Extending deterministic transport capabilities for very-high and ultra-high energy electron beams

Focused Very-High Energy Electron (VHEE, 50–300 MeV) and Ultra-High Energy Electron (UHEE, > 300 MeV) beams can accurately target both large and deeply seated human tumors with high sparing properties, while avoiding the spatial requirements and cost of proton and heavy ion facilities. Advanced testing phases are underway at the CLEAR facilities at CERN (Switzerland), NLCTA at Stanford (USA), and SPARC at INFN (Italy), aiming to accelerate the transition to clinical application. Currently, Monte Carlo (MC) transport is the sole paradigm supporting preclinical trials and imminent clinical deployment. In this paper, we propose an alternative: the first extension of the nuclear-reactor deterministic chain Njoy-Dragon for VHEE and UHEE applications. We have extended the Boltzmann-Fokker-Planck (BFP) multigroup formalism and validated it using standard radio-oncology benchmarks, complex assemblies with a wide range of atomic numbers, and comprehensive irradiation of the entire periodic table. We report that \(99\%\) $99\%$ of water voxels exhibit a BFP-MC deviation below \(2\%\) $2\%$ for electron energies under \(\text{1.5 GeV}\) $\text{1.5 GeV}$ . Additionally, we demonstrate that at least \(97\%\) $97\%$ of voxels of bone, lung, adipose tissue, muscle, soft tissue, tumor, steel, and aluminum meet the same criterion between \(\text{50 MeV}\) $\text{50 MeV}$ and \(\text{1.5 GeV}\) $\text{1.5 GeV}$ . For water, the thorax, and the breast intra-operative benchmark, typical average BFP-MC deviations of \(0.3\%\) $0.3\%$ and \(0.4\%\) $0.4\%$ were observed at \(\text{300 MeV}\) $\text{300 MeV}$ and \(\text{1 GeV}\) $\text{1 GeV}$ , respectively. By irradiating the entire periodic table, we observed similar performance between lithium ( \(Z=3\) $Z=3$ ) and cerium ( \(Z=58\) $Z=58$ ). Deficiencies observed between praseodymium ( \(Z=59\) $Z=59$ ) and einsteinium ( \(Z=99\) $Z=99$ ) have been reported, analyzed, and quantified, offering critical insights for the ongoing development of the Evaluated Nuclear Data File mode in Njoy.