Statite Dynamic Shell, aka, Stapleton Dyson Shell
The Standard Story
The continued increase of the human population, expanding into the solar system and later to other star systems, is a common assumption in 20th century science fiction. People move into orbiting space habitats at the L4 and L5, terraform Mars, etc. When planetary systems are exhausted, the expansion continues into more space habitats orbiting the sun, perhaps manufactured from the asteroids, Mercury, and Venus. Some propose dismantling the Earth to build more habitats, eventually capturing most of the energy from the Sun.
Nikolai Kardashev characterized future supercivilizations by the energy they capture and use.
A type I supercivilization captures all the power reaching their planet from their star for artificial uses. For the Earth, that is 174 petawatts, 1.74e17 watts incoming, of which perhaps 120 petawatts reaches the surface - the rest is reflected into space. Plants intercept about 20 petawatts (2e16 W), and convert 200 terawatts (2e14 W) into material animals (and now biofuel-guzzling machinery) can eat. Current global artificial power production is about 15 terawatts (1.5e13 W).
A type II supercivilization captures all the power emitted by their star. Our sun emits 380 yottawatts (3.8e26 W) visible light, UV, and infrared, 2 billion times more power than the earth intercepts, and 25 trillion times more power than human artificial power production.
A type III supercivilization captures all the power emitted by all the stars in their galaxy. Our galaxy emits perhaps 40 trillion yottawatts, (4e37 W), more than two heptillion (2e24) times more power than human artificial power production.
So, a supercivilization capturing all the power emitted by the Sun with a shell of habitats would be a Type II supercivilization.
Olaf Stapleton wrote about type II and type III supercivilizations in his 1937 science fantasy novel Starmaker. Freeman Dyson wrote about how such supercivilizations might appear as highly luminous, compact infrared sources in 1960, Search for Artificial Stellar Sources of Infrared Radiation. He described them as shells, an assembly surrounding a star - he did not claim they would be solid or round.
Because of this paper in Science, a journalist misleadingly named these sources Dyson Spheres, a source of confusion ever since. Dr. Dyson wishes they were named something else, as I will do below.
The "Dyson" "Sphere"
The scare quotes are intentional - the name is wrong, as is the description. I will describe the idea the label has come to describe, before disposing of it.
A Miscellany of Physical Pathologies
The area of a sphere is 4πR² - the area facing in one direction (like the sun) is πR², so the average surface illumination is ¼ of the total. Add in atmospheric reflection, and the average illumination (visible light and near IR < 2 μm wavelength) reaching the Earth's surface is about 250 W. If this was somehow duplicated across the inner surface of a huge sphere, and radiated into deep space on the outer surface,