NTER: Nuclear Thermal-Electric Rocket

There is a type of nuclear propulsion that can have most of the acceleration of a nuclear thermal rocket but also the high Isp of an electric thruster. 

Let’s have a look at nuclear ‘thermal-electric’ engines and their advantages.

The title image is from 'dV: Rings of Saturn', here.

Limits of Nuclear Thermal Rockets

Nuclear thermal rockets (NTR) work by heating up a propellant. Heat flows from the nuclear fuel to the propellant, raising its temperature. The higher the temperature, the faster the propellant expands in a nozzle, allowing for higher exhaust velocities.

                                                            

It is evident that higher temperatures allow for higher exhaust velocities. Nuclear rocket designs have always tried to push the temperatures up to the limit that their materials can handle.

From Project Rover, we have 2750K as the maximum temperature that was sustained. This is not enough to break up the hydrogen propellant into individual H ions, so the exhaust velocity they could have achieved in vacuum is 8.86km/s or an Isp of 904s. 

Project Timberwind went further with carbide fuel particles that could handle 3100K, and the Russian nuclear space program ramped up the temperatures to 3500K.

By operating at these higher temperatures, they gain a major step up in exhaust velocity by causing the hydrogen propellant to thermally decompose. The result is an exhaust with half the molar mass.

At 3500K, an exhaust velocity of 12km/s is possible, which is an Isp of 1233s.

This of course is an excellent level of performance. An exhaust velocity four times greater than that of chemical rockets but with propulsion systems with a similar power density means that spacecraft can perform missions with four times the deltaV requirements.

For example, a hydrogen-propelled nuclear thermal spaceship with the same overall mass as a chemical-fuel spaceship could go to the Moon and back four times or reach Mars twice as fast.

But what if we wanted to go even further?

This is where the limits of nuclear thermal rockets impose themselves.

At temperatures over 3200K, you must accept that the nuclear fuel will get eaten away by hot hydrogen because the protective materials used to shield the uranium fuel, such as Zirconium or Niobium ceramics, fail.

At 4000K, the use of carbon materials is unsustainable as carbon readily vaporizes even without being attacked by superheated propellant. Perhaps temperatures as high as 4500K are possible with the most heat-resistant material we’ve discovered yet; Tantalum Hafnium Carbide.

But, even at 4500K, the exhaust velocity achievable is 13.7km/s, only 14% better than with the conventional materials.

A known solution to this to accept that the reactor will melt, or even operate in a gaseous state. This is the idea behind liquid core or gaseous core rockets.

A liquid or vapor core nuclear rocket can produce core temperatures as high as 6000K. 

A gas core rocket can produce even higher temperatures.

These are promising solutions, but we will not be focusing on them in this post. They have problems of their own, such as spewing out radioactive fuel along with the propellant, and have not yet been demonstrated to work.

Instead, let’s look at the real world alternative.

The Nuclear Electric Alternative

If the temperatures required to achieve higher exhaust velocities are too great to handle, then it is smart to side-step the challenge and use another form of propulsion.

Electric propulsion does not heat up the propellant but accelerates it in other ways. Exhaust velocities of 60km/s are being produced by space probes right now, and 210km/s has been demonstrated. 

Nuclear reactors are the preferred method for providing a reliable source of power in space that does not depend on distance from the Sun or finite stores of chemical fuels. A few dozen kilograms of uranium can release megawatts for years.

This power can be converted into electricity by moving heat from a high temperature (reactor) to a low temperature (radiator) and forcing the temperature gradient to do work with something like a turbine.

The efficiency of the process depends on how work is extracted. A thermoelectric device might have an efficiency of 10%, a turbine 40% and a magnetohydrodynamic generator 60%. These efficiencies are lower than those on the ground because we have to reduce the temperature gradient and maintain the cold end (the radiators) at a relatively high temperature so that the cooling surfaces required stay manageable.

Radiating away the heat from a 100 Megawatt heat source at 400 Kelvin would need the spaceship to extend radiator surfaces totalling 69,000m^2. Even lightweight carbon fins would impose a mass of 345 tons, and this is without the pumps and piping required to move the heat around. Increasing the radiator temperature to 800 Kelvin might halve the generator’s output but it would reduce the radiator mass down to 43 tons. When dealing with spacecraft that are very sensitive to mass increases (as each kg gained requires exponentially more kg of propellant to be added), this is a worthwhile tradeoff.

The electricity generated is then used to power an electric propulsion system.

‘Ion’ or ‘plasma’ engines are of this sort. They feature very high exhaust velocity but very low power density. While a nuclear thermal rocket enjoys 100kW to 1MW per kg, an electric engine would struggle to produce more than 2kW per kg. Most modern examples achieve less than 1 kW per kg.

The low power density of the electric propulsion system, the mass of the radiators and mass of equipment like turbines all add up to create a nuclear-electric rocket (NER) where each kW of power is paid for by several kilograms of mass.

This, coupled with the higher exhaust velocities cutting thrust (exhaust velocity and thrust have an inverse relationship), means spacecraft that necessarily accelerate very slowly. Uncrewed cargo craft won’t mind the wait. Human transports and crewed ships would prefer to use much more propellant to speed up their interplanetary trips.

The poor Bimodal rocket

There have been attempts at trying to gain the benefits of both nuclear thermal and nuclear electric propulsion.

A previously proposed solution is the bimodal rocket (BNTR). In one mode, it is a thermal rocket. In another mode, it is a reactor the provides heat to a generator that powers an electric propulsion system.

