The Martian Moons Exploration (MMX) spacecraft is a JAXA mission to Mars and its moons Phobos and Deimos. MMX will carry the Circum-Martian Dust Monitor (CMDM) which is a newly developed light-weight ($mathrm{650,g}$) large area ($mathrm{1,m^2}$) dust impact detector. Cometary meteoroid streams (also referred to as trails) exist along the orbits of comets, forming fine structures of the interplanetary dust cloud. The streams consist predominantly of the largest cometary particles (with sizes of approximately $mathrm{100,mu m}$ to 1~cm) which are ejected at low speeds and remain very close to the comet orbit for several revolutions around the Sun. The Interplanetary Meteoroid Environment for eXploration (IMEX) dust streams in space model is a new and recently published universal model for cometary meteoroid streams in the inner Solar System. We use IMEX to study the detection conditions of cometary dust stream particles with CMDM during the MMX mission in the time period 2024 to 2028. The model predicts traverses of 12 cometary meteoroid streams with fluxes of $mathrm{100,mu m}$ and bigger particles of at least $mathrm{10^{-3},m^{-2},day^{-1}}$ during a total time period of approximately 90~days. The highest flux of $mathrm{0.15,m^{-2},day^{-1}}$ is predicted for comet 114P/Wiseman-Skiff in October 2026. With its large detection area and high sensitivity CMDM will be able to detect cometary meteoroid streams en route to Phobos. Our simulation results for the Mars orbital phase of MMX also predict the occurrence of meteor showers in the Martian atmosphere which may be observable from the Martian surface with cameras on board landers or rovers. Finally, the IMEX model can be used to study the impact hazards imposed by meteoroid impacts on to large-area spacecraft structures that will be particularly necessary for crewed deep space missions.
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