Power transmission via radio waves can be made more directional, allowing longer-distance power beaming, with shorter wavelengths of electromagnetic radiation, typically in the microwave range.[68] A rectenna may be used to convert the microwave energy back into electricity. Rectenna conversion efficiencies exceeding 95% have been realized.[citation needed] Power beaming using microwaves has been proposed for the transmission of energy from orbiting solar power satellites to Earth and the beaming of power to spacecraft leaving orbit has been considered.[69][70]Power beaming by microwaves has the difficulty that, for most space applications, the required aperture sizes are very large due to diffraction limiting antenna directionality. For example, the 1978 NASA study of solar power satellites required a 1-kilometre-diameter (0.62 mi) transmitting antenna and a 10-kilometre-diameter (6.2 mi) receiving rectenna for a microwave beam at 2.45 GHz.[71] These sizes can be somewhat decreased by using shorter wavelengths, although short wavelengths may have difficulties with atmospheric absorption and beam blockage by rain or water droplets. Because of the "thinned-array curse", it is not possible to make a narrower beam by combining the beams of several smaller satellites.For earthbound applications, a large-area 10 km diameter receiving array allows large total power levels to be used while operating at the low power density suggested for human electromagnetic exposure safety. A human safe power density of 1 mW/cm2 distributed across a 10 km diameter area corresponds to 750 megawatts total power level. This is the power level found in many modern electric power plants. For comparison, a solar PV farm of similar size might easily exceed 10,000 megawatts (rounded) at best conditions during daytime.Following World War II, which saw the development of high-power microwave emitters known as cavity magnetrons, the idea of using microwaves to transfer power was researched. By 1964, a miniature helicopter propelled by microwave power had been demonstrated.[72]Japanese researcher Hidetsugu Yagi also investigated wireless energy transmission using a directional array antenna that he designed. In February 1926, Yagi and his colleague Shintaro Uda published their first paper on the tuned high-gain directional array now known as the Yagi antenna. While it did not prove to be particularly useful for power transmission, this beam antenna has been widely adopted throughout the broadcasting and wireless telecommunications industries due to its excellent performance characteristics.[73]Wireless high power transmission using microwaves is well proven. Experiments in the tens of kilowatts have been performed at Goldstone in California in 1975[74][75][76] and more recently (1997) at Grand Bassin on Reunion Island.[77] These methods achieve distances on the order of a kilometer.Under experimental conditions, microwave conversion efficiency was measured to be around 54% across one meter.[78]A change to 24 GHz has been suggested as microwave emitters similar to LEDs have been made with very high quantum efficiencies using negative resistance, i.e., Gunn or IMPATT diodes, and this would be viable for short range links.