Efficient Charged Cluster Beam Transport Using COMSOL Multiphysics

A. Khatibi1, M. Van Spronsen1, G. Held1
1Diamond Light Source Ltd, Harwell Science and Innovation Campus, Oxfordshire, United Kingdom
Published in 2026

Efficient transport and confinement of charged nanoclusters are essential for localized deposition in size-selected cluster beam systems. In magnetron sputtering and gas aggregation sources, both neutral and charged clusters are generated with broad size distributions. A quadrupole mass filter (QMF) is therefore used to select charged clusters, while neutral clusters continue travelling approximately along the central chamber axis. Electrostatic beam steering is required to direct the charged size-selected cluster beam toward the sample holder. During commissioning of the cluster source at beamline B07 at Diamond Light Source, extremely low cluster current was measured at the sample holder when using the original four-plate electrostatic deflector geometry. Although retarding field analysis confirmed the presence of charged clusters, deposition current measurements indicated poor transport efficiency to the sample region, suggesting substantial beam spreading within the chamber. To investigate this behaviour, electrostatic field calculations and charged particle tracing simulations were performed using COMSOL Multiphysics®. A three-dimensional geometry of the our deposition chamber was developed including the QMF outlet, electrostatic grid, mesh assembly, chamber walls, and sample holder. The Electrostatics and Charged Particle Tracing interfaces were used to calculate electric field distributions and simulate charged cluster trajectories under experimentally relevant conditions. The simulations revealed that the original deflector geometry generated strong transverse electric field components, resulting in significant beam divergence and inefficient transport of charged clusters toward the sample holder. Based on these findings, a cylindrical tube deflector geometry was designed and implemented. COMSOL simulations predicted improved electrostatic confinement and beam steering due to the more symmetric field distribution generated by the cylindrical geometry. Experimental validation confirmed successful localized deposition of mass-selected Pd clusters together with significantly increased sample current at the deposition region. Further simulations demonstrated that small low-energy clusters remained highly sensitive to electrostatic perturbations and still exhibited trajectory divergence during transport. To improve confinement of low-energy clusters, an Einzel lens-inspired electrostatic focusing geometry was designed and evaluated using COMSOL simulations. This work demonstrates the importance of simulation-guided ion optical optimization for improving charged cluster transport, spatial confinement, and deposition efficiency in size-selected nanoparticle beam systems.

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