Estudo experimental e numérico da força de levitação magnética em supercondutores de alta temperatura crítica
Sanchez, Elmer Saavedra
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In this research work we propose, in general, to address the issue of magnetic levitation force between a superconducting material and a permanent magnet. This is a very current and relevant mainly from a technological standpoint, as it allows, among others, the design of machines such as motors, generators and trains based on the principle of levitation. Thus, the research proposed here has been very inclusive, treating the subject of levitation not only from the experimental point of view, but also theoretical. In the experimental approach we have built, assembled and calibrated an experimental station that measures the levitation force, vertically and horizontally, of a permanent magnet on a sample of high critical temperature superconducting materials of the type YBa2Cu3O7-d. Within this scope, we also have developed the ability to prepare the samples using various types of chemical methods and routes that resulted in samples with different textures and properties, where the measurement of the levitation force also pointed out differences between them. The samples had their quality assessed by (a) magnetic characterization (through measures of AC magnetic susceptibility) and (b) structural characterization (through measures of x-rays diffraction and measurements of scanning electron microscopy). In the theoretical approach of this issue, we developed a program allowing simulating the magnetic levitation force by obtaining the relations of force between the permanent magnet and the superconducting material. In this numerical study we have considered the analytical expressions of classical electromagnetism to write the integral equation of the derivative of the current density inside the superconductor, as a function of the geometry and the settings of the applied field. Next, we used the Method of Moments to write the integral equation in its analytical formulation matrix, in which the current density at each point in time is obtained by a simple rule of integration (Euler method). Thus, were also calculated curves for superconducting magnets in the shape of a finite cylinder in which it was measured the levitation force between a permanent magnet and a superconductor, both in the finite and cylindrical geometry. Finally, we compare both results, theoretical and experimental, for sets of samples with different geometries and obtained following different preparation methods.