Abstract
Sub-atomic particles impinging on metallic surfaces is a commonly encountered load case in nuclear engineering, medical physics, and particle research. Microbeam X-ray therapy is a promising cancer therapy that can be applied using high-power, spatially fractionated X-rays generated by an electron beam hitting a metallic target. For a clinical microbeam therapy X-ray source, an impinging electron beam of a power of 1 MW onto a rectangular focal spot of 0.05 × 20 mm size is needed, with a penetration depth of 0.1 mm. This corresponds to a heat flux input of 1 TW/m2 on the surface, an order of magnitude higher than that encountered in state-of-the-art nuclear fusion reactors and conventional imaging X-ray sources. Thus, it is essential to simulate and validate the thermo-mechanical capability of the metallic target’s material to withstand this extreme heat flux. This paper introduces a simplified mathematical model for evaluating temperature during the impact of such an electron beam on a rotating metallic target with a tungsten focal track. The model dissects the maximum temperature requirement into local and global temperatures at the focal spot and focal track, respectively. Numerical simulations based on surface heat flux loading and volumetric heat loading are also presented in this work. Further, the local temperature around the focal spot is modeled in a separate numerical model of a much lower scale with a minimum mesh element size of 10 μm and volumetric heat loading. This differs from the state-of-the-art numerical simulations, in which electron beam impinging on metals is modeled as purely surface heat flux loads. A metal target design of Titanium-Zirconium-Molybdenum (TZM) alloy structure and tungsten focal track is presented and is shown to withstand the thermal requirement of not exceeding the melting point of tungsten and TZM alloy. The simulation temperature results agree with the mathematical estimates within an error of 10 %. Results of various discretization levels are presented, and the spatial and temporal grid independence of the numerical simulations are validated. Further, a novel validation strategy is proposed to address the lack of available test facilities to replicate this extreme heat flux load case. The critical parameters describing the high heat flux loading are identified as temperature, thermal strain, thermal stress, and strain rate. Scaled-down test specifications are determined to use a test facility of power less than 100 kW and recreate the critical parameters. With the numerical simulation model validated using the scaled-down test, it is proposed to verify the material’s capability to withstand the concentrated 1 MW heat load numerically without requiring a 1 MW test facility.