The advantage is that it can perform a high-powered burn out of inner orbits and deep gravity wells, like our Low Earth Orbit, maximizing Oberth gains. It then slowly increases its velocity with a high Isp electric engine to shorten its interplanetary trip.

The problem with this approach is that switching between the two modes of propulsion requires that equipment for both types be present at all times. This means that you need the nozzle of a nuclear thermal rocket as well as the radiators for an electrical generating system. The equipment for the mode not in use becomes dead weight.

Furthermore, nuclear cores cannot be made hot and powerful for the thermal mode as well as stable and endurant for the electric mode. The 3000K+ temperatures and high pressures that made a good nuclear thermal mode clash with the need to reduce temperatures and protect the nuclear fuel so that it can provide heat for days to months on end. All designs end up compromising on performance.

The result is sub-optimal performance in either mode. A lower temperature thermal mode with diminished Isp and thrust, and a reduced efficiency electric mode with diminished power output.

The true hybrid

The nuclear thermal-electric rocket (NTER) design is meant to combine the two different types of propulsion into a true hybrid that does not waste the fact that cryogenic propellants are wasting their cooling capacity (as Alan Bond put it) in NTRs and NERs.

There are many variants possible, but we will explain the design using one of the most promising of them: the intercooled Brayton-cycle nuclear thermal-electric rocket with magnetohydrodynamic booster. It will be using liquid hydrogen as propellant.

Let’s follow the journey of the liquid hydrogen from the propellant tanks, through the nuclear electro-thermal rocket and out of the nozzle. The pressure, temperature and other numbers being mentioned are only indicative of what would be expected from this design.

The short version is that the hydrogen makes two passes through the reactor core. Once at high pressure, another time at low pressure. Many megajoules of energy are extracted from each kilogram of hydrogen that makes these loops. The energy is converted into electricity, which is used to further accelerate the thermal exhaust going down the nozzle using an electric booster.

1-Cooling

The hydrogen starts out as a cryogenic fluid. A small impeller or autogenous pressurization of the propellant tanks pushes it out at a low pressure.

The fluid passes through a heat exchanger. It absorbs heat from one of the steps below and becomes a cool gas (perhaps 150 Kelvin) with low pressure (1 bar).

About 2.2 MJ of heat is absorbed for every 1 kg of hydrogen that passes through.

2 – Compression

The cool hydrogen gas can now pass through a two-staged compressor.

The first stage multiplies the pressure 50-fold. It releases the hydrogen at a pressure of 50 bar. Compression heating raises the gas’s temperature to 468K. We use temperature changes to track how much energy is consumed or released, as pressure differences are recovered in later steps. The first stage of the compressor requires 4.54 MJ of energy per kg of hydrogen.

The warm hydrogen passes through an intercooler. This is where the heat absorbing ability of cryogenic hydrogen is exploited. Liquid hydrogen from the propellant tanks is used to bring the 50 bar hydrogen’s temperature down to 313K.

The second stage compressor multiplies the pressure 3 times. It produces warm hydrogen gas at 150 bars and a temperature of 430K. It would require 1.68MJ/kg of hydrogen.

The total energy consumed by the compressor stages is 6.22MJ/kg.

3 – High pressure heating

The warm hydrogen enters the high pressure section of the reactor core. By passing over the fuel elements, it absorbs energy and reaches a temperature very close to that of the uranium fuel itself. In this example, it will be 2500K.

4 – Expansion

The hot hydrogen enters a turbine. It expands, decreasing in pressure and temperature. The turbine blades are propelled by the hydrogen’s expansion to extract 29.18MJ/kg. The blades will need to be hollow so that they can be actively cooled in order to survive the initial 2500K temperatures.

Hydrogen exits the turbine at a temperature of 698K and a pressure of 1 bar.

5 – Generator

The turbine and compressors are connected by a single shaft. That shaft can be connected to an electric generator. Energy consumed by the compressors and extracted at the turbine allows for a net gain. In this example, it is 22.96MJ/kg.

6 – Low pressure heating

The turbine’s exhaust now passes through the low pressure segment of the reactor. It is heated again to 2500K and Cesium is added. The Cesium would represent a tiny portion of the hydrogen flow (0.1% or less by mass) but greatly increase its electrical conductivity.

7 – Nozzle with booster

The nozzle is ringed with electromagnets. They act upon the conducting exhaust gases like an electric plasma rocket to further accelerate the exhaust. Electricity comes from the turbine-driven generator.

Without any electric boost and a large vacuum-optimized nozzle, the rocket’s exhaust velocity would be 8.45km/s, which is an Isp of 862s. However, adding the 22.96MJ/kg gained from the generator allows for an exhaust velocity of 10.8km/s, or an Isp of 1104s!

Naturally, this is an ideal scenario where everything is 100% efficient. It would more realistic to add perhaps just 17MJ/kg to the hydrogen, increasing the Isp to ‘only’ 1046s.

This is still a very significant improvement. We are obtaining greatly improved Isp from a solid nuclear core, without the increase in temperatures that would otherwise be needed from a purely thermal rocket. On the contrary, the 2500K temperature allows for greatly improved core endurance and reduces thermal stresses on all components involved.

Only one mention of this type of propulsion exists outside of a handful of scientific papers: the game “dV: Rings of Saturn”. It features plenty of hard SF technologies, including an example of this type of propulsion system. The engine is called the “Rosatom-Antonov K-37: Turbine Nuclear Thermal Rocket with Lorentz-effect accelerator” which uses the steps described above to achieve an exhaust velocity of 15km/s, impossible for a solid-core nuclear rocket otherwise.

Here you can watch an excellent start-up sequence made for that engine.

