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starship-design: Re: Protons vs Electrons for Relativistic Electric Thrusters
The way I see it, Accelerating Protons will ALWAYS be better than
accelerating electrons if you want to keep charge neutrality. If you
want to dump a proton for every electron, you need to carry the protons
along with you, and that huge mass requirement negates the advantage of
using lighter-mass propellant.
Let me put it this way; We will have a given amount of Energy (E) to
accelerate every proton/electron pair. We want to do it in a way that
will give us the maximum momentum boost. Before I was (incorrectly)
using the equation E^2 = (P c)^2 + (m c^2)^2, forgetting that the E was
actually the Kinetic Energy PLUS the Rest Mass Energy. If we want E to
only stand for Kinetic Energy, the equation becomes:
E^2 + 2 E (m c^2) = (P c)^2
In the low energy limit (E << mc^2), this goes to the well-known
E = p^2/(2m). In the high energy limit (E >> mc^2) it looks like a
photon, with E = P c. Comparing the momentum given by this equation for
protons and electrons, its a no-brainer. Both have the same first term,
but the second term is much greater for protons: Protons are always
better (or as least as good) as electrons for propellant.
Now without charge neutrality requirements, electrons do have a
redeeming value; you dont need to carry as much propellant mass on your
ship. But since you have to carry the protons along anyway, you might
as well use Them for propellant.
Im not saying we should focus completely on protons, though. For very
high energy/mass ratios, electrons are practically identical.
Therefore, if there is some reaction that produces fast-enough
electrons, it would probably be more efficient to use the electrons as
propellant rather then catch the energy and transfer it to protons. An
example here would be the Monopole-induced proton decay which makes 800
MeV positrons. This is probably on the border-line of where it would be
worth it to switch to a proton. If you take the 800MeV and transfer it
to a proton, you get nearly twice the momentum that you have in the
800MeV positron. So here it would depend on what sort of capture
efficiencies you can manage; if your efficiency dropped below 50% it
wouldnt be worth it to switch to a proton. (Actually, this case is a
no-brainer. You no longer have to dump a proton for charge neutrality;
its a positron so you only have to dump an electron. We would
definitely want to keep the positron as propellant.)
So the example I just gave made me realize that having positrons
available makes my claim invalid: if you can dump positrons at ANY
energy, then electrons keep their original advantage of being light; you
dont need to lug extra protons along for charge neutrality. In fact, I
would guess that for an antimatter engine, the optimal design would be
to get all the energy from the anti-protons, but keep the positrons
around to dump for charge neutrality, and use electrons as propellant.
One additional way I can see still using electrons as propellant is if
you are somehow able to keep charge neutrality by capturing electrons
from interstellar space. Perhaps strong fields could deflect the
protons (which would be beneficial in its own right) and capture enough
electrons, thereby keeping charge neutrality without carrying along
extra protons. I see lots of problems here, though...
So assuming we are limited to keeping charge neutrality with protons,
the question of propellant should be switched from proton/electron
debate to a proton/alpha debate. The higher the mass particle, the
higher the momentum we can get from a given energy, but now we are
dealing with carrying more mass in the ship to use as propellant. I
would guess we would want to keep the ship as light as possible, which
would point to protons. But of course alphas would still the propellant
of choice in a fusion engine; if we have them around anyway as a
reaction product, we might as well use them as propellant!
Wow, now Ive done it. I started out by saying that protons are the best
propellant, but my exceptions to this rule (Fusion, Antimatter,
Monopole-catalyst) seem to cover most of the possibilities! Okay; I
still claim that protons are the best propellant for a rotating black
hole engine. Any takers?