iontom

Antimatter Economics for Interstellar Extended Mod

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Hello! I'm working with @FreeThinker of the Interstellar Extended mod to try and get his antimatter engine spacecrafts to be more accurate. Primarily, we want to make sure we have the correct exhaust ISP and reactor output for an antimatter reactor. We're looking at beam-core specifically, but while we are at it, looking ant anti-matter catalyzed fusion or being open to  even more efficient alternatives would be great. 

Here is the mod forum link (you can find the mod itself on CKAN)

Now, there are a few designs out there in existence which we can reference as-is. However, many of these have specific mission parameters in place at the get go. They also include a surplus of mass for use as shielding against gamma rays generated from the use of the antimatter. That goes way beyond what is necessary in Kerbal, modelling shielding from gamma rays would be a a lot of work. Also, depending on the configuration of the reactor, that shielding might already be in place.

Different Physics than Tsiolkovsky

The first and most important thing to realize is that the traditional rocket equation no longer holds. Some of your mass wet mass is literally annihilated and converted into energy. This means that you can reach substantially higher delta-V than simply calculated from your Isp.

You can read more detail from this source, but here are the basic eqs.

{\frac {M_{0)){M_{1))}=\left({\frac {1+{\frac {\Delta v}{c))}{1-{\frac {\Delta v}{c))))\right)^{\frac {c}{2I_{\text{sp))))

The problem for KSP is that once you take the derivative of this to model the fuel loss, you can't solve it symbolically for the total Isp. 

Ship Designs

There are a few different designs out there, some in the VERY early stages of NASA Tech Readiness Level, others are far ahead in fiction alone. Here's a list from Orion's Arm which I summarize below as well, and add ACF.

  • Antimatter Catalyzed Fusion
  • Pulsed Explosions
    • AIMStar
  • Solid Core - (ISP = 1000 s) high energy conversion efficiency, but very high thrust and low ISP - little thermal decay
  • Gas Core (ISP = 2000 s)
  • Plasma Core (ISP = 10^5 s)
  • Beam Core (ISP = 10^7 s)
    • Project Valkerie
    • Project Frisbee
  • Gamma Ray Photon Rocket

Right now the mod is focused on Beam Core, Gamma Ray photon rockets are well beyond the scope of any serious study right now.

Here's two charts which show the propellent/dry mass and antimatter/dry mass ratios. Beam Core is the best, hands down. For every 1 mT of dry mass, to reach 33% light-speed, you'd only need roughly 2 mT of fuel, or 4 mT for acceleration and decelleration.

antimatterGraph2TB.jpg

 

For Anti-Matter, for 1000 kg dry mass reaching 33%, you'd roughly hit parity. You'd want an amount of antimatter nearly equal to your dry mass. Or twice that if you need to decelerate too.

antimatterGraph3.jpg

Or seen this way at just direct mass 10^6 g is 1 mT

antimatterusage-1.png

Antimatter Storage Density and Energy Requirements

So first, we should look at mechanisms for storing antimatter - it needs to be tight. Generating antimatter is important as well, but the mods that @FreeThinker has does a great job at that. We actually do have antimatter stuck in the Van Allen Belt, and so does Jupiter. It can be harvested. And it's already used, it occurs naturally in lightnight strikes, and PET Scans used in hospitals are actually generating positrons from isotope decay to track gamma rays being generated inside your body. Insane right?

Antimatter is NOT for energy production, it's for energy transport. It is the most efficient fuel known to physics. 

r8AcmYW.png

Antimatter can be stored in a number of ways, but here are the most prominent. Antimatter can be an anti-proton, a positron, or anti-hydrogen. Conceivably you could have heavier anti-particles, or exotic anti-particles, but those are for another time. Some of those particles though, pions, are created and destroyed during the annhilation process of larger particles.

