This thesis presents a novel study on Second Generation High Temperature Superconductors, which covers their electromagnetic characteristics and AC loss analysis. Lorentz Force Electrical Impedance Tomography (LFEIT) is one of the most promising hybrid diagnostic scanners with burgeoning potential for biological imaging, particularly in the detection of cancer and internal haemorrhages. The author tried a novel combination of superconducting magnets together with the LFEIT system. The reason is that superconducting magnets can generate a magnetic field with high intensity and homogeneity, which could significantly enhance the electrical signal induced from a sample, thus improving the Signal-to-Noise Ratio (SNR). The author developed four magnet designs for the LEFIT system using the Finite Element Method (FEM) package, COMSOL Multiphysics, and found that a Superconducting Halbach Array magnet can achieve all the requirements (magnetic field properties, geometry, portability, etc.) for the LFEIT system. The optimization study of the superconducting Halbach Array magnet has been carried out on the FEM platform of COMSOL Multiphysics, with 2D models using H-formulation based on B-dependent critical current density and bulk approximation. Optimization focused on the location of the coils, as well as the geometry and number of coils on the premise of maintaining the total amount of superconducting material used in the design. The optimization results showed that the Halbach Array configuration based superconducting magnet is able to generate a magnetic field with an intensity of over 1 Tesla and improved homogeneity. In order to efficiently predict the optimization performance, mathematical formulas were developed for these optimization parameters to determine the intensity and homogeneity of the magnetic field. The mathematical model for the LFEIT system was built based on the theory of the magneto-acousto-electric effect. Then the basic imaging of the electrical signal was developed using Matlab. The magnetic field properties of the magnet design were imported into the LFEIT model. The LFEIT model simulated two samples located in three different magnetic fields with varying magnetic strength and homogeneity. Even if there are no actual alternating currents involved in the DC superconducting magnets mentioned above, they have power dissipation during normal operation (e.g. magnet ramping) and under different background fields. This problem generally goes under the category of “AC loss”. Therefore, the AC loss characteristics of HTS tapes and coils are still fundamentally important for HTS magnet designs, even if they are normally operating in DC conditions. This thesis starts with the AC loss study of HTS tapes. The investigation and comparison of AC losses on Surround Copper Stabilizer (SCS) Tape and Stabilizer-free (SF) Tape have been carried out, which includes AC loss measurement using the electrical method, as well as the real geometry and multi-layer HTS tape simulation using the 2D H formulation by COMSOL Multiphysics. Hysteresis AC losses in the superconducting layer, and eddy current AC losses in the copper stabilizer, silver overlayer and substrate were concerned in this investigation. The measured AC losses were compared to the AC losses from the simulation, using 3 cases of different AC frequency: 10 Hz, 100 Hz, and 1000 Hz. The frequency dependence of AC losses from Stabilizer free Tape and Copper Stabilizer Tape were compared and analysed. A comprehensive AC loss study of a circular HTS coil has been fulfilled. The AC losses from a circular double pancake coil were measured using the electrical method. A 2D axisymmetric H-formulation model using FEM package COMSOL has been established, which was able to make consistency with the real circular coil used in the experiment. To model a circular HTS coil, a 2D axisymmetric model provided better accuracy than a general 2D model, and was also more efficient than a 3D model. Three scenarios were analysed: (1) AC transport current and DC magnetic field, (2) DC transport current and AC magnetic field, (3) AC transport current and AC magnetic field. The angular dependence analysis on the coil under the magnetic field with the different orientation angle  was carried out for all three scenarios. For scenario (3), the effect of the relative phase difference ∆ between the AC current and the AC field on the total AC loss of the coil was investigated. To summarise, a current/field/angle/phase dependent AC loss (I, B, , ∆) study of circular HTS coil has been carried out, which could potentially benefit the future design and research of HTS AC systems. The AC losses of horizontally parallel HTS tapes have been investigated. The AC losses of the middle and end tape of three parallel tapes have been measured using the electrical method, and compared to those of an individual isolated tape. The effect of the interaction between tapes on AC losses has been analysed, and compared with finite element method (FEM) simulations using the 2D H formulation implemented in COMSOL Multiphysics. The electromagnetic induction around the three parallel tapes was monitored using COMSOL simulation. The electromagnetic induction and AC losses generated by a conventional three turn coil were simulated as well, and then compared to the case of three parallel tapes with the same AC transport current. The analysis demonstrated that HTS parallel tapes could be potentially used in wireless power transfer systems, which could have lower total AC losses than conventional HTS coils. By using FEM simulations, cases of increasing number of parallel tapes was considered, and the normalised ratio between the total average AC losses per tape and the AC losses of an individual single tape have been calculated for different gap distances. A new parameter is proposed, Ns, a turning point the for number of tapes, to divide Stage 1 and Stage 2 for the AC loss study of horizontally parallel tapes. For Stage 1, N < Ns, the total average losses per tape increased with the increasing number of tapes. For Stage 2, N > Ns, the total average losses per tape started to decrease with the increasing number of tapes. The analysis demonstrates that horizontally parallel HTS tapes could be potentially used in superconducting devices like HTS transformers, which could retain or even reduce the total average AC losses per tape with large numbers of parallel tapes.