the main issue is that the exhaust would be helium, and then after the second ship uses it it would become Beryllium I think, and then Oxygen, and so on. fusing together heavier elements is harder then fusing lighter ones. so with each pass through a fusion engine the process becomes harder. Another main issue is that there is nothing slowing the exhaust down, so it is going backwards with same force it pushed the ship forward. so when the second ship hits the exhaust it will get pushed back or destroyed by the incredibly fast helium cloud, and if it succeeds in scooping it up and accomplishing helium fusion without being pushed back too hard, then the next ship has to catch the exhaust without being hit and pushed back, and then successfully fuse beryllium. magnetic funneling could theoretically direct, compress and ingnite fusion of the matter without it touching your ship, but it would not be easy. and I'm not certain it is possible at all. I may be wrong as to what order of elements you would get. I am assuming that 100% of matter is fused, so all the hydrogen makes helium, so all that is left to fuse is helium. so it follows a exponential increase in the amount of protons, which will give you the atomic number on the periodic table. if any matter is not fused by the first ship then hydrogen could be fused with helium making lithium. this is the process by which different elements are produced by stars. The idea is clever, but I do not think it is feasible in short you would need to catch the mass without it impacting you so much that it pushes you back. you would need to be able to fuse together increasingly heavy elements

It's a difficult problem, but not for the reasons you state. In space, everything is moving. You won't have to try to fuse helium, because the helium will be somewhere else by the time the next rocket gets there. You also won't have to worry about your rocket spitting a particle beam out the back end, because rockets aren't well collimated. The exhaust will spread out and be meaningless to any other rockets, unless you're absurdly close. However, it's really, really hard to fuse protium. On top of that, you have to fuse it without slowing it down, so you're trying to do incredibly difficult fusion on a moving target. If you slow it down, you get drag, which kills the benefits of the rocket.

you forget that they are in vacuum, and so the exhaust will not spread out anywhere near as much as in atmosphere. For example when the curiosity Rover was dropped onto mars, the exhaust from the sky crane dug a hole straight down into the martian ground. The thin Martian atmosphere was unable to spread out the exhaust plume enough to disperse the force, so the exhaust hit the ground with close the the same force it left with. fun fact the curiosity rovers first job was to investigate this hole/crater made by the exhaust to study the soil further down then the surface. And the OP's original idea was that the convoy sticks close enough together to catch each other exhaust and reuse it for fuel. so they would be that close to each other. As for the rockets not fusing their reaction mass I guess I was mistaken. I need to re-read how the engines work in EP.

It would be tricky but by adjusting distance and making your scoops wide enough to allow for dispersal it could happen. There would certainly be loss, but that could be compensated for. My concern is diminishing returns on accelerating mass...how fast you can push the hydrogen per stage would decrease as the exhaust velocity approaches c! "Last one in line gets a relativistic particle beam to the face!"

Chernoborg wrote:

My concern is diminishing returns on accelerating mass...how fast you can push the hydrogen per stage would decrease as the exhaust velocity approaches c! "Last one in line gets a relativistic particle beam to the face!"

A trailing ship would always be moving at pretty much the same speed as the one in front, so in their local inertial frame it would never be relativistic.

Won't the exthaust disperse very quickly because it is made of charged particles? The electrons and protons might recombine to hydrogen but I'm no plasma physicist. But the greatest problem I see is that the particles are moving in the wrong direction with great speed. If you collect them you will add their momentum to your own and therefore loose forward momentum. If you somehow avoid that, the time they will spend in your reaction chamber will be very short, maybe too short to impart any momentum on them. I'm sure there are more problems. Consider the following: Two identical ships travel together, one behind the other. We just assume the second ship gets every single exthaust molecule from the first. If the molecules are stopped the second ship would get just as much momentum in the wrong direction (backwards) as the first got in the right direction (forward). As it is an identical ship the momentum it can get from expelling the molecules backwards is exactely the same as it lost from collecting them. It stands still. If it just doubles the velocity of the incoming molecules it gets just as much momentum as the first ship did. But if the reactor can accelerate fast moving molecules to double their velocity, why didn't we do that in the first ship? Throw away all the parts except the reactor and we can transport even more.

I'm not sure what the concept of temperature means in the context of a dilute plasma in vacuum. How large are realistic fuel flow rates anyway?

The Bussard ramjet is a concept with a major flaw; when you scoop up the hydrogen in front, you need to accelerate it to your own inertial frame. This is, effectively, a form of drag. First you're accelerating a small amount of hydrogen, which loses you speed, and then you shoot it out of a rocket to gain you speed. The net effect of this is that you can't actually go faster than the engine's exhaust velocity. What then happens when you string along a bunch of Bussard ramjets like you propose is that the first ramjet accelerates some hydrogen from rest to its current speed v_e, then shoots it out the back at a relative velocity -v_e, returning it to rest. Then the next ramjet comes along, accelerating the hydrogen to v_e, and then shoots it out with a velocity -v_e, returning it to rest, whereupon it's accelerated by the third ramjet... As you can see, there's no actual gain here, you're just accelerating the same reaction mass several times, instead of accelerating more mass only once. (You do actually gain a little from not having to deploy the scoop on the trailing ramjets, but Bussard ramjets are pretty terrible anyway, so why bother trying?) You could go with a RAIR, but there's really no need to string them along; rocket #1 has to accelerate the hydrogen stream to some greater velocity. Then rocket #2 has to accelerate the hydrogen stream from that greater velocity to an even greater velocity, which rocket #3 then has to accelerate even further velocities... This is probably more difficult than just accelerating three ships in the first place. What you're actually doing here is making a very powerful engine and then splitting it into several parts among several rockets; you might as well just build one spaceship, rather than hassle with several, if you have rocket engines that powerful. In short, your idea is unworkable because it's just a roundabout way of making a single very big rocket, and there's no actual gain anywhere on the process.