Chibuikem U. | Rensselaer Polytechnic Institute ## Introduction Project Elara, a student-led research group at Rensselaer Polytechnic Institute, seeks to apply maser (Microwave Amplification by Stimulated Emission of Radiation) devices to the development of space-based solar power technologies. The design incorporates giant mirrors placed in geostationary orbit to concentrate solar energy onto a transmitter. This transmitter will power a maser which transmits a beam with a frequency in the $1-12$ $\text{GHz}$ range through the atmosphere to an Earth-based array, after which it can be distributed to the grid. As they possess longer wavelengths than visible-light lasers, masers cannot be assumed to interact with the environment the same way a visible light laser would. A comprehensive understanding of the operational parameters of free-electron masers, particularly their susceptibility to atmospheric attenuation, noise, and output coherence, is essential to ensure that their qualities are pertinent to this application. This review synthesizes the literature on these properties and how each may affect the efficacy of Project Elara's design. ## Atmospheric Attenuation A primary factor distinguishing masers from lasers is their sensitivity to the Earth's atmosphere. Masers typically operate within the microwave and radio regions of the electromagnetic spectrum, where rotational transitions of atmospheric gases, primarily water vapor ($\ce{H2O}$) and oxygen ($\ce{O2}$), cause significant resonant absorption. This absorption is dependent on the beam frequency, with the first three absorption bands centered at frequencies of $22.2$ $\text{GHz}$ ($\ce{H2O}$), $60$ $\text{GHz}$ ($\ce{O2}$), and $188.8$ $\text{GHz}$ ($\ce{O2}$) at $1$ $\text{atm}$, $20$°$\text{C}$, and a water vapor density of $7.5$ $\mathrm{g/m^3}$ (Ippolito 1981. pp. 6-7)[^1]. Project Elara plans to operate its masers in the $1-12$ $\text{GHz}$ range to minimize the attenuation coefficients of oxygen and water vapor, and thus normal weather conditions present little issue. The effects of inclement weather, including rain and dust storms, on the attenuation of the microwave beam must also be considered. Ippolito (1981)[^1] analyses attenuation in clouds, fog, and rain with varying water droplet sizes at $20$ °$\text{C}$. In rain, when droplet size is considered, attenuation is lowest in the $1-2$ $\text{GHz}$ range, with lower rain rates of $2.5$ $\text{mm/hr}$ leading to low attenuation until $9$ $\text{GHz}$ instead. (Ippolito 1981. p. 14)[^1]. At all cloud and fog densities examined, attenuation is determined to be lowest in the $1-2$ $\text{GHz}$ range at $0$°$\text{C}$, after which attenuation is directly proportional to frequency over the $1-100$ $\text{GHz}$ range shown (Ippolito 1981. p. 14)[^1]. Kocifaj (2021)[^2] considers dust storms by modelling the size-distribution functions of aerosols in arid regions and calculating the corresponding microwave attenuation. Microwave attenuation in dust storms is determined to be directly proportional to frequency, for all relative humidities and particle origins examined (Kocifaj 2021, p. 6)[^2]. As Project Elara employs frequencies at the lower end of the examined range, attenuation is minimized even with rain, fog, clouds, or charged particles in the beam's path. ## Noise and Coherence In addition to attenuation, water vapor and oxygen produce phase dispersion in the microwave beam that interferes with coherent beam combination. The International Telecommunication Union (ITU) shows the specific phase dispersion as near-zero for $1-12$ $\text{GHz}$ electromagnetic waves at $1$ $\text{atm}$, $15$°$\text{C}$, and a water vapor density of $7.5$ $\mathrm{g/m^3}$ (ITU 2022, p. 17)[^3]. Thus, if ideal conditions are assumed, simulating the Earth's atmosphere may not be necessary for experiments intended to model space-to-Earth transmission. Inclement weather's effect must be considered however. Ippolito (1981)[^1] measures the differential phase shift from $4-100$ at various