MatterBeam

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  1. I am really impressed by the level of effort you're putting into this, with mission badges, edited photos and full descriptions. Love it all!
  2. I found that the deltaVs required for braking just could not be handled by chemical propulsion once you accelerate the trajectories. For example, that trip to Mercury required over 14km/s braking burn. A hypergolic stage of 320s Isp would need a mass ratio of 86.5! The only real option is solar-electric. And nuclear-electric is the only option for performing one of the very high deltaV braking burns at the Outer Planets.
  3. This is from the latest ToughSF blog post: http://toughsf.blogspot.com/2019/05/starship-lite-from-rapid-interplanetary.html Starship Lite: from rapid Interplanetary to Interstellar Elon Musk stated that a stripped-down SpaceX Starship could become an interplanetary boost vehicle able to push probes towards the farthest objects in our Solar System. What other missions could the Starship ‘Lite’ do, and how quickly? Near SSTO Rockets performance scales favourably with size. A larger rocket dedicates less mass to propellant tanks, engines and other equipment relative to the quantity of propellant it can hold. In technical terms, bigger rockets have better mass ratios. The SpaceX Starship, planned to stand 55m tall, 9m wide and at 1350 tons on the launchpad, increasing to 118m and 4,400 tons once mounted on top of its giant booster stage, makes the most of its size. Art by Charlie Burgess. Despite being made of steel, the launcher manages a dry mass of 85 tons. The addition of landing legs, longer propellant tanks and large delta wings likely brings this closer to 90 tons. This gives it a mass ratio of (1350/90): 15. The current versions of the Raptor engines it uses have a sea-level Isp of 330s and a vacuum Isp of 360s. The average Isp over the course of a launch is about 350s. Tsiolkovsky’ rocket equation gives us the deltaV we can expect from the Starship: DeltaV = ln(Mass ratio) * Isp * 9.81 The deltaV is in m/s. The mass ratio is the dimensionless ratio of full to empty weight. Isp is in seconds, and multiplying it by 9.81 gives the exhaust velocity in m/s. We find that it can produce 9.3km/s of deltaV. This is enough to reach Low Earth Orbit, and validates claims that it can act as a single-stage-to-orbit vehicle. Art by Charlie Burgess. However, these figures are for a Starship with no payload onboard except the vehicle itself, and no reserve propellant to perform a powered landing. Placing 100+ tons in LEO requires the help of the ‘Superheavy’ booster. Starship Lite Elon Musk presented two versions of the Starship back in 2017: a crewed version and an uncrewed tanker or cargo-carrier version. The 85-90 ton figures are for the crewed version. It has to have a large habitable volume, life support systems and other contributors to a larger dry mass. The uncrewed version can dispense with all that. Its dry mass is reported to be 60-75 tons. The mass ratio increases to 18-22, as good as that of the Falcon 9 booster stage. This tweet from Elon Musk introduces what we’ll be calling the Starship Lite – a stripped-down version with no features meant for re-entry, recovery or holding a payload. It would be a naked steel tank with an engine at the bottom and used solely in space. Starship Lite has a mass ratio of 30, from a wet mass of 1200 tons and a dry mass of 40 tons. It is unknown why the wet mass is lower than previously stated. The engines can be optimized for the vacuum environment – the addition of huge nozzles increases their Isp to 380s. Going through the deltaV equation again, we find a value of 12.7km/s. It will likely resemble the vehicle on the right. Art by 'teamonster'. The vehicle could start out sitting in Low Earth Orbit, fuelled and ready to go. It could be a regular Starship that was converted in space instead of returned to Earth. Filling it up would take about 12 tanker launches. Alternatively, it could be boosted into an extremely elliptical orbit, reaching out to beyond the Moon in apoapsis (400,000km) and just above the atmosphere in periapsis (200km). Tankers would struggle to match its orbit and deliver more fuel, increasing the number of launches required to fill it up to 70 (!). For the following sections, we’ll attach various payloads to the Starship Lite and work out which missions can be carried out and how quickly they can get to their destination. Ultima Thule and beyond In that same tweet, Elon Musk talks about Starlink satellites converted into probes. They would have a solar-electric propulsion system with an Isp of 1600s, so with the mass ratio of 2, they’d have a deltaV of 10.9km/s. Between the elliptical orbit giving some starting velocity, a fully fuelled Starship Lite and the probes with their efficient engines, we can look forwards to some pretty extreme missions. Adding up the deltaV amounts, we can already tell that the probes can be put into trajectories that escape the Solar System. This is what probes Voyager I and II accomplished. Let’s look for the time required to reach the original goal: 2014 MU69 ‘Ultima Thule’. The asteroid orbits at a distance of 44.5 AU from the Sun on average. Because we don’t have a launch date, and we can assume that the launch will be optimally timed and won’t need an inclination adjustment, we can do some simple calculations. First of all, the Starship Lite is loaded with a couple of modified Starlink satellites. Let’s suppose 4 of them fit within a 1 ton payload. Mass ratio is reduced to 29.3 To escape Earth, the loaded vehicle burns all of its propellant at periapsis. It is already travelling at 10.9km/s, to which it adds 12.6km/s of deltaV. This gives it an initial velocity relative to Earth of 23.5km/s. The Oberth effect is significant. Even after gravity slows down the Starship Lite, we expect it to shoot away into interplanetary space at a whopping 20.9km/s. Earth orbits at 1 AU from the Sun at 29.7km/s. The escape velocity from the Sun at Earth’s orbit is 42km/s. Our Starship Lite leaves Earth and enters interplanetary space 50.7km/s. Another way of putting it is that the Starship is going faster than the Sun’s escape velocity… so it will continue travelling beyond the Solar System and go interstellar. After millions of years, it will meet another star system. A true star ship. Kerbal Space Program, modified to represent the real Solar System, can give decent approximations of the trajectories possible. If the screenshots taken look too small to read on your screen, right click and open them to full size in a new tab. We position a target in Ultima Thule’s rough orbit and send off a model of the Starship Lite to meet it. We find that Ultima Thule can be intercepted after about 6 years and 10 months. Our Starship Lite would pass the asteroid by at a blistering 28.6km/s! Let’s add the deltaV from the probes’ electric engines on top. They can raise the velocity at which they escape Earth by another 10.9km/s, allowing for a total of 31.8km/s relative to the Earth, or an incredible 61.6km/s relative to the Sun. The increased velocity shortens the travel time to 4 years and 7 months and the modified Starlinks cross the asteroid’s path going even faster. The biggest challenge would be resolving the asteroid in the probe’s cameras before it is out of sight again! To the planets, quickly There is plenty left to explore in the Solar System despite decades of probes and dozens of robotic missions. Scientists would love to be able to send a heavy probe loaded with instruments, RTGs, propellant and radiation shielding for long-duration missions to places such as Mercury or Uranus. The Cassini-Hyugens mission put a lander on Titan and orbited Saturn for 13 years. It represented a 5.7 ton payload. Using the payload capacity of the Starship Lite, we can put together a bigger, heavier and more capable probe. Since we want the probe to spend a long time doing science instead of flying past like at Ultima Thule, we need to have a way to brake and insert the probe into an orbit around its destination. This means that the probe needs propulsion capability. Now, working out the optimal probe mass ratios, power densities, ion engine endurance and all the other factors that go into proper mission design would take weeks of work and accurate simulation tools. ToughSF does not have access to those resources… so we will cut short the work by fixing the probe mass at 25 tons. Depending on the mission parameters, those 25 tons could be nearly entirely dedicated to scientific equipment (24 tons dry mass, 1 ton propellant), entirely filled with propellant (1 ton dry mass, 24 tons propellant) and anything in between. The exact propulsion type is left open. A hypergolic-fuel system with 320s Isp, where a lightweight 2 ton probe carries along 23 tons of propellants would have a deltaV capability of 7.9km/s would be ideal for a rapid gravity assist maneuver deep in Jupiter’s gravity well, where the radiation environment makes solar power tricky at the very least. A Starlink-like electric engine would work best when braking into orbit around Venus or Mercury, where abundant sunlight allows for decent acceleration. Going further, we could even expect a nuclear-electric power system and a HiPEP-derived 6000s Isp engine slowly accumulating velocity in the Outer Solar System; with a mass ratio of just 1.5, it would have a whopping 23.8km/s to perform a braking maneuver at Uranus or Neptune. Furthermore, we won’t be using the complicated and expensive elliptical orbit as a starting point. While it might be worth it for a once-in-a-lifetime opportunity to visit an interstellar asteroid leaving the Solar System, it would be too expensive of an option for the exploration of our planets. Instead, we will assume a straightforward and cheaper 1,000km starting altitude. We can go ahead and focus solely on the outbound trajectory from Low Earth Orbit. Where could Starship Lite position this 25 ton probe and how quickly could we get there? A 25 ton payload increases the Starship Lite’s dry mass to 65 tons. This decreases the mass ratio to 18.46, and its deltaV capability to 10.9km/s. From Hohmann trajectory data, we know that this is enough to reach every single body in the Solar System. However, relying on these trajectories means sometimes waiting for many decades for the probe to reach its destination. Instead, we will look at higher energy trajectories. We rely on