Electron-Photon cascades

We propose a novel mathematical framework for modelling electron-photon cascades using stochastic differential equations (SDEs) and the theory of branching processes. This approach enables us to capture the intricate, multi-dimensional, and infinite activity nature of these cascades. By building our model from first principles, we derive a comprehensive set of SDEs that describe the energetic, angular and spatial evolution of the cascade particles. Our framework extends previous ideas of Oppenheimer and Landau, modelling the average number of electrons in the system and energy disposition of the cascade. Our new perspective  gives a “probabilistic” path-wise interpretation of the cascade that will agree with the average properties.