Wednesday 19 July 2017

All the Radiators

Every spaceship will have radiators. Energy such as sunlight, reactors, habitats and rocket engines accumulates as heat unless it is removed through radiation. 
We will look at how this critical component works and then at existing, future and possible designs. 
Stefan Boltzmann

On Earth, heat leaves a vehicle through conduction, convection and radiation. In the vacuum of space, only radiation works to remove excess heat. 
The International Space Station's radiators.
Spaceships are exposed to sunlight in space, which they absorb as heat through the hull. The various equipment on-board produces waste heat through their various inefficiencies, at different rates and temperatures. Even the crew contributes to producing waste heat. If this waste heat is not removed, it will accumulate and increase the spaceship's temperature until it melts. Radiators are critical for this reason.

Radiators work by emitting electromagnetic energy. It consists of photons of a wavelength determined by the radiator's temperature.
Guess what temperature this exhaust manifold is at.
Examples include the infrared wavelengths our body emits (300K), the red-orange visible wavelengths molten iron emits (1430K) and the bright white of the sun's surface (5800K). 

For our purposes, we will focus on the energy removal capacity of a radiator. The rate is measured in watts: the waste heat watts absorbed and produced by the spaceship's systems, to be compared to the waste heat watts radiated away by a radiator. The relationship between the energy removal capacity and the radiator's temperature is given by the Stefan Boltzmann equation:
  • Waste heat removed: E * A * Sb * Temperature^4
E is the emissivity of the radiating surface. It is a property between 1 and 0. Extremely black surfaces approach 1 emissivity. Shiny surfaces have lower emissivity. 
A is the surface area of a radiator, in square meters. Make sure to count it twice for a double-sided radiator. 
Sb is the Stefan Boltzmann constant, equal to 5.67*10^-8.
Temperature is in Kelvin.

Design factors

Using the Stefan Boltzmann equation, we can quickly see that a radiator with better emissivity, higher surface area and higher temperature removes more waste heat. 
On the left, 1100K radiators. On the right, 2700K radiators. The latter is actually handling three times as much waste heat. 
On spaceships, it is important to use the lightest possible components for each task. A spaceship with lighter radiators will accelerate faster and have more deltaV, meaning it can go further and do more for less propellant. 

If we want a lightweight radiator, we want it to have the highest emissivity. We can accomplish this by using naturally dark materials, such as graphite, or painting over shiny metals with black paint. 

A larger radiator weighs more. We therefore want the smallest radiators possible. To compensate for lower surface area, we can increase the operating temperature. A small increase in temperature leads to a massive increase in waste heat removed. This means that hot radiators are massively lighter and smaller than cold radiators. 

Further considerations

The ISS's EAC system
A typical radiator accepts coolant from a hot component. The coolant's component exit temperature is the initial temperature at the radiator. The radiator serves as an interface that radiates away the coolant's heat, leading to a lower radiator exit temperature. The coolant is fed back to the component to complete the waste heat removal cycle.
Note how the maximum temperature the heat exchanger's maximum temperature, delivered to the steam, is the lowest temperature of the liquid sodium in the reactor core.
Heat only flows from a hot object to a cooler object. A radiator can therefore only operate when the component's temperature is higher than the radiator's coolant exit temperature. For example, if a nuclear reactor operates at 2000K, the radiator must work at 2000K or less. 

A reactor from COADE. The reactor operates at 2907K but the radiator receives coolant at 2400K.
The difference between the entry and exit temperatures in a radiator depends on many factors, but generally we want the largest difference possible. This difference in temperature is especially important for power generation. A large difference means more energy can be extracted from a heat source. It also means that less coolant is needed to cool a component.

This creates problems with realistic designs.
A general solution is to use two sets of radiators operating at different temperatures: one low-temperature circuit and one high temperature one. It works fine when your low temperature waste heat is a few kilowatts from life support and avionics. Other solutions have to be found for components that must be kept at low temperatures yet generate megawatts of waste heat, such as lasers.

This design has three sets of radiators of decreasing area for different temperature components. 
For low temperature high heat components, heat pumps must be used. They can move waste heat against a temperature gradient, allowing, for example, a a 1000K radiator to cool down a 500K component. However, this costs energy. Moving heat from 500K to 1000K costs 1 watt to the pump for every watt moved. A realistic pump will not be 100% efficient and will require more than 1 watt to move a watt of waste heat. 

  • Pump power: (Waste heat * Tc / (Th - Tc)) / Pump Efficiency
Pump power is how many watts the heat pumps consume. Waste heat is how many watts must be removed from the component. Tc is the component's temperature. Th is the radiator's temperature, both in Kelvins. Pump efficiency is a coefficient.
The refrigeration cycle is an example of a heat pump.
A coolant must generally be kept liquid. This imposes a lower and upper limit to the coolant temperature; any colder and it will freeze and block the pipes, any hotter it boils and stops flowing. Water coolant, for example, can only be used between 273 and 373K. More importantly, it limits the temperature difference that can be obtained from a radiator.

Large temperature differences require that the coolant spend a long time inside the radiator. This requires larger radiators or long, circuitous paths for the pipes. As the coolant becomes colder, it radiates at lower rates, meaning that the last 10 kelvin drop in temperature can take exponentially more time than the first 10 kelvin reduction. There are strong diminishing returns. 

There are also structural concerns. Large temperature differences impose thermal stresses. These might be too great to handle. Lightweight, stressed radiators are prone to reacting badly to any sort of battle damage, making radiators a weak-spot for any sort of warship.

The ISS radiators' support spars. A spaceship under acceleration will need much more support.
All in all, we must keep in mind that there is a restricted range of temperatures between the hot and cold ends of a radiator, and that its performance cannot simply be obtained by using the Stefan Boltzmann equation on the maximum temperature. We cannot use a simple average either, because the coolant loses heat at a quadratically declining rate as it moves from higher to lower temperatures. 

Here is an example of 1 kg of sodium at 1000K being cooled by a 0.8 emissivity one-sided 1m^2 radiator panel:

We can see that it takes 17 seconds for the sodium to cool down from 1000K to close to its melting point of 370K. Any cooler and it'll solidify in the pipes. If we average the radiated watts, we get a value close to 11.46kW. This corresponds to an average radiating temperature of 545K.  