Nuclear Thermal-Electric Variants and Performance

We will now go through a list of potential variants, each with their own advantages and disadvantages, and work out a likely performance level. As the technology progresses or assumptions change, the performance that is calculated will also change. We will use a ‘near future’ set of performance assumptions and then extrapolate to a ‘further future’ where materials have improved and technology has progressed somewhat.

Simple Thermal

It is important to establish a reference point to see what the relative advantage the NETR has over the NTR.

A large-scale engine that can be built from proven designs would achieve a power density of 1 MW/kg and operate at 2800K using current technology. This gives it an Isp of 912s (8.9km/s) using liquid hydrogen and 635s (6.2km/s) with liquid methane.

A more advanced version would operate at a higher temperature and use stronger, lighter materials. 3200K core temperature allows for a liquid hydrogen Isp of 1214s (11.9km/s) and a liquid methane Isp of 679s (6.6km/s).

Note that at this point, increasing the temperature up to the absolute limits of currently understood materials technology (<4200K) would only increase Isp by 15% over the advanced design, but the use of dense refractory ceramics would cut into the power density.

Thermoelectric

In this variant, the Seebeck effect is used to generate electricity. A thermoelectric couple stands between a heat source and a cold sink so that the temperature gradient drives electrons to produce a current.

We have a >2800K heat source available and cryogenic propellants as the cold sink. No single thermoelectric generator can handle such a huge temperature gradient in one step. It is more likely that multiple generators are stacked on top of each other, each only handling a smaller temperature gradient. The maximum temperature that can be handled today by thermoelectric materials is about 1300K.

Propellant would first need to be pumped to the stack of thermoelectric generators (TEGs) to keep the cold end at a low temperature. If it is 500K, then 7MJ/kg of cooling can be obtained from liquid hydrogen, and 1.43MJ/kg from liquid methane.

Heat can be delivered to the top stack of thermoelectric generators by a heat pipe directly connected to the nuclear reactor’s core. It extracts electricity from the temperature difference between the hot end and the cold end. The ideal Carnot efficiency across 500 to 1300K is 61.5%.

The efficiency of a thermoelectric device is given by:

Efficiency = (1-Tc/Th) * ((1+ZT)^0.5 -1) / ((1+ZT)^0.5 + Tc/Th)

Tc is the cold end temperature in Kelvin.

Th is the hot end temperature in Kelvin.

ZT is a characteristic value depending on the thermoelectric materials.

Using modern thermoelectric materials with a ZT of 1.2 across to 500K to 1300K temperature range, an efficiency of 16% is to be expected.

A negligible amount of inefficiency comes from having to pump the propellant through the piping from the propellant tanks, through the heat exchangers and into the reactor core.

This means that the 7MJ cooling capacity of liquid hydrogen is spent handling the (1-0.16): 84% of reactor heat that is wasted. 1.33MJ becomes electrical energy. Liquid methane’s 1.43MJ/kg cooling capacity becomes 0.27MJ of electricity.

An advanced thermoelectric generator that could handle 2000K temperatures and have a ZT=2 could raise its efficiency to 27%. It would extract 2.59MJ of electricity from the cooling capacity of hydrogen, and 0.53MJ from methane.

Advantages of this design include having nearly no moving parts and only a single passage of the propellant through the reactor. It would be tough and reliable. Tens of thousands of hours of operation are expected.

Disadvantages are the low efficiency and great weight of the thermoelectric generators.

Thermionic

The high temperatures available from the reactor core can cause metals to directly emit electrons. This is the thermionic effect that can be used to produce electricity.

Two plates, an emitter and a receiver, are held close to each other. The emitter is heated to a high temperature, causing it to release electrons. Electrons jumping the gap between the two plates and are collected as an electrical current. However, the receiver absorbs all of the thermal radiation from the receiver, which is the main source of inefficiency. We want the temperature gap to be as high as possible, so a receiver with a low emittance and low temperature is ideal. The emitter can be made of materials like molybdenum or tungsten; in fact, it is even more temperature resistant than the nuclear core and can therefore be as hot as we want. The cold end is a problem though.

In previous examples of nuclear thermionic power, having a low temperature receiver conflicted with the need to have a high radiator temperature to get rid of the waste heat into vacuum. We have access to cryogenic propellant which can absorb heat even at very low temperatures, so this is not as much of a problem.

We know that high efficiencies are already possible. A Japanese solar propulsion research effort produced a thermionic converter (TIC) that held an emitter at 1850K and cooled the collector to 1100K. They managed 57% of the maximal Carnot efficiency, resulting in 23.2% actual efficiency.

A modern nuclear thermo-electric rocket using a thermionic converter could raise an emitter’s temperature to 2700K, only slightly less than the core temperature by using heat pipes, which do not require any electricity to move heat (only a temperature difference).

An electric pump or exhaust bypass drives a low pressure pump to push propellant through a heat exchanger that cools the thermionic collector. It could hold it at 1000K.

The maximum Carnot efficiency across this temperature gradient is 64.3%. Near term performance might be 30% of this maximum, achieving 19.3%.

Hydrogen can absorb 14.2MJ/kg when heated from liquid to 1000K. With the thermionic converter’s efficiency, we can produce 3.4MJ of electricity from each kilogram of hydrogen.

Methane absorbs 3.4MJ/kg in the same situation, which allows 0.81MJ of electricity to be produced.

The hot gases from the collector are then sent into the reactor to be heated themselves up to the 2800K core temperature, and then pushed through a nozzle.

The electricity produced by the thermionic is then used to accelerate the exhaust from the nozzle.

