Interstellar VASIMR Bussard ramjet scoop powered by fusion

[scienceguy]

Some time ago some of us here were calculating what speed a VASIMR craft could get to if it had a 1 kg/kW power source. It was concluded that the mass of propellant made the trip to alpha centauri prohibitively long (something like 1500 years).

What if we used a Bussard ramjet scoop and got our propellant from the hydrogen sitting in space (1 molecule per cubic centimeter)? If you pair this with an ideal fusion power source (I know, this may be a long time coming), then it appears you can get to 0.10c in 48 years.

From the VASIMR Wikipedia page

http://en.wikipedia.org/wiki/VASIMR

For the engine requiring 200 kW, the exhaust velocity of the propellant is 50 km/s and the force produced is 5 N. Assuming propellant is hydrogen (the only thing available in interstellar space):

p = mv = (1.67E-27 kg)(5E4 m/s) = 8.4E-23 kgm/s

Force produced by 1 hydrogen atom:

F = dp/dt = (8.4E-23 kgm/s)/ 1 s = 8.4E-23 N

Assuming the spacecraft is 2E5 kg and the acceleration we want to accelerate at 0.02 m/s^2,

F = ma = (2E5 kg)(0.02 m/s^2) = 4000 N

Getting thrust from these hydrogen atoms,

4000 N/8.4E-23 N/atom = 4.8E25 atoms required per second.

In space

1 H2 atom per cm^3 means 2E6 atoms/m^3

(4.8E25 atoms/s)/(2E6 atoms/m^3) = 2.4E19 m^3/s of space must be taken in

Moving at an average of 0.05c, the area of space that needs to be scooped by the magnetic field is

(2.4E19 m^3/s)/(0.05(3E8 m/s)) = 1.6E12 m^2 = 1.6E6 on a side if area is a cube.

Magnetic field required to scoop this much area

Atoms are moving towards the ship (relatively) at 0.05c, so an acceleration per atom is needed:

0.05c = 1.5E7 m/s

Length atoms move is estimated to be 1/cos (pi/4) of distance needed to be scooped:

v^2 = 2ax
 
a = v^2/2x = (1.5E7 m/s)^2/2(2.1E7) = 5.4E6 m/s^2

That may seem like a huge acceleration but remember we are accelerating atoms:

F = ma = (5.4E6 m/s^2)(1.67E-27 kg) = 8.9E-21 N

F = qVxB

B = F/qV

B = 8.9E-21 N/(1.6E-19 C)(1.5E7 m/s) = 3.8E-9 T which seems too small...

Assuming 100% efficiency of a fusion reaction reacting 3He and 3He:

3He + 3He  4He + 2p + 12.9 MeV

200 kW needed per VASIMR engine

4000 N/5 N/engine = 800 engines

200 kW x 800 engines = 1.6E5 kW = 1.6E8 W

1 eV = 1.6E-19 J

1.6E8 J/s x 1 eV/1.6E-19 J = 1E27 eV/s needed to be generated

(1E27 eV/s)/(12.9E6eV/reaction) = 7.8E19 reactions/s

3He mass per reaction = 2x3x1.67E-27 kg = 1E-26 kg/reaction

7.8E19 reactions/s x 1E-26 kg/reaction = 7.8E-7 kg/s of 3He needed to react

t = v/a = 3E7 m/s / 0.02 m/s^2 = 1.5E9 s = 48 years of accelerating

1.5E9 s x 1.9E-6 kg/s = 2850 kg of 3He needed for fusion power.

At 1 kg/kW, 800 power sources for the VASIMR engines would have a mass of

1.6E5 kW x 1kg/kW = 1.6E5 kg

Thus 80% of the mass of the craft is just the power generators. Depending on how much power it would take to power the magnetic scoop at the front of the ship, the payload may have to be even smaller. However, what we see here is a way to possibly reach alpha centauri in 140 years (need to decelerate as well, possibly with magnetic scoop) or say epsilon eridani in 200 years or Gliese 581 in 300 years.

Edit: travel times

Edit: formula error

[Elmar Moelzer]

If you can do fusion, why dont you use that directly for the propulsion, instead of the detour over converting to electricity and then powering VASIMIR with it?

[scienceguy]

If you can do fusion, why dont you use that directly for the propulsion, instead of the detour over converting to electricity and then powering VASIMIR with it?

Good question. I guess I was figuring that we could get electricity directly from 3He-3He and use the hydrogen from space for propellant.

It would be better just to fuse the hydrogen from space...