Kerbal Space Program again to obtain approximations. Let’s start with Mercury. It is a difficult planet to get to. The latest attempt, BepiColombo, has to perform multiple flybys of Earth, Venus and Mercury before it can enter Mercury’s orbit 7 years after lift-off. We won’t be so patient! We’ll make for a single transfer to Mercury. We find that 10.9km/s is enough for a quick 55 day trip to Mercury. Venus is closer. Earth’s sister planet was last visited by JAXA’s Akatsuki probe in 2010, where it failed to reach the desired orbit due to a malfunctioning engine. It had to wait 5 years before it could try again. The ‘porkchop’ plots show us a way to get to Venus in a mere 30 days. Mars has had a permanent robot population since 1971. Insight, the newest inhabitant, took about 7 months to get there. According to our approximation, we could cut that down to 40 days with the Starship Lite. Jupiter is far away. Juno had 4 years and 10 months of drifting through space to reach the gas giant. A more energetic trajectory can carry a 25 ton probe to Jupiter in just under a year. Saturn can be reached with a Hohmann trajectory lasting 73 months. Cassini-Hyugens took about this long to have a look at the Solar System’s most impressive rings. If we had a Starship Lite sitting ready, we could have done it in just over 24 months. Uranus and Neptune will always take a long time to get to, as they are 19.2 and 30.1 AU from the Sun respectively. Voyager 2, the only probe to visit both planets, took 8 years and 5 months to fly past Uranus and a full 12 years to pass Neptune. Our faster trajectories mean a 4 year trip to Uranus and 7.5 years to Neptune. These long durations simply mean that chemical propulsion, even on the scale enabled by SpaceX vehicles, is not enough to cross over to the Outer Solar System in reasonable durations. It is much more likely that a good portion of the probe’s mass would be dedicated to electric rockets with high Isp that can shorten the trip and brake at the other end. Mars Express Elon Musk’s dream is Mars. Just how quickly could we get to Mars using the Starship Lite? It will depend of course on the payload we select for the mission. We also want to recover and reuse the Starship vehicle. Previous calculation assumed that once the payload separated from the vehicle, it would carry on into interplanetary or interstellar space, empty and discarded. Regular travel to Mars means that we would have to keep enough fuel in reserve to brake it into an orbit where it can be met by refuelling tankers. One complication with using the Starship Lite instead of the regular Starship is that it does not have any features that allow it to aerobrake. No heatshield, no wings and no fairings means it must rely solely on its own propellants. Let’s work out two scenarios: 10 ton fast, 10 ton staged and 10 ton ultrafast. In the 10 ton fast scenario, we have as the name suggests a payload of 10 tons. The dry mass of the Starship Lite is therefore 40+10: 50 tons. We work out a mass ratio of 24.2 and a deltaV capacity of 11.9km/s. When using 4.6km/s to leave a 1000km altitude Low Earth Orbit and 6.8km/s to brake into a ~31,000km altitude High Mars Orbit, we get a trip time of 120 days. The total deltaV is 11.5km/s. In the 10 ton staged scenario, the payload is separated from the Starship Lite before it starts its braking burn. This allows the payload to perform an aerobraking or aerocapture maneuver while the Starship brakes while 10 tons lighter. It is possible to accelerate by 5.36km/s leaving Earth to reach Mars in 95 days. After detaching from its payload, the Starship Lite can use its remaining 7.2km/s of deltaV to brake into a 170x800km Low Mars Orbit. The 10 ton ultrafast trajectory consumes the Starship Lite, because we are entering the atmosphere. The payload stages and performs an aerobrake or aerocapture maneuver, just like in the staged scenario, but the Starship Lite burns up alongside it. By not having to reserve any propellant for braking, we can take the most energetic trajectory possible. We find that using the full 11.9km/s deltaV capacity it has allows for a trip as short as 47 days. The only caveat is that we must hope the payload’s heatshield can withstand an entry into the Martian atmosphere at over 19km/s! Conclusion The Starship Lite would be an amazing booster for sending off probes to all of the Solar System’s planets with much reduced travel times, or carrying significant payloads to destinations rapidly. In the most energetic trajectories, it proves itself to be a true Star ship.
  4. Hi! I'm sorry if this has been asked before. Is these any way to run this calculator outside of KSP?
  5. This is from the latest Toughsf blog post: http://toughsf.blogspot.com/2019/05/actively-cooled-armor-from-helium-to.html Actively Cooled Armor: from Helium to Liquid Tin. We have seen designs for long ranged particle beams and powerful lasers. Could they be the end-all, be-all of space warfare? Not if we fend off their destructive power with actively cooled armor. Let's have a look at the different cooling solutions, from high pressure gas to liquid metal, and evaluate their relative effectiveness. Armor The armor curves away to hide the radiators from attack from the front. The traditional solution for defeating directed energy weapons such as particle beams and lasers is to use solid plates of armor. The armor material would ideally have a high heat capacity so that it doesn't heat up too quickly, and an excellent melting or boiling energy. Graphite excels in both. It is clearly superior when compared to steel or aluminium. We have written about the effectiveness of graphite when facing laser beams, and how we can use different techniques such as sloping, rotation and reflective surfaces to further increase the energy required to remove armor. However, certain techniques described in Lasers, Mirrors and Star Pyramids have limitations. Reflectivity in particular cannot be counted upon in all situations. While we might have broadband dielectric mirrors that effectively reflect a vast range of wavelengths, an enemy will eventually field lasers specifically meant to defeat them. They might select polarizations against which the mirror is less effective, they might use beams of wavelengths too short to reflect (usually below 200nm), or even replace lasers with particle beam weapons that ignore surface features entirely. What can we do against such mirror-defeating techniques? Can we increase the effectiveness of armor even further than what was calculated in Lasers, Mirrors and Star pyramids? Maximizing that energy value means you can get by with less armor and have more mass dedicated to winning tools such as propulsion or ammunition. Passive armor We can start with a reference to compare everything else to. Passive armor is simple in design and construction. It is made to handle as much heat as possible and prevent it from leaking into the spaceship. Graphite electrodes in an electric arc furnace. A good example, as mentioned above, is graphite. It first needs to be heated to about 3500K before it starts being degraded. At 4000K, it turns into a gas. Between its heat capacity and vaporization energy, it takes roughly 60 MJ/kg to vaporize. A stronger carbon-based material would take an equivalent amount of energy while also being physically strong. We can therefore expect graphite to handle a laser intensity of 8.5 MegaWatts per square meter for extended periods of time. This is a value calculated from the Stefan Boltzmann blackbody radiation equation, as it is the intensity required for a black surface to sit at an equilibrium temperature of 3500K. For the laser beam to start digging into the carbon at an appreciable rate, it must first overcome a 14.5 MW/m^2 threshold so that the temperature rises to 4000K, then it must add 60 MJ for each kilogram of carbon to be vaporized. We mentioned active cooling. Being able to remove 11 MW/m^2 using a coolant looping through the armor material significantly raises the damage threshold. In this case, it is increased to 19.5 and 25.5 MW/m^2 respectively. Two other techniques covered in Lasers, Mirrors and Star Pyramids are valid in all situations: sloping and rotating. We can add a good compound slope to the carbon surface: 80 degrees vertical and 67.5 degrees horizontal. This spreads the laser beam over a surface area about 15 times greater. Consequently, the laser now needs to reach an intensity of at least 292.5 MW/m^2. Rotation spreads the beam further. We could have a situation where the beam diameter is 12.56 times smaller than the armor’s circumference, and the average beam intensity is reduced by the same factor. All in all, carbon materials can survive 3.67 GW/m^2 for long periods of time or 4.8 GW/m^2 while ablating. If we have a 100 MW laser with a wavelength of 450nm, being focused by a 4 meter wide mirror, we would be able to damage a simple layer of carbon at a distance of 27,025 km. Using all the techniques just mentioned, the range is shortened to 1,300 km. Why shorten ranges? At very long ranges, space battles are boring with little room for tactical decisions. From here. We cover this issue in The Laser Problem: any moderately powerful laser can render maneuvers pointless. Warships cannot escape beam weapons. Even at distances where light lag becomes significant, the beam can be divided to cover a wider area while maintaining its destructive intensity. Shorter ranges allow for acceleration to matter more. Other weapon systems that do not have the supreme range of lasers and particle beams can come into play, such as missiles and kinetics. Angular separation starts to matter, allowing for flanking attacks against warships forced to be more well-rounded to fend off multiple weapons from different directions. It is also important from a narrative and visual perspective. Actions taken have a more immediate effect. Events happen quicker and the danger or relief is greater. It is easier to depict battles and the faster pace will be more agreeable to viewers. Actively cooled armor The 1,300 km figure given in the previous example is situational. It relies on the beam coming in from an ideal angle, which is straight down the edges of the star pyramid shape. If instead it came from a flanking angle, perhaps 80 degrees from the front, then the vertical slope of 80 degrees is completely negated. The benefit from sloping falls from a factor 15 to just 2.6, which makes the laser effective