“…Since β > α holds for any value of the geometrical and material characteristics involved, B 0 max (B 0 ) < B m max (B 0 ) ensues throughout, which confirms that the predicted enhancement of the critical field, disclosed by equation (26), like the concomitant attenuation of the external field, revealed by equation (30), cannot be exclusively ascribed to the shielding effect of the magnetic sheath, as argued in some previous attempts 21,41,42,43 . To appraise the relevance of the above results, we take a MgB 2 filament with radius R = 5.0 · 10 −4 m covered by a Fe sheath of thickness d = 2.5 · 10 −4 m and relative permeability µ = 50 (Refs.…”