starship-design: Re: Questions Regarding Relativistic Electric Thrusters

[TLG.van.der.Linden@tip.nl (Timothy van der Linden)]

Timothy replies to Rex's 1/25 letter:

>A critical component of most of the interesting interstellar
>propulsion concepts (e.g., fusion-powered rockets, antimatter-
>powered rockets, beam-driven sails in the deceleration phase) is a
>relativistic electric thruster.

Actually a *relativistic* thruster is probably not useful for a fusion
powered design, since such designs in general have a optima for rather
"slow" exhaust velocities (less than 0.1c).
So only beam-powered or anti-matter powered ships are candidates for
relativistic thrusters.


>The sample questions are as follows (I haven't tried to address
>any of them, so some may not be well thought out):
>
>1. What is the best exhaust particle?  Electrons, protons, alphas,
>   etc.?  What is the best parameter to compare them by?

Actually to determine an optimum we should first decide what we want to
optimize. This may seem a trivial question but it really isn't.
High velocities have a low momentum:energy ratio, but of course need a lot
less mass. So you always have to weigh between how much mass and how much
energy.
Also one would want to use most of the repulsion mass that is taken with the
starship, this almost certainly means that one needs to use ions (thus not
electrons).
For the highest exhaust velocity, one should take the particle with the
highest charge:mass ratio, this would have been an electron, so the next
best thing would be a proton:

Formulas in SI units.

U=q dV
U=m c^2 (gamma-1)

q dV=m c^2 (gamma-1) --> gamma=q/m ((dV/c^2)+1)

>2. Is there an electron energy that gives the same performance as
>   protons? (from the so-called "mass amplification" with
>   increasing velocity)

Do you mean: For what exhaust velocity y is the total relativistic energy of
a electron the same as for a proton with exhaust velocity x?
(If not, what do you mean with performance?)

Mp:Me = 1:1836

E=gamma m c^2

GAMMAp Mp c^2 = GAMMAe Me c^2 -> GAMMAe/GAMMAp=1836

                    2
      Vp + 3370895 c
Ve = -----------------       
          3370896

(Ve, Vp are exhaust velocities of electron and proton)

>3. Can we estimate relative thruster weight per unit thrust?
>   Thruster size? (to compare the different options)


>4. What disadvantages/advantages accompany motion of electric
>   charges?
>   a. What is the effect on performance (e.g., exhaust velocity)
>      of charging of the ship due to incomplete charge
>      neutralization?

It probably is neglectable,  if one however only exhaust ions and not
electrons, then a serious problem will rise in a matter of seconds (probably
less).

>   b. What is the effect on performance of charge neutralization
>      effected by dumping oppositely charged particles (at zero
>      velocity, say)? 

This depends on the amount of dumped mass compared to the amount of
exhausted mass.  In the case of exhausting electrons and dumping the protons
and neutrons it would seriously harm performance.

In general dumping mass always decreases performance. The rate at which it
decreases performance depends besides technical problems also on the kind of
fuel (f-factor) that is used.

>   c. Will the current of the exhaust beam generate a magnetic
>      field strong enough to deflect interstellar protons (ionized
>      by a stripping foil out in front of the ship) away from the
>      ship, to save shielding?

If the core of the linear accelerator is in the same direction as the ship
moves, the magnetic field in the forward direction will be almost zero. (I'd
like others to verify this.)

>   d. Could the electric charge from incomplete neutralization
>      create an electric field, around a sharp point out in front
>      of the ship, strong enough to deflect interstellar protons
>      as in c, above?

Ah, I notice you are assuming the incomplete neutralization is negatively
charged.
I think (after having done a very rough calculation) that this might be
possible, however I've little experience with charges of many positive
magnitudes Coulomb.

>   e. Could electrodes on the sides of the particle beam at the
>      exit end of the accelerator be used to steer the "jet"
>      (and hence the ship)?
>   f. Is there a possibility of entrainment of interstellar
>      protons by the particle beam to cause jet augmentation?

This depends on the exhaust velocity and the velocity of the ship. If the
exhaust velocity is smaller than the velocity of the ship (not unthinkable
when using fusion) then this is clearly not useful, since the protons need
to be decelerated. (In a few cases the protons could be fused first, the
gained energy might shift the border between useful and not useful a bit).

>   g. What might be the damage caused by impingement of the
>      very-high-powered particle beam on another object in space?

What objects did you have in mind?

Timothy