Saturday 5 October 2019

The Expanse's Epstein Drive

We aim to take a fictional propulsion technology from The Expanse, and apply the appropriate science to explain its features in a realistic manner.
This also applies to other SciFi settings that want a similar engine for their own spacecraft.
The Epstein Drive

Title art is from here.
Central to the setting of The Expanse is a very powerful fusion-powered engine that allows spacecraft to rocket from one end of the Solar System to the other quickly and cheaply.

It reduces interplanetary trips to days or weeks, allows small shuttles to land and take off from large planets multiple times and accelerate at multiple g’s for extended amounts of time.

Such a propulsion system is known as a ‘torch drive’: huge thrust, incredible exhaust velocity and immense power inside a small package. 

Fusion energy can certainly provide these capabilities. Using fuels like Deuterium provides over 90 TeraJoules of energy per kilogram consumed. Proton fusion, the sort which powers our Sun, could release 644 TJ/kg if we could ever get it to work.
The Epstein Drive (art Gautam Singh) is described in The Expanse as a breakthrough in fusion propulsion technology. A short story provides some details. A small spaceship equipped with this engine could reach 5% of the speed of light in 37 hours, averaging over 11g’s of acceleration. A magnetic bottle is mentioned. Since we don’t know the mass of the vehicle or what percentage of it was propellant, we can’t work many useful details.

The main book series and the TV show focus on the adventures of the Rocinante and its crew. We know that it uses laser-ignited fusion reactions and water as propellant. Again, we don’t have a mass or propellant fraction, so we cannot get definitive performance figures. However, we have detailed images of its interior and exterior. Note that there are no radiator fins or any heat management system visible.
The cross-section also reveals that there is very little room for propellant. Despite this, it can accelerate at over 12g’s and has reached velocities of 1800km/s while averaging 5g. Presuming that it can slow down again and jet off to another destination, this implies a total deltaV on the order of 4000km/s, which is 1.33% of the speed of light.

Official figures for the masses of spacecraft from The Expanse do exist. In collaboration with the TV show’s production team, SpaceDock created a series of videos featuring ships such as the Donnager-class Battleship for which a mass of 250,000 tons is provided.
Using the battleship’s dimensions, we obtain an average density of about 20 to 40 kg/m^3. For comparison, the ISS has a density of 458 kg/m^3. We will use this average density for now, but you can read the Scaling section below to understand how different mass assumptions for the Rocinante don't 'break' our workings so far. 

Applying the battleship density to the Rocinante's size gives us a mass of about 130 to 260 tons. It is likely to change a lot depending on what the ship is loaded with, seeing as it is almost entirely made up of empty volumes. We’ll use a 250 tons figure for an empty Rocinante and add propellant to it as needed.

Let’s put all these numbers together.
The Epstein drive technology allows for >250 ton spacecraft to accelerate for several hours at 5g with bursts of up to 12g, achieving a deltaV of 4000km/s, while not having any radiators and a tiny propellant fraction.

Can we design a realistic engine that can meet these requirements?

The Heat Problem
The biggest problem we face is heat.

No engine is perfectly efficient. They generate waste heat. Some sources of waste heat are physically unavoidable, however performant the machinery becomes.

Fusion reactions result in three types of energy: charged kinetic, neutron kinetic and electromagnetic.
Charged kinetic energy is the energy of the charged particles released from a fusion reaction. For a proton-Boron reaction, it is the energy of the charged Helium ions (alpha particles) that come zipping out at 4.5% of the speed of light.

We want as much of the fusion reaction to end up in this form. Charged particles can be redirected out of a nozzle with magnetic fields, which produces thrust, or slowed down in a magnetohydrodynamic generator to produce electricity. With superconducting magnets, the process of handling and using charged kinetic energy can be made extremely efficient and generate practically no heat.

Neutron kinetic energy is undesirable. It comes in the form of neutrons. For deuterium-tritium fusion, this represents 80% of the fusion output. We cannot handle these particles remotely as they have no charge, so we must use physical means. Neutron shields are the solution; the downside is that by absorbing neutrons they convert their all of their energy into heat. This is a problem because materials have maximum temperatures and we cannot really use radiator fins to remove the heat being absorbed.
Electromagnetic radiation is another unavoidable source of heat. Mirrors can reflect a lot of infrared, visual and even ultraviolet wavelengths. However, fusion reactions happen at such a high temperature that the majority of the electromagnetic radiation is in the form of X-rays. These very short wavelengths cannot be reflected by any material, and so they must also be absorbed. 

With this information, we can add the following requirements:
-We must maximize energy being released as charged particles.
-We must minimize heat from neutron kinetic and electromagnetic energy.

Thankfully, there is a fusion reaction that meets these requirements.
Diagram from here.
Helium-3 and Deuterium react to form charged Helium-4 and proton particles. Some neutrons are released by Deuterium-Deuterium side reactions, but by optimizing the reaction temperature, this can be reduced to 4% of the total output. An excess of Helium-3 compared to Deuterium helps reduce the portion of energy wasted as neutrons down to 1%. Another 16% of the fusion energy becomes X-rays. Other ‘cleaner’ source of fusion energy exists, using fuels such as Boron, but they cannot be ignited using a laser.

An optimized Deuterium and Helium-3 reaction therefore releases 1 Watt of undesirable energy (which becomes waste heat if absorbed) for every 4 Watts of useful energy.

If this reaction takes place inside a spaceship, then all of the undesirable energy must be turned into heat. However, if it is done outside the spaceship, then we can get away with only absorbing a fraction of them. It's the idea behind nuclear pulsed propulsion. 

How else do we reduce the potential heat a spaceship has to absorb?


A fusion reaction produces a sphere of very hot plasma emitting neutrons and X-rays in all directions. A spaceship sitting near the reaction would eclipse most of these directions and end up absorbing up to half of all this undesirable output.

If the fusion reaction takes place further away, less of the undesirable output reaches the spaceship and more of it escapes into space.

It is therefore a good design choice to place the fusion reaction as far away as possible. However, we are limited by magnetic field strength.
The useful portion of the fusion output, which is the kinetic energy of the charged particles, is handled by magnetic fields to turn it into thrust. Magnetic fields quickly lose strength with distance. In fact, any magnetic field is 8 times weaker if distance is merely doubled. 10 times further away means a field a 1000 times weaker. If we place the fusion reaction too far away from the source of these magnetic fields, then the useful fusion products cannot be converted into thrust.

We could calculate exactly how far the fusion reaction could take place from the spaceship while still being handled by magnetic fields, but whether you use magnetic beta (magnetic pressure vs plasma pressure) or the ion gyroradius (turning radius for fusion products inside a magnetic field), it is clear that kilometres are possible with less than 1 Tesla. For a setting with the Expanse’s implied technology level, generating such field strengths is easy.

What does this all mean for a fusion engine?
If we can generate a magnetic field strong enough to deflect fusion particles at a considerable distance, then we can convert a large fraction of the fusion output into thrust while only a small fraction of harmful energies reaches the spaceship.

The Rocinante is about 12 meters wide. If we describe it as a square, it has a cross-section of about 144m^2. A fusion reaction taking place 20 meters away from the spaceship would have spread its undesirable energies (neutrons and X-rays) over a spherical surface area of 5027m^2 by the time they reach the Rocinante. This means that 144/5027= 2.86% of the fusion reaction’s energy is actually intercepted by the spaceship.

Increase this distance to 200 meters and now only 0.0286% of the fusion reaction’s harmful output reaches the spaceship. A much more powerful fusion output is possible.

Finally, we need a heatshield.
NASA heatshield materials test.
Despite only a portion of the fusion output being released as neutrons and X-rays, and a small fraction of even that becoming radiation that actually reaches the spaceship, it can be enough to melt the ship.

We therefore need a final barrier between the fusion reaction and the rest of the spaceship. A heatshield is the solution.

This heatshield needs to enter into a state where it balances incoming and outgoing energy. With no active cooling available, no heatsinks or external fins, the heatshield has to become its own radiator.

The Stefan-Boltzmann law says that a surface can reach the state described above at its equilibrium temperature. It can be assumed that emissivity is high enough to not matter (over 0.9).

Equilibrium temperature = (Incoming heat intensity/ (5.67e-8))^0.25

Equilibrium temperature is in Kelvin.
The heat intensity is in Watts per square meter (or W/m^2)

Using this equation, we can work out that an object sitting under direct sunlight in space (at 1 AU from the Sun, so receiving 1361 W/m^2) would have an equilibrium temperature of 393 Kelvin.

A concentrating mirror focusing sunlight to 1000x intensity (to 1.36 MW/m^2) would heat up an object to the point where radiates heat away at a temperature of 2213K.

For a fusion-powered spaceship, you want this temperature to be as high as possible. Higher temperatures means that the incoming heat intensity can be greater, which in turn means that the spaceship can shield itself from more powerful fusion outputs.

Tungsten, for example, can happily reach a temperature of 3200K and survive a beating from 5.95MW/m^2.

Graphite can handle 3800K before it starts being eroded very quickly. That’s equivalent to 11.8MW/m^2.

Tantalum Hafnium Carbide is the current record holder at 4150K. Keep it below its melting temperature at 4000K, and we would see it absorb 14.5MW/m^2. Scientists have also simulated materials which could reach over 4400K before they melt.
This heatshield needs to rest on good insulation so that it doesn’t conduct heat into the spaceship. A design similar to the Parker Solar Probe’s heatshield mounting can be used. Low thermal conductivity mountings and low emissivity foil can reduce heat transfer to a trickle.

Proposed design

Let’s talk specifics.

We will describe now a fusion-powered rocket engine design that can perform most similarly to the Expanse’s Epstein Drive as shown on the Rocinante.
It is based on this refinement to the VISTA fusion propulsion design. Like the VISTA design, a laser is used to ignite a fusion fuel pellet at a certain distance from the ship and a magnetic coil redirects the fusion products into thrust. The rear face of the spaceship takes the full brunt of the unwanted energies and re-emits them as blackbody thermal radiation.
The refinement consists of a shaped fusion charge that can be ignited by laser slamming a portion of the fusion fuel at high velocity into a collapsing sphere, raising temperatures and pressures up to ignition levels.

Instead of the fusion products being released in all directions, a jet of plasma is directed straight at the spaceship. This increases thrust efficiency up to 75%, as the paper cites.
Somewhat similar magnetic nozzle configuration from this MICF design.
Meanwhile, the X-rays and neutrons escape the plasma in all directions.
The Epstein Drive is assumed to be a version of this. Instead of a spherical firing squad of lasers (as can be found in the NIF facility) that requires lasers to be redirected sideways with mirrors, a single laser is used for ignition. It is less effective but it means we can dispense with mirrors hanging in space. 
We will also be using Deuterium and Helium-3 fuels instead of Deuterium and Tritium. They are harder to ignite, but give much more useful energy (79% comes out as charged particles). By adjusting the fusion temperature and ratio of Helium-3 to Deuterium, we can increase this output to become 83% useful while neutrons fall to 1% of the output and X-rays represent 16%.

Also, using powerful magnetic coils, we will be igniting the fusion pellets at a much greater distance from the physical structures of the engine. We can take the 'nozzle' to actually be a mounting for the magnetic coil and everything with a line of sight to the fusion reaction to be covered in a heatshield. More importantly, the engine will be much, much smaller than the 120m diameter of the VISTA design.

The Rocinante has a cross-section area of 144m^2. Its heatshield will be a black metal carbide that can reach an equilbirium temperature of 4000K. It is separated from the hull with insulating brackets that massively reduce the heat being conducted to the 300K interior.

The heatshield needs to be thick enough to fully absorb X-rays and neutrons from the fusion reaction (it might be supplemented by boron carbide in cooler <3000K sections).

At 4000K, the heatshield can handle 14.5MW/m^2. The rear of the Rocinante can therefore absorb 2.09GW of heat.

The magnetic field acts on a fusion reaction 300m away from the hull. It acts like a spring; it requires no energy input to absorb the kinetic energy of the charged fusion reaction products and transmit it to the spaceship. Using figures from the cited paper, thrust efficiency is 75%.

Thanks to this arrangement, only 0.0127% of the unwanted energies from the fusion reaction are intercepted and absorbed as waste heat by the heatshield.

Some of the heat can be converted into electricity using to power the laser igniting the fusion reactions. The generator can be of the superconducting magnetohydrodynamic type, and the laser could be cryogenically cooled. This makes them both extremely efficient. The electrical power that needs to be generated to run the laser can be very small if the fusion gain is extreme (small ignition, big fusion output).

