Radiation

Radiation. Scary word. Makes us think of fallout and glowing waste.
The truth is, most radiation is harmless. That warm feeling of sunlight on skin? Radiation. Microwave ovens? Strong radiation sources. Same for wi-fi, cellphones, broadcast TV, radio, infrared heat lamps, blacklights and remote controls.

Radiation takes two forms: electromagnetic and particle.
 Electromagnetic radiation is packets of energy carried by photons (or one could say waves of energy). This is defined by the electromagnetic spectrum. Most of this radiation is harmless or even useful as long as it is at the visible level or below.



 Ultraviolet light tends to degrade materials, especially plastics, and causes sunburns; on Earth as well as in space, any structural material needs to be protected from UV. Paint is a good option, as is using UV-resistant metals. Hard UV can disrupt electronics and is very damaging.
 Above that, x-rays and gamma rays are penetrating ionizing radiation. That means they can travel through material like aluminum and skin to do their damage in the blood-forming organs, reproductive organs and other places you generally don't want damage. It's called ionizing because the photons have enough energy to ionize or knock an electron out of a molecule (like DNA); that can mangle or destroy the molecule. Mangled DNA leads to cancer. Mangled proteins can lead to cell death. Too much cell death causes problems like the lining of your digestive system disintegrating into slop; very unpleasant. X-rays and gamma rays can have overlapping energy levels; it is common to call a photon an x-ray if it was generated by an electron and to call it a gamma ray if it was generated by an atomic nucleus.
 Hard gamma rays can have enough energy to do further damage; like breaking a rack of billiard balls, the initial photon has so much energy it can plough through many molecules and knock electrons all over the place. If they have enough energy, more exotic reactions like pair production can occur. This is when the photon has more energy than an electron and its antimatter pair (a positron) and passes close to a heavy nucleus; the extra energy actually produces new matter in the form of an electron and a positron. Most of the time these particles recombine and spit out two gamma rays with up to half the energy of the first one.
 Protecting against electromagnetic radiation usually means heavy atoms. Lead is a traditional material. Uranium and thorium can be useful, as can other heavy elements like barium, bismuth, tungsten, mercury and gold. The shielding effect occurs when the photon strikes a nucleus, which absorbs the energy and then re-emits photons at lower energy levels.

Particle radiation is high-speed particles. There are several types with their own sources and properties.
 Neutron radiation is formed of high-energy neutrons and is almost always the result of a nuclear fission or fusion process. Neutrons have no charge and interact mostly with atomic nuclei; they are not stable in free space and are normally only seen near radioactive material or during solar particle events. Sometimes these neutrons will fuse with nuclei, a process called neutron activation. This can make a material radioactive even when it is not normally so; this is the reason that the parts of a nuclear reactor become radioactive after the reactor has been running. Neutron shielding can be just like EM shielding, but often also includes materials that are very good at absorbing neutrons. Examples include boron, hydrogen, carbon, hafnium and many lanthanides.
 Beta radiation is formed of electrons (or positrons). The energy in a beta particle is lost through bremsstrahlung or braking radiation; the particle is deflected by another charged particle and the change in path causes an x-ray to be emitted. For positrons, when they strike an electron they annihilate into two gamma rays. Shielding against these particles can be done several ways, but one successful method is to start with a dense, heavy material that will intentionally force the beta particle to produce many x-rays followed by progressively lighter shielding that will further split and distribute the energy until it is no longer harmful.
 Bare protons are very common in space as a component of the solar wind and as cosmic rays. They are similar in behavior to beta particles but are much more massive; they tend to carry much more energy and require thicker shielding.
 Alpha radiation is a high-energy helium nucleus, two protons and two neutrons. These particles carry a lot of energy but do not penetrate well at lower energies. Alpha particles on Earth are easily stopped with a sheet of paper. Some radioactive materials like Radon gas emit alpha particles when they decay; breathing these in can expose the lungs directly to alpha radiation and cause very heavy damage. In space, alpha particles are usually cosmic rays and have vastly more energy and penetration power. These particles are formed or ejected during supernova explosions. Shielding is similar to beta radiation, a heavy-element skin with lighter elements to dissipate the bremsstrahlung x-rays. Very high energy alpha particles can cause a particle shower, where the first impact generates several high-energy particles that keep traveling into the material. The only way to protect against this is with very thick shielding.
 A proton is basically a hydrogen nucleus and an alpha particle is basically a helium nucleus. Heavier elements can be cosmic rays; these are called high-Z GCR (galactic cosmic rays) and are thought to be produced in supernova explosions. Elements as heavy as iron are commonly seen in this form, with heavier elements much more rare. These particles carry extreme amounts of energy. Stopping them with shielding is not realistic unless you can bury your habitat deep inside some other object.