Positrons might end up being easier to store, but they have much less mass-energy than an anti-proton. Positrons are 0.5 MeV, Anti-Protons are 938 MeV. Ultimately, a LOT of your dry mass will end up being just the components necessary to house the stored anti-matter.

  • Penning Traps - generally pretty large and energy demanding, but can hold large amounts of either anti-protons or positrons. These get a lot better with superconductors. These could potentially scale up into larger electromagnetic holding cells - but it's still pretty risky to keep it all in one place.
  • Micro-Trap Arrays (source)-
    • "Atom chips are now being proposed for trapping antiprotons, positrons and antihydrogen." - Source 
    • Intended for positrons at the moment, but microtrap arrays are also used in Quantum Computing and a lot of solid matter physics experiments. You can trap heavy ions in these things, it happens all the time, and these microarrays are far safer. If one fails, you might have an explosion, but not necessarily a chain reaction.
    • A microtrap array would probably be much heavier than a large penning trap, but it could still remain relatively small since you can arrange the traps in 3 dimmensions. It's hard to get a good estimate on possibly storage limits, because most of the time these traps are used in QC where you are trying to have only one atom per trap, not several. But - if you include "cooling lasers" to the mix, it might be possible to scale things up pretty large. 
    • There are no listed numbers available for max storage capacity for Microtraps in a serious large scale use - however - "It was computationally shown that each microtrap with 50 µm radius stored positrons with a density (1.6 × 10^11 cm−3 ) even higher than that in conventional Penning-Malmberg traps (≈ 10^11 cm−3 ) while the confinement voltage was only 10 V" Source
    • 2q3n41e.png
    • Since microtraps are basically tiny coils on a wafer, once can see how these could easily scale up. Taking the mass of a positron at 9.1e-31 kg, and the number of positrons at 10V, which is 10^8, you get  1.45e-20 kg/trap.
    • Each trap takes up 50 micron radius, which gets you to a number of 1.47e-9 kg per square meter. So the surface area required to reach 1mT of antimatter is... 6.76e11 m^2
    • So that's still a lot, and mostly because positrons are so tiny, but you could fold a lot of surface area into a tiny volume if you wanted to. If you stacked all of those traps linearly, you would be 41,000 km long, but only 50 nm wide.
    • Now... I think I did my math right, but I wouldn't mind being checked. You could possibly fold that 41,000 km into thin sheets that were 100m x 100m - assuming that EVERY microtrap has a spacing of 50 nm, I calculated that you could fit the entire aparatus into a box which is 100m x 100m x 164m, or roughly a box that is 117m^3 - again, that's for 1 mT of Antimatter
    • Bump that up to 120m^3 for posterity, and you get a figure that says you have 5.7e-4 kg/m^3 of antimatter, or 0.57 g/m^3
    • Now, let's say that you bump up the potential from that 5-10 V to something more like 100 V, you now would have 12 KG/m^3, because storage scales logarthimically AND folded arrays scale cubic. You also could possibly shrink the trap size but retain a similar positron count.
    • Realistically, you probably will want more space between the cells - but you'll run things at a somewhat higher voltage because otherwise you can't store enough. The "dry weight" here would probably be comparable to an average data center, but I'll have to calc that out when I have more time.
  • Buckyball, CNT, Physical Binding- more coming soon.
  • Neutral Molecular Binding - look up positron dynamics, this  is a very promising technique too, definately a hell of lot easier to create en-masse than a 3D circuit of microtraps that is ~100m in diameter.

Here is the chart @FreeThinker put together for his storage estimates on his antimatter tanks. - I will review tomorrow - but I think splitting tank types might be a good idea, since tech level will determine storage capacity.

Diameter 0.625m 1.25 m 2.5 m 5.0 m 10 m 20 m
Antimatter (mg) 1695 13192,25 105538 844304 6754432 54035456 432283648
Antimatter (kg)   0,013 0,1 0,84 6,75 54 432
Tank Mass (kg) 25 50 100 200 400 800 1600
Tank Mass (ton) 0,025 0,05 0,1 0,2 0,4 0,8 1,6

Antimatter Beam Core Reactor Energy

More to come on this soon - will try to derive from the charts above. Help appreciated.

