Dyson Spheres (and their variants) are a type of megastructure built around stars to collect a large fraction of their energy output. Dyson swarms, shells, bubbles, and Matrioshka brains are all types of Dyson sphere. The optimal type of Dyson sphere depends on the star, intended purpose, and how many materials you have.
Types of Dyson sphere[]
First, let us consider possible uses of a Dyson sphere. First, sheer power output. Second, habitation. After these, all manner of applications, ranging from weapon to pushing laser to gigantic computer, must be considered. The types of Dyson sphere required for these are listed below:
Dyson swarms[]
The most common type of Dyson sphere, a Dyson swarm is a swarm of small, light-absorbing objects, be they solar panels, O'Neill cylinders, or even ringworlds. The least expensive type by far is a Dyson swarm of mirrors and solar collectors to harness the energy coming from the star.
While the solar panel and O'Neill cylinder types can be built incrementally, from a starting investment of usually under a hundred million tonnes of material, they are also usually much more expensive than the ringworld type due to economies of scale in construction. Middle options, like the rungworld, a circumstellar chain of O'Neill cylinders, can sometimes serve as a middle ground between these two extremes, as they have the benefit of being able to manufacture the O'Neill cylinders in bulk, and can have passages allowing for a larger interior ecosystem than a single O'Neill cylinder. Ringworlds also have less expensive ecosystem maintenance due to their vast size.
Dyson bubbles[]
Dyson bubbles are a specialized type of Dyson swarm designed to work around high-luminosity stars. A Dyson bubble must have a very high luminosity-mass ratio to work, as the solar panels around the star take the form of "statites," objects which use radiation pressure from the star to hover without orbiting. These must use very low-mass materials for the panels, but have the advantage of being able to harness 100% of the star's light. It is worth noting that the use of reflective materials is strongly recommended. Not only are reflective materials supported by radiation pressure twice as efficiently, but most of the light reflected will be reflected onto another mirror, increasing the effective radiation pressure. While this will diminish, as no material is a perfect reflector, the radiation pressure will be 20 times greater for a material that reflects 95% of the light that hits it than for a material that absorbs all of the light. Be careful, though, as if there is too much radiation inside of the bubble, the star might decide to flare, or in extreme circumstances, even explode.
Dyson shells[]
Dyson shells are a kind of Dyson sphere designed to capture 100% of a star's light by use of an actively supported shell around the star. Circumstellar rings held in place by neodymium magnets can spin faster than orbital velocity to provide an upward force to the shell, counteracting gravity. These can also be used for habitation by placing the shell at a distance where the stellar gravity is optimal for your species, providing a surface on the outside. Power can be beamed via microwave to receivers on a ring orbiting the star at orbital velocity, which can have giant LED bulbs in parabolic mirrors supply light to the surface. Bulbs can be turned on and off to simulate the day-night cycle, and can even provide seasons by inclining the orbit of the ring. Disclaimer: this only works around stars where the habitable zone is approximately at 50% of the radius where stellar gravity is around 10 m/s^2, which is a group that encompasses only the very smallest red and brown dwarfs.
Nicoll-Dyson beams[]
A Nicoll-Dyson beam is essentially an array of mirrors designed to focus the energy of a star into a giant lens, which focuses the light into a tight beam. These are actually relatively inexpensive to build if you are creative (e.g. using Fresnel lenses, not the conventional kind), and are best built around the largest and brightest stars, for obvious reasons. These can either be used as tight beams of light or to propel relativistic kinetic missiles via laser propulsion. Nicoll-Dyson beams do have a nonmilitary use, that of beam-powered spaceship propulsion for near-lightspeed interstellar travel.
However, the beam can have wildly different power outputs depending on the star used. If a tiny red dwarf with only 10^22 W of power is used, one can expect a yield of around 2.39 teratonnes of TNT equivalent per second, enough to burn a 100 km-wide mark in a planet if moving at 100 km/s. If, on the other hand, a blue hypergiant with 10^33 W of power is used, planets can be completely destroyed almost instantaneously. Of course, these beams move at the speed of light, so are only ideal for defensive purposes. However, an RKM with a thousand times the energy needed to destroy a planet is an almost unstoppable weapon.