Finally, a radiator suffers stresses when a spaceship accelerates. Some types of radiator break or disperse under strong accelerations, so the spaceship's performance needs to be considered before selecting a design.

Solid Radiators
A straightforward design used today.

It consists of a slab of metal run through with hollow tubes for a coolant to flow. The waste heat conducts out of the coolant and into the radiator material, which radiates it away from its exposed surfaces.  
This design has a rather high mass per area and low temperature limits, making it one of the worst performing designs. The maximum temperature is whatever keeps the radiator materials both solid and strong, which is important as many metals rapidly lose strength as they approach their melting point. 

The coolant must remain liquid throughout the cooling cycle, so this limits the temperature difference that can be achieved. Using metals such as tin or salts such as sodium allows for better temperature differences, but pumping them requires specialized, sometime non-reactive, sometimes power consuming equipment.

Multiple radiators will shine their heat into each other and lose efficiency.
The arrangement of radiators around a spaceship must take into account inter-reflection, which is when one radiator's heat is intercepted and absorbed by another radiator. This reduces their efficiency. Anything more than two radiators per axis absorbs some of the heat of another radiator... at four radiators, only 70% of the heat escapes to space, at eight radiators, the efficiency falls to 38%. 

NASA has studied solid radiators for use in its Nuclear Electric Propulsion concepts. It has specified 2kg/m^2 area density as a requirement for any thermal management system. The ISS's radiators mass 8 kg per square meter, or 2.75kg/m^2 if we only consider the exposed panels.

So far, only bare carbon fibre radiators operating at 800-1000K have reached this area density. 

An alternative design achieves better area density by removing the coolant loops and pumps. The heat pipe has a hot end and a cold end, separated by a vacuum.

Heat Pipe moving waste heat into a heatsink. 
Solid coolant is boiled away and then condensed on the cold end, then re-circulated through capillary action or centrifugal acceleration. This method allows for high operating temperatures and does not require any pumps of moving parts, but high mass per area negates many of its advantages.

On a warship, radiators are a weakpoint. Bright, exposed and hard to defend, they are easy to hit and once the are damaged, they can render a spaceship unable to function. They can mission-kill a warship without ever having to penetrate any armor. Redundant radiators impose a mass penalty. Covering the radiators in plates of armor massively decreases their thermal conductivity between coolant and exposed surfaces, which in turn reduces their efficiency. 

Solutions for reducing the vulnerability of radiators include pointing them edge-on to the enemy, moving them to the back of the ship, or using retractable designs.

On the right, the radiators are exposed the enemy fire. On the left, the hull bulge protects the radiators from damage.
If all radiators are retracted, the spaceship must rely on heat sinks for its cooling needs. A megawatt heat source can boil off a ton of water in less than seven minutes, so this will only work over very short time periods. 

A compact collapsible and retractable radiator design.
High temperature solid radiators run into issues, such as having to deal with the coolant boiling, or having to contain enormous pressures to keep fluids in a supercritical state. The solution is to use solid blocks of metal instead of coolant. Running these blocks like a train around tracks allows for robust radiators that can handle strong accelerations and temperatures up to the boiling points of the coolant blocks (4000K in some cases, if the tracks are actively cooled). The smaller the blocks, down to the size of pinballs, the faster they cool down and the shorter the track has to be, leading to mass and area savings. 

Moving radiators

One of the biggest reasons why solid radiators are so massive is that they need coolant pipes, pumps and heat exchangers to move waste heat from equipment to exposed surfaces.

To greatly reduce the area density, we can devise a radiator that does not require bulky coolant loops. Instead, we move the radiator.

Moving radiators rely on the radiator material itself to move through a heat exchanger, out into space to radiate away the heat, then back in.

Advantages include simpler construction, less fragile designs, less power consumed and very larger temperature differences between the hot and cold ends. This ends up giving them better kg/m^2 and kW/m^2 ratings. However, there are many more moving parts and the radiating surfaces are only a fraction of the volume the radiators take up. Unless very lightweight materials are used, the support structure will negate the mass advantage of such a radiator.

From High Frontier.
A disk-and-drum design has a heat exchanger shaped like a drum, rolling against a radiating disk. The hoola-hoop radiator is a large disk held at the tip by a drum heat exchanger. 
The belt loops are held edge-on to the sun. Angled loops would suffer less from re-absorption of radiated heat on the internal surfaces, which is more important at higher operating temperatures. 
If the wheel or loop is replaced by a flexible or track-linked belt, it can be made to follow various paths. A 'belt-loop radiator' could bring the radiator closer to the spaceship and reduce the structural strength required to survive accelerations or vibrations.
A wire-loop configuration uses black carbon filaments as the radiating surface. They are flung out of the heat exchanger and held in place by centripetal force. Using high tensile strength materials allows for extremely lightweight loops.
From High Frontier. Uses carbon nanotube materials for the wires. 
Rollers can guide the wires instead of centripetal force, thereby becoming an even lighter version of the belt-radiator. High tensile strength materials would be needed, as this allows the rollers and motors to hold the wires under tension to prevent them from sliding around or tangling.
A rotating disk radiator is a moving radiator where the central component is a spinning disk. Coolant fluid is sprayed at the hub. The low vapour pressure liquid's surface tension causes it to spread into a thin, even film over the disk. As the disk rotates, centripetal force causes the film to flows as it cools to the collector troughs on the edges. This configuration does away with heavy heat pipes and radiator pumps, but requires the use of very low vapour pressure fluids. The disk can be angled inwards, outwards or canted to deal with spacecraft acceleration.
Bubble-membrane radiators are a 3D version of the rotating disk radiator. Hot coolant is sprayed against an inflated membrane, causing it to spread out into a thin film that very effectively loses its heat. Spinning the membrane causes the liquid film to pool at the bubble's equator, where it is collected and recycled. 
Advantages includes allowing the use of high vapor pressure coolants and very light construction. Disadvantages include having to contain high pressure vapours in a container that must remain light and transparent.

Electric radiators

The designs mentioned so far use physical structures to hold the radiators in place. This imposes some restrictions, such as having to stay within the temperature limits of the support structures, and larger radiators need heavy support to survive even light accelerations. 