Magnetic Nozzle Exhaust Velocities

I will expand on this soon. Basically though, it's variable based on what reactor you use, but enough sources out there claim an upper limit of about 10,000,000 ISP, while some only predict 100,000. ISP, Exhause Velocity and Delta V are again related, but not via the traditional ratios of the rocket equations. See above.

ALRIGHT - this is my first draft - I'll update this first post with relevant information as we revise things. Also - I'll probably post another thread for the MagScoop Sail too - since that can handle the bulk of deceleration (interstellar 'wind' drag) andthus cut your fuel needs down by nearly half.

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One of the biggest problems of antimatter is storage density. The fishbee design mentions it stores the antimatter at 1/10 of the density of Liquid Hydrogen, which mean is storage density is only 7.085 g/L !!

Now here comes the kicker, according to the Frisbee document it uses a dry tank of 26600 Ton to store 160000 Ton of hydrogen AND 165 000 TON OF ANTIMATTER !!!.

uwUZTRI.jpg

Notice it has 2 propellant tanks, one tank of 7.7 KM and a second about 10 times as big filled with antimatter !!

Looking at the design it would mean the 165 000 ton Antimatter is stored with about 24000 ton storage tank, which give it a dry/wet mass ratio of 6,875 !!

Now that is extremely good, but it does mention 2 addition requirements:

The tanks would only  have to operate in deep space far away from the fun and the vessel will never accelerate faster than 0.01 g

Our tanks needs to able to survive launch and earth atmosphere !!

 

 

Edited by FreeThinker

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Wow, yeah, it seems counter-intuitive that you need more antimatter than matter. I guess the numbers there are pretty close. I'd think you'd want 1:1 but maybe there are losses during the annihilation? (165k tons of antimatter and 160k hydrogen.)

I think the tricky thing to understand here is that the mass ratio actually changes as you move faster and use up more fuel.
http://www.wikiwand.com/en/Antimatter_rocket

Eq.III can be integrated and the integral evaluated for M_{0} and M_{1}, and initial and final velocities (v_{i}=0 and v_{f}=\Delta v). The resulting relativistic Rocket Equation with loss of propellant is[2][20]

Of note: variable a is the original mass ratio of dry/wet. You're solving for the actual total trip mass ratio with this monster.

{\frac {M_{0)){M_{1))}=\left({\frac {(-2I_{\text{sp))\Delta v/c^{2}+1-a-{\sqrt {(1-a)^{2}+4aI_{\text{sp))^{2}/c^{2))})(1-a+{\sqrt {(1-a)^{2}+4aI_{\text{sp))^{2}/c^{2))})}{(-2I_{\text{sp))\Delta v/c^{2}+1-a+{\sqrt {(1-a)^{2}+4aI_{\text{sp))^{2}/c^{2))})(1-a-{\sqrt {(1-a)^{2}+4aI_{\text{sp))^{2}/c^{2))})))\right)^{\frac {1}{\sqrt {(1-a)^{2}+4aI_{\text{sp))^{2}/c^{2))))

What bother me is that they are just assuming the Isp to be the desired final velocity of 0.69c, which is m/s, instead of just determining seconds. However, since Isp is always shown here as a relation to c, it always cancels out - with the exception where you have Isp*Delta-V. But for an interstellar trip where you plan to use all of your fuel - those values would be the same.

However, that's not a safe assumption to make for kerbal, because you might use a secondary propulsion method to deccelerate (IE magsails and a small fusion drive so you can dump the huge antimatter tanks). The thing to do would be to probably calculate out the max delta V for a particular stage given the amount of onboard fuel and applying an energy conversion.

