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In this paper, we consider a charged massive fermionic quantum field in theidealized cosmic string spacetime and in the presence of a magnetic fieldconfined in a cylindrical tube of finite radius. Three distinct configurationsfor the magnetic fields are taken into account: (i) a cylindrical shell ofradius $a$, (ii) a magnetic field proportional to $1/r$ and (iii) a constantmagnetic field. In these three cases, the axis of the infinitely long tube ofradius $a$ coincides with the cosmic string. Our main objectives in this paperare to analyze the fermionic condensat (FC) e and the vacuum expectation value(VEV) of the fermionic energy-momentum tensor. In order to do that, weexplicitly construct the complete set of normalized wave-functions for eachconfiguration of magnetic field. We show that in the region outside the tube,the FC and the VEV of the energy-momentum tensor are decomposed into two parts:the first ones correspond to the zero-thickness magnetic flux contributions,and the seconds are induced by the non-trivial structure of the magnetic field,named core-induced contributions. The latter present specific forms dependingon the magnetic field configuration considered. We also show that the VEV ofthe energy-momentum tensor is diagonal, obeys the conservation condition andits trace is expressed in terms of the fermionic condensate. The zero-thicknesscontributions to the FC and VEV of the energy-momentum tensor, depend only onthe fractional part of the ration of the magnetic flux inside the tube by thequantum one. As to the core-induced contributions they depend on the totalmagnetic flux inside the tube, and consequently, in general, are not a periodicfunction of the magnetic flux.

Fermionic vacuum polarization by a magnetic tube in the cosmic string spacetime