from a distance (15/2.6)^0.5: 2.4 times greater. In other words, a warship that sustain laser fire from the front at 1,300 km is vulnerable to flanking attacks out to 3,122 km. The benefit from rotation also varies with distance, as it changes the size of the beam’s spot relative to the target’s circumference. Intensity reduction by rotation = Beam spot radius / (3.142 * Armor radius) The reduction is a dimensionless number. Beam spot radius and armor radius are in meters. The beam spot radius decreases linearly as the distance decreases. If the warship is being shot at a distance two times closer, then the benefit from rotation is twice as great. This inverse relationship means significant gains from rotation at close distances and small gains at long distances. Distances, mirror sizes, beam wavelength, warship radii and even spot shapes are all variable, so we are unlikely to ever have one single number to describe the effect of rotation. What technique instead can we rely upon in all situations? Can we increase armor effectiveness without the enemy having to sit in certain positions and relative angles? Active cooling is the solution. We looked at figures of 11 MW/m^2 being removed by flowing water over hot surfaces. Further research shows fusion diverters and rocket engine chambers surviving 100 MW/m^2. We can go further, to absorb much more power. For the sake of comparison, we will be using a standardized model where a flat plate of armor sits under the glare of a laser beam. It conducts heat through a heat exchanging surface to a coolant flow underneath. The armor is 1cm thick and the coolant flow channel 1cm wide. We will calculate the power required to pump coolant to a certain velocity, and won’t allow velocities that cause turbulence in liquid or supersonic compression in gases. The heat is radiated away using simple 1mm thick carbon fiber radiators. There are fourth factors to consider for a proper comparison. The first is the heat that can be removed per square meter. The second is the pumping power requirement. The third is battle damage resistance, which is not as straightforward. The last is the radiator surface area required to handle the heat. We won’t be working out the effect of thermal conductivity as in most cases it is not the limiting factor. Gas cooled armor Gas cooled rocket nozzle Gases are an interesting coolant as they have no upper temperature limit. If the armor material is carbon and it can withstand a 3500K temperature, then we can select any gas and heat it up to that temperature in the heat exchanger. We are looking for the gas with the highest heat capacity. High heat capacity means less gas needs to flow through the heat exchanger to pick up the heat and carry it away. Less gas means reduced pumping power. We also want a gas that doesn’t condense at lower temperatures. Hydrogen is the best. However, it is reactive. It will chemically reduce the carbon and degrade it. Helium is a second-best alternative that is chemically inert. We want it entering the armor at 500K, heating up to 3500K and exiting to be cooled in a radiator back down to 500K. If it does not reach the desired temperature in one pass through the heat exchanger, it can be recirculated through at the cost of doubling the pumping power. The speed of sound in helium at 500K is 1315m/s. At 3500K, it is 3480m/s. We are limited to pumping below the smaller figure, so let’s give it Mach 0.9 (1183m/). This means we can push 1.13 kg/s under each square meter of armor at 1 bar of pressure, and 28.25 kg/s at 25 bar. Helium absorbs 5.19 kJ/kg/K. Over a temperature rise of 500 to 3500K, 28.25 kg/s will absorb 439.7 MW/m^2. Pumping power requirement depends on the pressure drop across the heat exchanger. It will be the highest of all designs considered in this post. The radiators happily handle the heat using 4994 m^2 and 5 tons of mass. Pumps will most likely resemble those of rocket engines. Gaseous cooling has the advantage that it can increase its performance with increased pumping pressure, and can maintain some degree of functionality while sustaining battle damage. A sudden increase in temperature is not so dangerous as pressure build-up can be vented into space. However, they have the highest pumping power requirements. While we are ignoring thermal conductivity in our calculations, gaseous cooling using helium has the lowest thermal conductivity of all the fluids we will be considering. This imposes certain design restrictions on the heat exchanger interface with the gas, which is trouble when we want the gas to be flowing through it at near Mach speeds. Metal vapor cooled armor Helium has high heat capacity but low density. We need a lot of pumping power to push enough volume through the heat exchanger to draw a decent amount of heat away. Metal vapour prepared for use as a lasing medium. The gases with the highest densities are metal vapours. The same volume brings a lot more mass throughput and therefore cooling capacity. We want a metal that is dense but boils easily. Mercury is ideal. It boils at 630K, so we’ll set the minimum temperature to 750K to prevent it condensing back into a liquid. As before, we heat it up to 3500K. Boiling mercury. The average density of a mercury vapor at 25 bar, between 750 and 3500K, is 48.7 kg/m^3. It would have a heat capacity of 104 J/kg/K and a speed of sound of 227 m/s at 750K. Putting all this together, we expect to push 99.5 kg/s through the 1cm wide heat exchanger and extract 28.5 MW/m^2. This is a much lower performance than with. Pumping requirements are a significantly lower. It is estimated that mercury vapours remove 5 kW of heat from the armor for every watt of pumping power, which is about 20% better than for helium. Only 1563 m^2 of radiators weighing 1.6 tons are needed to handle the heat. The reduced pumping requirements means that you can use many smaller pumps to push the mercury gas through heat exchangers, which helps with redundancy. However, a sudden pressure drop from holes created in the armor are likely to cause the mercury to suddenly expand, cool and revert to its liquid form. The droplets would quickly block gas flow through narrow channels in the heat exchanger. Another difficulty is that mercury can solidify completely behind unheated or damaged armor. Re-establishing a coolant flow is impossible unless the mercury is boiled again to clear the heat exchanger’s channels. Armor would have to ‘go hot’ before battles and prevented from cooling down too much when not under beam attack. Water cooled armor The traditional cooling liquid is water. It is much denser than a gas, has good thermal conductivity and very high heat capacity. Water’s temperature range is its main limit. If we use it as a liquid, we impose that we use very low temperatures to reject heat from the radiators. Consequently, huge radiating areas would be needed. If we use it as a gas at the same temperatures as helium or metal vapours, it will corrode the heat exchanger and chemically attack everything it touches. Instead, we use a phase change design. High pressures allow water to stay liquid beyond the standard 373K boiling point. It is then heated into steam, up to the maximum temperature the heat exchanger can handle without corrosion. After passing through the radiators, it condenses back into water. The complicated phase diagram of water. At 25 bar, we can retain liquid water at 480K. That will be our minimum temperature. It has a density of 1197 kg/m^3. We find steam turbine coatings such as chromium steel able to resist 873K steam for thousands of hours, or chromium-niobium alloys at 923K. That will be our maximum temperature. Steam has an average heat capacity of 2.56 kJ/kg/K between 480 and 920K. The phase change from liquid to gas also absorbs energy. For water, this is a whopping 1840 kJ/kg when starting from 480K. Adding the heat absorbed by the phase change and then rise in temperature, we obtain a total of 2966 kJ/kg. We cannot allow turbulent flow through the heat exchanger, as this drastically decreases the heat transfer rate. Based on a fluid’s Reynolds number and viscosity, we can estimate the maximum velocity before the start of turbulent flow. In this case, it can only be 24 m/s when passing through a 1cm gap. With that flow rate, we get as much as 286.8 kg/s passing through the heat exchanger removing 850 MW/m^2. This is impressive performance. The pumping power requirements are drastically lower than any gas (on the order of 2 kW of heat removed per watt of pumping power). Water has the advantage of gaining most of its heat removing capacity through its phase change when cooling armor from as low as 373K. Increasing the temperature of the armor and therefore of the heat exchanger only improves performance. Another advantage is that it is likely to serve a second role as propellant on spacecraft. Electric, nuclear and solar rockets can all use water. The consequences are that the coolant needed for the armor’s active cooling does not have to be dead weight, and that after being heated into steam, it can be pushed through a nozzle instead of passed into radiators. During battle, if radiators are hidden or destroyed, the armor can still be kept cool by using water as an open-cycle coolant. There are downsides though. Water increases in volume over a thousand-fold between liquid and gaseous states. Designing a phase change heat exchanger where liquid enters one side and gas exits the other is tricky to do, and is unlikely to work after receiving battle damage. In fact, creating a hole in the heat exchanger would release pressure and allow the water entering as a liquid to suddenly boil and practically explode in the pipes. Just like mercury, water can freeze into ice when not heated. Damaged pipes can see themselves blocked by this ice, cutting further cooling. Thankfully, the phase change from liquid into solid also takes a lot of energy, so there is usually plenty of time to re-heat the water and get it flowing again. The biggest disadvantage is the maximum temperature restriction on the armor and heat exchanger. Above 920K, the thin layer of water or steam in contact with the heat exchanger starts corroding the protective layer quickly. If the armor is at 3000K, it will be superheating a small quantity of steam to a vigorous oxygen-hydrogen plasma, even if the average temperatures within the heat exchanger as within bounds. Therefore, if the laser intensity overwhelms the cooling capacity