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A Halbach array is a specialized arrangement of permanent magnets designed to generate a strong, uniform magnetic field in the designated region. This unique configuration has been widely utilized in various applications, including magnetic levitation (maglev) systems, electric motors, particle accelerators, and magnetic seals. The advantages of Halbach arrays include high efficiency, reduced weight, and precise directional control of the magnetic field. Halbach arrays are commonly categorized into two configurations: linear and cylindrical. A linear Halbach array produces a concentrated magnetic field on one face and is frequently employed in maglev trains and conveyor systems to ensure stable and efficient operation. In contrast, a cylindrical Halbach array consists of magnets arranged in a ring, generating a uniform magnetic field within the cylinder while suppressing the external field. This configuration is particularly advantageous in applications such as brushless electric motors and magnetic resonance imaging (MRI) systems. Traditionally, the design of electromagnetic systems incorporating Halbach arrays relied on engineers’ expertise and intuition due to the complexity of the permanent magnet configuration. However, advancements in numerical methods, particularly topology optimization, have introduced a systematic approach to optimizing the shape and distribution of permanent magnets within a given design domain. In the context of Halbach array design, topology optimization aims to maximize the total magnetic flux within a designated region while simultaneously determining the optimal material distribution to achieve a specified design objective. This approach enhances the performance and efficiency of Halbach arrays, providing a more precise and automated framework for their development. In this paper, we propose a Cardinal Basis Function (CBF)-based level-set method for designing a circular Halbach array capable of generating a uniform magnetic field within a designated region. The CBF-based level-set method offers significant computational advantages by reducing the computational cost and accelerating the convergence process. This approach enhances the efficiency of the optimization process, making it a promising technique for the systematic design of Halbach arrays. 

High Voltage Direct Current (HVDC) technology is a cornerstone of efficient Offshore Wind Farm (OWF) power transmission. This review examines the integration of HVDC technology in OWFs, considering collection and transmission aspects. The analysis is structured around four key dimensions: economic considerations, connection topologies, converter designs, and technical modeling. It begins with an in-depth economic analysis, evaluating cost-effectiveness, reliability, and market dynamics, focusing on investment, operational costs, and lifecycle expenses. Building on this foundation, the review explores various collection and transmission architectures, highlighting their technical and economical trade-offs, and evaluates power converter designs for efficiency, reliability, and offshore adaptability. Finally, advanced modeling and simulation techniques are reviewed to optimize system performance, enhance reliability, and balance computational efficiency. Throughout each of the four sections, economic and technical constraints are considered together. This helps to improve understanding of how systems can be designed in a way that meets the constraints of both fields and to enhance feasibility on both dimensions. These insights provide a holistic framework for sustainable and economically viable Offshore Wind Energy (OWE) integration.