Scanning electron microscopy plays a central role in modern microscopy, with electron probe microanalysis (EPMA) offering quantification of the elemental composition of solid material samples. The working principle of EPMA is the illumination of the material with an electron beam, leading to atomic ionization and the emission of characteristic x-rays. In materials commonly investigated using EPMA, electrons undergo elastic scattering on nanometer length scales, whereas characteristic x-rays propagate micrometers before absorption or scattering. For the interpretation, simulation, or inversion of measurement data, accurate and efficient computational modeling of the transport phenomena is crucial, especially when the required resolution reaches the size of the volume illuminated by the beam. Whereas Monte Carlo simulation has traditionally been applied, the transport regime also allows for moment approximations of the linear transport equations. Moment approximations offer deterministic results and flexibility to apply adjoint approaches without variance increase, a concept that is crucial for efficient forward as well as inverse modeling in EPMA. The computational core that mainly determines the computational cost is a grid-based solver for linear transport (in continuous-slowing-down approximation) for heterogeneous media with varying scattering behavior. Dynamical-low-rank approximation (DLR) has emerged as a valuable tool to cope with the high computational requirements of linear transport codes. In this talk, we discuss the application of DLR to a mixed-variational framework for linear transport using spherical harmonics tailored for simulation in EPMA. A crucial component is the incorporation of the electron beam, which drives the system through boundary conditions and is treated consistently via the variational formulation and low-rank approximation. To mimic charge conservation in electron transport, standard low-rank integration algorithms must be adapted. Numerical experiments employing classical test cases for linear transport as well as simulations in EPMA-based scenarios indicate potential for a reduction in runtime, but also that the efficient application of DLR requires careful control of the truncation error.