A solution would be to use magnetic forces to hold the radiators in place. Strong magnetic can replace physical support structures for significant mass savings. 

Examples of such radiators include the flux-pinned radiator. Magnetic fields hold solid radiator components in place. Thermally conductive ribbons transport heat to the magnetic components.

However, there are complications. Most metals lose their magnetic properties as they are heated, becoming completely insensitive to magnetic fields above their Curie point. Careful selection of the materials used and control of the temperatures is required. 

A Curie point radiator operates around the temperature at which metallic dust particles lose their magnetism. Iron, for example, loses its ferromagnetism at 1043K.
A rotating electromagnetic scoop collects iron dust after cooling. 
The Curie point radiator uses metal filings or even liquid droplets. It is heated to above the curie point temperature and ejected into space, away from the spacecraft. A magnetic field is in place, but they are not affected by it. Iron can be released at temperatures of up to 3134K and collected at 1043K, but Cobalt has a Curie temperature as high as 1388K, is naturally black and boilds at 3400K, making it a better coolant. The small size of the particles or liquid droplets allows several megawatts of waste heat to be radiated away per square meters. 
Once the particles cool below the Curie point, they regain their ferromagnetism. They begin to be affected by the magnetic field and are drawn back to the spaceship to be collected.

Magnetic radiators are excellent solutions for combat damage - at worst, the enemy will disrupt cooling for a few seconds. However, they consume a lot of power and require heavy equipment to generate strong magnetic fields. Any unexpected acceleration or jolt from the spaceship can disperse all the material held in place by magnetic fields. 

An alternative electric radiators uses electrostatic forces to hold charged particles in place. One example is the ETHER charged dust radiator. Charged particles follow field lines and execute elliptical orbits between the heat exchanger and the collection point. Similarly to a liquid droplet radiator, charged particles can be mechanically dispersed and collected efficiently at the other end by oppositely charged scoops. 

The advantage of electrostatic radiators is that they consume less power, since creating a strong charge differential is easier than extending a strong magnetic field. The equipment is lighter and is less sensitive to temperature changes, since no superconducting or cryogenic equipment is used, and the charged particles can hold a charge across larger temperature differences than they can maintain their magnetic properties. 

However, the charge carried by the particles can be nullified by natural solar wind or if they come into contact with a conductor. This means they need a clear, short path between heat exchanger and collection point. 

Liquid droplet radiators

Liquid droplet radiators do not use any radiating surfaces - they expose the coolant directly to the vacuum. The resultant droplets have incredible surface area for their mass, allowing for rapid cooling and extremely low area density.

As the coolant does not need to be physically contained, it can be heated to very high temperatures and still cool down very quickly. There are no thermal stress constraints on liquids, so the temperature change can be as extreme or rapid as desired. They do not have to maintain magnetic properties or hold a charge either. This calculator can gives an approximation of an LDR's performance. At 1300K and using 50 micrometer droplets (a fine mist), area density can be as low as 0.047kg/m^2 with an effective performance of 57MW/m^2. This does not include the mass of the heat exchanger, droplet emitter and collector.
Solutions have already been devised for issues such as the droplets being blown away by solar wind, colliding and merging into larger droplets or moving at different velocities within the droplet sheet. 

Vapor pressure is still a concern - hot liquids in vacuum tend to evaporate quickly. Special low-vapor pressure coolants must be used, such as liquid gallium, aluminium or tin up to 1200K, lithium up to 1500K. Salting these liquids with a material such a graphite 'grit' or coating them with black ink is necessary to achieve high emissivity. Nano-fluids might allow even higher temperature liquids to be used. Reaching higher temperatures means accepting high coolant loss rates or enclosing the radiating volume in a membrane that condenses and collects vapors. The membrane has to be transparent at the radiating temperatures.   

Variations in liquid droplet radiators are mostly around how to contain and direct the coolant flow between ejection and collection points.   

A rectangular LDR has droplet emitter and collector arms of equal length. The collector arm can be made wider than the emitter to catch droplets deviated out of their path by unexpected movements or errors in droplet formation. It might be possible to move the collector arm above and below the droplet plane to intercept droplets when the spaceship is accelerating, as this would cause the droplet sheet to bend away from the plane. 

An ICAN-II design with rectangular liquid droplet radiators.
A triangular LDR saves mass by using a small collector dish instead of a long arm. However, it is less able to catch deviating droplets or compensate for spaceship acceleration.
Triangular LDR variants.
Some LDR designs dispose of the long arms and membranes and instead just spray the droplets into space. The momentum of the droplets makes them follow trajectories that land them right back at the collectors. A fountain LDR shoots droplets in front of an acceleration spaceship. They are scooped up once cool. This method of dispersing droplets produces the lightest possible designs, but there is a risk of droplet losses. 
Droplets are dropped from the spacecraft's 'front' and fall into collector arms at the mid-section.
It works best on spacecraft that gently accelerate over long periods of time, such as nuclear-electric craft on interplanetary trajectories. A shower LDR disperses droplets in front of the spacecraft and has the collectors simply collect them like a ram-scoop. It has less risk of dispersing the droplets than a fountain LDR but requires a long shower-head. 

Pressure membranes can be an addition to any liquid droplet radiator. They enclose the volume the droplets traverse. Benefits include re-condensing vapours from too-hot droplets, catching stray droplets, allowing for faster droplet velocity and a greater tolerance for droplet sheet instabilities. However, they must remain transparent to all wavelengths the droplets are radiating at, and hold in the vapour gas pressure. These are competing requirements: low wavelength absorption is done with very thin membranes, while high pressure requires thick membranes.  

Advanced radiators

Magnetically pumped and focused LDR:

Magnetically focused by the collector nozzle.
Ferrofluids at low temperatures and liquid metal at high temperatures can be used as coolant in liquid droplet radiators. They react to eddy currents and magnetic fields, allowing the coolant to be pumped without any moving parts through magneto-hydrodynamics. 
Schematic of the Mag-LDR patent, showing the dipole magnet.
Magnetic fields can also be used to recover a droplet sheet. Cyclical fields can push and pull on a group of droplets over distances proportional to the field strength. High strength fields could allow droplet sheets to extend over several dozens of meters before being recovered. They would also allow the LDR to compensate for its vulnerability to droplet sheets being dispersed and lost when the spacecraft accelerates by holding the droplets in place.