An advanced version of this is might manage to achieve 60% of the ideal Carnot efficiency between 3200K and 1000K, for an actual efficiency will of 41.2%.

Hydrogen now allows 9.9MJ of electricity to produced and methane allows for 2.4MJ.

The advantages of this design are that it can handle very high temperatures and extract more power using the cryogenic propellants. It is just as resistant to damage as the thermoelectric option.

Disadvantages are low power density, although much better than a thermoelectric converter.

One thermionic variant attempts to use three thermionic steps, all with the same emitter temperature but at higher and higher collector temperatures. Propellant gas moves from step to step, making the most of its cooling capacity in a sort of cascade.

For example, the first step could have the emitter at 2800K and the receiver at 500K. The second has the receiver at 1000K and the final step has the receiver at 1500K.

Continuing with the assumptions of the previous variant, thermionic efficiency between 2800K and 500K can be as high as 24.6%. Heating hydrogen from liquid to 500K absorbs 7MJ/kg, so 2.3MJ of electricity can be produced at this step.

The second step recycles the warm gases released from the first step and further heats them to 1000K. Another 7.35MJ/kg of cooling capacity is available, of which 1.76MJ can be extracted as electricity if we expect a thermionic efficiency of 19.3%.

In a third step, we further heat the hydrogen to 1500K. Thermionic efficiency falls to 13.9%, which is still enough to gain another 1.25MJ from the hydrogen.

A total of 5.3MJ of electricity of produced.

Re-doing the numbers for methane, we generate 0.47+0.45+0.41: 1.33MJ.

An advanced version might achieve 60% of the Carnot ideal, operate at a higher 3200K emitter temperature and add a 4^th stage that raises the collector temperature to 2000K.

The efficiencies of the stages are 50.6%, 41.2%, 31.8% and 22.5% with collector temperatures at 500, 1000, 1500 and 2000K.

The electrical power generated at each stage using 1kg of hydrogen would be 7.2MJ, 5.2MJ, 3.6MJ and 2.4MJ for a total of 18.4MJ.

The same figures for methane would be 2.5MJ, 1.3MJ, 1.2MJ and 0.87MJ, totalling 5.87MJ.

Clearly the advantage here is that the cooling capacity of the propellant is used much more efficiently. However, multiple thermionic converters would mean a reduction in overall power density.

Thermoelectric generators are limited in the maximum temperature they can handle. This limit can be broken by another variant, a hybrid having the collector of a thermionic converter act as the hot end of a thermoelectric generator.

Cryogenic propellant can first cool the cold end of a thermoelectric generator to 500K. The resulting warm gas is then used to cool the collector of a thermionic receiver to 1300K. This hotter gas passes over the hot end of the thermoelectric generator before entering the reactor core. The thermionic emitter meanwhile is directly heated by the nuclear reactor to 2800K.

Thermionic efficiency can be as high as 16% between 1300K and 2800K. Thermoelectric efficiency would also be 16% between 500K and 1300K.

Starting with hydrogen, we work out that the thermoelectric generator produces 1.33MJ of electricity, and the thermionic converter produces another 2.29MJ for a total of 3.6MJ.

Methane following the same path allows for the production of 0.27MJ and 0.63MJ, totalling 0.9MJ of electricity.

An advanced version of this with an improved thermoelectric generator of ZT=2 operating between 500K and 2000K, and a higher temperature thermionic converter working between 2000K and 3200K, would have efficiencies of 27% and 17% respectively.

It would extract 2.59MJ and 4.83MJ of electricity from each stage for each kg of hydrogen, a total of 7.4MJ. Each kg of methane yields 1.95MJ of electricity.

Also, thermionics can work with other power conversion systems to achieve a very high overall efficiency.

Thermophotovoltaic

Whereas the blackbody radiation from a high temperature thermionic emitter is a source of inefficiency, it can be used to produce electricity using thermophotovoltaic panels (TPV). A thermophotovoltaic cell works like a photovoltaic cells, found in solar panels, except that it can convert the wavelengths released by surface less bright than the Sun into electricity.

Current work focuses on increasing the efficiency of thermophotovoltaic systems using emitters at lower temperatures (1000 to 2000K), with efficiencies of 25 to 38% predicted. However, we can have a 2800K emitter directly heated by a nuclear reactor, emitting wavelengths with a peak at 1000 nanometers. The conversion efficiency can be as high as 56% using multi-junction Gallium-Indium-Arsenic-Phosphorus photovoltaic cells. As has been mentioned in a previous ToughSF post, efficiencies as high as 61% have been demonstrated.

The thermal radiation reaching these photovoltaic cells heats them up. Hot photovoltaics quickly lose efficiency. It is therefore important to maintain a temperature of about 300K, which we will accomplish using cryogenic propellant as a heatsink.

Using an efficiency of 50%, we find that a very high temperature thermophotovoltaic system can produce 4.2MJ of electricity when using liquid hydrogen as the heatsink.

An advanced version of this set-up is very unlikely to increase the efficiencies or temperatures much further. Power density could become better though.

The advantage of thermophotovoltaics is their good power density relative to thermoelectric or thermionic devices and an excellent overall efficiency.

However, having to operate at low temperatures means that only a portion of the cryogenic propellant’s cooling capacity is utilized.

Stirling

We now move to a very different method of generating electricity. It works using two pistons that exchange gases as one heats up and the other cools down. The motion of the pistons drive a generator.

The Stirling cycle is currently the largest working type of nuclear power generation for space, with NASA’s ‘Kilopower’. We can cite from a test report on the design: “The engine thermal efficiency ranged from 30-34% at approximately 50% of Carnot”.

