NUCLEATION OF SUPERCONDUCTING VORTICES BY EXCITING ACOUSTIC STANDING WAVES IN A TYPE - II SUPERCONDUCTOR

Abstract

Superconductivity nucleation phenomenon in superconductors under an applied magnetic field close to the upper critical field HC3 has been studied by many authors. Physicists Saint-James and De Gennes were the first to study the surface nucleation phenomenon for a semi-infinite super-conductor occupying the half space and placed in an applied magnetic field which is parallel to the surface of the superconductor. When the applied magnetic field is spatially homogeneous and close to Hc3, a superconducting layer or sheath nucleates on a portion of the surface at which the applied field is tangential to the surface. In the case of non-homogeneous applied magnetic fields, interior nucleation may occur first when the applied field is decreased below the upper critical field. The research is interested in the rotational velocity of a magnitude that would generate a fictitious magnetic field that exceeds Hc1 (the upper limit of the magnetic field for type – I superconductors). The magnitude of Hcl is around 0.2 T. This requires that the angular velocity, ω be around 109 s-1 and it is not possible to experimentally attain such a high value for a mechanical rotation. However, such local rotations could be generated in a superconductor by high frequency ultrasound and we could study the possibility of the nucleation of a vortex by sound. A superconducting cylinder rotated at an angular velocity of ω about its symmetry axis develops a magnetic moment 𝐌. It is this possibility of the nucleation of a vortex by sound that has been theoretically studied in this thesis. For a vortex to enter a superconductor, the Gibb’s free energy of the system must be lowered. Calculations that showed how sound enters the problem were done and equations connecting the generated magnetic fields Bs, rotating cylinder thickness d, rotational angular velocity Ω, ultrasound angular velocity ω, amplitude Uo and wavelength λ, were derived. Calculations and analysis revealed the following major results; the rotating cylinder thickness d and the ultrasound wavelength λ are connected by the equation, d = 0.5 λ; to achieve high rotational angular velocities, Ω desired for the superconducting cylinder, its thickness d must be kept very small; the generated magnetic field and rotational angular velocity of the superconducting cylinders are connected by the equation, Bs = 6.82 x 10-3 Ω. These results imply that it is possible to generate values of fictitious magnetic fields Bs, of the order 103 T that exceed Hc1