Design of a four-leaf clover-like heater for atomic comagnetometers via inverse topology optimization for high-uniformity magnetic fields

Traditional forward-designed heaters introduce interference magnetic fields under complex boundary constraints, which severely limit the sensitivity of Spin-Exchange Relaxation-Free (SERF) atomic comagnetometers. To address this, we establish an Inverse Boundary Element Method (IBEM) model and propose a novel inverse topology optimization method to design a four-leaf clover-like heater generating a highly uniform magnetic field. By discretizing arbitrary heating surfaces into triangular meshes, the method incorporates interlayer current ratios, regularization weights, and penalty factors into the inversion model, realizing an adaptive mapping from magnetic field requirements to source topology. To overcome matrix ill-posedness and local optima in the high-dimensional coupled optimization of current ratio-path topology, an adaptive collaborative particle swarm optimization (ACPSO) strategy integrating Tikhonov regularization and fitness sensitivity factors is developed. This strategy led to the successful generation and experimental validation of a highly magnetically symmetric double-layer four-leaf clover-like heater topology. Compared to traditional saddle coils, the newly designed heater reduces magnetic flow coefficients in the x, y, and z axes by 82.2%, 54.1%, and 60.5%, respectively, improving target-region magnetic uniformity by 72.4%. In system applications, this solution reduces Allan deviation by 29.2% and improves angular-rate sensitivity by 53.9%, while increasing the heating rate by approximately 30%. This work provides a novel theoretical and engineering framework for the synergistic thermal-magnetic optimization of high-performance quantum sensors under complex boundary conditions.