and the armor starts heating up to higher temperatures, we will start to see degraded heat exchangers and a decrease in cooling capacity. This is a self-reinforcing cycle that destroys the armor. Eutectic cooled armor Sodium-Potassium coolants for use in TOPAZ-II space reactor. Liquid coolants have much reduced pumping power requirements. Instead of water with its restrictive temperature limitations, we might select a coolant that can handle much temperatures. NaK properties. Eutetics are mixtures of two or more elements that have a lower melting point than either pure element. A prime example is sodium and potassium used as ‘molten salt’ coolant in nuclear reactors or solar energy storage facilities. Sodium and potassium melt at 371K and 337K respectively, but their eutectic mixture melts at just 260K. Looks a lot like mercury, but not toxic. From here. We will be using Galinstan. It is a mixture of gallium, indium and tin. It melts at 254K and boils at 1573K. With a density of 6440 kg/m^3, a heat capacity of 296 J/kg/K and a laminar flow velocity of 85m/s, we find that we can remove 1738MW/m^2 while radiating away heat at 500K. This incredibly performance is possible due to the fluid’s high density and high viscosity. Pumping requirements will be significant, and you’d need 490,606 m^2 or 491 tons of radiators for every square meter of armor receiving this intensity, but it is worthwhile when it can reduce ranges by so much. Galinstan would work perfectly inside a liquid droplet radiator. A note on the radiator requirements: this number is not to be used simply as it is presented. 490,606m^2 are only needed if the enemy beam covers an entire square meter with 1738 MW of power. It is much more likely that a much less powerful beam, for example 100 MW, is focusing its power onto a small spot, perhaps 27cm wide. This gives the same intensity (1738 MW/m^2) but the total heat that must be handled is only 100 MW. The radiator area needed to handle the heat is just 28,218 m^2. One advantage of Galinstan is that it remains liquid at very low temperatures, so there is a much reduced risk of it solidifying and blocking cooling channels. Another is that as an electrically conductive mix of metals, we can use electromagnetic pumping that can end up being more efficient and more damage resistant than conventional pumps. The main disadvantage is that lasers or particle beams can strike multiple spots along an armor surface without warning, so the coolant flow much be able to compensate for any heating across its entire surface. In other words, the pumps must consume large amounts of power to keep Galinstan flowing across the entire armor surface! Another challenge is when beam intensity overwhelms cooling capacity. 1573K is a decently high boiling point, but it is still lower than the 3500K that carbon materials can handle. A hot spot can create vapor bubbles in the Galinstan flow that could cause destructive cavitation or blocked flow in small channels of a hat exchanger. Liquid metal cooled armor There are liquids that can handle much higher temperatures without boiling. Liquid metals have the highest boiling points. To be a good coolant, we could use a metal with a fairly low melting point, a very high boiling point and the best heat capacity possible. There are many good choices, including plutonium, but we will look at these four in particular: tin, indium, aluminium and cerium. Indium has a melting point of 430K and a boiling point of 2345K. It has a density of 7020 kg/m^3 and a heat capacity of 233 J/kg/K. We work out that 2944 MW/m^2 can be removed between 500K and 2300K. Tin has a melting point of 505K and a boiling point of 2875K. It has a density of 6990 kg/m^3 and a heat capacity of 228 J/kg/K. We work out that 3666MW/m^2 can be removed between 550 and 2850K. Aluminium has a melting point of 934K and a boiling point of 2792K. It has a density of 2375 kg/m^3 and a heat capacity of 896 J/kg/K. We work out that 3767 MW/m^2 can be removed between 980 and 2750K. Cerium has a melting point of 1071K and a boiling point of 3697K. It has a density of 6550 kg/m^3 and a heat capacity of 192.4 J/kg/K. We work out that 2999 MW/m^2 can be removed between 1120 and 3500K. For all of the calculations, we limited the flow velocity to 100m/s, despite maximum laminar flow velocities reaching double and more. This gives a more plausible 1m^3 per second volumetric flow rate. We have ceramic pumps that can handle liquid metals, and we go further. The performance of liquid metal cooled armor far exceeds that of other cooling solutions. Indium is at the lowest risk of solidifying in the pipes, but has the highest pumping requirement and imposes the lowest temperature limit on the armor. Aluminium provides the best performance and the lowest pumping power requirement, but it is the most reactive of the metals and so needs a protective layer in between it and the carbon armor. Cerium, with its very high boiling point, is unlikely to ever create vapour bubbles in the heat exchanger and has the smallest radiators, but it is also at the greatest risk of solidifying inadvertently. Tin is the overall best choice. The danger of course is that a battle starts with the tin in its solid state. Directed energy weapons could add heat to an armor plate too quickly for the tin to melt and start flowing to draw it away. Ideally, the tin is constantly flowing at the minimum temperature, which is 550K in this case. For efficiency’s sake, it could be kept molten using waste heat from a nuclear reactor. However, pumping the metal would consume electrical power that has to be taken away from other systems. Liquid tin as a thermal transport coolant to a solar energy storage system. Spaceship designers could make use of the armor layer as another radiator. It would be durable and usable even in battle. Other than the sections under laser attack, it could be rejecting up to 3.5 kW of waste heat for each square meter sitting on liquid tin. This feature could compensate for the extra heat from a nuclear reactor that needs to operate at a higher power level to feed the pumps with electricity. Reduced beam ranges Let’s work out the effective range of a beam weapon facing a carbon armor layer using all the tricks available to us: rotation, compound sloping and active cooling. As before, we set the weapon to be a 100 MW laser of 450nm wavelength, being focused by a 4m wide mirror. The target will an eight-pointed star (octagram) pyramid 6m wide at the base and 17.3 meters long. This gives it a vertical slope of 80 degrees and a horizontal slope of 67.5 degrees. Each face of the octagram is 1.76m long, which means a total circumference of 28.1m. Before combat, the armor maintains a flow of liquid tin through it. It serves as a radiator which handles about 1.26 MW of heat on its own. During combat, 3.6 GW/m^2 can be absorbed when the liquid tin gets really hot. The maximum temperature we’ll allow is 2800K to prevent any hotspots from boiling the tin. The heated carbon also radiates another 3.5MW/m^2, but this is a tiny contribution. An enemy attacking the pointy end of the star pyramid would face a compound slope that spreads their beam over a surface area 15 times greater. This is a 15-fold reduction in intensity. Working it out, the armor can handle 54.2 GW/m^2 with ideal sloping. If the enemy attacked from the side, they would face only the horizontal slope that reduces intensity by 2.6-fold. The armor can only handle 9.4 GW/m^2 in that case. We can see already that the intensities the armor can handle are much greater than in previous examples. The laser we are considering can only produce an intensity of 9.4 GW/m^2 at distance of 812.6 km. If our warship is outnumbered, it would want to stay at least this distance away from its closest opponent. 54.2 GW/m^2 is only possible at a distance of 338.4 km. Our warship can get this close if it is confident that it can always face its pointy end to the enemy. What about rotation? In these scenarios, the benefits could be massive. At 338.4km, the spot radius of the laser is 2.4cm, and at 812.6km, it is 5.8cm. These are 1170.8x and 484.5x smaller than the circumference of our armor. In ideal conditions, it is a reduction in intensity of 1170.8x and 484.5x. A supremely confident commander could bring our warship to single-digit kilometres in front of the beam and expect to spread its power enough to never overwhelm its cooling capacity! There are important consequences for this sort of cooling capacity and reduction beam ranges. Many depend on the specifics of the setting where space warfare takes place. Laser attack, captured and edited from this Children of a Dead Earth video. In general though, we can reasonably expect that battles will revolve around achieving a flanking position, suppressing the cooling capability of the armor or preventing electrical generation that powers the pumps. The latter two objectives can be achieved by pulsed lasers, penetrating particle beams, kinetic strikes and other weaponry that are not continuous beams. At the very least, the threat of giant laser-equipped warships and their dampening effect on any sort of eventful space combat can be reduced or eliminated in science fiction.
  6. I followed for your excellent post on the RD-600 russian gas-core rocket. The quenching comes from the interaction between the photons generated by the lasing medium and the massive cloud of electrons surrounding an atom like uranium. Thorium, with 90 electrons, will very likely have the same quenching effect as Uranium, with 92 electrons.
  7. Only when cooled, and only up to 70% Look at this document: http://epubs.surrey.ac.uk/841789/1/Scott_Jarvis_Final_Thesis_280717.pdf With a powerful laser, you can just use a laser-thermal propulsion system. Even more lightweight and with greater overall efficiency than with intermediate electrical conversion steps. It has also been proven at 5000s Isp: http://toughsf.blogspot.com/2017/03/laser-launch-into-orbit.html
  8. Hi @Pak What were your reference documents for this design? I know it comes from a real life study!
  9. The direct thrust from a nuclear reactor laser is too small to matter. Because of this, a photonic propulsion system was not proposed or discussed in the blog post or the text I copied. Instead, the laser is used as a weapon or to beam power over long distances. You can estimate the acceleration from the power density. 1kW/kg gives an acceleration of 2.26 nanogees.