Matrioshka brain[]
A Matrioshka brain is a computational system that uses the power of a star. Usually built using the actively-supported shell technique, these objects contain many layers of computers operating at different temperatures, powered by each other's waste heat to maximize efficiency. Depending on the size of the star, these can get anywhere from 10,000,000,000,000,000,000 to 10,000,000,000,000,000,000,000,000,000,000 times as much energy as the theoretical maximum for personal computers set by the 110 V outlet, and can be that much more powerful. Typical uses involve bureaucracy, research, cloud processing, and artificial intelligence. The computational power of such a device is so great that most stars can simulate hundreds of millions of minds if a matrioshka brain with that purpose is built around them.
Starlifting mechanism[]
Another common use for Dyson spheres is the extraction of vast amounts of material from metal-rich, high-luminosity stars. This is mainly done by focusing large amounts of light to small regions of a star, and then using large balloons or a similar storage mechanism to transport the gas to refining plants, where valuable materials can be sifted out. The hydrogen produced can either be thrown back into the first star or used to assemble a new one. As for how much material can be removed, let us use the star Arcturus as an example (While Arcturus is not the best choice, as its metallicity is low, red giants such as it have very low escape velocities, as stars go, making the process that much easier.): Arcturus has an escape velocity of 90.1 km/s, meaning that 1 kg of material can be removed if 4.06 GJ of energy is added. As Arcturus has a metallicity of -0.52 dex, it has 10^-0.52 times the amount of non-hydrogen and helium elements as the sun, which means 0.405% of the star is useful. This means that it takes 1.00 TJ (a nice round number) of energy to extract 1 kg of useful material from the star. As Arcturus outputs 6.51x10^28 W of energy, 6.51x10^13 metric tons of material can be extracted every second. This is enough to build Mt. Everest 428 times every second, so starlifting can be an extremely profitable business in many situations.
Caplan Thruster[]
Caplan Thrusters are large stations built around stars. As the name implies, they are large fusion engines that are capable of moving an entire star. It could take potentially millions of years to get anywhere, but it does mean that you never have to get out of your system in order to go to other stars. This idea was originally proposed by Dr. Matthew Caplan in this paper [1], hence the name.
Star Choice[]
After choosing one of the above types, it is now time to choose a star to colonize. The smallest stars, red dwarfs, can have luminosities as low as 5 ZW, and the largest stars, luminous blue variables, blue supergiants, and Wolf-Rayet stars, can have luminosities as high as 5,000,000,000 YW.
For a ringworld swarm, degenerate stars are the best, with smaller red and orange dwarfs also being options. While red dwarfs offer the lowest prices, they have such low luminosities that comparatively not much land can be built (sometimes only a few hundred planets worth). For most other kinds of swarms, the size of the star does not matter when looking at cost per square kilometer, so the larger the star is, the better, except when the star is inherently unstable. While larger stars have shorter lifespans, even most O-type stars have at least 100,000 years left. As long as the death of the star is someone else's problem, preferably far in the future, no one will care. However, there is an exception for habitable swarms: stars with above a certain luminosity/mass ratio no longer benefit from added luminosity. This is because the construction of habitats requires non-hydrogen and helium building materials, typically carbon or metal based. As stars typically are only 0.5-5% non-hydrogen and helium elements, there remains a limit to the building material in a system, even using starlifting methods, which establishes an upper bound to the habitation space in a system. This means that habitable space maxes out around early A-type stars.
Dyson bubbles only work when around large stars, since their high luminosity-to-mass ratio is required.
Dyson shells for habitation will only work around extremely faint red dwarfs, or stellar- to intermediate-mass black holes. Any star larger than an extremely faint red dwarf will cook the shell, and any black hole larger than a few thousand solar masses will have such a high escape velocity that random meteorites have enough energy to punch through the shell like a thermonuclear weapon. This can be remedied, possibly by adding a thin Mylar layer above the outer shell to detonate random meteorites before they reach the surface. Using this method, what are called birch planets can be built around supermassive black holes. The Mylar should be patched when holes form.
Nicoll-Dyson beams work around anything, but only the biggest stars have the energy to destroy planets in less than a second. Luminous blue variables, blue supergiants, and Wolf-Rayet stars are strongly recommended.
Matrioshka brains will work much the same around anything, so the same factors used with dyson swarms apply.
References[]
1 - Matthew E. Caplan, Stellar engines: Design considerations for maximizing acceleration, Acta Astronautica, Volume 165, 2019, Pages 96-104, ISSN 0094-5765, https://doi.org/10.1016/j.actaastro.2019.08.027. (http://www.sciencedirect.com/science/article/pii/S0094576519312457)