Putting these percentages so far together, 0.00216% of the fusion reaction energy ends up as heat in the heatshield.

Using that percentage, it is now evident that we have a very large ‘multiplier’ to play with. For every watt that the heatshield can survive, 46,300 watts of fusion output can be produced.

A heatshield absorbing 2.09 GW of heat means that its Epstein drive can have an output of 96.8 TW. About 2.2kg of fuel is consumed per second if we assume 30% fuel burnup ratio.

83% of that fusion power is in the form of useful charged particles, and the magnetic field turns 75% of those into thrust. So, 62.3% of the fusion power becomes thrust power; which is 60.26 TW.

The effective exhaust velocity of a Deuterium-Helium3 reaction can be as high as 8.9% of the speed of light. This assumes 100% burnup of the fusion fuel. Because we are using an excess of Helium-3, this might be reduced to 6.3% of the speed of light.

With this exhaust velocity, we get a thrust of 6.37 MegaNewtons.

An empty 250 ton Rocinante would accelerate at 2.6g with this thrust.

We know it can accelerate harder than that but it cannot handle any more fusion power. So, it must increase its thrust by injecting water alongside fuel into its exhaust.

There is a linear relationship between exhaust velocity and thrust at the same power level, but a square relationship between thrust and mass flow.

Halving the exhaust velocity doubles the thrust but quadruples the mass flow rate. The Rocinante can have a ‘cruise’ mode where only fuel is consumed to maximize exhaust velocity, and a ‘boost’ mode where more and more water can be added to the exhaust to increase thrust.

It is useful to know this, as we must now work out just how much fuel (Deuterium and Helium-3) and extra propellant (water) it needs

1800km/s is done in the ‘boost’ mode, and then 2200km/s in the ‘cruise’ mode, for a total of 4000km/s. How much fuel and propellant does it need?

As with any rocket equation calculation, we need to work backwards.

Mass ratio = e^(DeltaV/Exhaust Velocity)

An exhaust velocity of 6.3% of the speed of light and a deltaV requirement of 2200km/s means a mass ratio of 1.123.
The 250 ton Rocinante needs to first be filled with 30.75 tons of fusion fuel. A 1:2 mix of Deuterium (205kg/m^3) and Helium-3 (59kg/m^3; it won't freeze) has an average density of 107.6kg/m^3, so this amount of fuel occupies 285m^3. It represents about 4.9% of the spaceship’s 12x12x40 m internal volume.  

And now the ‘boost’ mode. 5g of acceleration while the spaceships gets lighter as propellant is being expended means that thrust decreases and exhaust velocity increases gradually over the course of the engine burn. The propellant load can to be solved iteratively... on a spreadsheet.

Using 0.25 ton steps for water loaded onto the Rocinante, it can be worked out that an initial mass of 352 tons is required. This represents an additional 57 tons of water and 17.25 tons of fuel.

The full load is therefore 57 tons of water in 57m^3, and 48 tons of fusion fuel in 446m^3. Together, they fill up 8.7% of the Rocinante’s internal volume.

The thrust level during the acceleration to 1800km/s varies between 13.77MN and 17.27MN. It takes just over 10 hours to use up all the water.

Boosting to 12g would require that this thrust be increased further, between 33.05MN and 41.44MN. However, it could only be sustained for 106 minutes, until 751km/s is reached.
Official art by Ryan Dening.
In ‘cruise’ mode and with no water loaded, the Rocinante would have 3320km/s of deltaV and can cross the distance between Earth and Saturn in 10 to 12 days at any time of the year.

At 12g, it can sprint out to a distance of 21.2 thousand kilometres in about 10 minutes, and 0.76 million kilometres in an hour.


This proposed design can be easily scaled to adjust for different figures for mass, acceleration and deltaV.  

The variable will be the ignition point distance from the spaceship and therefore the magnetic field strength of the coils in the 'nozzle'. A stronger field allows for fusion products to be redirected from further away, so that an even smaller portion of the harmful energies are intercepted. 

If we assumed a ten times greater density for the Rocinante, for example, we would have an empty mass of 2500 tons. To adjust for this while maintaining the same performance, we would simply state that the fusion reaction is ignited 10^0.5: 3.16 times further away, or 948m. The 'multiplier' mentioned earlier jumps from 46,300 to 461,300, just over 10 times better than before. In other words, the fusion output can be increased 10 times and all the performance falls back in line with what was calculated so far. 


Beyond what we’ve seen on the show or read from the books, there could be some interesting consequences to having this sort of design.
Visually, for example, the rear end of spaceships would glow white hot. They cannot come close to each other while under full power, as then they’d expose each other’s flanks to intense heat from the fusion reactions.
You might have noticed from a previous diagram that a portion of the fusion plasma travels all the way up the magnetic fields without being redirected. This could be the reason why we see 'gas' in the 'nozzle'; it is simply the leaking plasma hitting a physical structure and being compression heated up to visible temperatures. 

A failure of the magnetic fields would immediately subject the heatshield to 5x its expected heat intensity. This would quickly raise the temperature by a factor 2.23, so it would turn from solid to explosively expanding gas. Not exactly a ‘failure of the magnetic bottle’, but a similarly devastating result.

On the other hand, the magnetic field passively provides shielding against most of the radiation that can affect space travellers. If it is strong enough to repel fusion protons, then it could easily deal with solar wind protons and other charged particles, as found in the radiation belts around Earth or Jupiter. This could be a reason why we don’t see thick blankets of radiation shielding all around the hull.

Our proposed engine design is pulsed in nature. We want smooth acceleration, so we want as many small pulses in such quick succession that the spaceship feels a near-continuous push. This can be achieved with as few as 10 pulses per second, or hundreds if possible.
However, even at 10 pulses per second, you need to shoot your fusion fuel from the fuel stores to the ignition point 300 meters away at a velocity of 3km/s. This can be accomplished by a railgun, and it is incidentally a good fraction of the projectile velocities used in combat.

Could the Belters in the Expanse simple have pointed their fuel injection railguns in the opposite direction to equip themselves with their first weapons?

Similarly, an intense laser is needed to ignite the fuel quickly enough to achieve an extreme fusion gain. Doing so from 300m away requires a short wavelength and a focusing mirror… which are also the components needed to weaponize a laser. If a laser can blast a fuel hard enough to cause it to ignite, then it could do the same to pieces of enemy spaceships, and all that is needed to extend the range is a bigger mirror. This implication can be countered by having an extreme fusion gain ratio - ie, a 10,000,000 fold ratio between the energy input of a laser ignition system to the fusion output. That means a 100TW reaction can be ignited by just a 10MW laser, which is far less likely to be weaponized.  

There is also a claim made where the Rocinante’s fuel reserves are ‘enough for 30 years’. This cannot mean propulsion. Even at a paltry 0.1g of acceleration in ‘cruise’ mode, the Rocinante can consume all of its fuel in just 40 days. Add in a lot of drifting through space without acceleration, and we’re still looking at perhaps a year of propulsion. It is much more likely that this claim refers to running the spaceship; keeping the lights on, the life support running and the computers working. That sort of electrical demand is easily met by the energy content of fusion fuels.

Finally, keep in mind that the propulsion technology described here is not specific to the setting of the Expanse. It respects physics and you can introduce it to any setting where real physics apply. In other words, it is a ready-made and scalable solution for having rapid travel around the Solar System without much worry about propellant, radiators, radiation shielding and other such problems!


  1. What would happen if heat is absorbed by fuel before being used in the reactor? If I remember correctly, hydrogen and helium can convey a lot of heat.

    1. You want the fuel to be solid and as cold as possible before ignition, so that your delicate shaping and arrangement of different layers survive intact. It is this arranagement which allows for very high fusion gains.

    2. Being this is 200 years in the future (I think it is 300 in the books) I would think antimatter factories would exist. You don't need much. Antimatter augmented fusion or Forward type antimatter propulsion would solve a lot of reaction mass problems. It would probably be more efficient than the Epsitein drive.

    3. Minor spoilers, but antimatter production does pop up in the later books. The quantities are very small, so not enough for a pure antimatter engine, but its use to ignite fusion reactions easily is described.

    4. Not a book reader. Yeah antimatter catalyzed fusion has been a topic in technical papers in the last 25 years. Pure antimatter propulsion would probably be even beyond the advanced technology of 200 years. Focusing of gammas is probably Kardashev II technology.

    5. I think absorbing the heat with the reaction mass would be a better idea. In my sci go, the torch drive is basically this, but the heat is absorbed by injecting the reaction mass in near the radiators

  2. I've thought about this myself, but reached a somewhat different conclusion given the numerous problems encountered by laser-driven fusion on Earth: impact fusion. Perhaps, they use extremely powerful magnetic fields around a loop as their exhaust port. A pellet of Deuterium/He-3 is wrapped in a lithium foil, then shot out the back towards the magnetic field at say 1000 km/sec (I've heard that as a ballpark for impact fusion). From the POV of the pellet, the magnetic field slams into it, heats it and compresses it, and just as the particle crosses the crux of the field, it fuses. The fusion products are expelled the other way, providing thrust. Some issues:
    1) You still need to absorb the waste heat from the reaction. That means that between your superconducting coil and the reaction chamber, you'll want some kind of heatshield. Depending on the temperature the coil can handle before it quenches, the rate of fire and the size of the pellet, it seems somewhat doable.
    2) Your coils would need backing, so they don't burst from the strength of their magnetic field. The tape material used would probably be some kind of REBCO with a nanotube backing. Or, you could use the heatshield to anchor the coils (carbon has both exceptional thermal properties, and exceptional strength properties).
    3) For lack of a better "flexible"is a magnetic field, and how does that flexibility scale with distance from the coil and field strength in Teslas? We can already do 40 T of field strength, but all magnetic fields are "bendy". You want the field to as closely approximate a sudden stop as possible.

    1. Oh you are quite right, this is far from the most efficient way of handling fusion. The great distance between the magnetic coil and the ignition point imposed by having to handle a whopping ~100TW fusion reaction makes magnetic control impossible. Limited to only lasers, you would have to rely on extremely fine control over the various instabilities that trouble modern fusion scientists at the NIF and elsewhere.

      You are describing the much more efficient and stable MICF design:

      Regarding the 'bendiness' of a magnetic field... it's usually not a problem. Like a spring, all that matters is that it stops compressing before it reaches the spaceship.

    2. Actually, the similar Gradient Field Imploding Liner approach seems to be a better match:
      Though, I must say, the speed estimated for the fuel nugget in that study was far lower than I had anticipated. 10 km/sec is around 100 times less than needed for impact fusion. I must be missing something... Either way, I guess that even if that were less optimistic, one could include a particle of fissile material in the core of such a nugget to be compressed into criticality and start a chain reaction (americium or U233 would do nicely; good neutronics). The study also used D-T fusion, but higher energy is probably possible with D-He (well, useful energy; you don't lose 80 percent of it to neutrons). 16 times the needed energy to fuse means 4 times the nugget velocity, all things being equal.
      I really don't like using lasers for fusion... all the billions poured into that approach only lead to use realising how even micro-scale instabilities dramatically affect the performance of the reaction.
      Or, if nothing else, you could approximate an Epstein drive with a nuclear pulsed thermal engine. Not quite the exhaust velocity, but still.... About the only realistic engine other than the above gradient fusion and NPTR that has both high ISP and (reasonably :P) high acceleration is the direct drive fusion one. The hypothetical advanced plasma magnet might also work:
      but it's not really an "engine" and can only do it moving away from the sun (though the potential is vast if it works).
      Question: if I have an idea pertaining to an RTG, where should I post it?

    3. The reason I'm asking is because there doesn't seem to be a blog post dedicated to RTGs, and I don't want to spam.

    4. Sorry for not answering sooner.

      You can post an RTG question here, no problem.