  10. This is from Nuclear Reactor Lasers: from Fission to Photon: http://toughsf.blogspot.com/2019/04/nuclear-reactor-lasers-from-fission-to.html Nuclear Reactor Lasers: from Fission to Photon Nuclear reactor lasers are devices that can generate lasers from nuclear energy with little to no intermediate conversion steps. We work out just how effective they can be, and how they stack up against conventional electrically-powered lasers. You might want to re-think your space warfare and power beaming after this. Nuclear energy and space have been intertwined since the dawn of the space age. Fission power is reliable, enduring, compact and powerful. These attributes make it ideal for spacecraft that must make every kilogram of mass as useful and as functional as possible, as any excess mass would cost several times its weight in extra propellant. They aim for equipment for the highest specific power (or power density PD), meaning that it produces the most watts per kilogram. Lasers use a lasing medium that is rapidly energized or ‘pumped’ by a power source. Modern lasers use electric discharges from capacitors to pump gases, or a current running through diodes. The electrical power source means that they need a generator and low temperature radiators in addition to a nuclear reactor… these are significant mass penalties to a spaceship. Fission reactions produce X-rays, neutrons and high energy ions. The idea to use them to pump a lasing medium has existed ever since the first coherent wavelengths were released from a ruby crystal in 1960. Much research has been done in the 80s and 90s into nuclear-pumped lasers, especially as part of the Strategic Defense Initiative. If laser power can be generated directly from a reactor, there could be significant gains in power density. The research findings on nuclear reactor lasers were promising in many cases but did not succeed in convincing the US and Russian governments to continue their development. Why were they unsuccessful and what alternative designs could realize their promise of high power density lasers? Distinction between NBPLs and NRLs Most mentions of nuclear pumped lasers relate to nuclear bombpumped lasers. They are exemplified by project Excalibur: the idea was to use the output of a nuclear device to blast metal tubes with X-rays and have them produce coherent beams of their own. We will not be focusing on it. The concept has many problems that prevent it from being a useful replacement for conventional lasers. You first need to expend a nuclear warhead, which is a terribly wasteful use of fissile material. Only a tiny fraction of the warhead’s X-rays, which are emitted in all directions, are intercepted by the metal tube. From those, a tiny fraction of its energy is converted into coherent X-rays. If you multiply both fractions, you find an exceedingly low conversion ratio. Further research has revealed this to be on the order of <0.00001%. It also works for just a microsecond, each shot destroys its surroundings and its effective range is limited by relatively poor divergence of the beam. These downsides are acceptable for a system meant to take down a sudden and massive wave of ICBMs at ranges of 100 to 1000 kilometers, but not much else. Instead, we will be looking at nuclear reactor pumped lasers. These are lasers that draw power from the continuous output of a controlled fission reaction. Performance We talk about efficiency and power density to compare the lasers mentioned in this post. How are we working them out? For efficiency, we multiply the reactor’s output by the individual efficiencies of the laser conversion steps, and assume all inefficiencies become waste heat. The waste heat is handled by flat double-sided radiator panels operating at the lowest temperature of all the components, which is usually the laser itself. This will give a slightly poorer performance than what could be obtained from a real world engineered concept. The choice of radiator is influenced by the need for easy comparison instead of maximizing performance in individual designs. We will note the individual efficiencies as Er for the reactor, El for the laser and Ex for other components. The overall efficiency will be OE. OE = Er * Ex * El * Eh In most cases, Er and Eh can be approximated as equal to 1. As we are considering lasers for use in space with output on the order of several megawatts and beyond, it is more accurate to use the slope efficiency of a design rather than the reported efficiency. Laboratory tests on the milliwatt scale are dominated by the threshold pumping power, which cuts into output and reduces the efficiency. As the power is scaled up, the threshold power becomes a smaller and smaller fraction of the total power. Calculating power density (PD) in Watts per kg for several components working with each other’s outputs is a bit more complicated. As above, we’ll note them PDr, PDl, PDh, PDx and so on. The equation is: PD = (PDr * OE) / (1 + PDr (Ex/PDx + Ex*El/PDl + (1 - Ex*El)/PDh)) Generally, the reactor is a negligible contributor to the total mass of equipment, as it is in the several hundred kW/kg, so we can simplify the equation to: PD = OE / (Ex/PDx + Ex*El/PDl + (1 - Ex*El)/PDh) Inputting PDx, PDl and PDh values in kW/kg creates a PD value also in kW/kg. Direct Pumping The most straightforward way of creating a nuclear reactor laser is to have fission products interact directly with a lasing medium. Only gaseous lasing mediums, such as xenon or neon, could survive the conditions inside a nuclear reactor indefinitely, but this has not stopped attempts at pumping a solid lasing medium. Three methods of energizing or pumping a laser medium have been successful. Wall pumping Wall pumping uses a channel through which a gaseous lasing medium flows while surrounded by nuclear fuel. The fuel is bombarded by neutrons from a nearby reactor. The walls then release fission fragments that collide with atoms in the lasing medium and transfer their energy to be released as photons. The fragments are large and slow so they don’t travel far into a gas and tend to concentrate their energy near the walls. If the channels are too wide, the center of the channel is untouched and the lasing medium is unevenly pumped. This can create a laser of very poor quality. To counter this, the channels are made as narrow as possible, giving the fragments less distance to travel. However, this multiplies the numbers of channels needed to produce a certain amount of power, and with it the mass penalty from having many walls filled with dense fissile fuel. The walls absorb half of the fission fragments they create immediately. They release the surviving fragments from both faces of fissile fuel wall. So, a large fraction of the fission fragment power is wasted. They are also limited by the melting temperatures of the fuel. If too many fission fragments are absorbed, the heat would the walls to fail, so active cooling is needed for high power output. The FALCON experiments achieved an efficiency of 2.5% when using xenon to produce a 1733 nm wavelength beam. Gas laser experiments at relatively low temperatures reported single-wavelength efficiencies as high as 3.6%. The best reported performance was 5.6% efficiency from an Argon-Xenon mix producing 1733 nm laser light, from Sandia National Laboratory. Producing shorter wavelengths using other lasing mediums, such as metal vapours, resulted in much worse performance (<0.01% efficiency). Higher efficiencies could be gained from a carbon monoxide or carbon dioxide lasing medium, with up to 70% possible, but their wavelengths are 5 and 10 micrometers respectively (which makes for a very short ranged laser) and a real efficiency of only 0.5% has been demonstrated. One estimate presented in this paper is a wall-pumped mix of Helium and Xenon that converts 400 MW of nuclear power into 1 MW of laser power with a 1733 nm wavelength. It is expected to mass 100 tons. That is an efficiency of 0.25% and a power density of just 10 W/kg. It illustrates the fact that designs meant to sit on the ground are not useful references. A chart from this NASA report reads as a direct pumped nuclear reactor laser with 10% overall efficiency having a power density of about 500 W/kg, brought down to 200 W/kg when including radiators, shielding and other components. Volumetric pumping Volumetric pumping has Helium-3 mixed in with a gaseous lasing medium to absorb neutrons from a reactor. Neutrons are quite penetrating and can traverse large volumes of gas, while Helium 3 is very good at absorbing neutrons. When Helium-3 absorbs neutrons, it creates charged particles that in turn energize lasing atoms when they enter into contact with each other. Therefore, neutrons can fully energize the entire volume of gas. The main advantages of this type of laser pumping is the much reduced temperature restrictions and the lighter structures needed to handle the gas when compared to multiple narrow channels filled with dense fuel. However, Helium-3 converts neutrons into charged particles with very low efficiency, with volumetric pumping experiments reporting 0.1 to 1% efficiency overall. This is because the charged particles being created contain only a small portion of the energy the Helium-3 initially receives. Semiconductor pumping The final successful pumping method is direct pumping of a semiconductor laser with fission fragments. The efficiency is respectable at 20%, and the compact laser allows for significant mass savings, but the lasing medium is quickly destroyed by the intense radiation. It consists of a thin layer of highly enriched uranium sitting on a silicon or gallium semiconductor, with diamond serving as both moderator and heatsink. There are very few details available on this type of pumping. A space-optimized semiconductor design from this paper that suggests that an overall power density of 5 kW/kg is possible. It notes later on that even 18 kW/kg is achievable. It is unknown how the radiation degradation issue could be solved and whether this includes waste heat management equipment. Without an operating temperature and a detailed breakdown of the component masses assumed, we cannot work it out on our own. Other direct pumped designs Wall or volumetric pumping designs were conceived when nuclear technology was still new and fission fuel had to stay in dense and solid masses to achieve criticality. More modern advances allow for more effective forms for the fuel to take. The lasing medium could be made to interact directly with a self-sustaining reactor core. This involves mixing the lasing medium with uranium fluoride gas, uranium aerosols, uranium vapour at very high temperatures or uranium micro-particles at low temperatures. The trouble with uranium fluoride gas and aerosols or micro-particles is the tendency for them to re-absorb the energy (quenching) of excited lasing atoms. This