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A Timepix3 detector with a 300<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo> </mo><mi mathvariant="sans-serif">μ</mi><mi mathvariant="normal">m</mi></mrow></semantics></math></inline-formula> silicon sensor has been studied as a novel radiation monitor for the mixed radiation field at the Large Hadron Collider at CERN. This work describes a test campaign carried out at Centro Nacional de Aceleradores with quasi-mono energetic protons (alphas) from 0.6 (1) to 5 (5.6) MeV, where orthogonal irradiations are used to obtain an energy calibration, and a low-energy angular scan to estimate the front dead layer thickness of the sensor. The detector is operated in hole collection mode and at a partial bias of 250<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo> </mo><mi mathvariant="sans-serif">μ</mi><mi mathvariant="normal">m</mi></mrow></semantics></math></inline-formula> at 50 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="normal">V</mi></semantics></math></inline-formula>, which increases the charge sharing among pixels to mitigate the signal saturation at high energy depositions. The data, supported by FLUKA Monte Carlo simulations of energy losses in the sensor, show that the Timepix3 monitor operates in a linear regime up to energy depositions of around 600 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="normal">k</mi></semantics></math></inline-formula><inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi mathvariant="normal">e</mi><mspace width="-0.21251pt"></mspace><mi mathvariant="normal">V</mi></mrow></semantics></math></inline-formula> per pixel and 2 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="normal">M</mi></semantics></math></inline-formula><inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi mathvariant="normal">e</mi><mspace width="-0.21251pt"></mspace><mi mathvariant="normal">V</mi></mrow></semantics></math></inline-formula> per cluster. As a result, the detector has been found to be suitable for measuring charged particle fluxes in the LHC mixed radiation field within the linear calibration regime, with the partial exception of inelastic nuclear reaction hits (mostly from neutrons).