Technical note: Dose voxel resolution determination for Monte Carlo electron beam simulation in thin targets

Background: Monte Carlo particle simulation has become the primary tool for designing low-energy miniature x-ray tubes due to the difficulties of physically prototyping these devices and characterizing their radiation fields. Accurate simulation of electronic interactions within their targets is necessary for modeling both photon production and heat transfer. Voxel-averaging can conceal hot spots in the target heat deposition profile that can threaten the integrity of the tube. Purpose: This research seeks a computationally-efficient method of estimating voxel-averaging error in energy deposition simulations of electron beams penetrating thin targets to inform the appropriate scoring resolution for a desired accuracy level. Methods: An analytical model to estimate voxel-averaging along the target depth was developed and compared to results from Geant4 via its wrapper, TOPAS. A 200 keV planar electron beam was simulated to impinge tungsten targets of thicknesses between 1.5- and 12.5- (Figure presented.). For each target, the model was used to calculate the energy deposition ratio between voxels of varying sizes centered on the longitudinal midpoint of the target. Model-calculated ratios were compared to simulation outputs to gauge the model's accuracy. Then, the model was used to approximate the error between the point value of electron energy deposition and a voxel-based measurement. Results: The model underestimates error to within 5% for targets less than 7.5- (Figure presented.) in thickness with increasing error for greater thicknesses. For the 1.5- (Figure presented.) target, calculations of the point-vs.-voxel energy deposition show an 11% averaging effect between the midpoint and a 1.5- (Figure presented.) voxel. Energy deposition profiles along the target depth were also calculated in the Monte Carlo for reference. Conclusion: A simple analytical model was developed with reasonable accuracy to guide Monte Carlo users in estimating the appropriate depth-voxel size for thin-target x-ray tube simulations. This methodology can be adapted for other radiological contexts to increase robustness in point-value estimations.