FM band to select an FM radio station.)

If you place very closely an electrically closed metal ring to one of the ends or onto your air core coil, then depending on the material of the ring whether it is para or diamagnetic, you could also see a change in the inductance.

In case of a solid piece of iron, the same eddy current effect would overrule the increase in inductance, introducing a big loss in magnetization in the Alu core case, too.  This is why soft iron cores in transformers are laminated.

rgds,  Gyula