Together, an LDR can become extremely lightweight for the area is covers, as no physical support structure has to span its length. 

Gas coolants: 

We have looked at solid and liquids as coolants. Gasses can be used too.

Gas coolants have been used in nuclear reactors already. Carbon dioxide and helium were selected as they are inert and support higher temperatures than water or sodium coolants. 

In space, the principal advantage of a gas coolant is that it can operate at much higher temperatures than liquid or solid coolants. The same gas could be run from a nuclear reactor to a radiator's tubes and back. It also allows for inflatable structures for the radiators, which can be much lighter than rigid equivalents.

Inflatable fin radiators.

Multiple roll-out fin radiators.

Inflatable bags are simpler and more rugged than roll-out fins but have lower surface area.
However, there are limitations and complications. Hot, pressurized gas can be very chemically reactive. While you can push a gas to 3000K+ temperatures, the walls of the pipes containing the gas must also survive these temperatures. Many of the mass savings that come from running a radiator at high temperatures are lost trying to contain and survive the gas coolant. Pumping gas requires much more power per kg moved than liquids, for example.

Another difficulty is the very poor heat transfer rate between a heat exchanger and a gas. A hot, low density gas like heated helium might have a thermal conductivity hundreds of times lower than a liquid like molten sodium. This leads to difficulties both at the heat exchange interface and the radiating surface interface. 

A lot of these issues can be solved by using a two-phase coolant loop, meaning it spends some of its time as a liquid and some of its time as a gas. Up to the heat exchanger, the coolant is in a liquid form. It flows through tubes using simple pumps. The heat exchanger is divided into many smaller tubes to increase the contact area between exchanger and coolant. 

Past the exchanger, the coolant expands. The pressure drop allows it to boil into a gas. This gas travels through a volume enclosed by a hermetic membrane. Through a combination of expansion decompression and the Stefan-Boltzmann law, the gas quickly cools and condenses on the membrane walls. This forms a thin film in microgravity that can be directed towards collection points, where the liquid is pumped back to the heat exchanger. 

Dusty Plasma radiator:

This radiator uses conductive plasma, manipulated by magnetic fields, to move and manipulate dust particles. 

The dust particles suspended in a plasma behave in fascinating ways, still being discovered by the dusty plasma field of research. Interesting behaviours include self-organising into quasi-crystalline structure, building DNA-strand-like bridges through plasma or collecting into disks with empty centres. This is all due to the self-repelling charges the dust particles gain inside the plasma. 

A better understanding of these behaviours can allow for a radiator to combine every advantageous characteristic: wide range of operating temperatures, very low mass per square meter, easily manipulated by electromagnetic and electrostatic forces, low vulnerability to damage and able to survive strong accelerations. 
A sheet of dust particles self-organizing into a 'plasma crystal'. 
The plasma can be quite cold and still serve to manipulate the dust particles. Low-temperature plasma does is safe to manipulate and is quite transparent to the wavelengths the dust particles will be radiating at, meaning it won't heat up or be blown away by thermal expansion. 

A simple dusty plasma radiator would have plasma trapped in magnetic loops, like coronal loops. Dust would travel along these plasma tubes. More advanced dusty plasma radiators would spray dust particles into a plasma and have it self-organize into thin planes for maximal radiating surface area. Simply changing the ionization state of the particles by running an electric current through the plasma would allow the dust to clump together and follow magnetic field lines straight back to a collector. 


  1. Crazy idea: Suppose a dusty plasma bed reactor could use the fission fragments directly as the coolant in a dusty plasma radiator?

    This is a trick that would only work well in space, of course, if at all-there might be interesting/undesirable reactions with a pressurized external environment.

    1. I don't think that would be very desirable. Fission fragments held close together heat up because they would capture neutrons from spontaneous decay and undergo fission, even if it is not at a self-sustaining rate.

      Even if you compensate for this, you'll be wasting the nuclear potential energy the moment you move it out of the reaction and all the while it is circulating through the cooling system.

      Finally, the cool dission fragments must thermally interact with the fragments that stayed in the reactor, to bring the average temperature down. This means some sort of heat conduction between hot fragments and cool fragments. Since the fragments in a dust bed reactor are not supposed to clump together, it will not allow direct conduction of heat, so the cooling effect of the cold fragments is minimal...

    2. Hmmm.

      I was looking at the concept diagram on wikipeda for dusty plasma bed reactors when I thought this up-the way to generate electricity seems to be decelerating the fission fragments, not capturing their heat.

      Unless you have a secondary, Carnot heat engine based generator, hot fission fragments don't seem to be something you want to have around, and the obvious solution of simply letting them escape into space means you'd have a FFRE thrusting away the whole time the reactor's on.

    3. Hey Matter Beam. I'm wondering about the calculation of the 5x5 dusty plasma radiator.
      In comparison, what would a lithium droplet system handle at the same dimensions?

    4. Lithium droplets, of 0.1mm diameter and spaced by 1mm, arranged into a stack of 10 sheets covering 25m^2, released at 1500K, would radiate over 720kW before being recovered at 1130K. The main benefit is that it would only mass about 21.3 grams, giving it an astonishing 33.75MW/kg heat rejection capability.

    5. Thank you very much man. I have no idea how to use that radiator calculator (yet), but I'm learning so much from just perusing this site.

  2. Are there any estimates how much the dusty plasma radiator can emit heat per square meter (or cubic meter?)?

    1. Its hard to say as little experimentation has been done on large-scale dusty plasma. However, watching videos of experiments such as these:
      we can surmise that the dusty plasma will act like a liquid droplet radiator with droplets around 1 micron in diameter and spaced at about 10 microns.

      The liquid droplet radiator calculator tells me that a sheet 5m wide and 5m long, containing 1 micrometer carbon particles ejected at 2000K, can remove ...

      the calculator is not longer available. :(
      I'll use this cached version:

      We get 9.8m^2 effective radiating area and a waste heat capacity of 8728MW.

      That's... terawatts of waste energy dealt away.

      A solid radiator of 5x5m operating at 2000K would at most handle 45MW.