    5. Well, I was thinking about how I could do a high power non-dynamic RTG. RTGs generally suffer from low power due to the rather low efficiency of thermoionic and betavoltaic type devices. Use of Stirling systems enables substantially higher efficiency (see the KRUSTY reactor developments) but have issues with wear and tear, are heavy, as well as varying dynamic heat and power loads. A major advantage of classical RTGs is their lack of moving parts enabling very rugged operation.
      After some research I stumbled upon the fission fragment reactor idea. Direct energy conversion either through the use of Venetian Blind type systems, or MHD systems could very well be easily used to make an RTG. Take the material that would usually be a red hot block of material, ground it up, suspend it electrostatically, collect the fission products in an ion beam, and produce power. With no moving parts, but bypassing the tirany of the Carnot heat cycle. And because it's not an actual reactor, you don't really need to maintain a fission reaction.
      You can even use thermovoltaics to collect some of the energy from the fraction of ions that hit other dust particles instead of escaping the chamber (thus heating them up).
      My choice for fuel would be... unconventional:
      I wanted an alpha emitter, since alphas travel slower, and enable the use of smaller collection and fuel chambers. Polonium-210 is king, with it's staggering power output. I also expect it to be produced in decent quantities in lead-bismuth cooled reactors (which, being fast reactors, would be useful on space missions and bases). That means the super-RTG could get refuelled easily.
      Another useful quality of polonium is that it is self-grinding because of its' powerful emission (which spalls dust particles, as well as any unwanted chemical bonds; this is why it starts to turn to vapour far bellow its' actual vaporisation temperature ). What's more, since the concoction is electrostatically suspended, you don' have to use gadolinium additive as an alloy (weight and volume savings).
      Less useful qualities: short half-life (expected for such an energetic isotope). Also... crazy dangerous (easily dispersed, easily absorbed, heavy metal toxicity).
      I've tried searching for a way to estimate the opacity of a block of say 16 cubic cm of Polonium that is ground and distributed into a volume...say... a quarter of a cubic meter. That way I could figure out how many of the alphas escape, and try optimise the shape of the cloud into, say, a disk for a Hall type collector. But it's apparently quite tough. Would you have any ideas?

    6. I'm sorry to say, but a fission fragment or dusty plasma reactor definitely undergoes fission. If you look at any reactor designs using that technology, it definitely features neutron moderators to induce criticality. The majority of their output (~85%) is fission fragments. In a thin enough cloud of fission fuel, the fragments can escape entirely and get collected by electrostatic or electromagnetic devices for direct energy conversion.

      Perhaps you mean a non-fissioning version of this reactor? You will get power from radioactive decay, and you might be able to collect the output in the form of alpha particles directly.

      Alpha particles have near zero penetrating power. So, it will always be absorbed as heat by any dust particle it encounters. It might be interesting to look at the maths behind the dust cloud density and replace parameters for fission fragments by those of an alpha particle.

    7. That is essentially what I was saying...but trying to be coherent in a noisy environment is a losing proposition. Apologies :)
      Yes, I meant to say using nuclear decay instead of artificially induced fission (nuclear engineers are apparently quite careful about using the two terms; got scalded for using them wrongly).Alpha particles are essentially small, heavily charged and fast fission products. By using decay you just need to contain the fuel, rather than being bogged down by heavy stuff like moderators and sensors, or deal with neutron activation or embrittlement. And avoid (well... to an extent; radionuclides are still scrutinised) the political problems of private companies having the ability to use/refine fissionables away from planetary oversight.
      When I have time, I'm gonna look over the original FFR paper. The problem there was, as I recall, that they were building a rocket, and merely suggesting a reactor, with little details given on how the collection system would work, or it's estimated efficiency (better than heat engines was about the gist of it). I'll try and see if they have any public papers about subsequent designs inspired by that.
      Thank you for your suggestions and time!

    8. No problem.

      Try papers like these:, and accessing them with sci-hub is you are unable to do so otherwise.

  3. Does a ship using an engine like this need another set of reactor to provide electricity for the systems onboard?

    1. You would need a power source to run the laser, but that can be easily accomplished by drawing energy through superconducting coils and the MHD effect actin on fusion products. By slowing them down, they are converted into electricity directly.

  4. I really love your blog, keep up the good work.

    While the challenge of recreating The Expanse's shipdrives prohibited radiators, wouldn't using them boost the efficiency of the design immensely? How much better could we get with active cooling and radiators? And what would be a decent coolant for a 4000K + heat shield? Cerium? Liquid tungsten dropplet radiators?

    1. Thank you.

      Being able to use radiators means that you can handle much, much more waste heat. This helps bring the fusion reaction closer to the spaceship, so that you can handle the fusion products with weaker magnetic fields and a greater thrust efficiency. This means even less propellant is required!

    2. So this would potentially lead to designs similar to those proposed in the NTER post, with large radiators for use during high-efficiency cruise, which are retracted during combat?

    3. The problem with fusion drives as NTERs is that their power output greatly exceeds the cooling capacity from the flow of fuel and propellant going through them.

      Hydrogen gas might absorb 60MJ/kg before heat exchanges start melting. But, out of that same kg, a fusion drive would release 100TJ... it is not really possible to match those numbers.

      Also, a fusion engine will need a large nozzle. A magnetic nozzle cannot be kept hidden inside armor; it has to be large and exposed. This creates an obvious wekspot that you cannot retract like you can do with radiators.

    4. @Matter Beam

      I think he is referring to the fact that in a boost mode you can actively cool the rear of the spacecraft with the water or whatever you use to boost it. Therefore, meaning you can use radiators and even without radiators squeeze out a little more performance than if it wasn't actively cooled by reaction mass.

    5. @Bob

      That is an option, but the doing the maths shows that the water flow does not contribute significantly to the cooling effect.

      Heating water up to 3000K should absorb about 6MJ/kg. In the blog post, I worked out that the water flow rate for boosting to 5g was 1 to 2 kg/s, and 12g acceleration might require about 5kg/s at most. So, this water flow is absorbing about 30 MW. This is understandably tiny compared to the gigawatts of heat that is bombarding the heatshield.

  5. I hate to be a naysayer here, but it seems to me that such a high-thrust fusion engine would require prohibitively large magnetic fields. Looking through your sources and solving for detonation distance, magnetic fields in excess of 50 Tesla are required to deflect the plasma from a single 6 TJ pulse.
    When doing the numbers myself, I keep finding a direct relationship between increased thrust/weight (really thrust to area, as I am assuming the mass of a heat shield) and increased pulse rate with smaller individual pulses. A 30m diameter coil with 1.6 GA running around it (generating a B field of roughly 66T) is used for my assumptions. Assuming a pulse energy of 500 MJ, each pulse produces 13.6 kg*m/s of impulse. In order to produce 250 KN of thrust (what I would set as the minimum for a torchdrive ship of 250 tons) a detonation rate of around 18,000 is required. Now this seems, if not impossible, highly impractical. With this coil arrangement, the maximum efficient detonation distance is around 400m. The waste thermal energy released by 18,000 500 MJ pulses every second would quickly heat the 30m diameter heat shield well past 4000K (4460K to be more precise).
    This is a great idea, and I want to thank you for continuing your work and everything you put into this blog.

    1. Hi Spencer.

      The strength of a magnetic field is not related to the power output of the plasma it works with. 1 proton or 10 trillion protons are deflected just the same.

      My own calculations show that it takes an average field strength of 26 microtTesla is necessary to get 17.5% C protons to turn around in a U-turn with a radius of 300 meters. The initial field strength needed to create an average field strength of 26 uT over 300 meters is just... 6.67 milliTeslas!

      Also, the effective size of the nozzle is huge, and it could be increased even further if we use Mini-Magnetosphere Plasma Propulsion type designs.

    2. Hi MatterBeam,

      More than a year on but I'd like to revisit this. When a fusion pellet explodes in a magnetic field, the field does not remain stationary as you have depicted in this diagram. Instead, by Lenz's Law, the hot conductive plasma actually excludes magnetic field lines and pushes the preexisting ones aside, distorting the magnetic field lines. Thus, the magnetic nozzle that you have drawn is really not as rigid as is made out to be, and a straightforward calculation of the B field strength assuming that the fusion products will spiral along those field lines is results in a severe overestimation of the sort of power that you can achieve. In this sense, the ability of the field to contain the fusion plasma jet really DOES depend on its strength.

      Indeed, the field lines (yes, these are multi-Tesla fields) are often distorted so much in these fusion pellet designs that they basically line up next to the fusion coil itself, which basically means with one coil you will get basically no collimation at distance. The plasma will basically expand unconstrained and in a spherical shell, with a very tiny fraction bouncing off the magnetic coil at close range. In order to fully capture a large portion of the plasma and redirect its momentum, you need a nozzle-shaped array of coils, which unfortunately reintroduces the issue of intercepted radiation and waste heat. See NASA's HOPE MTF reference design as an example, or Hyde's Fusion Rocket.

      All hope is not lost though, the idea of a standoff explosion with a very collimated exhaust is I believe the correct way to go. We can talk of the fuel pellet containing a sort of disposable lightweight coil around it, which is energised moments before ignition and survives just long enough to collimate the rapidly expanding fusion plasma towards a distant pusher plate. In this case the ship itself doesn't even need to provide a remote magnetic field, it is self-generated by the pellet upon ignition.

    3. Hi! I missed you comment, so I'm replying now.

      I based my findings on the papers I read (and cited here). Perhaps there is a misunderstanding here.
      -The exhaust is directed out of the fusion pellet by hydrodynamic (pressure/fluid) forces rather than magnetic forces. There are no magnetic coils within the mass of frozen hydrogen fuel.
      -The exhaust then expands through space until it encounters the magnetic fields of the magnetic nozzle.
      -The magnetic fields do no work. As long as they are strong enough to deflect a single alpha particle, then can deflect terawatts of power. The limitation is how much the physical structure can survive in terms of heat and radiation, and I already tailored that to match the desired thrust from the fusion reaction.

      Does this clear things up?

    4. Hi MatterBeam,

      My point is that the assumptions that you've laid out, specifically the 4th one, do not hold for a rapidly expanding plasma, though they may hold for a single alpha particle. A conductive plasma moving through a magnetic field sets up all sorts of induced currents within itself that act to oppose the original magnetic field. This means that on the whole, the magnetic field is not as stiff and rigid as you are making it out to be, but rather deflects and deforms with significantly less resistance, when impinged upon by a plasma. This is exactly why fusion research is so hard, because even with the low pressure plasma in those tokamaks, the plasma still finds ways to distort the multitesla fields our best superconducting coils can put down. This would certainly be the case for a torch drive where the pressures of the exhaust are necessarily much higher (you need to propel the ship at multiple g's).

      As such, the thing I mentioned about the magnetic coil within the pellet was a method to bypass this limitation and get the magnetic field to within inches of the plasma, so that it can actually act to collimate the plasma, and/or set up that M2P2 field configuration you've mentioned elsewhere in the comments section. It was not an incorrect interpretation of the article because it was supposed to be a suggested improvement.

    5. (continued from previous)

      Something else I'd like to address is that the reason I might appear to be talking past you is that, to my knowledge, we appear to be operating on differing assumptions in terms of what exactly is used to collimate the flow.

      You mention the use of hydrodynamics to shape the flow, inspired I suspect by Freeman Dyson's work on shaped nuclear charges a la Casaba Howitzer. Several things I'd like to point out with respect to that:

      1. You need an inert moderator in order to generate such a jet. That impacts specific impulse greatly as the fusion energy has to be shared with inert byproducts, cooling the exhaust.

      2. Collimation via this means is an extremely inefficient use of fusion energy, in terms of collimated exhaust generated. An article you wrote on shaped charges confirms this. The tighter the collimated beam, the more energy inefficient the focusing process.

      Based on these 2 facts, such a hydrodynamically shaped charge would suffer a specific impulse far below the theoretical limit for fusion. And given how the engine performance in the Expanse appears to already be pushing the ragged edge of that envelope, I do not believe that they would be using such an inefficient means of charge focusing.

      That leaves us with the magnetic field itself to perform focusing of the jet and also push off it to generate thrust. And while it can do a really good job, as per the illustration you provided of a plasma charge exploding against the magnetic field, note also how close the charge is to the coil in terms of coil diameters. This is not an illustration quirk, but a geometric necessity. Owing to the springiness of the magnetic fields I described in my last 2 comments, you cannot trust the magnetic field to remain extended as it would with single charged particles. Instead, what often happens is that the magnetic field will distort and press itself close to the physical coil, as in NASA'S HOPE MTF design. You NEED the coil to be that close in order to push off the exhaust at all, a problem which you cannot tackle just by increasing the field. This then prevents you from distancing the coil as was the intent of the whole design. You need a field of several tesla at the point of detonation, and if the coil is very far from the target in coil diameters, you are going to need a truly monstrous coil to get that level of B field, not to mention the expanding plasma is going to simply nullify some of your hard work by setting up induced magnetic fields.

      Which is why I proposed a a magnetically focused charge as a tweak to your otherwise very solid design. You can keep the ship based magnetic coil to act as a pusher plate, but the collimation is now handled by a magnetic coil surrounding the mostly moderator-less pellet, remotely energised by the parent spacecraft and surviving long enough to collimate the expanding fusion plasma into a very tight beam pointed at the magnetic pusher plate.