Now, I wish I had mathemetica right now to evaluate that monster. It might be easier to write a small program to handle it. Ultimately the "a" value and the max delta-V will be variable based on how much fuel you have to convert to energy and what the efficiency is.

I'm not sure how this is moddable into Kerbal though, since from what I understand, KSP only cares about determining thrust based on Isp values. We might have to solve for the trip duration mass ratio (M_0/M_1), and use the standard 0.69 for the I_sp value, and then plug it all in, and then reverse solve for the "classical" I_sp that KSP uses.
https://wikimedia.org/api/rest_v1/media/math/render/svg/41bae943b77f591d8b298ee431cc3b8736b58589

But I don't think that ALL that is needed to get the storage density and engine working properly in the game - I think it's just important for trip planning. You would have to feed in your target delta-V, and then it would spit out the final fuel ratio you should be using. And depending on how you choose to accelerate/decelerate your fuel use will be different.

So if you use a laser sail or beamed energy to reach 0.1c, then antimatter to go from 0.1c to 0.5c, then magsail to brake down to 5000 km/s and fusion to decelerate the last stretch - you'd only need to calculate the fuel ratio for the antimatter portion which was 0.4c delta-V. And of course I think the Fusion Reactors have a similar Fuel Ratio calculation problem too. Any Build Assistants are going to have to be a lot more complicated.

For now, I think boosting the ISP of the magnetic nozzle and determining empirically the antimatter storage capacity per cubic meter is probably the best bet for getting it to work with tweakscale. You might also at some point make multiple types of antimatter storage - since they will have different effective dry masses. A magnetic nozzle vs a microtrap vs bound neutral molecules will all have varying support mass within the fuel tank itself.

Another funny thing is that the size of the magnetic nozzle isn't studied super closely in any of those studies, but maybe when calculating the thrust, have some sort of formula check the size and apply a simple modifier. You likely would want your magnozzle size to match your reactor size.

Phew this stuff is tricky!

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2 hours ago, iontom said:

I think the tricky thing to understand here is that the mass ratio actually changes as you move faster and use up more fuel.
http://www.wikiwand.com/en/Antimatter_rocket

Eq.III can be integrated and the integral evaluated for M_{0} and M_{1}, and initial and final velocities (v_{i}=0 and v_{f}=\Delta v). The resulting relativistic Rocket Equation with loss of propellant is[2][20]

Of note: variable a is the original mass ratio of dry/wet. You're solving for the actual total trip mass ratio with this monster.

{\frac {M_{0)){M_{1))}=\left({\frac {(-2I_{\text{sp))\Delta v/c^{2}+1-a-{\sqrt {(1-a)^{2}+4aI_{\text{sp))^{2}/c^{2))})(1-a+{\sqrt {(1-a)^{2}+4aI_{\text{sp))^{2}/c^{2))})}{(-2I_{\text{sp))\Delta v/c^{2}+1-a+{\sqrt {(1-a)^{2}+4aI_{\text{sp))^{2}/c^{2))})(1-a-{\sqrt {(1-a)^{2}+4aI_{\text{sp))^{2}/c^{2))})))\right)^{\frac {1}{\sqrt {(1-a)^{2}+4aI_{\text{sp))^{2}/c^{2))))

Notice that I have already solved this problem when developing the Daedalus Engine, basically I calculate the relativistic mass and adjust the effective Isp. It works quite well and prevents you from being able to travel faster than the speed of light.

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Cool - glad to know that the Daedalus has an effective ISP calc. 

Regarding antimatter storage - I still need to find some time to review and finalize tank mass calcs from the microtrap array numbers I had. I didn't have any knowledge of the trap mass. But I'd like to compare them against the numbers you are using right now.

I think the issue though is that with the scaling you present - there's only an exponential trend while increasing the tank size. Once you start adding multiple tanks, the ratio of fuel to dry mass no longer scales, not even linearly. Your antimatter payload and your dry mass will just continue to keep the same ratio, since the ratio for 2 tanks or N tanks is the same as just 1 tank. Unless you are doing a calculation somewhere that I don't see.