    2. Wow, and I was trying to stick big retractable panels to my semi hard sf warships :p
      I really hope this radiator is explored in near future, it can save a lot of mass on spaceships.
      I have am idea, since the radiator is cold plasma with some particles in it, wouldn't it stop radiation if it was thick enough?

    3. Actually, it has been pointed out to me that the Liquid Droplet Radiator calculator on that website is wrong. It mixes up diameter and radius and outputs MW instead of kW.

      Use a new and updated calculator found on this excellent webpage:

      It reveals that the micron-particle radiator described above would emit 17MW at 2000K. It would still be massively more performant that an equivalent solid radiator in terms of kW/kg.

      The plasma in a cold-plasma/hot-particle dusty plasma radiator would be very thin and completely useless for blocking any sort of radiation.

    4. Thanks for the calculator, I will be using it in the future!
      I think I will try to put these radiators on my rocket drawings, instead of trying to fit big "normal" panels somewhere, which brings a question, how would the dusty plasma radiator look? A knob sticking out of spacecraft and surrounded by glowing mist of particles around it? Would that be correct?

    5. There's a bunch of other useful calculators on that page, be sure to use it often!

      Personally, I would avoid using dusty plasma radiators unless your technology level can handle fusion reactions in Tokamaks or is regularly handling antimatter in magnetic bottles. That is the level of magnetic technology that would be needed for dusty plasma radiators.

      It would be strange if you can handle a dusty plasma but cannot contain a fusion reaction with the same magnetic fields.

      How would it look?

      Well, there might be a continuous or pulsed design. A continuous design has the dust particles emerge from a heat exchanger and get dragged along by the plasma out and back to a collector, so they'd make faint loops that are white hot at one end and dull red or cold black on the other end. The pulsed operation spit a jet of plasma, flatten it, eject dust particles, have the dust spread rapidly into a plasma crystal configuration, then pull everything back in with a magnetic field manipulation. The whole cycle would take less than a second. It might resemble the spitting flames from a sport's car exhaust. It would be an interesting look on a spacecraft.

    6. "The plasma in a cold-plasma/hot-particle dusty plasma radiator would be very thin and completely useless for blocking any sort of radiation."

      Is there any difference between the plasma used in radiator and the plasma for radiation shielding on future spaceship?

    7. Ah, yes. The plasma shielding referred to by NASA over here ( is technically an electromagnetic anti-particle shield. The ultra-high velicity cosmic rays that are the biggest danger to astronauts in deep space are composed of charged particles. The plasma is there to generate a strong electromagnetic effect to deflect them from the spaceship's path.

      The sort of radiations I was talking about are those more frequently encountered by spacecraft using nuclear power: gamma rays, neutrons and so on. These are not charged particles and are not affected by magnetic fields. A plasma 'shield' is useless here - you'd need solid layers of anti-radiation protection.

  3. I came across something on NextBigFuture where panels essentially radiated infrared energy through atmospheric "windows" into space (

    While not a radiator per se, it does provide a passive means for keeping structural elements or structures like a lunar dome cool when exposed to raw sunlight.

    I wonder if you can expand on the idea of a "cooling laser" which crops up from time to time in Science Fiction (I remember reading about it first in David Brin's "Sundiver"), although the concept seems very counterintuitive to me (especially since lasers are power hogs and generate a great deal of waste heat of their own).

    1. I see a use for those mirrors as an external hull material on commercial spaceships and as a focusing lens for solar-thermal heat engines. By reflecting away sunlight, with can be over 1300W/m^2, the cooling needs of a spaceship can be greatly reduced. Sunlight can be concentrated to heat a working fluid in a heat engine (Carnot cycle) to 3000K. Between 3000K and 300K (temperature of the returning coolant from a radiator), we can get incredible efficiencies (90% or more).

      Cooling lasers do not conventionally cool things, hence the misunderstanding. Basically, they are special application items only used on gasses at extreme cryogenic temperatures. We're talking sub-kelvin temperatures where even helium heat pumps are ineffective.

      A gas at such temperatures still moves. Atoms drift at random velocities in random directions. They do not normally absorb photons from the laser because it is of the wrong wavelength - the gas is transparent. Atoms that move away from the laser see it Doppler shifted to a longer wavelength (like an ambulance siren moving away). Atoms moving towards the laser see the wavelength as shorter. This is critical. The doppler shifted wavelength in the latter case is absorbed by the atoms.

      So, the atoms moving towards the laser absorb a photon. Photons have momentum. The atom's momentum in one direction absorbs a photon's momentum in the opposite direction. The atoms ends up slowing down. They eventually re-emit the photons, creating a group of atoms with less energy than they started with.

      Over time, the velocity of the atoms in the gas is lowered. This means the gas becomes cooler.

      However, as you might have understood, laser cooling is not a closed system. Energy is consumed (laser generator) to move heat out of the gas, leading to more total energy but less energy in the gas.

  4. The post often mentions having the radiator operating at temperatures well over 1000 K. To get much work out of a heat engine the input temperature has to be well over the temperature of the heat sink (ie: the radiator for space applications) 1.5 to 2 times in Kelvins. Nuclear or solar thermal engines that I've seen written about never seem to have operating temperatures much over 1000 K & are often less. This seems to be a limitation of the materials available. Won't we have to go for radiators operating well below 1000 K to get our heat engines to work?

    1. Space applications is a pretty broad term if we include all the fictional possibilities a spacecraft might have.

      If we follow NASA's well-reasoned by very narrow set of restrictions, then the radiators must operate within the confines of the reactor temperature range. Since the solar powered designs only have to content with direct sunlight heating of the hull, and nuclear designs rarely have core temperatures greater than 1300K (limited mostly by the solid-state heat transfer systems), then radiators will not have a lot of headroom.

      The consequence of this is that the radiators will be pretty massive for the performance. At 1000K, a radiator will only remove about 45kW/m^2. This is fine for the tens-to-hundreds of kilowatts of waste heat these designs expect.

      But what about a future where megawatts of heat are expected? Gigawatts? What if there are other concerns, such as the radiator being shot off by enemy fire?

      In these cases, a smaller radiator becomes a much more critical issue.

