A capture–compression limit for passive intakes of atmosphere-breathing electric propulsion

Preprint of a manuscript submitted to Acta Astronautica. Code and data: https://doi.org/10.5281/zenodo.24025948 An atmosphere-breathing electric thruster depends on a passive intake that collects the free-molecular flow ahead of the spacecraft and raises its density before ionisation. Intake designs are compared through their collection efficiency and compression ratio, but there is no upper bound against which a design can be rated. We derive such a bound. For free-molecular flow and walls described by any mixture of specular and diffuse reflection, a reciprocity identity reduces the compression gain to the ratio of two transmission probabilities. Maximising that ratio at fixed capture is a Neyman–Pearson problem whose solution is an ideal angular filter, so that the gain cannot exceed W_f/sin²θ*, where θ* is the half-angle of the cone that contains a fraction W_f of the incoming flux. Combined with the particle balance of a thermalised collection chamber, the bound limits the chamber density ratio to about 2√π S³ √(T∞/T_w), with S the orbital speed ratio, and gives an explicit operating limit when the thruster draws gas. Test-particle Monte Carlo results for 222 intake configurations are consistent with the bound, and an independent DSMC code reproduces the underlying transmission probabilities for eight test configurations. For a specular three-dimensional compound parabolic concentrator, simulated point estimates of the gain were within 3% of the bound for acceptance angles up to 2/S and within 7% across the tested cases; it loses half its gain when the flow is misaligned by about its acceptance angle. Published intakes, compared on the same definition of compression, operate at about 1–5% of the limit. With Maxwell walls the gap can be closed only if most wall collisions are specular: at a diffuse fraction of 0.1 a concentrator with an acceptance angle of 1.5/S keeps about 62% of the limit. Walls whose scattering depends on molecular speed fall outside the theorem: in the cases tested, Cercignani–Lampis–Lord walls whose tangential accommodation is much weaker than their normal accommodation exceeded the limit by up to a factor of 2.3.