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Casimir energy and force induced by an impenetrable flux tube of finite radius

A perfectly reflecting (Dirichlet) boundary condition at the edge of an impenetrable magnetic-flux-carrying tube of nonzero transverse size is imposed on the charged massive scalar matter field which is quantized outside the tube. We show that the vacuum polarization effects outside the tube give rise to a macroscopic force acting at the increase of the tube radius (if the magnetic flux is held steady). The Casimir energy and force are periodic in the value of the magnetic flux, being independent of the coupling to the space-time curvature scalar. We conclude that a topological defect of the vortex type can polarize the vacuum of only those quantum fields that have masses which are much less than a scale of the spontaneous symmetry breaking.