      Because the plasma is already collimated, all the magnetic pusher plate needs to do is to sit there and wait for the plasma to hit it, as per your Rocinante diagram. Additionally, if the pellet coil field is strong enough, it will link up with the magnetic coil to create an M2P2 field for further focusing, although I wouldn't personally count on it.

      I hope you don't take this as an attack on your work. I agree wholeheartedly with your general layout of tightly focused shaped charge hitting magnetic pusher plate, and agree that this is probably THE path to go in order to achieve torchship level performance. I just wanted to bring into consideration a detail which would lend greater authenticity to this concept.

  6. I have a few honest questions, mostly about the differences between what you're describing here and what is depicted in The Expanse. I'm just trying to make sure sure I'm not confused or misunderstanding something.

    Am I correct in thinking that your system (on its own) isn't feasible for launching from (or landing on) a body with nontrivial gravity? It seems like there's no way to move the fusion explosion close enough to the ship for sane-sized landing legs while still producing sufficient thrust. Also, it wouldn't work in an atmosphere because of drag, heating, etc. acting on the fusion pellets.

    Ships would need to be very careful using your engine near other vehicles, stations, etc. not the sort of "coming in hot" flying from the show, right? In fact, it seems like ships would either need some other sort of propulsion for use near anything valuable/inhabited, or else use RCS to gently drift out to a safe distance before firing up the fusion drive.

    1. That is a valid concern and a real problem for a near-future fusion engine.

      However, the Expanse has good control over fusion ignition and can throttle between thrust and exhaust velocity very well.

      It is therefore likely that they enter a very low exhaust velocity mode for takeoff and landing.

      For example, if the Rociante wanted to land and then take off from Earth with minimal awrodynamic heating, it would need 20km/s deltaV

      It can use 50 tons of water (so maybe 300 tons empty, 350 tons full) to do this.

      The Rocinante can reduce its exhaust velocity to the point where it achieves a TWR of 1.2. At 350 tons, this 5.15MN.
      With a mass ratio of 350/300: 1.167, you'd need an exhaust velocity of 129km/s to achieve the necessary deltaV.

      Now let's work out the engine power output.

      Power = 5.15e6 x 129e3 / 2 = 3.34e11 Watts.

      That's 334GW. Huge but nothing like the maximum it can handle.

      The lower power also means you can bring the fusion reaction much closer to the spaceship. This helps counter the disruption caused by igniting fusion within atmosphere, as you'd be imposing stronger magnetic fields and more intense laser pulses...

    2. I would also tend to believe that additional reaction mass from air between the craft and the fusion pulses would significantly increase thrust. You could probably get away with an order of magnitude less power than even your 300GW number and still achieve enough thrust for liftoff at low altitudes. If the radiation shield at the back of the craft can works as a semi-orion absorption plate, then atmospheric operation should be incredibly efficient.

    3. That's right. Also, the air can absorb high energy X-rays pretty well, so we also get a big boost in the energy available from the fusion reaction (and a corresponding decrease in unwanted heating).

  7. Hi, I really love your work~ especially the "particle field armor" & the "dusty plasma radiator" which seem to be your own ingenious creation, I wish we can see them in future Sci fi series soon.
    Some points after reading this post:
    I still find the radiator indispensable: energy efficiency of high power laser is notoriously low, so the igniter laser will need radiator during prolonged acceleration. Dusty plasma radiator seems impractical here, because the acceleration...old fashioned panels with strong bracing is
    Also, strong magnetic field needs strong structural support, let's re-design the Rocinante to have a magnetic torus field running through the long axis of the ship, so the hull as a whole
    can support this field. The problem is whether human body can sustain strong field, at least for several hours to days...
    Such a whole-ship-field can also accommodate the particle field armor and dusty plasma radiator
    during actions since actions will mostly take place during coasting.
    Practically, this post leads us to a spinal main laser design, so the other end, or the "head" of the ship can be equipped with your conical laser amour, with a delicate but robust shutter integrated with it, so a beam of high energy siege laser can be brought for the enemy stations
    to bear.
    While facing a barrage of enemy kinetic or even nuclear warheads, this engine seems to provide
    similar active defense effect to that of cabasa howitzer purposely deployed near one's own ship.
    If the opponent fields siege laser, which one below will be a better defense? The conical graphite armor with active cooling, or the plasma ball of fusion? It is known that plasma can "block" laser: high energy plasma with very high electron density can resonate and absorb UV or even X ray laser beam.
    If the fusion fireball is indeed more efficient at eliminating incoming energy and kinetic threats, then after reading the older posts of kinetic exchange, I think the scenario below may be plausible:
    Accelerate violently from home base circling one planet or moon into solar escape orbit and then
    swivel to face the opponent with your rear, so you can decelerate to capture into opponent's orbit surrounding a certain planet or moon, at the same time, you can handle all the incoming threats with the fireball. The ship could be armed as a killer bus, it can release a saturated barrage, or "fleet" of self-guided kinetic and nuclear warhead, their ultra high relative speed will ensure annihilation of the first front of the opponent, then this ship can leisurely use its siege laser to reduce orbit industrial bases of the opponent to partially processed resources. The total-wrecked front defense of the enemy will also become a rich pool of resource for you the invader.
    Lastly, the same unavoidable weak point as the design of Orion Pulse Nuclear: how to protect the laser beam shutter at the center of the heat shield? If high pulse frequency is needed, this may
    become a problem.
    It seems that the magnetic field lines act just like the mechanical springs of the pusher plate, so I assume the actual acceleration delivered to the mechanical part of the ship structure is not that violent as that delivered to the pusher plate of The Orion, is this correct? On the other hand, I can recall that in the famous "electromagnetic initial confinement" design of John Slough using Li ring and a pulsed field, pusher plate is necessary to buffer the initial impact, despite having a electromagnetic nozzle.

    1. It also seems that we can accelerate the shaped pellet using laser ablation, just like in the linear field implosion layout, and the pellet will be compressed at the existing point, again similar to linear implosion, but the pellet does not reach critical until a last pulse of the igniter laser trigger that event when the safe distance is reached

    2. Hi!
      A lot to answer here!

      -Thanks for the compliment. I hope it does inspire people.
      -We have working examples of lasers with an efficiency of 85%, thanks to cryogenic cooling:
      -Strong magnetic fields can drag along metal particles at high G's, so a dusty plasma radiator could work well (although it might leak a bit if exposed to the punishing radiation of fusion detonations).
      -Magnetic fields can be cancelled out by an inner tube of magnets. This would create a volume inside the ship free of strong magnetic fields.
      -A plasma that can block a laser is hot enough to roast the ship it is protecting. Think of it this way: the Sun's core is opaque to X-rays but also sits at millions of Kelvin. It is easier to generate a plasma-penetrating X-ray beam than to recreate the conditions at the core of the Sun to protect yourself from that same beam.
      -The extreme kinetic energy of high speed projectiles can be turned against them. If you place a very lightweight sheet of paper in front of a projectile travelling at several hundreds of kilometers per second, then the energy released by the collision is enough to make the projectile explode into harmless dust. So, you can employ very simple protection to defend against these projectiles, so long as you give yourself enough room between the explosion and the ships being protected.
      -Multiple laser pulses indeed create the best fusion ignition conditions.

  8. Once again very impressive, Matter Beam. Have you/will you be doing similar calculations for the MCRN Donnager?

    Thank You,


    1. Thanks, Keith

      The design I described can be scaled up to the Donnager. It would have to run at about 1000x power to produce the same acceleration with 1000x the mass... but the Donnager might have more fuel reserves and accept a lower exhaust velocity to get more thrust at a lower power level.

  9. Very impressive work! Thank you for writing this!

    The "gas in the nozzle" detail did get me wondering though: am I right in imagining this design would still produce a visible "drive plume", albeit one visually separated from the ship itself by the distance to the ignition point?

    1. You are correct. In fact, about a trillionth of a percent of the drive's power ends up being released as visible light. That means the 100 TW reaction releases only 15.3 kW of visible light.

  10. Excellent analysis -
    I'm curious about whether incorporating some aspects of the Gleason/Tau Zero idea of a Plasma Magnet Drive for magnetic confinement. The plasma-magnet skips the superconducting magnet and instead relies on a rotating electric field to drag plasma around to generate a magnetic field.
    Estimates are 10kW of electricity generate a 30km magnetic field.

    This would seem to open up some interesting options: longer distances for detonation, some aspect of "orion medusa" motion where detonation inflates the magnetic field and the field "jellyfishes" along, and the possibility of trapping a column of plasma between the ship and the detonation point to acts like the ionized shockwave of a reentry capsule.

    1. A magnetic field drops very rapidly in strength, but it can be carried much further by a conducting plasma. This gives the Sun its massive magnetosphere, but is also exploited by plasma sails.

      A plasma sail creates it's own tiny magnetosphere that expands until it equalize in pressure with the ambient pressure. This is on the order of nanopascals/nanoteslas. You can see how a small magnetic field generated by 10kW currents can expand to 30km.

      The magnetic nozzle of an Epstein drive doesn't retain a plasma to extend its reach, and of it did, it would have to equalize with the pressure of the expanding fusion plasma. Necessarily, it would be much much smaller.

    2. Not sure if quotes are bad form, but I hope this helps for references

      -- Matter Beam - A plasma sail creates it's own tiny magnetosphere that expands until it equalize in pressure with the ambient pressure. This is on the order of nanopascals/nanoteslas. You can see how a small magnetic field generated by 10kW currents can expand to 30km.

      Yep, but IIRC that's the classic mini-mag setup. The ring currents for a plasma magnet would extend to a radius of ~10km. Per Cent-Dreams-

      -- The Plasma Magnet Drive: A Simple, Cheap Drive for the Solar System and Beyond
      Two polyphase magnetic coils (stator) are used to drive steady ring currents in the local plasma (rotor) creating an expanding magnetized bubble. The expansion is halted by solar wind pressure in balance with the magnetic pressure from the driven currents (R >= 10 km). The antennas (radius ~ 0.1 m) are shown expanded for clarity.

      I'm sure that there would be an "in universe" explanation of "magnetic ring current OFF" or "magnetic ring current ON" to switch between modes but if a 10kw current creates a nanotesla magnetic field stretched into a ~20km diameter sail blocking solar wind plasma, it is still bouncing particles moving at up to 750 km/s or about 0.2% of light speed. Some plasma magnet sail figures calculated about 2 weeks for an outbound craft to reach O.2% light speed by "just coasting" on the stellar wind.

      -- Matter Beam The strength of a magnetic field is not related to the power output of the plasma it works with. 1 proton or 10 trillion protons are deflected just the same.

      Which I'm having trouble visualizing. If a plasma mag-sail at nano-tesla power is abble to bounce solar wind plasma moving at 0.2% of light speed when stretched over a 20km diameter, then (ballpark) that same power focused down to 2km should bounce 2% light speed plasma, and focused down to 200m should bounce 20% light speed plasma (not addressing how to calculate magnetic field strength for a ring-current at 20km, 2km, 200m *(or perhaps 20m or even 2m if you can focus that accurately).

      -- Matter Beam - My own calculations show that it takes an average field strength of 26 microtTesla is necessary to get 17.5% C protons to turn around in a U-turn with a radius of 300 meters. The initial field strength needed to create an average field strength of 26 uT over 300 meters is just... 6.67 milliTeslas!--

      So, perhaps SOME of this is in the ballpark for 2m, 20m, 200m a magnetic-bottle and perhaps a 2km or 20km plasma-magnetic boosted bottle?

    3. Think of the magnetic field as a spoon, and the charged particles as tap water.
      You can make a light trickle or full blast from the tap, and they get deflected all the same way (just with proportionally more force exerted).

      A stronger magnetic field can:
      -Bounce the same particles from further away (making a U-turn 600 meters from the spaceship instead of 300 meters away)
      -Bounce faster particles in the same distance (0.02 C particles in 100 meters instead of 0.01 C particles in 100 meters).

  11. Interesting point about the Mini-Mag nozzle,

    It occurred to me that a magnetic nozzle should be inherently variable, not just in geometry (e.g. from a wide-open-umbrella shape to a narrow-pencil shape).
    Since you are changing volume, by changing the "bell" shape, you ought to be able to create a MHD "squid" drive in an atmosphere. If you have a source of ions, or can ionize the atmosphere, and start with a large diameter field (like an umbrella) and then construct the diameter (like closing an umbrella you should get a MHD jet.

