The elementary interaction force between a dislocation loop and the flux line lattice of a type II superconductor

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Abstract
The elementary interaction force f between prismatic dislocation loop and the flux line lattice due to both first- and second-order strain field interactions is computed. A new Fourier transform method for defects radially symmetric about the flux line direction is developed and used to compute the second-order interaction as well as to check the results of the first-order interaction calculated previously by the Peach-Koehler formula. Small interstitial loops are attracted to flux line cores by the first-order interaction and repelled by the second-order interaction whereas small vacancy loops are repelled by both interactions. For both interactions, the maximum interaction force f p of a loop much smaller than the flux line spacing a 0 increases with loop diameter D approximately as D 2. For larger loops f p increases less rapidly with D, goes through a maximum at D≈a 0/2 and rapidly decreases to zero at D≈a 0. For still larger D the sign of the interaction force is reversed (repulsive pins become attractive). A pattern of maxima and sharp minima in f p is observed as D is increased further. The minima are pinning interferences, caused by neighbouring flux lines exerting equal and opposite forces on opposite sides of the loop.