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?

Distance.

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.

83% of that fusion power is in the form of useful charged particles, and the magnetic field turns 75% of those into thrust. So, 41.5% of the fusion power becomes thrust power; which is 60.25 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.

Scaling

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. 

Consequences

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!

23 comments:

  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.

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    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.

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  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 term...how "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.

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    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: http://www.projectrho.com/public_html/rocket/realdesignsfusion.php#id--MICF_Fusion_Spacecraft

      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.

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    2. Actually, the similar Gradient Field Imploding Liner approach seems to be a better match:
      http://www.projectrho.com/public_html/rocket/realdesignsfusion.php#id--Gradient_Field_Imploding_Liner
      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:
      https://www.centauri-dreams.org/2017/12/29/the-plasma-magnet-drive-a-simple-cheap-drive-for-the-solar-system-and-beyond/
      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?

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

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    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.

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  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?

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    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!

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    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?

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    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.

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  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.

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    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.

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  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.

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    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...

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    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.

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    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).

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  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
    necessary
    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.

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    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

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    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: https://www.academia.edu/11448147/SHEDs_Funding_Enables_Power_Conversion_Efficiency_up_to_85_at_High_Powers_from_975-nm_Broad_Area_Diode_Lasers
      -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.

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

    Thank You,

    Keith

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    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.

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