Design and performance of a compact triplet quadrupole focusing system for 90 kV EB-PBF micro-beams

A compact triplet quadrupole focusing system was investigated for the micro-beam melting mode of a 90 kV, 10 kW electron beam powder bed fusion column. To satisfy the long working-distance and limited-space constraints, the quadrupole magnets were designed using pole-profile shimming, magnetic shielding, and end chamfering. Two-dimensional pole shimming reduced the dodecapole harmonic component, while three-dimensional shielding and chamfering suppressed fringe-field overlap and controlled integrated harmonic errors within the compact triplet layout. A CST–Python co-simulation workflow was then established to tune the three excitation currents using three-dimensional magnetic fields and space-charge particle tracking. Baseline optimizer screening showed that particle swarm optimization provided the most suitable starting region, and a time-varying PSO-based refined search further improved the focusing performance. The optimized excitation currents compressed the transverse RMS beam radii to 97.0 μm and 96.9 μm at the target plane. The corresponding equivalent FWHM diameter, R50, R90, and peak power density were 153.1 μm, 131.1 μm, 201.6 μm, and 4.93 kW·mm-2, respectively. Current-perturbation analysis showed that the maximum focusing deviation remained below 0.6% under ±100 ppm ripple. Prototype magnetic-field measurements further showed that, after current calibration, the relative deviations in both the central gradient and effective magnetic length were below 2% for all three magnets in the assembled triplet. These results demonstrate the feasibility of compact quadrupole-based micro-beam focusing for high-voltage EB-PBF applications.