precipitation rates, finding it to be non-negligible across the $4-35$ range at any precipitation rate from $12.5-150$ $\text{mm/hr}$ (Ippolito 1981. p. 14)[^1]. Another concern is the atmospheric noise temperature. Ho (2007)[^4] analyses atmospheric noise for both ideal atmospheric conditions and rain, and at varying elevation angles. For angles of $30$°-$90$° and within the $1-12$ $\text{GHz}$ range Project Elara is concerned with, the atmospheric noise temperature is below $10$ $K$ with clear skies and below $20$ $K$ with a water vapor density of $15$ $g/m^3$ and a columnar liquid content of $0.5$ $\mathrm{kg/m^2}$. This noise is relatively low, but its effects on the efficiency of the energy acquisition should be considered along with the effects of the phase shift, especially in moist conditions. ## Power Losses A significant limitation to masers as a medium of space-to-Earth power transmission is beam divergence. The minimum divergence for Gaussian beams is governed by the diffraction limit, where the half angle of the beam is proportional to its wavelength and the transmitting aperture's diameter (Bridges 1975. p. 2346)[^5]. Selecting frequencies in the $1-2$ $\text{GHz}$ range ($\lambda\approx15-30$ ) will result in beam divergence thousands of times greater than that of an optical laser, and still many times larger than that a frequency of $12$ $\text{GHz}$ ($\lambda\approx2.5$ $\text{cm}$) would produce. This presents a dilemma: the wavelengths which pass through the atmosphere with the least attenuation and produce the least atmospheric noise reach the Earth's surface most diffuse. This trade-off must be addressed in the design of the maser and the ground-based array receiving the beam. ## Conclusion Masers operating at frequencies of $1-12 \text{ GHz}$ present as excellent candidates for space-to-Earth power transmission. This range minimizes atmospheric attenuation and noise temperature across a wide range of weather conditions, with $1-2$ $\text{GHz}$ presenting optimal performance. The primary challenge with this implementation arises from beam divergence, as the GHz ranges which are most optimal for atmospheric transmission diverge most significantly. ## References [^1]: Ippolito, L.J. "Radio Propagation for Space Communications Systems." Proceedings of the IEEE, vol. 69, no. 6, 1981, pp. 697--727. DOI.org (Crossref), https://doi.org/10.1109/PROC.1981.12049. [^2]: Kocifaj, Miroslav, et al. "The Nature, Amplitude and Control of Microwave Attenuation in the Atmosphere." Journal of Geophysical Research: Atmospheres, vol. 126, no. 17, Sep. 2021, p. e2021JD034978. DOI.org (Crossref), https://doi.org/10.1029/2021JD034978. [^3]: Attenuation by atmospheric gases and related effects, document Rec. ITU-R P. 676-13, International Telecommunication Union, 2022. [^4]: Ho, Chungkai, Kantak, A., Slobin, S., Morabito, D.. \"Link Analysis of a Telecommunication System on Earth, in Geostationary Orbit, and at the Moon: Atmospheric Attenuation and Noise Temperature Effects.\" The Interplanetary Network Progress Report, vol. 42-168, p. 1-22, Feb 2007 . [^5]: Bridges, William B. "Divergence of High Order Gaussian Modes." Applied Optics, vol. 14, no. 10, Oct. 1975, p. 2346. DOI.org (Crossref), https://doi.org/10.1364/AO.14.002346. [^6]: Magyar, G., and L. Mandel. "Interference Fringes Produced by Superposition of Two Independent Maser Light Beams." Nature, vol. 198, no. 4877, Apr. 1963, pp. 255--56. DOI.org (Crossref), https://doi.org/10.1038/198255a0. [^7]: Aryshev, A., et al. "Observation of the Stimulated Coherent Diffraction Radiation in an Open Resonator at LUCX Facility." Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, vol. 763, Nov. 2014, pp. 424--32. DOI.org (Crossref), https://doi.org/10.1016/j.nima.2014.06.056. [^8]: Garrido-Villén, Natalia, et al. "Atmospheric Attenuation and Scintillation Effects on the Range of EDM Instruments." Journal of Surveying Engineering, vol. 141, no. 3, Aug. 2015, p. 05015001. DOI.org (Crossref), https://doi.org/10.1061/(ASCE)SU.1943-5428.0000142.