This is an interesting piece of information. It tells us that if have Stirling generator (STG) with the appropriate materials (perhaps tungsten carbide with an inert helium gas as the working fluid), we could have the hot end be directly heated by a nuclear core to 2800K, and the cold end by cooled by cryogenic propellant.

A 1000K cold end means that the Stirling generators works across a 2800K to 1000K temperature gradient, allowing for a maximum Carnot efficiency of 64%. If the generator manages half of this maximum efficiency, we get 32%.

The cooling capacity of liquid hydrogen heated up to 1000K is 14.2MJ/kg. 32% efficiency means that 6.7MJ of electricity can be produced for every kg of hydrogen used.

Using liquid methane allows for 1.6MJ of electricity to be produced.

A more advanced Stirling design would use a free piston inside a linear generator to achieve 63% of the Carnot maximum. When paired with a 3200K hot end from a higher temperature nuclear core and the same 1000K cold end as previously, we can expect an overall efficiency of 43%.  

The electricity that can be generated when using hydrogen increases to 10.7MJ, and with methane to 2.6MJ.

The main advantage of Stirling generators is that they can achieve a better percentage of the maximum Carnot efficiency and have generally better power densities than the alternatives. The gas in the cylinders can be different from the coolants used to increase or reduce their temperature, so they could theoretically handle very high temperatures without worry of chemical degradation.

The disadvantage though is that they work across a large temperature gradient, so they have to be made robust and therefore heavier, and they have several moving parts that reduce their operating lifetime. On spacecraft, they might need to include a vibration absorber.

Brayton Intercooled

This is the design we described earlier when explaining the nuclear thermal-electric concept. Propellant is used to drive a Brayton cycle. Energy is extracted from the temperature difference between the heat exchanger and the turbine exit and is used to drive a shaft which spins an electrical generator.

The process depends on a number of factors, such as the pressure ratio and the heat capacity of the gases involved. Therefore, it is not possible to use a simple percentage figure for the efficiency.

Using the ‘modern’ nuclear core as out heat source, we would expect temperatures as high as 2800K to be used to maximize efficiency. However, turbine blades must bear the brunt of these temperatures. They have to spin at high speeds and maintain sufficient strength to not break off or slowly elongate. What’s worse is that with a turbine on a spaceship, it is not really possible to cool the turbine blades using cold air from the exterior or cold water from an endless reservoir. The result is hard limits on the temperatures that turbogenerators can work with.

The highest a typical uncooled nickel-based turbine blade can handle is 1200K. 

More recent alloys based on niobium have managed several hundreds of hours under 1700K conditions, but the best we have are silicon nitride or silicon carbide ceramics that have been tested for thousands of hours up to 2000K.

Let’s run some numbers using hydrogen.

We’ll start with two compressor stages, each increasing the gas pressure 10-fold. Temperature increases by a factor 1.95 after each stage. An intercooler between the stages absorbs some heat.

If we set the entry temperature at 410K, the hydrogen will exit the first stage compressor at 800K. It enters the intercooler, where cold liquid hydrogen is used to absorb the heat added by the compression. The compressed gas is cooled down to 410K while the liquid hydrogen is heated into a 400K gas, ready to be sent into the compressor. 5.7MJ of heat energy is exchanged per kilogram. Going through the second stage compressor allows it to reach 100x the initial pressure and a temperature of 800K.

We heat the hydrogen in the reactor core to 2000K.

High pressure, high temperature hydrogen now enters the turbine stage to be expanded so that its energy can be extracted as mechanical work. Expanding across a 100-fold pressure difference lowers the temperature by a factor 3.8, so it exits at 526K.

The compressors have consumed 11.4MJ to compress each kilogram of hydrogen. The turbine can extract 23.2MJ, so the net result is 11.8MJ for each kg of hydrogen. It is then converted into electricity by an alternator.

If we apply real world efficiencies to these steps (95%, 90% and 95%), we are more likely to gain 8.4MJ instead. This is an overall efficiency of about 52%.

The turbine exhaust goes through the reactor core again to be re-heated an exit through a nozzle, where the electrical energy gained is used to increase exhaust velocity.

Methane in this same Brayton cycle consumes 1.1MJ/kg in the compressors, extracts 6.4MJ/kg in the turbine and gains a net of 5.3 MJ of electricity for each kilogram used. With a realistic overall efficiency of 56%, this is 4.4MJ.

A more advanced turbine can use hollow turbine blades made of ceramic materials actively cooled by a liquid metal heat pipe. Hafnium carbide can form the outer layer while silicon carbide forms the core. This arrangement minimizes the use of the very dense hafnium-rhenium-tungsten alloy while exploiting the fact that the interior of the turbine blade can be kept at the <2000K temperatures where the lighter silicon carbide retains its strength.

Active cooling is how we manage to increase turbine performance with existing materials, only that we are applying the concept here to much improved materials.

Thanks to these improved materials, we can operate at 2800K.

We will also use bigger compressors to reach even higher pressures, perhaps 500 times the initial pressure. This is similar to the performance of simple turbopumps on rocket engines today, like the Raptor, where pressure at the exit is 643 bar.

To maximize the intercooling effect, we can separate the compression into three stages. In between each stage is an intercooler that makes use of the cryogenic propellant’s cooling capacity.

Let’s run the numbers on a sample design.

Three compressors aiming to multiply pressure 500-fold could be arranged to achieve 10x, 10x and 5x. This would increase the temperature of hydrogen gas 1.95x, 1.95x and 1.59x respectively.