[Nilof]

Fusing hydrogen from space is very hard though. the p-p chain is bottlenecked by weak processes which makes it impractical. CNO-cycle fusion is possible, but your terminal velocity will still be fairly low as you waste a lot of energy braking the interstellar hydrogen down in your reference frame.

Bringing fusion fuel with you for energy and using interstellar hydrogen only as reaction mass does seem like the best solution. IIRC Alan Bond was one of the first to propose this idea in his RAIR concept.

[Elmar Moelzer]

Fusing hydrogen from space is very hard though. the p-p chain is bottlenecked by weak processes which makes it impractical. CNO-cycle fusion is possible, but your terminal velocity will still be fairly low as you waste a lot of energy braking the interstellar hydrogen down in your reference frame.

Bringing fusion fuel with you for energy and using interstellar hydrogen only as reaction mass does seem like the best solution. IIRC Alan Bond was one of the first to propose this idea in his RAIR concept.

Then I have to ask again, why you would use the interstellar hydrogen as a reaction mass and not use the fusion products directly?

[Excession]

You have completely neglected drag from the scoop.

[Elmar Moelzer]

You have completely neglected drag from the scoop.

That one is actually very minimal compared to the thrust generated by the fusion reaction, see "Bussard Ramjet".

[Excession]

You have completely neglected drag from the scoop.

That one is actually very minimal compared to the thrust generated by the fusion reaction, see "Bussard Ramjet".

It is anything but minimal. Unless you find some way to recover all the losses from collecting and compressing the interstellar medium, there will always be a speed beyond which the drag forces exceed the thrust of the engine. And if you need to accelerate the material up to the ship's velocity (in other words, if your engine cannot work with propellant flowing through it at several percent of the speed of light), then that top speed cannot be higher than the rocket's exhaust velocity...

[DLR]

The drag problem alone makes the classical Bussard ramjet unworkable. But there's an upside to it. The drag of a huge magnetic sail could be used to slow interstellar spacecraft moving at signficiant fractions of c down without the use of propellant. That's nothing to sneeze at.

If you combine a fusion rocket with a magnetic sail you can use all your propellant to accelerate the spacecraft, reaching the destination twice as fast as if propellant had to be used to slow down as well.

My favourite interstellar propulsion system is the mass-beam. Self-replicating robots would construct huge solar power stations near Mercury. The energy from the stations would be used to accelerate "smart" nanoscopic particles towards a spacecraft with a magnetic sail. Prior to impact, the particles would be ionized by onboard lasers and deflected by the magnetic sail, pushing the spacecraft towards ever higher velocities. The great thing about mass-beams is that you overcome the mass-ratio problem associated with rockets. Depending on the power of the mass-beam, the technology would theoretically allow you to reach arbitrarily high velocities.

At the destination star, the magnetic sail could be redeployed to slow the spacecraft down by dragging against the interstellar medium and later the incoming stellar wind.

Source:

http://www.gdnordley.com/_files/2way%20EML%20&%20PB%20prop.pdf

[Elmar Moelzer]

It is anything but minimal. Unless you find some way to recover all the losses from collecting and compressing the interstellar medium, there will always be a speed beyond which the drag forces exceed the thrust of the engine. And if you need to accelerate the material up to the ship's velocity (in other words, if your engine cannot work with propellant flowing through it at several percent of the speed of light), then that top speed cannot be higher than the rocket's exhaust velocity...

You are right, it is not quite a trivial as I initially suspected. It depends on where you aim your spaceship relative to the solar wind. Personally, I never found the design particularly interesting anyway. It requires massive ships for once. The other problem is the fact that the interstellar medium is less dense than Bussard expected. I think interstellar travel will require some other technology. Right now, I think we should focus on getting into earth orbit. We are still a long way from doing that right.

[KelvinZero]

Fusing hydrogen from space is very hard though. the p-p chain is bottlenecked by weak processes which makes it impractical. CNO-cycle fusion is possible, but your terminal velocity will still be fairly low as you waste a lot of energy braking the interstellar hydrogen down in your reference frame.

Bringing fusion fuel with you for energy and using interstellar hydrogen only as reaction mass does seem like the best solution. IIRC Alan Bond was one of the first to propose this idea in his RAIR concept.

Then I have to ask again, why you would use the interstellar hydrogen as a reaction mass and not use the fusion products directly?

You get way more thrust for the same energy if you have more reaction mass.

Thats why a battery powered car can get up to 100km/hour in seconds but the same battery power converted to light  would barely move you at all. The car has the entire Earth to push against.

[Elmar Moelzer]

You get way more thrust for the same energy if you have more reaction mass.
Thats why a battery powered car can get up to 100km/hour in seconds but the same battery power converted to light  would barely move you at all. The car has the entire Earth to push against.