    The really interesting question is whether the entire volume in the "bell" would have to be ionized into plasma, or whether you could use a "bell" of plasma to move and compress bulk un-ionized air.

    1. The ignition laser for the fusion drive can be used to ionized the air directly.

      An ionized plasma tends to expand very rapidly and slam into the magnetic fields, although it will be slowed by down by the surrounding air. Since the magnetic fields cannot transfer thrust from hot but neutral air, this is a direct loss!

    2. Ah, my fault for mixing terms, I was thinking "plasma magnet nozzle" but typing "min-mag".

      You may remember the "magneto-aero-capture" idea of replacing drag chutes with a plasma magnet to create a magnetosphere with a diameter of several meters to act as an aeroshell during atmospheric reentry. Idea was, inject a few grams of plasma initially, those are trapped by a magnetic field, that magnetosphere impacts the atmosphere and generates the standard reentry shockwave and plasma; however the neutral atmosphere molecules are also trapped by charge exchange, and you drag along an electrical "aeroshell" of ionized gas and charged air molecules held in place by the magnet.

      Well, if you can make an electro-static parachute to slow you down in bulk atmosphere, you ought to be able to "flap" that parachute like a jellyfish to move forward.
      I'm thinking that a drive that uses a "magnetic bottle" to contain fusion plasma in space, could use those same magnets to create a magnetic bottle of ions and statically charged air to contain bulk molecules in an atmosphere.

      Consider the "magnetic nozzle" that extends over 300 meters behind the Epstein drive in space. Reverse-the-polarity and imagine that "magnetic bottle" reaching up over 300 meters into the atmosphere above the vehicle. Quickly shrink that bottle and you have an electrostatic jet engine.

      Other way I tried to think of this, if the ship somehow creates electrical power from plasma flowing FROM behind and venting to the sides, then reversing that process should pull ions from forward of the ship through the nozzles and vent them directly aft - a much larger version of the MIT "Ionic Wind" model plane demonstration of direct electrostatic flight.

    3. "Consider the "magnetic nozzle" that extends over 300 meters behind the Epstein drive in space. Reverse-the-polarity and imagine that "magnetic bottle" reaching up over 300 meters into the atmosphere above the vehicle. Quickly shrink that bottle and you have an electrostatic jet engine.

      Consider the "magnetic nozzle" that extends over 300 meters behind the Epstein drive in space. Reverse-the-polarity and imagine that "magnetic bottle" reaching up over 300 meters into the atmosphere above the vehicle. Quickly shrink that bottle and you have an electrostatic jet engine."

      Could this be a valid alternative to conventional combustion-powered jet engines, or does the required power consumption prohibit this?

      Thank You

    4. Conventional jet engines do not produce an ionized exhaust, so it won't interact with magnetic fields. You are forced to use physical components to direct and expand the exhaust.

      Also, the '300 meters' does not actually describe the size of a magnetic nozzle. The magnet field expands out to infinity from the coils. It gets weaker, very quickly. 300 meters is the distance at which a charged particle from a fusion reaction can meet the field and be deflected 180 degrees without touching the coils... it is like the minimum space needed for a truck to make a U-turn.

      A stronger field is not 'bigger', it just makes the fusion particles turn around in a shorter space.

      The simple coil I am describing is different from the 'bird cage' designs that are typically used for fusion propulsion. The fusion reaction there is enclosed in magnetic fields. In the Epstein drive, you are forced to place the fusion reaction pretty far away so as to not melt everything.

    5. This comment has been removed by the author.

    6. Re-edited

      --Conventional jet engines do not produce an ionized exhaust, so it won't interact with magnetic fields. --

      However, electromagnetism works perfectly well on simple charged molecules, it's not limited to fully ionized plasma. Consider simple charged molecules, like the negatively charged ice particles that power cloud to ground lightning -

      Or, consider how you can easily change the trajectory of bulk water from a faucet with a simple-static-charge-from-a-balloon. That's simply a polar molecule moving through a static electric field (basically similar to a polar molecule experiencing a magnetic field).

      Same thing for a microwave oven - it "grabs" polar molecules using electromagnetism and spins them around, and you don't need a plasma for the microwave to work. (However there ARE tons of videos about trapping plasma in an upside down beaker in a microwave.

    7. You are referring to electrostatic effects. Those don't extend far enough to protect the spaceship from 100TW of fusion output.

      Within an atmosphere, it is even worse, because you are going to reach electrical breakdown limits (sparks spontaneously jumping across) well before you create an electric field large enough to matter. At least magnetic fields mostly ignore air!

      But let's flip this around. What are you trying to do exactly?

    8. --What are you trying to do exactly?--

      Account for the fact that any conducting medium (e.g. plasma) moving in a magnetic field will necessarily generate rings of electrical current, which then generate reinforcing magnetic fields - e.g. a dynamo-

      By analogy, the solar magnetic field is "entrained" into the solar wind, charged particles moving with the magnetic field, which explains why measurements of the interplanetary magnetic field at 1 AU were ~10^-9 Tesla instead of the predicted 10^-11 Tesla.
      Magnetic field strength estimates can be off by 100 fold if you don't account for the charged particles that are caught in the magnetic field.

      Fortunately, this makes the Epstein drive MORE plausible.

      It seems like it also raises a possible Orion-Medusa situation where the motion of charged particles expanding away from a fusion pellet in a magnetic field, would necessarily generate currents which then reinforce the magnetic field- A form of peristaltic drive, where the Epstein drive's magnetic field swells and then sort of "squid-squirts" along...

    9. It would be interesting to see whether we can engineer plasma-magnetospheres that can survive being blasted by fusion explosions, and can then hold on to that energy.

    10. Well, it occurs to me that the pellets will be spin stabilized AND launched by some form of rail gun, so realistically I'd expect a bit of MHD effect from the spinning fusion pellet.

      Next, if you assume some sort of metal sabot to accelerate non-metal pellet, then you might even gain a bit of neutron and x-ray shielding, so perhaps a sabot of boron carbide-cadmium-hafnium.

      That leads to my-idea for a laser fusion target- an aerogel pellet. Aerogel to ensure that laser heating is most effective and heat is not wicked away into the core of a pellet, or if the pellet IS wobbling, that the laser heat a VERY small volume of material, making it easier to reach fusion temperature.

      Other ideas- an aerogel pellet with a spiral internal structure to promote rotation at detonation, and an overall conical shape with a reflective interior. Conical to focus the beam, conical to ensure that detonation starts at the far end so that detonation essentially pushes the pellet towards the ship.

    11. Frozen fuel in a fusion pellet is not conductive enough to create any measurable MHD effect.

      Rotation at detonation is usually avoided because it can cause uneven heating of the fuel.

      The most energy efficient ignition method being devised current is the hotspot ignition method. An extremely powerful laser pulse causes a tiny spot on the surface of the fuel pellet to reach millions of degrees K, with only a few joules. The heated fuel explodes, creating a shockwave. The shockwave is strong enough to create ignition conditions, so fusion starts to occur. The fusion liberates energy and drives the shockwave to be stronger, leading to a 'burn wave' that travels through fuel pellet, both releasing energy and igniting more fuel.

      This process happens so fast that rotation, MHD effects and so on are frozen in time in comparison.

    12. --Frozen fuel in a fusion pellet is not conductive enough to create any measurable MHD effect--

      IIRC, metallic hydrogen is conductive and magnetic?

    13. That is true. It acts as a metal, hence the 'metallic'.
      The problem is that we have no idea whether it is metastable.

  12. Hello,

    Apologies if I am being a killjoy or an arrogant asshole, but I have a problem understanding how this drive you described could possibly be made real.

    The problem is this. You need the fusion far from the rear of your spaceship to minimize the neutron and gamma flux. Sure. Got it. But you also need your magnetic noozle to intercept majority of your protons. I can not see how you could do it both ways.

    If your lasers make thermonuclear detonation 300 meters from the ship- how are you going to make most of the protons travelling toward the rear. Lasers beams travel the opposite direction so they cannot impart necessary momentum .

    The answer from your diagram is : magenetic field. The problem is that it must be very strong. You argue that miliTeslas are enough to deflect high speed protons from the rear. That is probably true. But the goal is not just that. Before you deflect it from your ship's back you need to direct them THERE first. And to do this you need strong magnetic field near the point of pellet fusion. Picture yourself a proton travelling from the ignition point perpendicularly to the axis of firing lasers. If you want have over 50% engine efficiency you need to make a 90 degree turn either towards the ship or away from it, imparting its kinetic energy to the field. Even if you choose the latter scenario (proton imparting energy and drifting farther from the ship), probably easier way you still need probably miliTeslas of field near the Ignition Point, at the very Least , bacause farther from there the field only gets weaker. And if you have miliTeslas 300 meters from the ship, then 3 meters from it you are going to have thousands of Teslas if (100^3=1000000) .If the Rocinante is 30 meters long then tip of the ship will still eperience Teslas of magnetic field. They will be travelling in friggin' flying MRI scanner :D, with their saliva undergoing electrolysis once they move their head. Assuming there is an equipment that can handle this. You could solve this by placing magnets closer to the ignition point, but obviously this will create problem of the excessive amount of neutrons radiating your coil , heating it and causing severe embrittlement. To sum up: I can't see how this could be done. The fusion physics can be harnessed but the engine geometry is an insurmountable obstacle. Sorry if I'm arrogant or something, I have no degree in science. if I'm wrong feel free to pinpoint my errors.

    1. No worries, I enjoy questions and discussion.

      A section before the diagram explains how a directional fusion explosion is made possible:

      "It is based on this refinement to the VISTA fusion propulsion design. Like the VISTA design, a laser is used to ignite a fusion fuel pellet at a certain distance from the ship and a magnetic coil redirects the fusion products into thrust. The rear face of the spaceship takes the full brunt of the unwanted energies and re-emits them as blackbody thermal radiation.

      The refinement consists of a shaped fusion charge that can be ignited by laser slamming a portion of the fusion fuel at high velocity into a collapsing sphere, raising temperatures and pressures up to ignition levels.

      Instead of the fusion products being released in all directions, a jet of plasma is directed straight at the spaceship. This increases thrust efficiency up to 75%, as the paper cites."

      So, there is no need for a magnetic field to get the fusion exhaust to travel in a cone aimed at the spaceship. The shaped charge does this job for us.

      Regarding your field strength question:
      My own calculations show that it takes an average field strength of 26 microtTesla to get 17.5% C protons to turn around in a U-turn with a radius of 300 meters. The initial field strength needed to create an average field strength of 26 uT over 300 meters is just... 6.67 milliTeslas!

  13. Yeah, I admit i missed that shaped-charge part. Still I find it hard to believe that it can be done that simple. The rough analogue of Orion drive nuclear shaped charges requires something like 90% of mass being devoted to shaping the actual nuke which is less than 100 kilograms in mass

    I am not sure I sure I follow your equations carefully but you seem to asume roughly 1:1 fuel propellant (moderator) proportion. But this seems completely unrealistic to me. While the paper you cite is serious it does not seem to give specific mass ratios of moderator and fuel (though the pictures indeed suggest that they are comparable). However there is other problem. Tha paper says that VISTA "actual" (i.e. before applying the shaped charge proposal) efficiency is 60% and they are improving it to 75 % with those shaped charges. Obviously this ratios protons because about 75 % of D-T energy escapes as neutrons. Still it suggests that those shaped charges offer modest improvent of efficiency. Most of that supposed VISTA efficiency is the result of ignition point being CLOSE to the COIL (ca 15 meters). So you would not get the same 75% efficiency with your ignition point being placed 300 meters from ship. You miliTesla coil would intercept and deflect less than a percent of protons probably. Vista high efficiency being caused primarily by proximity of ignition assumes already modest amounts of fusion energy produced and hence modest ISP (155 km per second) and delta v (about the same). This is no Rocinante.

    1. Fusion ignition techniques do not always need a moderator, especially if aneutronic fuels are being used. DHe3 fusion releases up to 80% of its energy as heavy alpha particles.

      I am not sure which type of efficiency you are referring to, but I used the paper as a reference for 75% of the fusion products being shot in one direction being possible. 75% of the 80% of fusion output that becomes thrust means 60% over all propulsive efficiency.

      And, even if we only intercepted 1% of fusion products for some reason, this does not mean that they become *slower*. The exhaust velocity would be the same... but thrust (Newtons of force) would be 100x less than you would otherwise expect.

  14. Ok, Let me clarify. First of all THOSE fusion ignition techniques seem to require moderator. It is required for shaped charges. How do you make shaped charges without some stuff wrapped up over the fuel that undergoes fission or fusion?

