In an experiment we need 2 tesla (T) field in the interaction regime. We have a permanent magnet which has magnetic field ~0.5 T at its surface. The interaction region is very close to the surface of the magnet. As per intuition and as described in several places the magnetic field can be focused if we place a magnetic material above the permanent magnet. I have made a setup like this figure
Here the diameter of the permanent magnet is 25 mm. The bottom of the mild steel core is 25 mm and top is 12 mm. The area is decreased by factor of ~4 hence the field should increase to 2 T at the exit, but i could not get the field more than 0.2 T at the top. The geometry works perfectly for low magnetic field strengths but not here.
please help in solving the problem, should I use some specific material or some other geometry.