If hydrogen gas enters the turbine inlet at a temperature of 200K, it exits the first compressor stage at 390K. The compressor consumes 2.66MJ for every kilogram that passes through.

The first intercooler reduces the hydrogen’s temperature back down to the compressor’s entry temperature. In a heat exchanger, hydrogen gas cools down from 390K down to 200K and cold propellant heats up from 22K to 166; this is an exchange of 2.66MJ of heat for every kilogram.  

The second compressor stage also consumes 2.66MJ/kg and releases 390K gas. It passes on the gases to a second intercooler that reduces their temperature to 358K. From the cold side of this intercooler’s heat exchanger, we get the gases at 200K that will go to feed the turbine inlet. From the hot side, we get the gases at 358K that will enter the final compression stage.

In the third compressor, 3.1MJ are consumed and compression heating causes the hydrogen gas temperature to increase from 358K to 571K. The hot pressurized hydrogen is then fed into the nuclear reactor core.

Hydrogen exiting the core sits at 2800K. A turbine expands it down a 500-fold pressure gradient. The expansion cools the hydrogen back down to 460K and 38.2MJ of energy can be extracted from each kg of hydrogen having passed through the turbine. It is converted into electricity by an alternator.

The net energy produced as electricity in this design is 29.78MJ. With realistic efficiencies, this is 27.4MJ.

We work out that the overall efficiency is 76%.

Methane used in this design allows for a realistic energy gain of 8.4MJ/kg. Methane’s overall efficiency is 73%.

A lot more energy is being extracted by these turbines for each kilogram of cryogenic propellant than with the previous generators. Turbines are also very lightweight for the power they handle, and they can be paired with electrical generators that are already achieving over 15kW/kg in power density. Superconducting versions of the latter could achieve 40kW/kg. Put together, we can see a power conversion system that exceeds the performance of previous examples ten-fold in terms of watts per kilogram of equipment mass.

This advantageous level of performance is why turbomachinery is the preferred method of generating power on Earth and in space.

One of the disadvantages of turbines using ceramic blades however is that they are brittle at lower temperatures and prone to cracking if heated up too quickly. They generally have a shorter lifetime than generators with few to no moving parts, shorter still if they start getting knocked around by impacts during combat or buffeting during re-entry.

This makes turbomachinery relatively fragile.

It is also possible to add a regenerator when the exhaust from the turbine is cooler than the gases going through compressors.

For example, if the entry temperature to the compressor was 400K and the exit temperature was 781K, while the turbine exhaust temperature is 526K, like in the modern 2000K design above, then we use the turbine exhaust as the cold side of a heat exchanger and the compressor gas as the hot side.

The regenerator allows these gases to reach an intermediate temperature. In this case, the average of 781K and 526K is 653K. The cooling effect on the compressor gas is therefore 128K. 1.8MJ of heat energy regenerated in this manner can reduce the need to use up the cryogenic propellant’s coolant capacity by the same amount. That cooling capacity can be better used elsewhere.

In the advanced Brayton generator example described previously, two intercoolers are used between three compression stages. The first intercooler uses up most of the cryogenic propellant’s cooling capacity, so the second stage can only reduce the hydrogen gas’s temperature by 32K before it enters the third stage.

Using a regenerator would have allowed a much more significant temperature reduction and a corresponding decrease in the compression consumption of the third compressor stage, as it would be working with cooler gases.

This translates into significant portion of that saving ending up as more electricity at the end. The question however, is whether the increased weight from the regenerator allows for a gain in overall efficiency that does not significantly affect overall power density.

The other variants possible using a Brayton cycle are a Double Loop design, where the exhaust of one turbine is fed into a second turbine, or a Closed Loop, where cryogenic hydrogen is only used to cool down turbine exhaust so that it can be recycled, much like a radiator would do.

Magnetohydrodynamic

This is yet another completely different method of generating electricity. A magnetohydrodynamic generator (MHD) uses magnetic fields to slow down a conductor moving through it. The kinetic energy of the conductor is directly converted into electricity.

Hydrogen, methane or other good rocket propellants are not well suited for use directly in an MHD generator, as they need to be ionized to become good conductors (as plasmas), but this only occurs at very high temperatures. As they cool down while going through the MHD generator’s ducts, they become neutral gases again.

Several solutions have been proposed: seeding the propellant with elements that easily ionize at lower temperatures, ionizing the propellant with an electron beam or having a closed loop MHD generator where a separate fluid is kept.

A closed loop is what we’ll focus on for now instead of the open cycle. It circulates an easily ionized element like cesium, potassium, rubidium or xenon between a heater, MHD duct, cooler and pump. The heater transfers thermal energy from the nuclear reactor core. Extreme temperatures are possible. The hot fluid travels down the MHD ducts, where some of its energy is extracted. In doing so, the fluid loses pressure and temperature. It then passes through a cooler, where we will bring in cryogenic propellant to act as a heatsink. The cooler fluid is then pumped back up to the design pressure to go through the loop again.

Technically, this is another Brayton cycle. Compared to a turbine, the MHD variant gains the ability to handle any temperature but loses the ability to extract most of the fluid’s energy. There are designs for MHD generators that work with 4000K temperatures and higher, something impossible to send through a turbine.

Let’s consider a MHD generator realizable today.  

Helium is used, seeded with potassium. The hot end temperature is 2800K, like the reactor core providing the heat. The cold end temperature is limited by the point at which potassium stops being ionized and returns to being a neutral atom. This happens at about 1000K.  

This means that the maximum Carnot efficiency is 64%. Inefficiencies in the MHD generator and the pumping requirements means only about half of that is available, so overall efficiency is 32% with the help of intercoolers and regenerators.