    This is one thing. BUt my main objection is this. The Japanese paper you cite, which describes the shaped charges, explicitly states that they are supplementing VISTA design. Not just ANY fusion design but VISTA. And on the very first page they state that the original VISTA design entails 60% efficiency. What kind of efficiency do they have i nmind? I do not know? Nyrath's RHO states 32 %. But the point is that this is irrelevant. The thing is that those Japanese scientists say something like this: "We are building on 60 % efficiency design and improving it to 75 % using shaped charges". So those charges account only for "modest" 15 % increase of the efficiency, regardless how that efficiency is defined. So it is not really those charges that account for this high efficiency. So what does? The answer is simple: it is proximity of the magnetic coil in VISTA design. The ignition point i s placed 10--15 meters from magnetic coil. The coil (according to picture on Nyrath's page) lies within 100 degree angle drawn from ignition point. So if shaped charge is able to put 75% of charged particles within that 100 degree angle, this is enough to put them within strong magnetic field inside the coil. Sure, you do not need to put all of it inside the coil -this is just to illustrate that you have pretty big angle here. Those Japanese charges do not seem to collimate particles in the narrow beam- the do not need it and if the could the guys would probably try to exploit proposing different fusion drive design.

    Now, your Epstein drive has ignition point spaced 300 meters from the coil, which is supposed to have about 12 meters in diameter. So in your case ,your coil is placed within about 2.4 degree angle not 100 degree angle like VISTA. So If VISTA coil intercepts 60-75% of charged products, your coil will intercept just about one thousandth of it or so. Sure your magnetic field works outside the coil but the same is true about VISTA. To make your design work you would need shaped charges with 30-40 times smaller collimation angle that those suggested by Japanese paper. and I seriously doubt those are attainable, at least not without have mass penalty in the form capsule that helps shaping of the fusion explosion.

    Your last remark is true to the extent that the fraction of products retains the same velocity as the rest of them. It is just the thrust that suffers. But obviously the result is similar : ion drives have large isp but their low thrust makes them poor candidates for workhorse of space exploration. Alas, If you drive will be intercepting just one thousandth of fusion energy it will not be much better.

    1. At ignition ALL charged particles are within the magnetic field and will impart thrust, regardless of direction. The question then become how much they impart before their motion carries them outside the field (those that are not flying directly toward the ship).

      Strengthening the magnetic field allows you to capture more momentum over smaller distances.

      Creating magnetic free zones within a magnetic field is trivial, so it doesn't really matter how strong you make the field, you can create a magnetic free zone within the ship.

      So, with pretty much everything unobtainium, it comes down to the engineering; the actual theory seems to be workable.

    2. fgough: You are correct.
      You can cancel out a magnetic field by adding loops around your spaceship with an equal current running in the opposite direction to that of the external electromagnets. It is not exactly trivial from an engineering standpoint, but easy to design.

    3. frgough, matter beam

      If we were to follow your reasoning then we can, in principle ignite fusion a kilometer from ship or a milion kilometers. The magnetic field has no boundaries, it extends to infinity and if we do not assume any realistic constraints then we can imagine everything, even Bussard's scoop with magnetic field extending hundreds, thousands of kilometers strong enough to serve as weapon of mass destruction. There are stars that have weaker magnetic field than this. This is not engineering. Engineering can not be that much divorced from (actual) reality. The Vista design definitely assumed that moist of particles will be placed in the vicinity of magnetic coil (vicinity= within the radius equal about to the diameter of the coil), for drive to be effective. So it seems that further magnetic field is not strong enough to properly deflect particles. Sure, by placing ignition point farther from the ship (say n times farther) you can decrease strength of the field, for nozzle to be effective. But to retain similar efficiency the noozle diameter must be correspondingly increased (also n times). And this requires increasing the field strength by factor of third power of n (n^3) if i am correct. It is unlikely that this is going to be economical and viable. And if not then either we drastically improve the fusion charges directivity (also unlikely without some loads of moderator around them, decreasing actual ISP OR thrust) or we are left with inefficient drive intercepting one thousandth of energy. And this is the only thing we can possibly count on.

      As for applying magnets to cancel each other -I also doubt it. First of all it also involves mass penalties and the cancel is probably partial. At one point the cancellation is perfect, in the other no so much. Also all of this is happening inside spaceship's interior full of dedicated avionics prone to any disturbances, even more so to Tesla scale magnetic fields. To say nothing about delicate fusion lasers capable of fusing stuff half a click away. And final problems concern energy and thermodynamics. All of you assume that magnetic field is going to be free produced with high temperature superconductors, without heating the coil. Truth is the main coil and cancelling coils will require ginormous energy and also cooling and will fill crampy ship's interior with magnetic fields which will not ba capable of fully cancel each other. And all of this in ship no bigger than boing 747.....All of this is a fairy tale not hard sf.

    4. This comment has been removed by the author.

    5. "So, with pretty much everything unobtainium, it comes down to the engineering; the actual theory seems to be workable."

      Obviously this may be....correct. If you assume at least one unrealistic stuff like shaped charges or superconductors working in high temperatures, then you are ok. But this is trivial for me. Fusion drive is theoretically possible, it is those "specific" that make it unworkable.. So if theory does not solve these obstacles it does not tell me anything new and does not make the drive itself any more likely.

    6. trident:
      If you place your ignition point too far away, then the cone of plasma would expand to the point where charged particles pass through a magnetic field that is too weak to deflect them very much. Their kinetic energy is lost. Therefore, if you want to place the ignition point further away, you need to *increase* the magnetic field strength to increase your 'capture area'.

      Creating a field-free zone inside a spaceship that is protected from galactic cosmic rays by a magnetic field:

    7. Matter Beam

      I know. The point is fgough seemed to downplay this suggesting that: "ALL charged particles are within the magnetic field and will impart thrust, regardless of direction". I agree that they will do but since the thrust imparted will be small it does not really matter. That was my point. The fact that it all happens inside the magnetic field does not matterr per se. Techically we are probably. all inside magnetic fields of distant objets like Jupiter.

      I seriously doubt you can do magnetic field strong enough to intercept most of electric particles. Assuming that 12 m diameter coil enables you to intecept everything within the radius of 12 meters with 6 militeslas, this gives you capture efficiency of about 0,0004 if i coalculate correctly. Now If you increase fild strength 1000 fold you can increase the radius 10fold and area 100fold, That way with 6 Tesla field you attain 0,04 efficiency. Poor reasult with magnetic field twice that of MRIs.

      As for your source: I am a little familar with proposition of shielding astronauts against cosmic rays. I cannot proerly review a source, yet what I understand of this, prompts my scepticism. First of all the are talking oabout relatively weal field 1 tesla-range, you need few Teslas and it is still not strong enough. Also while there is remark on page 18 that "cancelling field is easy" no details are present to back this claim. Others are more sceptical:

      Also others working in the topic are cautious :
      "Much detail has yet to be determined. An active shield system may not be practical without on-board power systems comparable to those envisioned in science fiction, but the concept should not be dismissed on the basis of an incorrect analysis.

      An active deflector shield system could never replace passive shielding or biological advances, but it can offer options, particularly for EVAs, extending the longevity of hardware and preventing secondary activation of the ship׳s hull and systems. It seems the only credible theory for deflection of GeV particles."

      I interpret this that they are sceptical about utility of strong magnetic fields both because of power consumptions and technical diifficulties. Prof. Bamford for example tries to minimize the required strength using plasma, Prof. Parker seems to be sceptical even of this.

      You also must realize two things:

      1.Cancelling magnetic field probably will never be ideal: You cannot erase magnetic field uniformly for several meters without building compensating coil every meter. And if compensating coil is too strong it will create problem of its own. If you believe you do try simply to draw a schematics of this.

      2. All of these magnetic fields will be working inside the spaceship especially inside the rear filled with fusion igniting laser and electronic controlling it. Unless you are able to build laser without electric cables or to cancel tesla strong field on the length of few meters without creating another powerful field, I can't see how you can manage the feat. You want your ship to run powerful laser from its back, having, at the same time a powerful magnet installed there, intefering with laser power supply, and all of this with being cooled enough to enable room temperature 10 meters further....

      And if we were to return original shape-charge idea, how are you going to direct protons toward the rear but no neutrons?

    8. We are designing plausible science fiction, not presenting something for NASA to give a grant on. So, yes, we make some assumptions. Nothing in the assumptions is contraindicated by physics, and is not even particularly implausible. We already have liquid nitrogen temperature superconductors and are seeing steady advancements in that area. Laser efficiency is steadily increasing.

      Again, this is plausible science fiction.

      If you are dumping on the ideas here, you are basically relegating yourself to solar powered NEXT ion thrusters and multi-stage LOX rockets for surface to orbit. Because launch loops, beanstalks, closed gas core nuclear light bulbs, etc. all have the same "insurmountables" you are complaining against here.

      Matterbeam did a very good job of designing a plausible system that allows for a very easy "suspension of disbelief."

    9. I admit I may be overly critical. Apologies,I will try less so. Still I do not get this "hard-sf" standards according to which you can not invent new physics or introduce technobable but you can propose fancy materials with unrealistic properties. Properties of matter are physics too, AFAIK they can be derived from physical constants and laws. I can't see how magnetic field can not interact with laser if they both excite atoms and rely on electricity. Sems unworkable in principle, no matter how powerful laser and magnet you get, as long as they are close to each other.

      Indeed I do not like those other fancy stuff you mentioned. I believe that if we are going to colonize planets we will do it as "God, Zubrin, and Musk intended", that is by using chemical and solid -nuclear rockets. Or we will build solar satellites and start beaming microwaves, first to Earth for electricity, and then to drive ships using solar sails. This stuff I can (possibly) believe in.
      Alright thank you for talk and apologies for playing spoiler. I will now go to to torment guys theere with my questions and doubts ;).

  15. Hello Matter Beam:
    I'm sorry but from the above I didn't get whether or not a scaled-down version of this would be a viable alternative to a conventional jet engine or if it would be too power-consumptive to be economical.

    Also, OT: Our friend Robert Zubrin re-examined ( the feasibility of artificial black hole propulsion (and some other related uses) as originally discussed by Louis Crane and Shawn Westmoreland in 2009, and I was curious if his engineering analysis were sound.

    Thank You,
    Keith H

    1. --I didn't get whether or not a scaled-down version of this would be a viable alternative to a conventional jet engine--

      I HAVE thought about this a bit, but more in terms of trying to address the problems of the Bussard ram jet - that your drag force from COLLECTING interstellar protons (H+) is actually LOWER than the thrust you obtain from BURNING that interstellar hydrogen.

      Could there be a method to take the Zubrin "dipole drive" and resurrect the old Bussard ramjet concept?

      One thought, THE RIGHT HAND RULE. If you can project a conical magnetic field, you should get roughly 4 cones of ions. The inner cone will consists of Beta particles/ electrons moving in a tight clockwise spiral path determined by -1 charge /mass. The outer cone will be Protons moving in a wider counterclockwise spiral path determined by +1 charge/mass. The third cone will have a mix of deuterium, tritium, Helium 3. The fourth cone will be Alpha particles/helium nuclei, and a smattering of other charged particles.

      Focusing on the 1st and 2nd cones, it seems, well, interesting, to consider a magnetic field "sorting" protons from electrons by using a magnetic field to create "Van Allen Belts" where protons are in a tight orbit, while electrons are in a wider orbit.

      Assume an actual metal "scoop" which is significantly wider than the proton gyration radius, but still significantly narrower than the electron gyration radius.

      You've now created a cloud of protons directly ahead of the vessel (which can be accelerated by a negative charge) and a cloud of electrons in a ring outside the ship (which can be accelerated by a negative charge). You accelerate the protons into the fuel scoop, and then accelerate the electrons with a charge far behind the ship.

    2. Hmm, edit isn't working
      - actual metal "scoop"-
      That should have been "scoops" the smaller for electrons with a tight gyration radius; and a larger scoop for heavier protons with a larger gyration radius.

    3. Keith:
      You could do a pulsed external fusion jet engine, but it is a rather wasteful use of the fusion fuel and you lose a lot of the Isp advantage that makes fusion power great.

      I have read Zubrin's latest paper, and the maths does work out. However, Hawking radiation is very hard to use because it comes out as gamma rays, and the Thrust to Weight will always be very poor. There are other ways of using black holes that are more convenient.

