The generation of a uniform magnetic field plays a pivotal role in various engineering applications and experimental endeavors, contributing to scientific progress and technological innovation. In the context of plasma experiments, a uniform magnetic field significantly enhances the intensity of gas discharge processes, effectively minimizes the diffusion losses of plasma particles to chamber walls, and markedly improves the overall efficiency of plasma generation. Plasma experiments have stringent requirements in terms of the three-dimensional distribution of the magnetic field and uniformity of magnetic induction intensity. To meet these demands, a dedicated magnet system must be designed to produce a magnetic induction intensity of 1000 Gs with a uniformity of ±1% within a cylindrical spatial volume of Φ45 mm×150 mm.

The Helmholtz coil is an effective device for generating uniform magnetic fields over small, localized areas. Finite element modeling was utilized to systematically compute the magnetic induction intensity distributions for coils of varying diameters. The analysis revealed that increasing the coil radius improves magnetic field uniformity while correspondingly decreasing the overall magnetic induction intensity in a nonlinear correlation. This insight allows for informed trade-offs in optimizing the design of devices to balance cost and performance. By integrating the specified design requirements alongside considerations of cost-effectiveness and manufacturing feasibility, a viable engineering scheme was proposed. The three-dimensional distribution of the magnetic field was discussed in detail for a configuration featuring four pancakes per coil and a coil radius of 250 mm. Through iterative simulations, the final magnet design achieved a uniformity of 1000×(1±0.52%) Gs, demonstrating superior precision exceeding initial expectations. The key structural components of the comprehensive system are the magnet coils, water cooling mechanisms, power supply units, and adjustable supporting brackets. Detailed specifications were provided for the power supply, ensuring stable and efficient operation, as well as for the water cooling system, which maintains thermal stability to prevent overheating and ensure long-term reliability.

To validate whether the magnetic field distribution meets the established design criteria, experiments were performed using a magnet system. Measurements were conducted using a high-precision three-axis Gauss meter, which provided accurate readings across the targeted volume. The results conclusively demonstrated that within the Φ45 mm×150 mm three-dimensional cylindrical space, a magnetic field uniformity of 1000×(1±0.66%) Gs was attained, fully complying with and even surpassing the required ±1% tolerance in practical implementation. The designed uniformity (±0.52%) was slightly superior to the experimental value (±0.66%), where three primary contributing factors were identified and analyzed in depth. Overall, the experimental data underscore the high performance of the system and confirm the successful integration of all system components.

This paper details the process for optimizing the design of a uniform magnet system based on finite element calculations. Detailed analyses of three-dimensional magnetic field distributions for various structural configurations were presented, illustrating the nuanced interplay between design parameters and performance outcomes. Experimental analyses following the completion of machining and assembly yielded results that align closely with the designed parameters. Specifically, the measurements confirm that within the prescribed three-dimensional spatial domain (Φ45 mm×150 mm), the magnetic field uniformity reaches 1000×(1±0.66%) Gs, where the distribution pattern and induction intensity fully satisfy design specifications. The magnet system has been successfully deployed in real-world applications. Future work can build upon this foundation to explore scalable designs, thereby creating a positive feedback cycle for advancing magnet design.