Numerical and Analytical Study of the Magnetic Field Distribution in a Three-Solenoid System

This study investigates the magnetic fields produced by a three-solenoid system configuration using both traditional numerical solvers and fractional integral methods. We focus on the role of mesh resolution in influencing simulation accuracy, examining coils with dimensions 80 mm × 160 mm and a radius of 15.5 mm, each carrying a current of 200 A. Magnetic field behavior is analyzed along a line parallel to the central axis at a distance equal to half the solenoid’s radius. The fractional integral formulation employed provides a refined understanding of field variations, especially in off-axis regions. Comparisons with the Poisson solver highlight consistency across methods and suggest pathways for further optimization. The results support the potential of fractional approaches in advancing electromagnetic field modeling, particularly in accelerator and beamline applications.