If we set the cooler temperature to 500K, then 7MJ/kg of cooling capacity can be obtained from liquid hydrogen, and 1.43MJ/kg from liquid methane.

This translates into an electrical energy gain of 3.29MJ for each kilogram of liquid hydrogen consumed, or 0.67MJ for each kilogram of liquid methane.

A lot more can be done with a more advanced MHD generator and a higher temperature nuclear reactor.

For one, the helium/potassium mix can be heated to 3200K. This increases the maximum Carnot efficiency to 68.8%, assuming the same exit temperature of 1000K.

We can also use superconducting magnets for the MHD generator and the electric motors turning the compressors. It might allow us to use an overall efficiency figure of 66%.

Putting all these advanced features together, and assuming a similar cooler temperature of 500K, we can manage to gain 13.5MJ from liquid hydrogen or 2.78MJ for liquid methane.

Of course, the MHD generator cycle can be greatly improved. 1000K gases at the exit of the MHD duct are hot enough to drive another power generating cycle. It can be another Brayton cycle using a turbine, where we can extract another 40% of the remaining energy between 1000K and 500K, which would improve overall efficiency of the advanced MHD design to 79.6% (and the energy gain by a whopping factor of 1.66x, to 22.41MJ with liquid hydrogen and 4.6MJ with liquid methane). Or, a humble TEG device that can only obtain a few percent of the remaining energy but does not add any moving parts.

There are several advantages to an MHD generator. It has a very high power density, no moving parts except for the pumps and the nuclear reactor would only need to have one single-pressure section that the propellant goes through once. It can easily be used as a topping cycle to power generating systems that cannot handle extreme temperatures but are able to use the MHD’s exhaust. In fact, it is best to have Magnetohydrodynamic, Brayton and Thermionic/Thermoelectric all working in series. 

Each cycle operates best at a certain temperature range. Magnetohydrodynamic generators thrive at extreme temperatures, turbines prefer lower temperatures that their turbine blades can handle, while thermoelectric generators can operate at low temperatures. Overall efficiencies using a 'combined' cycle approaches 80%. The highest power density combination is likely to be a turbo-MHD design.

However, having a high temperature fluid mixed with reactive metals going round and round a loop will lead to corrosion issues that reduce the lifetime of the generator. The magnets, which need to stay cold to maximize efficiency, have to be placed right next to superheated gases. Superconducting magnets have even bigger issues with thermal management.

Electric boosters

In this section, we’ll have a look at how the electrical energy produced by the generators in the previous section can be employed to increase exhaust velocity.

ResistoJet

A resistojet is a simple heating device that has propellant run over tungsten or other refractory material so that temperature is increased through conduction.

Tungsten can handle temperatures as high as 3500K. This is usually higher than the temperatures of the nuclear cores themselves, as they are under other design constraints (such as surviving the intense radiation).

If we employ a resistojet as the electrical booster to a ‘modern’ nuclear thermal rocket, we can raise the temperature of the exhaust from 2800K to 3500K. This might seem like a minor increase, but there is a significant benefit that comes with hydrogen propellant thermally decomposing into individual atoms (H2 to H). This halves the average molar mass of the exhaust, meaning that Isp increases from 912s (8.94km/s) to 1270s (12.4km/s).

For an advanced nuclear core already operating at 3200K, the benefit is so minor as to be negligible since it has already thermally decomposed the hydrogen and would only receive an Isp increase from 1213s (11.9km/s) to 1270s (12.4km/s).

Efficiency is said to be about 80%.

Arcjet

An arcjet heats up propellant to very high temperatures using electric arcs. It is not limited by the melting point of any material, but it does suffer from constant erosion of its electrodes.

Temperatures as high as 12,000K are achievable, and since the exhaust gases have already been heated up by a nuclear reactor, we can dismiss ionization losses and only look at the 80-90% thermal efficiency.

In this electric booster, we are not temperature limited but energy limited.

Any propellant entering the electrical booster should be considered a plasma (or soon will be!). This means that it has a heat capacity ratio of 1.66 and a fixed heat capacity of 20.37J/mol/K.

In practical terms, it takes 20.37kJ to heat up 1kg of monoatomic hydrogen by 1 Kelvin, and 6.36kJ to heat up 1kg of methane thermally decomposed into its constituents (average molar mass 3.2g/mol) by 1 Kelvin.

If we have 6MJ available for each kg of hydrogen propellant, we can increase the temperature by 265K (assuming 90% efficiency) from 3200K to 3465K, with a corresponding increase in exhaust velocity of just 4%.

Those same 6MJ delivered to an arcjet running on methane would increase temperature by 849K from 3200K to 4049K, increasing exhaust velocity 12.4%...

Microwave, Laser and RF Induction heating

These are improved methods for further heating propellant.

Microwaves or lasers can be used to directly heat propellant, with the choice being made depending on how well their wavelengths are absorbed.

RF Induction uses an alternating magnetic field to act on a conductive propellant.

Efficiency with these methods can be good (>60% efficiency lasers) to great (>90% efficient induction coils) and they have no temperature limits. Erosion is not a problem, so they can operate for a very long time. Power density is also improving every year.

Unlike resistojets or arcjets, there are no practical temperature limits, only the heat flux that the walls can handle. 

Electromagnetic acceleration

This category of electric booster uses electromagnetic forces to directly accelerate the propellant using Lorentz, Hall or Ponderomotive effects. More electrical energy directly becomes kinetic energy, making them much more effective than simply heating the propellant.

