Would the electron cyclotron-maser emission mechanism affect Proxima b's ability to retain an atmosphere? In a recent arXiv preprint, Pérez-Torres et al. &quot;Monitoring the radio emission of Proxima Centauri&quot; claim the detection of radio emissions synchronised with the orbit of the planet Proxima b. They explain this as the result of electron cyclotron-maser (ECM) emissions, making the Proxima–Proxima b system a scaled-up analogue of the Jupiter–Io or Jupiter–Ganymede systems.
Would this mechanism make it more difficult for Proxima b to retain an atmosphere?
This mechanism, being actively emitting in the radio-wavelengths, is certainly negligible for the overall atmospheric energetics at Proxima b. One can conclude this by taking the band luminosities from the cited paper ($\rm 2.51\times10^{20} erg/s$, p.3, first paragraph) and compare them to the solar constant at the planets orbit, which should amount to $\rm9\times10^{23}erg/s$.
The latter is however only the thermal energy contribution given by the stellar effective temperature, there might be other significant chunks of energy contributed in the UV and X-bands.
The luminosities thus considered would be important for driving both bulk escape and jeans escape. Being negligible in the radio-range, shows that this process is unimportant for the retention of a bulk atmosphere via thermal mechanisms.
In terms of non-thermal mechanisms it's possible to imagine that there would be some resonant absorption of the ECM emission at the planetary radius, driving scattering of heavier species. Considering however the scalings of the cyclotron frequency $f=qB/{2\pi m}$, and the fact that the magnetic field is weaker at the planet compared to the emission region at the star, the scattered particles would have to be lighter than electrons. Those particles do not exist in atmospheres in significant numbers, only in particle accelerators.
Hence we can conclude that non-thermal processes driven by ECM heating will also not play a role for atmospheric escape.