      There's a point to make about power density too. A low temperature radiator will struggle to reject more than a few kW per kg. A nuclear reactor is very likely to produce a megawatt per kilo or more. Therefore, it is more mass efficient to have small radiators and a larger reactor to compensate for the smaller heat difference. These are lessons agreed upon from Children of a Dead Earth.

  5. Much of what is being discussed can almost be hand waved away by going to external power. This has a multitude of other advantages, since it disconnects you from the tyranny of the rocket equation and provides much higher performance at a lower cost per spaceship (the ultimate being millions of nano-mirrors being accelerated by high energy lasers).

    Most of the engineering challenges are being dealt with in a large, well equipped station in orbit or o a moon or asteroid (which is even better since you now have access to a huge heat sink, and the optical or microwave train is securely anchored on a massive platform), and all you need to deal with in the spaceship itself is hotel power and having sufficient backup in batteries or maybe an RTG to run things when you are off the beam.

    1. Handwaving by using external power only goes so far! Even the poor efficiency of waste heat reclamation generators that are indirectly heated by the uncontained products of a fusion reaction (neutrons, gamma rays, x-rays ect) can amount to several gigawatts if the main drive is putting out terawatts.

      Imagine a 1000 ton spaceship that you want to accelerate at 1G using a 2Mm/s exhaust velocity drive. The total output is a comfortable 10TW. The fusion reaction is proton-Boron for its widely available reaction products and very low neutron emissions.

      However, even this reaction produces 0.2% of its energy as neutrons. A spherical explosion would release maybe 10% of its neutrons in the direction of the spaceship. This would heat up the radiation shields as they intercept neutrons. From this heat, we could run a sodium-loop MHD or even a gas turbine, getting back maybe 40% of the energy.

      Total energy reclaimed? 800MW.

      Even externally-driven kinetic impacts create plasma explosions. Moving plasma in a magnetic field can be reflected for thrust... or partially slowed down to produce electricity.

      We can certainly reduce the problem by decreasing the multipliers between engine power and laser power again and again, but there are limits to plausibly low efficiency that make torch-level outputs dangerous for dynamic combat no matter what.

      Maybe 0.1g acceleration?

    2. There are a few notable problems with hand-waving the problem to external power supplies, even if the external supply is 100% efficient. The problem is that you now have to deal with all the infrastructure required to provide that external power support.
      There is going to be power drain involved with any transmission of power, as a result of distance. This means that much more power has to be generated.
      There will also be problems with assuring reception of the transmitted energy, as well as assuring the energy is available to transmit. If something comes between you and the power source, you pretty much have an instant loss of power.
      The next problem is that the source still needs to deal with that waste heat. Granted, if the source is on a planet or large asteroid, you can probable get away with dumping that heat into the surface... but while that is perhaps a good solution for a couple ships, it gets much more difficult when you are trying to handle the loads of an entire space fleet.
      Then there is the vulnerability issue. Your power sources are going to become prime targets, and they are unlikely to be as manoeuverable.
      Finally, beamed power supplies don't work very well at distances if you need any kind of manoeuverability. Even a milliarcsecond of error could prevent the receiver from collecting the power... which slows your ship down considerably if it has to send planned manoeuvering info to the source in time for the latter to adjust the transmission to cover for the manoeuver. The situation is even worse if something interferes with handling.

      Beamed power is okay if you have a very carefully planned science mission, but it is not particularly helpful for military operations.

    3. I agree with your points, except maybe with the milliarcsecond accuracy of power transmission requirement.

      If you have boatloads of power available, you can afford to cut your efficiency by spreading the beam over a large area. If your target is 10m across, spread the beam over 100m and compensate for the transmission inefficiencies by just producing more power.

      Accepting such a large spot size allows for the use of longer wavelength lasers, such as microwaves, that in turn mean that huge antennae or phased arrays can be made cheaply.

      Another point not made here is that stationary power sources can use very flimsy waste heat management systems. Things like massive liquid droplet radiators without membranes, or flux-pinned superthermal radiators extending over kilometers. If the rock never has to move, it can send its coolant loops over very long distances without having to worry about losing them due to vibration disturbances and other such issues.

  6. Is it possible to double the dusty plasma radiator into a plasma shield blocking cosmic rays and solar storm or the another way around?

    1. You could use the same equipment that generates and handles the plasma in a dusty plasma radiator for creating a plasma shield in front of the spaceship.

      This will help in situations where the incoming particles are going so fast that even hitting a plasma can vaporize them. This is the case when a spaceship is travelling between stars at fractions of C.

      The plasma can be used in interplanetary travel to boost a magnetic field. This allows it to effectively deflect relativistic charged particle radiation: cosmic rays.

      Performing these functions simultaneously would be difficult however. The magnetic manipulations required to expel, spread and recover the dust particles are not the same as those needed to deflect cosmic rays or hold a plasma in place.

      But... it might work if you create pockets in the magnetic field for the dusty radiator to act, or if you use the dusty plasma in a different plane from the plasma shield. The systems in that case would be adjacent instead of multi-functional.

  7. A quick thought as to why you might actually want physical radiators: integrating the radiators as physical elements to stiffen the spacecraft.

    If we picture a spaceship shaped roughly like the traditional paper airplane we have a series of triangular "fins" which will keep the structural spine of the ship fairly rigid. While the Earthbound paper airplane has the point forward, a nuclear powered spaceship would be "point backwards" to prevent the reflection and scattering of neutrons and radiation being emitted from the reactor.

    Depending on the length of the spacecraft, trusses, rings or other structural elements can be placed periodically along the length of the radiators, joining them together to provide more cross bracing and potentially fluid transfer between radiator units to reroute around damaged sections. Since radiators which face each other are less efficient, the image which comes to mind is a 4 finned "dart" with fins speed 90 degrees apart, the reactor at the "point" and the crew areas at the base. If the structure is large enough, the gentle rotation around the axis can provide artificial gravity to crew modules strung along the connecting ring between the ends of the radiators.

    Maybe not the traditional vision of a spaceship, but one which is strong and relatively lightweight for most missions.

    1. That might work for sturdy solid radiators. The kind which are simple blocks of metal with hollow tubes drilled through them for coolant to run through.

