How could astrophysical jets, emitting matter from black holes be used as energy sources by a space-faring nation? How could they be able to collect and use this form of energy?
This is basically a solar sail on steroids. Unlike solar sails, which rely on a relatively gentle wind of particles, you need something much more sturdy. Rather than trying to capture the relativistic particles, since most of them are ionized, you can simply try to steal some of their kinetic energy by setting up a large electrostatic field. Instead of a solid sheet of photon-absorbing material, you instead want a large thin wire grid through which you can pass current.
Inverse Ion Drive
Shooting ions through a charged grid at high speed is exactly the function of an ion thruster. If you already have high speed ions, then instead of speeding them up, you just want to slow them down and capture their momentum. So this "sail" is really like a giant ion drive operating in reverse. If you have materials sufficiently sturdy to survive the jet in the first place, then you can stack several of these sails in series. Each one might only capture a fraction of ion energy, but as they pass through each sail, they slow down and you steal more momentum. It may be possible to stack enough of them that the very last layer is a proper solar sail, where you can literally catch the ions to steal 100% of their momentum, and then dump them over the side (at 0 relative velocity, so you don't have to accelerate them as dead weight).
Of course, you need to charge your grids to actually interact with the ions usefully, and this takes power. But you can also harvest power as the ions move through a magnetic trap, which operates like a kind of linear particle accelerator in reverse. Thus, the jet can power both your ship and the ion grid.
Of course, a relativistic jet is going to bombard any spacecraft with a pretty tremendous amount of energy. Probably the most sustainable way to survive this is to create a powerful magnetic field which simply diverts most of the ions around your ship proper (but not so much that they occlude the sail). Again, the magnetic field can itself be powered by the jet (though you need seed energy to power the shield before you enter the jet!).
A simpler solution would be to just create a massive shield which can absorb/deflect 100% of the jet without fancy grids or generators or magnetic shields. Unfortunately, there may not exist any material which can withstand the power density involved. The most obvious solution would be to just get an adequately large asteroid as the shield, park your ship on the lee side, and push it into the jet, letting the asteroid ablate away until you reach your destination. Unfortunately, the asteroid is likely to get hotter and hotter, unable to dump enough energy to stop from melting into a metal plasma long before you reach your destination. But all of this depends on how far away you are from the jet, how collimated the jet is, etc.
The Penrose mechanism - how to extract energy from a black hole
- Throw an object with a certain trajectory into the black hole
- Once in the ergosphere, break the object in two to give them a certain trajectory
- is absorbed by the black hole decreasing its cinetic spead
- gets out the ergosphere with a superior spead and a total energy superior to the mass energy of the original object.
Also from what I see in the article, if you break the object in more than two pieces, the speed stacks with the number of object you throw into the black hole.