has prevented any lasing action from being realized in all experiments so far. As this diagram shows, uranium fluoride gas absorbs most wavelengths very well, further reducing laser output. If there is a lasing medium that is not quenched by uranium fluoride, then there is potential for extraordinary performance. An early NASA report on an uranium fluoride reactor lasers for space gives a best figure of 73.3 W/kg from what is understood to be a 100 MW reactor converting 5% of its output into 340 nanometer wavelength laser light. With the radiators in the report, this falls to 56.8 W/kg. It we bump up the operating temperature to 1000K, reduce the moderator to the 20cm minimum, replace the pressure vessel with ceramics and use more modern carbon fiber radiators, we can expect the power density of that design to increase to 136 W/kg. Uranium vapours are another option. They require temperatures of 4000K and upwards but if the problem of handling those temperatures is solved (perhaps by using actively cooled graphite containers), then 80% of the nuclear output can be used to excite the lasing medium, for an overall efficiency that is increased four-fold over wall pumping designs. More speculative is encasing uranium inside a C60 Buckminsterfullerene sphere. Fission fragments could exit the sphere while also preventing the quenching of the lasing material. This would allow for excellent transmission of nuclear power into the lasing medium, without extreme temperature requirements. Nuclear-electric comparison With these numbers in mind, it does not look like direct pumping is the revolutionary upgrade over electric lasers that was predicted in the 60s. Turbines, generators, radiators and laser diodes have improved by a lot, and they deliver a large fraction of a reactor’s output in laser light. We expect a space-optimized nuclear-electric powerplant with a diode laser to have rather good performance when using cutting edge technology available today. With a 100 kW/kg reactor core, a 50% efficient turbine at 10 kW/kg, an 80% efficient electrical generator at 5 kW/kg, powering 60% efficient diodes at 7 kW/kg and using 1.34 kW/kg radiators to get rid of waste heat (323K temperature), we get an overall efficiency of 24% and a power density of 323 W/kg. A more advanced system using a very powerful 1 MW/kg reactor core, a 60% efficient MHD generator at 100 kW/kg with 1000K 56.7 kW/kg radiators, powering a 50% efficient fiber laser cooled by 450K 2.3 kW/kg radiators, would get an overall efficiency of 30% and a power density of 2.5 kW/kg. Can we beat these figures with reactor lasers? Indirect pumping The direct pumping method uses the small fraction of a reactor’s output that is released in the form of neutrons, or problematic fission fragments. Would it not be better to use the entire output of the nuclear reaction? Indirect pumping allows us to use 100% of the output in the form of heat. This heat can then be converted into laser light in various ways. Research and data for some of the following types of lasers comes from solar-heated designsthat attempt to use concentrated sunlight to heat up an intermediate blackbody that in turn radiates onto a lasing medium. For our purposes, we are replacing the heat of the Sun with a reactor power source. It is sometimes called a ‘blackbody laser’ in that case. Blackbody radiation pump At high temperatures, a blackbody emitter radiates strongly in certain wavelengths that lasing materials can be pumped with. A reactor can easily heat up a black carbon surface to temperatures of 2000 to 3000K – this is what nuclear rockets are expected to operate at anyhow. Some of the spectrum of a blackbody at those temperatures lies within the wavelengths that are absorbed well by certain crystal and gaseous lasing mediums. Neodymium-doped Ytrrium-Aluminium-Garnet (Nd:YAG) specifically is a crystal lasing medium that has been thoroughly investigated as a candidate for a blackbody-pumped laser. It produces 1060 nm beams. Efficiency figures vary. A simple single-pass configuration results in very poor efficiency (0.1 to 2%). This is because the lasing medium only absorbs a small portion of the entire blackbody spectrum. In simpler terms, if we shine everything from 100 nm to 10,000 nm onto a lasing medium, it will convert 0.1 to 2% of that light into a laser beam and turn the rest into waste heat. With this performance, blackbody pumped lasers are no better than direct pumped reactor laser designs from the previous section. Instead, researchers have come up with a way to recover the 99 to 99.9% of the blackbody spectrum that the lasing medium does not use. This is the recycled-heat blackbody pumped laser. An Nd:YAG crystal sits inside a ‘hot tube’. Blackbody radiation coming from the tube walls passes through the crystal. The crystal is thin and nearly transparent to all wavelengths. The illustration above uses Ti:Sapphire but the concept is the same for any laser crystal. Only about 2% of blackbody spectrum is absorbed with every pass through the crystal. The remaining 97 to 98% pass through to return to the hot tube’s walls. They are absorbed by a black carbon surface and recycled into heat. Over many radiation, absorption and recycling cycles, the fraction of total energy that becomes laser light increases for an excellent overall efficiency. 35% efficiency with a Nd:YAG laser was achieved. The only downside is that the Nd:YAG crystal needs intense radiation within it to start producing a beam. The previous document suggests that 150 MW/m^3 is needed. Another source indicates 800 MW/m^3. We also know that efficiency increases with intensity. If we aim for 1 GW/m^3, which corresponds to 268 Watts shining on each square centimetre of a 1 cm diameter lasing rod, we would need a 1:1 ratio of emitting to receiving area if the emitter has a temperature of at least 2622K. From a power conversion perspective, a 98% transparent crystal that converts 35% of spectrum it absorbs means it is only converting 0.7% of every Watt of blackbody radiation that shines through it. So, a crystal rod that receives 268 Watts on each square centimetre will release 1.87 W of laser light. We can use the 1:1 ratio of emitter and receiver area to reduce weight and increase power density. Ideally, we can stack emitter and receiver as flat surfaces separated by just enough space to prevent heat transfer through conduction. Reactor coolant channels, carbon emitting surface (1cm), filler gas, Nd:YAG crystal (1cm) and helium channels can be placed back to back. The volume could end up looking like a rectangular cuboid, interspaced by mirror cavities. 20 kg/m^2 carbon layers and 45.5 kg/m^2 crystal layers that release 1.87 W per square centimetre, with a 15% weight surplus for other structures and coolant pipes, puts this component’s power density at about 250 W/kg. The laser crystal is cooled from 417K according to the set-up in this paper. Getting rid of megawatts at such a low temperature is troublesome. Huge radiator surface areas will be required. As we are using flat panel radiators throughout this post, we have only two variables: material density, material thickness and operating temperature. The latter is set by the referenced document. We will choose a 1mm thick radiator made of low density polyethylene. We obtain 0.46 kg/m^2 are plausible. When radiating at 417K, they could achieve 3.73 kW/kg. It is likely that they will operate at a slightly lower temperature to allow for a thermal gradient that transfers heat out of the lasing medium and into the panels, and the mass of piping and pumps is not to be ignored, but it is all very hard to estimate and is more easily included in a 15% overall power density penalty for unaccounted-for components. A 100 kW/kg reactor, 250 W/kg emitter-laser stack and 3.73 kW/kg radiators would mean an overall power density of 188 W/kg, after applying the penalty. Gaseous lasing mediums could hold many advantages over a crystal lasing medium. They require much less radiation intensity (W/m^3) to start producing a laser beam. This researchstates that an iodine laser requires 450 times less intensity than an equivalent solid-state laser. It is also easier to cool a gas laser, as we can simply get the gas to flow through a radiator. On the other hand, turbulent flow and thermal lensing effects can deteriorate the quality of a beam into uselessness. No attempts have been reported on applying the heat recycling method from the Nd:YAG laser to greatly boost efficiency in a gas laser. Much research has been performed instead on direct solar-pumped lasers where the sunlight passes through a gaseous medium just once. The Sun can be considered to be a blackbody emitter at a temperature of 5850K. Scientists have found the lasing mediums best suited to being pumped by concentrated sunlight – they absorb the largest fraction of the sunlight’s energy. That fraction is low in absolute terms, meaning poor overall performance. An iodine-based lasing medium reported 0.2% efficiency. Even worse efficiency of 0.01% was achieved when using an optically-pumped bromine laser. Similarly, C3F7I, an iodine molecule which produces 1315 nm laser light, was considered the best at 1% efficiency. Solid blackbody emitters are limited to temperatures just above 3000K. There would be a great mismatch between the spectrum this sort of blackbody releases and the wavelengths the gaseous lasing mediums cited above require. In short, the efficiency would fall below 0.1% in all cases. One final option is Gallium-Arsenic-Phosphorus Vertical External Cavity Surface Emitting Laser (VECSEL) designed for use in solar-powered designs. It can absorb wavelengths between 300 and 900nm, which represents 65% of the solar wavelengths but only 20% of the radiation from a 3000K blackbody. This works out to an emitter with a power density of 45.9 kW/kg. The average efficiency is 50% when producing a 1100nm beam. Since it is extracting 20% of the wavelengths from the emitter, this amounts to 10% overall efficiency. Using the numbers in this paper, we can surmise that the VECSEL can handle just under 20 MW/kg. The mass of the laser is therefore negligible. With a 100 kW/kg reactor, we work out a power density of 3.1 kW/kg. VECSELs can operate at high temperatures, but they suffer from a significant efficiency loss. We will keep them at 300K at most. It is very troublesome as 20 MW of light is needed to be concentrated on the VECSEL to start producing a laser beam. 90% of that light is being turned into waste heat within a surface a few micrometers thick. Diamond heatsink helps in the short term but not in continuous operation. Radiator power density will suffer. Even lightweight plastic panels at 300K struggle to reach 1 kW/kg. When paired with the previous equipment and under a 15% penalty for unaccounted for components, it means an overall power density of 91 W/kg. This illustrates why