In this study, the conventional simulations on particle beam extraction was performed using a plasma-based or particle-in-cell method. Subsequently, its validity was verified through comparisons with the conventional simulation results using the finite element method. A three-dimensional finite element method was employed as a tool to simulate the motion of charged particles that are constrained by a specific geometric structure and subjected to various specified forces. This study investigated the features of carbon-ion beam extraction and the effects of the particle beam conditions on the three-electrode extraction system of a gaseous ion source by simulating the ion beam properties using the COMSOL Multiphysics software package. The AC/DC module in this software package was used to simulate the electrostatic field, whereas the Particle Tracing Module in the package was used to extract the ion beam. This package was used to analyze the beam trajectories and their dependence on particle properties under electrostatic boundary conditions, using bidirectionally coupled particle tracing. Consequently, Twiss parameters and root mean square (rms) beam emittance of the particle beam were calculated for the particle positions and divergence in their phase space. The feasibility of the particle beam extraction performed using this approach was confirmed through comparisons with the simulation results obtained using other ion source extraction programs. Furthermore, the effectiveness of a more user-friendly multiphysics based simulation was evaluated based on the rms beam emittance.
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