Basically - to hit the the desired cruise speed of 0.3c, you'd need mass parity if 1:1. So maybe something like if you have 8x or 10x the 40m fuel tanks, you would be able to hit 1:1 needed. Unless I'm missing something.

eupYvst.png

BUT - I still need to calculate out fuel/dry ratio for microtraps and overall storage for neutral molecule positron binding, or even CNT/Buckyball containment. One of those might be a little more efficient. Still - I think this scaling ratio is always going to be the problem.

BTW - somebody just posted this mod for a Bussard scoop. I like that its a functional scoop with code, but don't think it does decelleration though, and I like the model by @SasquatchM  better.

 

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13 hours ago, iontom said:

 think the issue though is that with the scaling you present - there's only an exponential trend while increasing the tank size. Once you start adding multiple tanks, the ratio of fuel to dry mass no longer scales, not even linearly. Your antimatter payload and your dry mass will just continue to keep the same ratio, since the ratio for 2 tanks or N tanks is the same as just 1 tank. Unless you are doing a calculation somewhere that I don't see.

@SasquatchM  better.

 

 
 
1

Good point. A possible implementation would be that part mass would be not only depend on the size of the tank, but also it connected neighbours. It could look if it is connected to another antimatter tank and apply some bonus, that way connecting in a stack will be a good strategy to minimise dry mass.

Concrete: for each stack connected antimatter tank, its own mass would be reduced by 25% (up to 50% mass reduction when connected both on the top and bottom)

 

Edited by FreeThinker

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Thinking about a little more I come to the conclusion, a fixed dry/wet ratio would not be the best solution, instead, you would need the ability to customise it for a specific role. specifically it ability to withstand temperature and acceleration. By minimising both temperature and acceleration resistance, it should be possible to create an anti-matter tank with the spectacular dry/wet mass ratio of 1 : 6,875 for a 76000m x 20m diameter tank.

So what we need it the ability to configure it in the VAB and if people are foolish enough to scale it all down and try to launch it into space, it would instantly explode due to overheating or acceleration. So in order to maximise mass ratio, you would first have to launch the tanks empty into space (or build it in space) and then use a second vessel with the more resistant tank to fill it up in orbit.

Edited by FreeThinker

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Sorry for pulling a disappearing act. Been very busy with work and some other projects. I did get a group started called OpenSpaceProgram which you should follow and put some input into when you have the chance.

In another two weeks or so, I will probably get more involved in doing more quantitative modelling for this. I've been learning Python Juptyer notebooks which are really useful for this sort of work. Just let me know any hangups you want me to look into.

I do like that point on temp/accel resistance. 76 km tank in KSP. Scary stuff! :o

Edited by iontom

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On 27-6-2017 at 0:11 AM, iontom said:

I do like that point on temp/accel resistance. 76 km tank in KSP. Scary stuff! :o

 

It is fully functional in KSPIE, I still have to do some work on dynamic power requirements, the stronger tanks should require more power when under high g-forces. The electrostatic tank should also have increased power cost depending on the content. Could you figure out how this should scale? I also need some  realistic power requiment for the Diamagnetic antimatter tank

Edited by FreeThinker

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Alright here is the result:

wCRjpRD.png

This 1.25m container stores a levitating antihydrogen ball of ice almost 13.2 kg, which antimatter in the form of hydrogen.

this extreme form of storage it is based on diamagnetism.

0bihJzU.jpg

Notice that it does not like excessive high gee forces (>10 G) and temperature(>1000 K)

GLKmXjp.png

Notice the size of the ball grows with the amount of anti-hydrogen in the container

The mass of the container can be reduced in the  VAB by reducing gee force and temperature tolerance

Edited by FreeThinker

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You guys did a brilliant job and made a beautiful mod. This is a thank you because I enjoyed using your mod and hope you continue making great things!

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