      For most solid radiator designs I know, minimum structural mass required to survive acceleration is the objective. There's a margin for safety, so the radiator can support perhaps three times the rated acceleration, but there is certainly no 'leftover' support for handling the stresses of the spacecraft's thrust frame.

      Basically, the way I see it, radiators are made as light as possible because they're so big, and if they were made strong enough to become part of the spacecraft's structure, then they'd become extremely heavy and would impose a great mass penalty.

      Another issue is material strength at high temperatures. Most metals lose the majority of their strength well before melting point. A solid radiator is therefore much weaker in operation than its construction materials suggest. Also, you cannot integrate it into the spacecraft's support structure, like a giant radiating truss, because everything else attached to that truss would also be bathed in thermal radiations.

      I think it is best to stick to min-maxing and optimizing each component for what it does best. Paper-thin radiators glowing as hot as possible, support structure reaching for the best strength-to-weight ratio possible.

    2. @Matter Beam:
      Try thinking about this the other way around. You are not multi-tasking the radiator. You are multi-tasking a structural framework.
      All you need is the property of being a good conductor, and a direct connection to the heat source, and the space frame itself becomes a reasonably good radiator. Of course, in the case of the wings, this would assume that you already have a need for such wings. Once you have the need for the structure itself, modifying it to serve the function as a radiator can fairly easily be done with virtually zero extra mass. Granted, the radiator might not be as efficient (it will not run at structural melting point). However, if the mass is already required for something else, the efficiency will not be that important. The key is that the structure is already large enough to provide the required surface area for whatever efficiency rating you CAN work with.
      Actually, there is no reason why you CAN'T have the radiator integrated into the support structure. All that is required is a very good layer of insulation to protect sensitive items... and that insulation layer can ALSO be incorporated into the support structure.
      Remember that multitasking structures is nothing new. For instance, propellant flow is used as coolant. Aerofoils are used as propellant tank skins. Pilot couches and control panel are built into (are part of) the structural frame of fighters (when you remove the couch during ejection, the nose of the craft will already begin to fold with the least amount of stress).

      In high school, I actually built a paper airplane with the point at the rear for a physics class competition. It actually made the distance record (it hit the far wall in the auditorium)... although not necessarily because of this reverse design.

    3. The problem here is that structural framework and radiators have incompatible criteria for the characteristics that make then 'good' at their job.

      For a framework, we want the highest affordable strength-to-weight ratio with a good lifetime tolerance to alternating stress cycles and some resistance to heating and cooling by sunlight.

      For a radiator, we want to highest affordable waste heat removal capacity to weight ratio. This means operating paper-thin surfaces at very high temperatures if possible.

      Most materials lose their strength when heated. Most materials expand and warp when heated. Something like aluminium, which is great for building spaceships out of, loses over half of its strength when heated above 600K.

      Are there materials which you can drill full of hollow spaces for coolant to run through, that survive multiple heating cycles ranging thousands of kelvin up and down, that have good strength-to-weight ratio when heating to useful radiator temperatures of 1000K+?

      Definitely. We just have to precise that they're advanced carbon-carbon composites!

  8. Just a quick note, although I don't know whether anyone will be paying attention to such a late post (sorry). Although technically true, in a way, this does not mean that every shacecraft will necessarily have a structure dedicated to the purpose (that is, it might radiate, but it might not be a radiator per se).
    A ship's hull itself can easily function as a radiator... and, by default, if there is no other structure to perform the task, WILL function as a radiator, whether you want it to or not. You don't even necessarily need coolant flow. All you need is good condictivity, and a direct (conductive) physical connection to the heat source... up to a point (there is a point at which the area of a hull will not be sufficient to dissapate the heat from the source... say, a nuclear reactor attached to something the size of the ISS). You MAY need a specialised radiator, but it is NOT a given requirement for all craft/vessels.
    As for drives, in many designs, the need for a radiator is eliminated by using the propellant as a heatsink. As the propellant is ejected, so is the waste heat. This is fine, so long as you are dumping a lot of mass. It does NOT work so well for highly efficient drives, however (such as VASIMR, or any other ion drive); and must be supplemented by other means for even upper-mid level efficiency drives (gas-core NTR, for example).
    So, although the presence of a dedicated radiator will be a common feature, I would avoid making universal assertions.

    1. Quite right about the hull-doubling-as-radiator function.

      There are a few caveats however. Hulls aren't uniform surfaces, some of it covers spaces which need to be insulated and protected from micrometeorites, like crew habitats, or can be very thin around propellant tanks. Only some sections can be used to radiate heat... but if it has any significant thickness, such as due to armoring, it will have terrible thermal conductivity and the waste heat removal rate will be low.

      You also have to protect some areas from heat conducting up and down the hull for the radiating sections. You don't want your reactor heat from leaking into the cryogenic hydrogen tanks!

      Also, the point of coolant supply inside radiator panels is to make sure the surface is evenly heated. Conducting from a small area into a large hull section will cause the point of contact to be hot and the edges to cold, which is a poor use of the available exposed surface area.

      There are solutions to all of these problems, yes, but in most cases the extra work and requirements of creating double hull/radiator sections is best avoided by using dedicated radiators.

      The universal assertion that radiators are needed still stands. Even rockets which nominally dump their heat into propellant flow, such as chemical rockets, still need radiators to deal with heat that isn't work pumping into the propellant flow, or to deal with heat when the engines are off and you want to prevent propellant from boiling over... the Space Shuttle deployed radiators after all.

  9. Something I rarely see even in hard science fiction is the use of droplet radiators at surface bases. Gravity makes them very easy to operate, as does avoiding acceleration, so they are natural choices for high density cooling of industrial or power generating operation. Conceivably lower maintenance costs too, since low density means short plumbing and fewer pumps. Could be quite aesthetically pleasing too, giant glowing fountains of liquid metal droplets arcing gracefully in lunar gravity from a shining cone.

    Some places might be better served by just laying pipe into the ground, but that requires you to have a high local heat conductivity and no worries about melting the ground out from under your power plant.

    1. I like the idea for use on ice moons, of which there are plenty. Rocky moons are better off running a coolant loop straight into the surrounding super-cool rock, while Titan colonies can just run air through their reactors.

      For safety reasons, you'd want the droplets to be pretty small so that you are absolutely certain that they've cooled much below glowing temperatures before they hit the ground. That way any accident won't spray your ground infrastructure with molten metal!