an opaque pumping medium is unsuitable for direct pumping as it does not allow for recycling of the waste heat. Filtered blackbody pumping A high temperature emitter radiates all of its wavelengths into the blackbody-pumped lasing medium. We described a method above for preventing the lasing medium from absorbing 98 to 99.9% of the incoming energy and turning it immediately into waste heat. The requirement was that the lasing medium be very transparent to simply let through the unwanted wavelengths. However, this imposes several design restrictions on the lasing medium. It has to be thin, it has to be cooled by transparent fluids, and it might have to sit right next to a source of high temperature heat while staying at a low temperature itself. We can instead filter out solely the laser pumping wavelengths from the blackbody spectrum and send those to the lasing medium while recycling the rest. The tool to do this is a diffraction grating. There are many other ways of extracting specific wavelengths from a blackbody radiation spectrum, such as luminescent dyes or simple filters, but this method is the most efficient. Like a prism, a diffraction grating can separate out wavelengths from white light and send them off in different directions. For most of those paths, we can put a mirror in the way that send the unwanted wavelengths back into the blackbody emitter. For a small number of them, we have a different mirror that reflects a specific wavelength into the lasing medium. A lasing medium that receives just a small selection of optimal wavelengths is called optically pumped. It is a common feature of a large number of lasers, most notably LED-pumped designs. We can use them as a reference for the potential performance of this method. We must note that while we can get high efficiencies, power is still limited, as in the previous section. Extracting a portion of the broadband spectrum that the lasing medium accepts also means that power output is reduced to that portion. Another limitation is the temperature of the material serving as a blackbody emitter. The nuclear reactor that supplies the heat to the emitter is limited to 3000K in most cases, so the emitter must be at that temperature or lower (even if a carbon emitter can handle 3915K at low pressures and up to 4800K at high pressures, while sublimating rapidly). Thankfully, the emission spectrum of a 3000K blackbody overlaps well with the range of wavelengths an infrared fiber laser can be pumped with. A good example is an erbium-doped lithium-lanthanide-fluoride lasing medium in fiber lasers. We could use it to produce green light as pictured above, but invisible infrared is more effective. As we can see from here, erbium absorbs wavelengths between 960 and 1000 nm rather well. It re-emits them at 1530 nm wavelength laser light with an efficiency reported to be 42% in the ‘high Al content’ configuration, which is close the 50% slope efficiency. In fact, the 960-1000 nm band represents 2.7% of the total energy emitted. It is absorbing 125 kW from each square meter of emitter. If the emitter is 1 cm thick plate of carbon and the diffraction grating, with other internal optics needed to guide light into the narrow fiber laser, are 90% efficient, then we can expect an emitter power density of about 5.6 kW/kg. Another example absorbs 1460 to 1530 nm light to produce a 1650 nm beam. This is 3.7% of the 3000K emitter’s spectrum, meaning an emitter power density of 7.7 kW/kg. The best numbers come from ytterbium fiber lasers. They have a wider band of wavelengths that can be pumped with, 850 to 1000 nm (which is 10.1% of the emitter’s output), and they convert it into 1060 nm laser light with a very high efficiency (90%). It would give the emitter an effective power density of 23.4 kW/kg. More importantly, we have examplesoperating at 773K. The respected Thorlabs manufacturer gives information about the fiber lasers themselves. They can handle 2.5 GW/m^2 continuously, up to 10GW/m^2 before destruction. Their largest LMA-20 core seems to be able to handle 38 kW/kg of pumping power. It is far from the limit. Based on numbers provided by this experiment, we estimate the fiber laser alone to be on the order of 95kW/kg. Another source works out a thermal-load-limited fiber laser with 84% efficiency to have a power density of 695 kW/kg before the polymer cladding melts at 473K. We can try to estimate the overall power density of a fiber laser. A 100 kW/kg reactor is used to heat a 23.4 kW/kg emitter, where a diffraction grating filters out 90% of the output to be fed into a fiber laser with 90% efficiency and negligible mass. The waste heat is handled by 1mm thick carbon fiber panels operating at 773K for a power density of 20.2 kW/kg. Altogether, this gives us 11 kW/kg after we include the same penalty as before. If it is too difficult to direct light from a blackbody emitter into the narrow cores of fiber lasers, then a simple lasing crystal could be used. This is unlikely, as it has already been done, even in high radiation environments. Nd:YAG, liberated from the constraint of having to be nearly entirely transparent, can achieve good performance. It can sustain a temperature of 789K. We know that Nd:YAG can achieve excellent efficiency when being pumped by very intense 808nm light to produce a 1064nm beam, of 62%. It is hoped that this efficiency is maintained across the lasing crystal’s 730 to 830nm absorption band. A 3000K blackbody emitter releases 6% of its energy in that band. At 20 kg/m^2, this gives a power density of 13.8 kW/kg. We will cut off 10% due to losses involved in the filtering and internal optics. As before, the laser crystal itself handles enough pumping power on its own to have a negligible mass. The radiators operating at 789K will require carbon fiber panels. They’ll manage a power density of 22 kW/kg. Optimistically, we can expect a power density of 3.7 kW/kg (reduced by 15%) when we include all the components necessary. Ultra-high-temperature blackbody pumped laser We must increase the temperature of the blackbody emitter. It can radiate more energy across the entire spectrum, and concentrates it in a narrower selection of shorter wavelengths. Solid blackbody surfaces are insufficient. To go beyond temperatures of 4000K, we must consider liquid, gaseous and even plasma blackbody emitters. This requires us to abandon conventional solid-fuel reactors and look at more extreme designs. There is a synergy to be gained though. The nuclear fuel can also act as blackbody emitter if light is allowed to escape the reactor. Let us consider two very high to ultra-high temperature reactor designs that can do that: a 4200K liquid uranium core with a gas-layer-protected transparent quartz window and a 19,000K gaseous uranium-fluoride ‘lightbulb’ reactor. For each design, we will try to find an appropriate laser that makes the best use of the blackbody spectrum that is available. 4200K: Uranium melts at 1450K and boils at 4500K. It can therefore be held as a dense liquid at 4200K. We base ourselves on this liquid-core nuclear thermal rocket, where a layer of fissile fuel is held against the walls of a drum by centrifugal effects. The walls are 10% reflective and 90% transparent. The reflective sections hold neutron moderators to maintain criticality. This will be beryllium protected by a protected silver mirror. It absorbs wavelengths shorter than 250 nm and reflects longer wavelengths with 98% reflectivity. We expect the neutron moderator in the reflective sections, combined with a very highly enriched uranium fuel, to still manage criticality. The spinning liquid should spread the heat evenly and create a somewhat uniform 4200K surface acting as a blackbody emitter. The transparent sections are multi-layered fused quartz. It is very transparent to the wavelengths a 4200K blackbody emitter radiates – this means it does not heat up much by absorbing the light passing through. We cannot have the molten uranium touch the drum walls. We need a low thermal conductivity gas layer to separate the fuel from the walls and act like a cushion of air for the spinning fuel to sit on. Neon is perfect for this. It is mentioned as ideal for being placed between quartz walls and fission fuel in nuclear lightbulb reactor designs. The density difference between hot neon gas and uranium fuel is great enough to prevent mixing, and the low thermal conductivity (coupled with high gas velocity) reduces heat transfer through conduction. We might aim to have neon enter the core at 1000K and exit at 2000K. There is still some transfer of energy between the fuel and the walls because the mirrors are not perfect; about 1.8% of the reactor’s emitted light is absorbed as heat in the walls. Another 0.7% in the form of neutrons and gamma rays enters the moderator. We therefore require an active cooling solution to channel coolant through the beryllium and between the quartz layers. Helium can be used. It has the one of the highest heat capacities of all simple gases, is inert and is even more transparent than quartz. Beryllium and silver can survive 1000K temperatures, so that will set our helium gas temperature limit. A heat exchanger can transfer the heat the neon picks up to the cooler helium loop. The helium is first expanded through a turbine. It radiates its accumulated heat at 1000K. It is then compressed by a shaft driven by the turbine. If we assume that the reactor has power density levels similar to this liquid core rocket (1 MW/kg) and that 2.5% of its output becomes waste heat, then it can act as a blackbody emitter with a power density of 980 kW/kg. Getting rid of the waste heat requires 1 mm thick carbon fiber radiators operating at 1400K. Adding in the weight of those radiators and we get 676 kW/kg. A good fit might be a titanium-sapphire laser. It would absorb the large range of wavelengths between 400 and 650 nm. That’s 18.5% of a 4200K emitter’s spectrum. If we use a diffraction grating to filter out just those wavelengths, and include some losses due to internal optics, we get 125 kW of useful wavelengths per kg of reactor-emitter. The crystal can operate at up to 450K temperature, with 40% efficiency. Other experimentsinto the temperature sensitivity of the Ti:Al2O3 crystal reveals lasing action even at 500K, with mention of a 10% reduction to efficiency. We will use the 36% figure for the laser to be on the safe side. Based on data from this flashpumping experiment and this crystal database, we know that it can easily handle 1.88 MW/kg. The mass contribution of the laser itself is negligible. Any wavelengths that get absorbed but are not turned into laser light become waste heat. At 450K temperature, we can still use the lower density by HDPE plastic panels to get a waste heat management solution with 4.6 kW/kg. Putting all the components together and applying a 15% penalty just to be conservative, we