      The Zubrin dipole drive would work. However, it only works because it sidesteps one of the problems the Bussard ramjet had: trying to use the hydrogen it collected as fuel. A dipole drive uses an internal power source, the Bussard ramjet tries to use an external one.

      Also, your concept of a magnetic scoop is fine. Just remember that you receive drag from any particle that interacts with your magnetic field, whether you scoop it up or not. So, the particles you let you add drag but you cannot then use them as propellant, so that's a worse outcome.

    4. Thanks again, MB. Tell me more about how BHs could be more conveniently used...



    5. You exploit their orbital velocity to ignite fusion.
      Insert tiny masses of deuterium+helium3 into a low orbit around a black hole, you will find that it will be travelling at several thousand km/s. Insert another bunch of masses into a retrograde orbit.

      When those masses meet, the energy released by the impact is enough to ignite fusion. Deuterium-Helium3 fusion releases over 300TJ/kg, so you can get really good energy multiplication.

      To capture the energy being released (mostly as X-rays), you surround the black hole with a sphere of something relatively dense. You will catch the majority of the X-rays and absorb them as heat. Turn that heat into electricity!

  16. --Also, your concept of a magnetic scoop is fine. Just remember that you receive drag from any particle that interacts with your magnetic field, whether you scoop it up or not.--

    I found the gyration radius interesting as a mechanism for sorting.

    In one of Zubrin's dipole-drive talks, he mentioned that particles at any significant distance from the dipole drive would effectively see zero voltage up until the particles crossed over into region of the dipole electric field.

    Well, a weak magnetic field should sort the protons towards the center, with electrons towards the periphery.

    That raises the idea of a "bulls eye dipole drive?"
    An inner circle of the "bulls eye" is charged to accelerate protons, the outer ring has the charges reversed to acellerate electrons.

  17. Thanks again.
    What mass BH are you discussing here?
    Also, (theoretically) aren't there more efficient way to generate energy from a BH than nuclear fusion (

    Cheers, Keith

    1. The key requirement they mention is the need for a rotating black hole. Without one, you are stuck relying on other means of producing energy (6% mass-energy conversion isn't bad though, that's 16x better than fusion).

  18. Much obliged. For energy capture (from neutral emission) is the efficiency proportional to the density of the material, its thickness, etc.?

    1. It is exponential. You capture a lot more neutrons in the first few centimetres than in the last meter. Look at the shadow shields on atomic rockets for examples of how thick they need to be.

  19. Again, muchas gracias. Are moderated fast neutrons ever used to generate energy directly (through heat(as your description of x-rays absorbed by dense material) as opposed to becoming thermal neutrons for fissioning actinide fuel? (I'm not able to find this out so far in my research.)


    1. I don't think so. After all, neutrons are just 5% of the output of a fission reaction.

  20. Good to know. What about neutronic (as opposed to aneutronic) fusion reactions like D + D or D + T?


    1. They are still pretty bad in terms of neutron output. Look at the chart on Atomic Rockets here:

    2. Much obliged. So, neutronic reactions produce enough to create problem (requiring shielding) but not enough to realisaically use as an energy source, correct?


  21. Hello, i really love your article,just some question (forgive me if I say some idiopsy, i'm not a phisicist plus I'm not a good English speaker): if we had an heat-shield made in some ultra-futurist league with a sort of thermo-ionic or Seebeck effect on a decent scale, turning a significant fraction of heat waste , it would change something in the general picture?

    1. Not much will change.
      We can extract a lot more power from the magnetohydrodyamic effect between the fusion plasma and the magnetic field of the nozzle, than from the heat in the heatshield.

    2. But we still need big radiator's plates or we can have little ones that can be hide and not immediately noted like we see in the series?

    3. The series shows the spacecraft with zero radiators. They're not hidden, they're just not there!

      The only way to get smaller radiators is to increase their temperature, but that also makes them shine brightly, like hot lightbulbs.

  22. Fascinating, well written article. I wonder how possible this is with current day technology? It looks like the reaction doesn't need to become self-sustaining - you just fire the pellet, blast it, and repeat - and the laser/fuel railgun could conceivably be powered by a fission reactor, forgoing the need to develop a fusion reactor for power.

    1. Thanks James.
      It is not possible with current day technology, because we do not have an ignition system that produces more fusion power out of a reaction than it takes to ignite it yet.

  23. Hello, just struggling to follow where the 2.2 kg/s mass flow came from after you calculated the drive output of 96.8 TJ?

    1. It is the result of using this equation:

      Engine power = 0.5 * Mass Flow * Exhaust Velocity ^2

  24. As long as we're talking about black holes, how about temporary ones in an Orion type pulsed drive (or generator)? Apply sufficient compression (hey, easy, any Kardashev II civilization should be able to - grin!)to collapse a suitable body of matter, just anything you've got lying around, interplanetary dust or dirty socks or whatever, into a tiny black hole...which will then evaporate through Hawking radiation. Tuning the hole size and mass, you can get any desired evaporation rate from nanoseconds up. Then do it over, and over, and over... ALL the energy content of the matter should thus come out as energy: 100% conversion, less of course whatever energy you had to put in to collapse the stuff in the first place. And of course heat losses. Always, always, entropy takes its due!

    1. The issue is that compressing matter into a black hole consumes energy, and even if we perfectly extract the 353 TJ/kg potential of Deuterium/Helium3 fuel... we would need to consume about 7.65 million tons of fusion fuel to compress 1 gram of matter into a black hole.

      The Hawking Radiation from a black hole is released in all directions, so you'd lose at least half of it in an open propulsion system, and it is incredibly penetrating, so you'd need heavy shielding to just turn it into heat.

      None of this sounds practical!

  25. I often see a Deuterium + Helium-3 mix as the go-to fusion fuel in various sci-fi IPs, I assume due to the high energy gain per Kg. However, given that deuterium fuses with itself even in this mix albeit in small percentages, its not truly aneutronic, thus still requires heavy shielding around the reactor to prevent dangerous radiation expulsion and that shielding would eventually need to be replaced due to neutron activation, creating additional upkeep costs.
    I'm currently in the process of developing a sci-fi universe and I wanted the primary fusion approach to instead use pure Helium-3 + Helium-3 reactions. In my research I found that it does require higher temperatures to achieve, thus more power input, but in my mind the trade offs may be worth it since A) unlike the D+He3 reactions He3+He3 is truly aneutronic, creating only a Helium-4 atom and two protons which can be electromagnetically controlled, requiring virtually no shielding making it not only far safer, but also able to be scaled down significantly to smaller designs (Looks hopefully at micro fusion reactors, lol). And B) its generally more efficient given that 20% of energy from the reaction isn't be wasted on neutrons. I suppose I'm looking at it more from a power generation purpose than Propulsion, since with He3+He3, you can rely solely on direct energy conversion systems, but honestly I'm a little out of my depth dabbling in nuclear physics and finding detailed information on this stuff that I can understand has been a trying process. Just wanted to get your thoughts on this fusion approach to see if it will be legitimate for my story or is D+He3 fusion is just the better route to go

    Also, out of curiosity, the He3+He3 creates the two protons which are the important part for direct energy conversion, but it also creates that regular old helium-4 atom. Is there anything useful that can be done with that helium once its created, i.e. vented fusion exhaust for propulsion?

  26. Sounds like similar concept would work for regular fission pellets, right?
    How design would change if instead of D+He3 fuel pellets were made of e.g. plutonium? (other than that jets of neutrons would be needed to ignite the pellet instead of lazers).
    In principle it should be easier to make such plutonium rocket, right?

    1. You would use the same lasers to compress the plutonium until it reached a critical mass and exploded. Efficient use of the nuclear material would require surrounding the fuel with something like beryllium.

      You would also need to replace the magnetic nozzle with a physical nozzle because igniting the nuclear pulses from far away would give the fissile plasma enough time to cool down and become neutral.

      There would also be the problem of the increased neutron and gamma ray radiation.

      But aside from all that, it can be done!

  27. Dealing with the heat issue, is there a way to absorb the xray and/or neutron flux with a material which can be ejected out the nozzle? Perhaps even adding thrust? Granted it would require carrying extra mass for such "fuel" but it might be worth it if it mitigates the heat problem.

    1. Yes! This is open cycle cooling.
      The problem with this solution is that your engine performance has to account for all the resources you expend to run it. So if you shoot 1 kg per second at 10,000 km/s out of the nozzle, but need 10 kg per second of coolant as well, then your effective exhaust velocity is 10,000/(1+10) = 909 km/s.

      This would greatly reduce the maximum speeds that the Epstein drive could reach.

    2. Thank you for your answer! I was calling it a kind of "regenerative ablative cooling" as I didn't realize there was already a (better, proper) term for it.

      I'm happy to say I learned something new from your Epstein article: heretofore, I didn't realize there is no known material that efficiently reflects X-rays. Gold and iridium can do it but only at extremely narrow angles of incidence, making them mostly useless for things like lining fusion reaction chambers. Absorbing is the best we can do but, as you pointed out, not without some downsides.

      Perhaps Epstein's greatest discovery was some method of lowering the "coolant" requirement to the point where the amount of material needed made it feasible, that being the "efficiency" they speak of? Who knows what kind of improvements in materials science and electromagnetics might come in the next century or two? It would be an interesting thought experiment to see how much thrust could be obtained if the X-rays *in a fusion reaction chamber* could be reflected into useful thrust instead of waste heat. Sort of a "what if" take on your article to see if it makes Epstein's drive a workable thing?

      Your articles are very well done and very thought provoking! I look forward to seeing many more of them!

    3. This comment has been removed by the author.

    4. Removed prior comment due to math error. Here's the corrected one:

      Also, you mentioned 10kg of coolant per 1kg of "propellant"...did you get that 10kg figure from something specific or was it just a guess? I'm not a materials or electromagnetics wizard so I don't know what kind of materials would be best for such "coolant". However, if that 10kg of coolant was a much lower figure -- say 2kg -- then the math becomes 10,000/(1+2)=3,333 km/s. That's not 5% light speed but it's still pretty damned fast.

    5. Hi again, Prisoner881 Sorry for the late reply.

      Epstein cannot change the physics involved in fusion. There will always be a portion of the fusion energy that is emitted in the form of X-rays and neutrons... if we used a much more speculative technology, then an X-ray mirror would be an ideal solution. It would mean that the walls of a fusion reactor would not absorb any heat!

      The 10kg was just an example, to illustrate how the maths works out.

  28. I can't imagine how can I install MHD generator for this type of engines...

  29. "Other ‘cleaner’ source of fusion energy exists, using fuels such as Boron, but they cannot be ignited using a laser."

    What about the idea of using a laser to make the boron into plasma, and then another to do the stream of protons? I know this needs insanely precise timing, but...? I know it's also controversial whether it'd work. Your thoughts?

    1. We have the technology to create a stream of protons energetic enough to initiate proton-Boron fusion. It is called Laser-Plasma Wakefield Acceleration. However, we are unable to make the process efficient enough, or the fusion reactions numerous enough, to produce more energy than we put in for ignition.

      The ratio between input and output here is over a hundred times worse than with other fusion fuels.

      One major factor is that the ignition temperature is 10x higher. Because of the Stefan Boltzmann law, we can already tell that heat losses due to radiation are 10^4 higher... a big loss!

  30. Hi! Partway through the article but I just wanted to let you know that x-ray mirrors can be made with silicon and a really, really tiny cutting tool. (In this case a focused ion beam)

    Loving the article though!

    1. Indeed, grazing incidence mirrors do exist. However, they would not work to deflect harmful radiation from the engine, as they only change the angle of the X-rays by a tiny 1-3 degrees instead of the required 180 degree reflection we would need.

  31. I understood probably 4% of this article, but I love it and want more. I've never been so captivated by a single show for as long as I can remember, and this article touches on one of the two reasons I am.

    The first reason, not related to these physics, fall under the sociology discipline. Most futuristic sci-fi stories paint a picture of the universe's society as falling into one of two extremes. Either a distopian existence with a well defined group of heros and villains, or the polar opposite utopian society where humans have emotionally evolved into a species of peaceful knowledge seekers. There are a few exceptions, such as the movie Interstellar, but the larger society in that film was left too vague to say. I'm my opinion, the Expanse was the first Sci-fi show or film which hit the nail on the head.

    Humans, as a species, are a LONG way off from any sort of higher state of enlightenment where, as in Star Trek, the vast majority of people value knowledge over wealth, thus greed has been eradicated. Sorry Gene, it's a nice thought, but that type of optimism it's what puts the 'fiction' into science fiction for Star Trek. We're a tremendously flawed species in many ways, but for this argument, it's the lack of true compassion when faced with the need for more resources, regardless of scarcity. Most simply refer to it as 'greed', which is more precise enough to really capture the entirety of the characteristic, but will do for now.