    2. Yeah spraying your equipment with liquid metal is less than ideal. Wouldn't this be a good system for mid solar system environments (of which I can only think of the moon)? I'm not sure what lunar subsurface temperatures/thermal conductivities are like, but this system allows you to reject heat with at a very high density. If your local rock is pretty warm and insulative you'll run into issues with "saturating" your medium.

      For ice moons, you'll need to include an upward facing cone of mylar or something so that your radiated heat isn't sublimating the ground around the fountain itself. I think this system becomes more and more attractive as your need to minimize space increases. Crowded industrial zones, that sort of thing.

  10. Liquid metal splashing and encrusting the surfaces of habitats far away from the Sun can still compromise insulation and pressurization and cause thermal stresses which would further compromise the affected surfaces.

    The advantage of geo-cooling is that you can use heat conductivity instead of heat radiation. The lunar crust should be about 120K just under the surface, continuing to drop until it rises again to 300K temperature at 100km under the surface. Thermal conductivity of this layer should be between 1 and 10W/m^2/K.

    A reactor running at 1300K can dump about 1.2 to 12kW/m^2. This might not sound like much, but heat exchangers going into the ground do not have to be flat panels. There is no inter-reflection to worry about. Spiky 'toilet-brush' heat exchangers with spike-like loops of cooling digging deep into the ground can allow for very high surface areas using very small dug-out volumes, which makes it quite competitive compared to spraying metal into the air.

    Ultimately, the specifics get lost under the much more significant influence of other details and assumptions in the setting. For example, if the radiator must be installed next to a spaceport, the spraying objects into the air is a bad idea. Alternatively, a first colony would be very mass-conscious and a lightweight droplet radiator might be a smarter idea than tons of digging equipment.

    I don't personally think we will ever reach the point where industrial zones become 'crowded' on celestial bodies. There's just too much room to spread things out over without incurring significant losses due to transport between the more remote infrastructure locations. Add in the need to stay away from radiation sources and thermal emitters like above-ground radiators, then spreading out your structures and resources might just become a design habit.

    1. I don't doubt human capabilities to misplan and get crowded. I think a mature spaceport is actually one of the more likely places to see one of these. You want a lot of equipment and facilities all clustered together. Some of that is going to need significant cooling, but volume might be too valuable to use for cooling.

      I can think of one other situation where this system mighta lot of sense. Mobile heavy surface equipment. You'd need high density power for mining or construction that moves along the surface. High density cooling lets you keep your vehicle size small. You could tether to a dug cooling well if you're going to be there long enough, but when you need mobility or can't dig for practical reasons it's pretty appealing to use droplets. He3 lunar mining (as dumb as that is) would benefit from this, as would almost any ice moon application as you pointed out before. I can even imagine a mobile factory building solar cells on the night side of Mercury. All depends on your application and how much you value weight and density vs complexity.

    2. To expand on the spaceport thought, just don't allow flight paths that cross the stream of droplets. Monitoring them with a simple array of IR cameras should be easy. If you're really worried, use electromagnets to catch stray dust.

    3. I agree on all points. This is why I actively encourage discussions in the comment threads! You always come up with something I hadn't thought about, such as heat management in fixed and mobile applications on the surface.

      For surface mining, there's always gunk scraping operations. Gunk is the mixture of extraplanetary dust and surface ices that accumulates over time. When all you've got is an icy desert, every mineral you can get is precious. It might actually be the only source of heavier elements such as sodium and calcium on pure-ice moons such as Enceladus, until underwater or deep mining operations commence.

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  12. Sry out of the topic but i wanted to ask can m2p2 mag sail lose heat just like dusty plasma radiators. If yes how big magnets would you need. And can mono pole magnets somehow help.

    1. The M2P2 sail traps plasma within a magnetic bubble long enough so the rate at which the plasma leaks out isn't too high. It is a one-way flow of plasma.

      A radiator needs a coolant *loop*. The plasma would have to exit the craft, cool down, and come back. That is why the M2P2 mag sail cannot act as a radiator.

  13. What about marangoni flow radiator. Atomic rocket says its the best radiator with least weight and highest heat rejection in amy convention readiator.

    I dont know much about this radiator so it would be nice if you can educate me.
    Also how would it look like. And how does it performs in high accleration like 1g.

    And how does it performs against LDR.

    1. I'm extremely skeptical of that radiator being possible. It is literally just a bubble in space. No coolant I know of can have both the surface tension necessary to not just pop in the vacuum, and have a vapor pressure low enough at 1300K that it doesn't immediately turn into a gas that drifts away.

  14. That seems reasonable. Is there a limite to how hot can your radiator be, we have materials which can withstand much higher heat so why to run them on 1300k why not 3000k?

    Also whats the next blog you are working on??

    1. If you are running your radiators at 3000K, then heat will flow out of the radiators and into your spaceship and not the other way round!

  15. Yes this is great stuff! Thanks for all this information. Radiators would be such a huge issue in future spacecraft design yet they are usually completely dispensed with in science fiction. Amazing what an oversight that is. I did a little research and hopefully I can add to the discussion above. Laser cooling has had several important breakthroughs in recent years and researchers have now demonstrated that they actually can cool electronics using it. Zhang et al. cooled semiconductors using "optical refrigeration". There are some advanced concepts in there about "phonon annihilation" and such. The basic principle, as I understand it, is that the heat is converted into photon emissions at a higher frequency, thus transferring the energy from heat to radiated photons. In space this might work even more efficiently as one could conceivably have a heat sink that emits all the way up into the gamma ray spectrum and really dumps a ton of heat generated by reactors and such. Of course the crew would have to stay out of the emitters' line of fire or they'd be irradiated and die. The Israeli company SolCold even claims to have a two-layer nanotech paint that fluoresces with this anti-Stokes effect, so that incident sunlight actually cools the paint surface! They are already talking about using it to cool satellites.

    1. Thanks @brougham!

      I can imagine the effect acting as a heat pump to move heat from the interior to the exterior of a building on the ground, but in space, the only way out for heat is through blackbody radiation. I am not sure that any technology can bypass the limit imposed by blackbody radiation.

      I'll try and do more reading about it though.