obtain an overall power density of 2.2 kW/kg. 19,000: If we want to go hotter, we have to go for fissioning gases. Gas-core ‘lightbulb’ nuclear reactors will be our model. The closed-cycle ‘lightbulb’ design has uranium heat up to the point where it is a very high temperature gas. That gas radiated most of its energy in the form of ultraviolet light. A rocket engine, as described in the ‘NASA reference’ designs, would have the ultraviolet be absorbed by small tungsten particles seeded within a hydrogen propellant flow. 4600 MW of power was released from an 8333K gas held by quartz tubes, with a total engine mass of 32 tons. We want to use the uranium gas as a light source. More specifically, we want to maximize the amount of energy released in wavelengths between 120 and 190 nm. 19,000K is required. It is within reach, as is shown here. Unlike a rocket engine, we cannot have a hydrogen propellant absorb waste heat and release it through a nozzle. The NASA reference was designed around reducing waste heat to remove the need for radiators, but we will need them. Compared to the reference design, we would have 27 times the output due to the higher temperatures, but then we have to add the mass of the extra radiators. About 15% of the reactor’s output is lost as waste heat in the original design. It was expected that all the remaining output is absorbed by the propellant. We will be having a lasing gas instead of propellant in between the quartz tube and the reactor walls. The gas is too thin to absorb all the radiation, so to prevent it all from being absorbed by the gas walls, we will use mirrors. Polished, UV-grade aluminium can handle the UV radiation. It reflects it back through the laser medium and into the quartz tubes to be recycled into heat. Just like the blackbody-pumped Nd:YAG laser, we can create a situation where the pumping light makes multiple passes through the lasing medium until the maximum fraction is absorbed. Based on this calculator and this UV enhanced coating, we can say that >95% of the wavelengths emitted by a 19,000K blackbody surface are reflected. In total, 20% of the reactor’s output becomes waste heat. Since aluminium melts at 933K, we will keep a safe temperature margin and operate at 800K. This should have only a marginal effect on the mirror’s reflective properties. Waste heat must be removed at this temperature. As in the liquid fuel reactor, the coolant fluid passes through a turbine, into a radiator and is compressed on its way back into the reactor. Neon is used for the quartz tube, helium for the reactor walls and the gaseous lasing medium is its own coolant. Based on the reference design, the reactor would have 4.56 MW/kg in output, or 3.65 MW/kg after inefficiencies. If the radiators operate at 750K and use carbon fiber fins, we can expect a power density for the reactor-emitter of 70.57 kW/kg. 28.9% of the radiation emitted by a 19,000K blackbody surface, specifically wavelengths between 120 and 190nm, is absorbed by a Xenon-Fluoride gas laser. They are converted into a 350nm beam with 10% efficiency in a single-pass experiment. In our case, the lasing medium is optically thin. Much of the radiated energy passes through un-absorbed. The mirrors on the walls recycles those wavelengths for multiple passes, similar to the Nd:YAG design mentioned previously. Efficiency could rise as high as the maximal 43%. This paper suggests the maximal efficiency for converting between absorbed and emitted light is 39%. We’ll use an in-between figure of 30%. This means that the effective power density of the reactor-emitter-laser system is 6.12 kW/kg. The XeF lasing medium is mostly unaffected by temperatures of 800K, so long as the proper density is maintained. We can therefore cool down the lasing medium with same radiators as for the reactor-emitter (17.94 kW/kg). When we include the waste heat of the laser, we get an overall power density of 2.9 kW/kg, after applying a 15% penalty. A better power density can be obtained by having a separate radiator for each component that absorbs waste heat (quartz tubes, lasing medium, reactor walls) so that they operate at higher temperatures, but that would be much more complex. Aerosol fluorescer reactor The design can be found with all its details in this paper. Tiny micrometer-sized particles of fissile fuel are surrounded in moderator and held at high temperatures. Their nuclear output, in the form of fission fragments, escapes the micro-particles and strikes Xenon-Fluoride or Iodine gas mixtures to create XeF* or I2* excimers. These return to their stable state by releasing photons of a specific wavelength through fluorescence. Their efficiency according to the following table is 19-50%. Simply, it is an excimer laser that is pumped by fission fragments instead of electron beams. I2* is preferred for its greater efficiency and ability to produce 342 nm beams. Technically, this is an indirect pumping method, but it shares most of its attributes with direct pumping reactor lasers. The overall design is conservatively estimated at 15 tons overall mass, but with improvements to the micro-particle composition (such as using plutonium or a reflective coating), it could be reduced even further. It is able to produce 1 MJ pulses of 1 millisecond duration. With one pulse a second, this a power density of 66 W/kg. One hundred pulses mean 6.6 kW/kg. One thousand pulses, or quasi-continuous operation, would yield 66 kW per kg. The only limit to the reactor-laser’s power density is heat build-up. At 5% efficiency, there is nineteen times more waste heat than laser power leaving the reactor. We expect that using the UV mirrors from the previous design could drastically improve this figure by recycling light that was not absorbed by the lasing medium in the first pass through. Thankfully, the 1000K temperature allows for some pretty effective management of waste heat. Carbon fiber panels of 1mm thickness, operating at 1000K would handle 56.7 kW/kg. It would give the reactor a maximum power density of 2.4 kW/kg, including a 15% penalty for other equipment. If the reactor can operate closer to the melting point of its beryllium moderator, perhaps 1400K, then it can increase its power density to 8.3 kW/kg. Conclusion Reactor lasers, when designed appropriately, allow for high powered lasers from lightweight devices. We have multiple examples of designs, either from references or calculated, that output several kW of laser power per kg. The primary limitations of many of the designs can be adjusted in ways that drastically improve performance. The assumptions made (for instance, 1 cm thick carbon emitter or flat panel radiators) are solely for the sake of easy comparison. It is entirely acceptable to use 1mm thick emitting surfaces or one of the alternate heat radiator designs mentioned in this previous blog post. Even better, many of the lower temperature lasers can have their waste heat raised to a higher temperature using a heat pump. Smaller and lighter radiators can then be used for a small penalty in overall efficiency to power the heat pumps. Most of the lasers discussed have rather long wavelengths. This is not great for use in space, as the distances they beam has to traverse are huge and it multiplies the size of the focusing optics required. For this reason, a method of shortening the wavelengths, perhaps using frequency doubling, is recommended. Halving the wavelength doubles the effective range. However, there is a 20-30% efficiency penalty for using frequency doubling. Conversely, lasers which produce short wavelength beams have a great advantage. The list of laser options for each type of pumping is also by no means exhaustive. There might be options not considered here that would allow for much greater performance… but research on such options is very limited. For example, blackbody and LED pumping seems to be a ‘dead’ field of research, now that diodes can produce a single wavelength of the desired power. Up-to-date performance of those options is therefore non-existent and so we cannot fairly compare their performance to lasers which have been developed in their stead. It should be pointed out that a direct comparison between reactor and electric lasers is not the whole story. Reactor lasers can easily be converted into dual-mode use, where 100% of their heat is used for propulsion purposes. A spaceship with an electric laser can only a fraction of their output in an electric rocket. For example, the 4200K laser can have a performance close to the liquid-core rocket design it was derived from. Other, like the aerosol fluorescer laser, can both create a beam and heat propellant at the same time. A nuclear-electric system must choose where to send its electrical output and must accept the 60% reduction in overall power due to the conversion steps between heat and electricity at all times. Finally, certain reactor lasers have hidden strength when facing hostile forces. Mirrors work both ways. The same optics and mirrors that transport your laser beam from the lasing medium out into space and to an enemy target can be exploited by an enemy to get their beam to travel down the optics and mirrors and reach your lasing medium. The lasing medium, assumed to be diodes or other semiconductor lasers, has to operate at relatively low temperatures and so it will melt and be destroyed under the focused glare of the enemy beam. Tactics around using lasers and counter-lasers, something called ‘eyeball-frying contests’ can sometimes lead to a large and powerful warship being brought to a stalemate by a small counter-laser. A nuclear reactor laser’s lasing medium can be hot gas or fissioning fuel. They are pretty much immune to the extra heat from an enemy beam. It would render them much more resistant to ‘eye-frying’ tactics. This, and many other strengths and consequences, become available to you if you include nuclear reactor lasers in your science fiction. PS: I must apologize for using many sources that can only be fully accessed through a paywall. It was a necessity when researching this topic, on which little detail is available to the public. For this same reason, illustrations had to be derived from documents I cannot directly link to, but they are all referenced in links in this post.
  11. This is turning out to be really good. Supercruising already! Maybe try attacking some payloads to that plane? Also, how did you collect and display telemetry from the TV-2 launch?
  12. To produce a very high Isp engine, you can use simple particle beams and adjust the beam velocity to match your Isp and thrust requirements. There is no need to keep the beam focused after it exits your spaceship, so a Laser-Coupled Particle Beam is of no use here.
  13. I point you to the previous ToughSF post: http://toughsf.blogspot.com/2018/12/particle-beams-in-space.html It covers many of the points you just mentioned.