We are interested in electrodeless plasma thrusters. Because the source of our plasma is a nuclear reactor core emitting very high temperature gases, to which an easily ionized seeding material can be added, we will not have to suffer the losses from using equipment required to generate plasma. That already significantly improves our potential efficiency.   

Some of the simpler designs, like a Pulsed Inductive Thruster, are unusable as the propellant from the reactor is continuous.

Others like the ponderomotive plasma engine, based on the non-heating part of the VASIMR engine, the travelling wave plasma accelerator or an ELF design can directly convert electricity into kinetic motion with efficiencies exceeding 80% using a variety of propellants and have practically unlimited exhaust velocity (the VASIMR in high gear is supposed to reach an Isp of 30,000s!).

The use of superconducting magnets can bring the power density of the electrical booster to acceptable levels, so they do not affect propulsion mass requirements too much. Even better, they do not significantly increase the temperature of the exhaust, so they can operate for much longer with lighter materials.

A highly efficient power generating cycle using all the tricks in the book (recirculating, combined cycles, regeneration and so on) using these types of accelerator could push Isp up to 1800s. 

Use of radiators

Using cryogenic propellant as a heatsink does not mean that radiators must be excluded from designs that can use them.

Power generating cycles with higher temperature cold ends can radiate a lot of their waste heat away using relatively small radiators. Each 1m^2 of double-sided fins exposed to space can remove 7kW of waste heat when radiating at 500K, and 113.4kW at 1000K. Other radiator types can handle this waste heat with very little equipment mass, by spraying liquid droplets or electrostatically cycling dust in and out of a heat exchanger.

Therefore, we can have power generating cycles that use radiators in addition to the cooling capacity of propellant to extract even more electricity from each kilogram consumed. Every MJ removed using radiators is a MJ that doesn’t using up the propellant’s cooling capacity.

For example, in the modern thermionic converter design, the collector plate is to be held at 1000K. Each kg of liquid hydrogen used to cool it can absorb 14.2MJ, so 1 kg/s of that propellant flow can be replaced by 125m^2 of double-sided fins removing 113.4 kW/m^2.

A spaceship can use radiators to increase the total amount of electrical power it produces or reduce the rate at which propellant is consumed. Radiators can be extended or retracted to change the power output or rate of propellant consumption, which is a nice option to have when facing different situations such as combat (where radiators could be damaged) or prolonged accelerations (where a maximally efficient electric engine is preferred).

Power generating systems that can operate at different temperatures give even more options. Small radiators can be used to handle high temperature heat (like a thermionic converter operating between 2000 and 1500K) while lower temperature steps that would require heavy thermal management could instead use a flow of cryogenic propellant. When radiators need to be retracted, propellant handles all cooling requirements. If the extra power is not needed, the power generating cycle only works with the high temperature steps and cuts off the lower temperature ones.

Impact of the technology

Two types of spacecraft benefit the most from Nuclear Thermal-Electric propulsion technology.

The first are rapid transports that wish to minimize interplanetary travel times. The second are warships.

Rapid transports aim to travel along very energetic trajectories using a lot of deltaV. They want the rapid acceleration of nuclear thermal propulsion but also the Isp of nuclear electric propulsion.

Rapid acceleration is needed to escape low orbits near planets quickly, both maximizing the Oberth effect and reducing the amount of time spent traversing radiation belts. High thrust chemical engines are why Apollo missions could get to the Moon in 3 days at the cost of 4km/s of deltaV, but a proposed electrical propulsion system would take 9 months to slowly spiral its way there.

A nuclear thermal rocket can deliver this high thrust as well as double the specific impulse. With the thermal-electric design boosting Isp from around 1000s to nearly 2000s, the deltaV capacity is doubled again without losing much acceleration.

This NASA document describes how a spaceship with both high thrust and high Isp propulsion options ends up having better performance than either option alone. NTER can realize that ideal.

Warships benefit even more from nuclear thermal-electric propulsion.

It would have three competing requirements. The first is to generate electrical power so that it can use lasers, electromagnetic accelerators, active sensors and other energy-intensive equipment. The second is to protect itself from enemy fire. The third is to keep up with its targets and run away from missiles.

The first two requirements are in conflict with each other because generating electricity also produces waste heat, and getting rid of waste heat generally means exposing large radiator panels to space. These panels cannot be armored (it would defeat their function) and so become large weakspots that when damaged, prevent electricity from being generated.

The second and third requirements clash because deltaV needs must be met by large propellant reserves. The best propellants, like liquid hydrogen, are very voluminous and covering propellant tanks with armor becomes a massive penalty. An opponent can bring more weapons to the fight if they do not have the same mass penalty, while you would be completely at the mercy of missiles and kinetics if you cannot maneuver out of the way if you did not protect your propellant tanks.

All of these competing requirements can be met by a NTER.

By using propellant as a heatsink, electricity can be generated while radiators are retracted or not even part of the design. This means a fully armored spaceship with no weakspots can still generate the megawatts it needs to win a fight. Furthermore, the electrical output can be used to increase the exhaust velocity of denser, less optimal propellants like liquid methane. It is 6.7 times denser than liquid hydrogen, so the volume of propellant tanks for a given mass ratio is correspondingly smaller. Less armor is needed.

A warship using NTERs can eventually outrun spaceships using NTRs and outmatch spaceships using NERs in both protection and acceleration.

From a science fiction perspective, it can allow for an argument to be made as to why there are no visible radiators. NTER propulsion means that we can consider 'softer sci-fi' designs as valid from a scientific standpoint.

You do not have to compromise between realism considerations and your choice of spaceship 'look'.