We measure ionizing radiation in a variety of confusing ways depending on what effect you are trying to measure. Non-ionizing radiation is irrelevant; you can get an infrared burn or a visible-light laser burn but neither will increase your risk of cancer. Human exposure is measured in Sieverts (Sv), which is based on a series of weighting factors based on the type of radiation and how likely it is to reach important sites like the blood-forming organs. Sources are often measured in Gray (Gy), which is 1 joule of radiation absorbed per kilogram. Converting to Sieverts requires knowledge of the specific types of radiation and how and where they are absorbed into the body, but normally an exposure of 1 Gray results in 1 to 20 Sieverts of absorbed dose. Doses to plants and electronics normally use Grey.
 Radiation dose is cumulative; even the tiniest amount adds to your lifetime exposure. A very excellent chart showing a variety of sources is available courtesy XKCD / Randall Munroe. Average people in the U.S. are limited to 1 mSv (one thousanth of a Sievert) per year by the EPA; the average background radiation dose is about four times that value. On Earth, flight attendants and pilots typically have some of the highest career doses of non-radiation-worker occupations. Radiation workers are split between those who work in medical (medical radiologists) and those who work in nuclear energy (nuclear power plant workers), with some niche categories (backscatter imaging techs) also at risk of exposure. Under normal circumstances radiation workers receive very little exposure but because of the risk of accidents they are carefully monitored for exposure. The radiation worker exposure limit in the U.S. is 50 mSv per year, though most people barely exceed the background dose in a given year.
 Astronauts are in a class all their own. An astronaut in low-Earth orbit is limited to 500mSv per year. An additional lifetime dose limit of 1 to 4 sieverts applies depending on age, gender and space agency. (Younger people have lower limits and women who might bear children also have lower limits.) To put it another way, a middle-aged male NASA astronaut could be exposed to ten times the annual maximum dose of a nuclear power plant worker for eight years before the cumulative risk becomes career-ending. As you can see from the linked pdf, radiation limits are complex. This is because there are short-term (acute) effects and long-term (chronic or latent) effects. For example, the astronaut 30-day limits are 250 mSv in order to avoid nausea, vomiting and other symptoms of acute radiation sickness.

 Our proposed colony is formed of civilians. As a permanent colony there will be children; this is inherently necessary to be self-sustaining. As such, the upper limit for exposure can be no higher than the Earth radiation worker limit. This is a much more stringent limit than for astronauts, so most shielding designs for specific missions will be insufficient. We cannot simply assume 10cm of aluminum will be enough to protect average people, particularly when it may not be enough to protect astronauts on a trip to Mars. So, our upper limit for exposure is 50 mSv per year with an ideal goal of 4 mSv per year or less. Plants are very tough and can generally tolerate doses as high as 1 Gy per year
 Radiation in space can be somewhat unpredictable, but in broad strokes it varies with the solar cycle and has two main components. During solar minimum, cosmic rays (GCR) are at their highest because there is less solar wind to fight against. GCR during solar minimum produces about 620 mSv per year, with about 1% of that (6.2 mSv) as high-Z GCR. That means even with good shielding we can't expect to reach the ideal 4 mSv target in free space; it would take several meters of rock to cut the high-Z particles down to reasonable levels. There is historical evidence that the GCR could peak at higher levels than it does now, perhaps as high as 1500 mSv per year. We don't know on what timescale or how likely that is, but for a permanent habitat it pays to be prepared for the worst.
 The solar wind is a mix of protons, alphas and x-rays / gamma rays. Highest doses occur during solar maximum. The sun also sometimes has solar storms, solar particle events (SPE), coronal mass ejections, solar flares, etc. where the radiation levels can become very high for short periods. The background solar wind is roughly 120 mSv per year. The highest recorded radiation peak was during the 1972 solar particle event. This event produced a dose of 1.24 Sv behind 2g/cm² aluminum or about 1.82 Sv in free space (dose to blood-forming organs). We have indirect records that suggest much larger events can happen on rare occasions. For reduction of risk many studies take the highest likely event as 4x the dose of the 1972 event, so we will use 7.28 Sv as the one-day maximum dose from SPE. Since 8 Sv is roughly the dose that kills all exposed people even with advanced medical treatment, this is clearly a serious concern. We will also assume that one and only one dangerous particle event occurs per year. For a less pessimistic number, one could use 740 mSv per year as today's average dose and consider SPEs separately.