More thrust is important for shorter trips. For an interstellar flight, it is not that important. For that you want mostly Isp and you will loose a lot of energy due to conversion losses. You will also add a lot of weight for the conversion system. Plus, there are concepts for high thrust - high Isp engines that directly convert the fusion energy into thrust. A good example is the "fusion powered rocket" by MSNW LLC.
http://forum.nasaspaceflight.com/index.php?topic=30437.210

[KelvinZero]

Let me try again.
You get more velocity for the same amount of energy if you have more reaction mass to push against.

It potentially brings your fuel requirements down from exponential to proportional to the square of velocity.

[Elmar Moelzer]

Let me try again.
You get more velocity for the same amount of energy if you have more reaction mass to push against.

It potentially brings your fuel requirements down from exponential to proportional to the square of velocity.

Yes, I got you. Have you even looked at the link, I provided? The proposed fusion driven rocket has more thrust than VASIMIR because it uses a Lithium liner (which also compresses the plasma to fusion conditions) as a reaction mass.
If you use a fusion reactor to produce electricity to then drive a VASIMIR engine, you loose a lot of energy during the conversion process. Because of this a direct fusion driven engine is preferable if you can achieve the same thrust.

[KelvinZero]

Let me try again.
You get more velocity for the same amount of energy if you have more reaction mass to push against.

It potentially brings your fuel requirements down from exponential to proportional to the square of velocity.

Yes, I got you. Have you even looked at the link, I provided? The proposed fusion driven rocket has more thrust than VASIMIR because it uses a Lithium liner (which also compresses the plasma to fusion conditions) as a reaction mass.
If you use a fusion reactor to produce electricity to then drive a VASIMIR engine, you loose a lot of energy during the conversion process. Because of this a direct fusion driven engine is preferable if you can achieve the same thrust.

Sorry, I looked at it and concluded you had misunderstood my post because of the use of the word "thrust". Always be more specific when you reference something. You can't rely on my common sense to snap to the bit that is relevant because half the time on the internet the source of confusion is not on the facts, but what each person thought the argument was about.

I didn't see the relationship to the discussion of why it is useful to be able to push against some medium that you do not carry with you. I though you were saying "but you can create high thrust without pushing against such a medium"

Such a fusion rocket would still face the fundamental issue of fuel being related exponentially to velocity, instead of by a more efficient velocity-squared relationship. This is not related to the inefficiency of converting to/from electricity etc.

[cordwainer]

You just reinvented the ion ramjet. Also you do need to take drag forces of the interstellar medium on the scoop into account. Off the top of my head that means your trip time to Alpha Centauri is doubled and top acceleration is about 1/6th the speed of light.

[hcm1955]

Another power source that may be considered is laser. This elmenatest the requirement for an on board fusion reactor , and rates higher on the TRL.

[Vultur]

As for making the scoop itself... I've seen it described as ionizing the hydrogen and collecting it with magnetic fields. But do you really need to ionize it first?

As I understand it, atomic hydrogen (though not H₂) is paramagnetic. So it will be attracted into a magnetic field.

O₂ is also paramagnetic, and many oxygen-measuring instruments work by this principle - running oxygen-containing air through a magnetic field creates an air current proportional to the oxygen concentration, as the oxygen is pulled into the field. The air current pushes on a spinning 'dumbbell' and the force is measured.

Could a far more powerful version of the same principle (well, minus the dumbbell) be used to make a Bussard scoop?

[qraal]

The ionization issue is overstated - the Interstellar Medium is between 25-100% ionized depending on where you are. Plus slamming into all the neutral atoms/molecules with such a rapidly changing magnetic field is probably going to ionize them anyway. And if not that process, then the ions/electrons being snow-plowed by the magnetic field will do significant ionizing of the neutrals around them.

As for making the scoop itself... I've seen it described as ionizing the hydrogen and collecting it with magnetic fields. But do you really need to ionize it first?

As I understand it, atomic hydrogen (though not H₂) is paramagnetic. So it will be attracted into a magnetic field.

O₂ is also paramagnetic, and many oxygen-measuring instruments work by this principle - running oxygen-containing air through a magnetic field creates an air current proportional to the oxygen concentration, as the oxygen is pulled into the field. The air current pushes on a spinning 'dumbbell' and the force is measured.

Could a far more powerful version of the same principle (well, minus the dumbbell) be used to make a Bussard scoop?

[hcm1955]

Is it possible to replace the fusion reactor power source with a laser based power beaming design ?