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High-temperature superconductors (HTSs) including HTS bulks and tapes have potential applications in linear motion drive and magnetic levitation/suspension systems generating substantial advantages over conventional ones. When an HTS linear motor is integrated with an HTS magnetic suspension subsystem, it can inherit both merits of HTS linear motion drive and HTS magnetic suspension simultaneously and can be applied into various fields, such as the maglev and electromagnetic aircraft launch systems (EMALSs). Based on different HTS aspects and arrangements, three modes of HTS linear synchronous motor (HTSLSM) integrated with HTS magnetic suspension subsystems have been proposed in this paper. To verify the modes for the design of a practical HTSLSM, the structural features of these systems are described, the magnetization characteristics to obtain HTS bulk magnets, the trapped-field attenuation characteristics of the HTS bulk magnet exposed to external traveling field, and the magnetic field distribution characteristics for different permanent-magnet guideways have been studied with experimental verification. Based on the study, a demonstration prototype of a single-sided HTSLSM integrated with HTS magnetic suspension subsystems has been developed. Its performance and thrust characteristics have been obtained by experimental measurements and compared with theoretical results. With regard to practical applications, two modes of double-sided HTSLSM integrated with HTS magnetic suspension subsystems have been designed for the maglev and EMALS, respectively, and then, the 2-D finite-element-analysis models for the HTSLSMs were built to analyze their performance characteristics. The comprehensive simulations and experimental results constitute a framework for the structural and electromagnetic design of the HTSLSM integrated with HTS magnetic suspension for practical applications.