 Clearly some kind of shielding will be necessary. At the most basic level, more mass equals better shielding. There are some clever things we can do with the arrangement of different types of materials but in the end we still require an enormous amount of mass as shielding.
 First off, how do we determine how much shielding is needed? There are three similar ways to describe the effectiveness of a material: halving thickness, tenthing thickness and attenuation length. Halving thickness is the thickness of a material that will reduce the incident radiation by half. Tenthing thickness reduces radiation to 10% and the attenuation length reduces it to 1/e or about 63%. Old US government documents tend to be in terms of halving thicknesses but most recent references are in terms of attenuation length (or several related terms meaning essentially the same thing). I will use attenuation length throughout.
 To calculate how effective your shielding is you can find the attenuation length of a material then divide the material's thickness by that value. Add the result for each material and you will have the attenuation factor for your shield. If you want a percentage of radiation allowed through, take 1 / e ^ x where x is your attenuation factor; for example, a factor of 1 is 36.788% while a factor of 2 is 13.534%. For a percentage of radiation blocked, use 1 - (1 / e ^x); 63.212% for x=1 and 86.466% for x=2. Shielding has varying effectiveness depending on the type and energy of incoming radiation, so the reality is not as simple as looking up values in a table and doing some addition. Probably the best available reference for x-ray shielding is the XCOM database hosted at the NIST; I'm not sure there are any comparable references for high-energy particles.
 We know that we need to protect against up to 1500 mSv of cosmic rays, 120 mSv  of solar wind and 7280 mSv of solar particle event radiation. That's 8900 mSv per year. Let's break this into two parts; we know that the SPE radiation happens over only a few days so if necessary we can take shelter in a more heavily shielded area for the duration, so the baseline will use the 1620 mSv background radiation and a storm shelter will use the full dose. We want the baseline exposure to hit 4 mSv if possible, but in any case less than 50 mSv per year. The attenuation factor is simply ln(1620 / 4) or 6.0039, or a minimum of ln(1620 / 50) = 3.4782. Let's add in the SPE: with an attenuation factor of 3.5, the incoming SPE dose of 7280 mSv is reduced to dose * 1 / e ^ 3.5 or 220 mSv. This might be OK for professional astronauts but our civilians need better protection. The full factor of 6 would reduce the SPE to dose * 1 / e ^ 6 or 18 mSv, for an annual dose of 22 mSv. A proper storm shelter should reduce that SPE dose to no more than an extra year's dose, which is ln(7280 / 4) = 7.5066. So, whether we use 3.5 or 6 as our design value for the outer hull we need a storm shelter with at least a factor of 7.5 in total.

 Let's look at some possible shielding materials to get a feel for how much mass is needed to hit those numbers. First, attenuation from XCOM is given in units of cm²/g. When multiplied by the material's density in g/cm³ this yields the attenuation length in cm. I use the lowest published value for each material; for example aluminum's minimum attenuation is 0.02168 at an energy of 20 Mev. With the density of aluminum at 2.7 g/cm³ that yields an attenuation length of  17.08cm. For very high energy gamma rays (10^5 MeV) the attenuation is 0.03189 or a length of 11.61cm. This means the actual performance of the structure will generally be better than estimated, since each step assumes the worst possible energy for each material. Future work should include modeling the structure and simulating several years under a variety of conditions to see if any of the mass can be shaved off.

I will list the name, attenuation length and mass per square meter for several materials at an attenuation factor of 1:
Aluminum - 17.08cm - 15,683kg
Iron - 4.25cm - 11,386kg
Nickel - 3.55cm - 10,749kg
Tungsten - 1.29cm - 8,420kg
Silicon - 18.36cm - 14,542kg
Water - 59.86cm - 20,311kg
Polyethylene - 73.06cm - 24,096kg
Regolith - 27.77cm - 14,161kg
Olivine - 11.17cm - 14,624kg

 Even the best candidate, Tungsten, still requires over eight tons of shielding for each square meter of hull to reach an attenuation factor of only 1. Reaching 3.5 requires over two meters of water and reaching 6 requires 85 tons of regolith per square meter. Shielding is a major problem and requires far more mass than we can reasonably provide from Earth. If on a planet or moon then the simple solution is to bury the habitat under at least 2 meters of regolith. If the habitat is in free space then the only option is to harvest shielding from asteroids or other easy to reach sources of mass.

 A free-space structure will need a micrometeoroid shield (Whipple shield). For best results this is a 2mm aluminum sheet with a 10cm empty space beneath it. High-speed dust specks and chunks of rock hit the aluminum and explode into plasma and fine dust, which doesn't have enough energy to punch through the next layer. Next would be a nickel-iron layer 10mm thick (~30% nickel); this is strong enough to handle the Whipple shield debris, is made of relatively heavy atoms and is readily available in asteroids. Its purpose is to convert the energy of incoming particles into a shower of x-rays so the next layer can absorb it. Lastly is a layer of regolith one meter (104cm) thick, probably compressed and sintered in place or possibly formed into blocks and glued, welded or wire-wrapped into place. If olivine or other dense rock is available this layer can be half as thick. Overall the shield provides an attenuation factor of 4.02.  The storm shelter will need a further 3.5 attenuation lengths worth of shielding after considering the habitat's structure and furnishings.

 The necessary shielding scales with the surface area of the habitat, while the shielded area scales with the volume of the habitat. This square-cube relationship means that while good shielding is far too heavy for small habitats, it should be comparatively easy for very large habitats.
  One advantage: SPE radiation always comes from the direction of the Sun. A shadow shield that can be kept between the habitat and the Sun can be used to provide shielding against SPEs without having to cover the entire surface of the habitat. This will still require 7.5 - 4.0 = factor of 3.5, or just under 1 meter of regolith. My example habitat has a shield diameter of 128 meters and length of 215 meters; adding an extra meter of regolith all around the hull would cost 132,000 tons while the sun shield at 12,868m² costs only 19,300 tons.

 Later posts will outline my reference design in greater detail. Hopefully this post provides a decent background on radiation and how to protect against it.