    The Expanse is probably the most accurate portrayal of what our species will look and behave like, if we survive long enough to have colonized beyond Earth. The corruption, lack of empathy and compassion, focus on hording resources without sharing, and the ever present willingness and ability to cause pain, suffering, and death to our fellow humans is captured by the writers in every detail.

    The second reason, more germain to this article, is the writer's meticulous inclusion of real world physics as a major theme of the story is a breath of fresh air for this genre. Where most sci-fi stories ignore these limitations, which is nothing more than laziness in story telling, or create implausible and unrealistic technological capabilities in order to avoid having to address these limitations, The Expanse embraces these realities, and showcases them as major parts of the story telling. 'Inertia Dampeners', 'Subspace Communications', and 'Transporter Beams' sure would be handy for the crew of the Rosinante, but they are all based on fictional nonsense.

    Whenever discussing this unique characteristic of The Expanse with friends or online, I've always caveated that, yes, they did invent a propulsion technology which was needed in order for the narratives to actually work. I would explain that I felt that the rest of the true-to-science story elements more than made up for it. But after reading this peice, despite not understanding the granular details of how it would/could work, I'm thrilled to be able to eliminate that caveat for good. I get it, there is a big part of this explanation which is still steeped in theoretical nuclear and material science. However, I feel that this discussion allows the prospect of an Epstein Drive-like propulsion system actually being developed and widely used to catapult from total fiction up to bring actually plausable.

    So thanks for the extensive article, I'm a happier camper for reading it!!!

    1. I'm very glad to hear that! The Expanse built a realistic setting and then asked itself what would happen, instead of most scifi that write a story and then twist physics or invent fantastical technologies to make that story possible.

  32. Hi,
    Great article.
    I went ahead and figured out your calculations on an Excel sheet...because I currently have time!

    Anyway, I've hit a snag at calculating the mass flow of fuel at 96,8TW. You say that it consumes about 2,2kg/s of fuel. However, using the "Fusion Reactions" table, 1000MW burns 0,002831g/s...
    I can get 2,2kg/s using either 1000MW as 1e8W (which I doubt is where the mistake comes from) or by having 1000MW burns 0,02831g/s (10x more than what the table says...) ...Is there a mistake on the table? They have the same exact table at ProjectRho...Did you recalculate the burn value? Is it me that's making the mistake??? (Could happen!)

    Aside from that, I get values extremely close to yours. I'm blaming the difference on approximation of pi. I use the pure pi that Excel gives.


  33. Hello. Interesting.

    Have you heard about the concept of Shear Flow Stabilized Z Pinch Fusion Propulsion?,fusion%20concept%20with%20Q%20%3E1.

    "Building on the ZaP, ZaP-HD, and FuZE projects, scaling studies will be presented of an SFS Z-pinch as a fusion space thruster, which generates high exhaust velocities ( 10^7 m/s) and high thrust ( 10^6 N) with low system mass"

    10.000.000 (10 million) meters per second exhaust (that's quite a lot of ISP) and 1 million newtons of Thrust...

    Not an Epstein drive... but almost.

    1. Yes! I do know about the Z-pinch drive.
      I don't think it comes close to an Epstein drive's performance though... it's exhaust velocity is too low (10 million m/s is 3.3% of the speed of light, we've discussed the maximum 8.9% of the speed of light) and more importantly, its power density is too low.

      You can have all the exhaust velocity you want, but if its lacking thrust, it won't give us amazing performance!

      Thrust = Drive Power * 2 / Exhaust Velocity

      Maximum Acceleration = Power Density * 2 / Exhaust Velocity

    2. Isn't it Thrust = Mass flow rate * exhaust velocity? That would generate 41.5 MN, not 6.7 MN...unless I'm missing a step somewhere

  34. A thought: when decelerating, would they not be blind in the direction of travel? What if any sensors could see though their exhaust?

    1. That is correct. Sensors would have a hard time looking through the blazing exhaust plume. Canonically, these exhaust plumes are very long and wide, so trying to put sensors on a sort of telescoping periscope won't be practical either.

      The solution is to have a friend look down and sideways at your target, or to adopt a serpentine trajectory that gives you regular glances behind you.

    2. Or perhaps the Crazy Ivan.

      The Soviet submarine - er, the spaceship powered by the Epstein Drive - occasionally shuts down and turns around to have a look. All going well, they turn back and fire it up again.

    3. You're going to have to hope that the engines can be switched on and off again very quickly!

    4. The switching off, presumably, is quick - just turn the lasers off. You might waste some fusion pellets, but... Now, turning off is another matter :)

      What do you do for takeoff from a planet? The full 98TW of power is equivalent to a 24kt nuclear bomb every second, which even if your ship can survive, presumably the locals will be unhappy.

      Is that where you use the afterburner and put lots of water in?

    5. Regarding the switching on/off problem: you need to store the electrical charge needed to power the lasers and ignite fusion. Multiple re-ignitions might mean that a lot of electrical charge needs to stored if your recharging systems cannot keep up.

      Takeoff from a planet is very simple. Your Isp requirements are quite low and the atmosphere acts as an excellent radiation absorber and exhaust mass multiplier.

      For example, imagine the Rocinante only wants to dedicate half of its 57 ton water reserves for a planetary landing. That's about 28.5 tons of propellant against an initial mass of 355 tons. Mass ratio is 1.0757.

      The Rocinante does not look like it has large heatshields, airbrakes or even grid fins. It seems like it cancels out orbital velocity under propulsive power and hovers all the way down. If the deltaV for a landing like this is about 10 km/s, then its required exhaust velocity is 137 km/s. That's an Isp of 13,969s.

      Acceleration would probably top out at 2g. That would need 6.72 MegaNewtons of thrust.

      Thrust power is exhaust velocity times thrust divided by 2. In this case it is 137,000 x 6,720,000/2 = 460.32 GW.

      This is only a tiny fraction of its maximum output!

  35. This, both the article and comment thread, was awesome and amazing to read for three reasons:

    1) I love The Expanse and seeing their tech conceptualized in even at-a-bit-of-material-science stretch is brilliant!

    2) I'm futurist and space nerd and I love reading about this stuff... I get a lot of the concepts well enough to follow this... okayly, though I'm nowhere near the math or actual details of the physics.

    3) I'm working on my own hard SF space RPG system, and finding some parameters to make fusion torches work with minimal Space Magic is a godsend. I hope you meant by what you said about using it if we needed (with credit to you!), because I plan to make extensive use!

    One thing I haven't been able to figure out for myself, from this, and maybe one of you really well educated folks can help; at what point / distance / "saturation" of local operation does the x-ray waste become problematic for nearby structures? Obviously, the version of the Roci in this article couldn't fire up her drive right next to Tycho Station (I mean, Amos might, but...).

    But, how close could they be, before the x-ray output becomes more intense than the background radiation the station is presumably already shielded against? And, how might that range change if you've got dozens, or hundreds, of intense x-ray sources accelerating away from and braking toward the structure?

  36. I assume there is no way to use cascade vanes or this
    and create reverse thrust right?

    1. You could use another magnetic loop to 'reflect' charged particles backwards and get some reverse thrust.

      Getting the loop and its mounting to survive the fusion blasts would be problematic however.

  37. Hello, I'm trying to design a similar drive for my own Sci-Fi setting but I'm having problems recalculating these values (mDot, F, Ve,...) using the formulas on Atomic Rockets. It seems I'm missing something. Do you have more detailed calculations I can take a look at?

    1. Hi!

      I can help if you provide some details or numbers you already have.

    2. This comment has been removed by the author.


    3. 'A heatshield absorbing 2.09 GW of heat means that its Epstein drive can have an output of 96.8 TW. About 2.2kg of fuel is consumed per second.'

      I'm assuming the mass flow is calculated by:
      mDot = F / Ve = 6.37 MegaNewtons / 6.3% C = 6.37E6 N / 18886925 m/s = 0.34 kg/s? How do you arrive at 2.2 kg/s?

      I'm assuming I'm making an error here, because with the given F and Ve I get about the same Thrust power as in the article.

      Im also not sure how you calculate the afterburner (H2O) part.

  38. Daft question I know but if you were to ignite the fusion reaction 300m away from the rear of a ship, how would you keep it 300m away as the ship is propelled forwards? Does the magnetic field somehow 'tow' the small sun you just generated? Or do you need to use lots of smaller reactions to 'pulse' the ship along in a more efficient version of the Orion Project idea?

    1. The wave of plasma that the fusion reaction throws out is travelling at several thousand kilometers per second. It crosses that 300m gap in a few tens of microseconds. The spaceship doesn't move much during this time.

  39. At 2.2 kg/s fuel consumption the 30,750 kg of fuel are used up after only 3.88 hours (30,750 / 2.2 ~ 11,3977. 11,3977 / 3,600 ~ 3.88). At 2.6 g this results in only 363.4 km/s, not 1800 km/s or even 4000 km/s. I don't understand how these numbers were arrived at.

    And do I understand it correctly that the idea is to redirect all or most ions resulting from a fusion reaction, occurring 300 meters away, with a magnetic field at the rear of the ship? If so, I guarantee that this does not work and neither is it the design in the article you cite and show a diagram of. What they use is a funnel (with coils producing a magnetic field) directly at the reaction site, not hundreds of meters away.
    And even if such a humongous, completely otherworldy, magnetic field could be generated that a large fraction of the ions, starting out 300 m away and flying away isotropically at thousands of km/s could be redirected towards the ship within microseconds (see below) and get reflected to produce thrust, this does not work in principle for the largest portion of the generated fusion energy because of the conservation of momentum:

    When this field pulls on ions and changes their velocity and thus their momentum, an opposite change in momentum is transferred to the ship, so it will get DEcellerated during that process. Afterwards, during reflection this will be reversed but only partially. So even theoretically, only the velocity component of the initial (!) ion velocity in the direction of the flight vector could be used, i.e. the cosine of the angle between them. So let's say the goal is to collect all ions up to an angle of 60° (at which the "usable" velocity-component is already down to 50%) - this reduces the number of ions by 75%, so only 1/4th of the ions are available and only the cosine of the respective angle, as a fraction of their kinetic energy is usable. I tried for a minute but then gave up with my attempt to set up the integral for this case but the result will obviously be somewhere between 50 and 75%, so in total ~13-19% of the kinetic energy of the ions could be used at most.
    And just to give a perspective on the scale of the required magnetic field: the average velocity of a tritium ion at 150 million K, ~ the temperature required for T-D fusion, is very roughly 1,000 km/s, a lot less than your quoted 8,9% c (~27,000 km/s) for the alpha particles produced during He3-D-fusion. Even for these much lower velocities they need the enormous magnetic fields applied in fusion reactor designs like ITER. And they need that locally, not at a distance of 300 m. And note that the redirection of the ions needs to happen rightaway, within microseconds (after 1 millisecond, an ion traveling at 27,000 km/s is already 27 km away and the magnetic field there is practically zero (~10,000th of the strength at 300 m anyways)) and I'm pretty sure at ITER they have much more time and hence, the field can be much weaker.
    Another issue is how this field, even if it were feasible, would funnel in ions from far away but reflect the ones that are very close (?).
    Sorry to be so negative but I think these points needed to be made. Also, maybe I'm wrong about them, or some of them, in which case I'd be happy to learn something.

  40. Nice post thank you Trevor

  41. How would the performance change if the D-He3 mixture ratio was optomised to get the full 0.089c of exhaust velocity? Specifically, how would this change the amount of thrust the engine can produce (assuming the 300 m ignition distance remains unchanged)?

    1. To get maximum exhaust velocity, you use the perfect 1:1 ratio of fusion fuels and aim for 100% burnup.
      You would then get 30% less thrust than the example I calculated. On the other hand, your mass ratio to get 2200 km/s deltaV in cruise mode decreases from 1.123 to 1.085... which I do not think it a good tradeoff!

    2. Thanks for the quick reply! I assume the 30% decrease / 70% multiplier just comes from dividing the example above's exhaust velocity by the optomised mixture's? Also, if possible, I'd enjoy a post like this that covers the ISV Venture Star's antimatter drives, since there's enough canon information about them to "fill in the blanks" in a very similar manner.

    3. That's right, for the same power output the thrust must decrease if you raise the exhaust velocity.
      I do plan to write an antimatter propulsion post eventually!