starship-design: Re: Relativistic Electric Thrusters

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

Timothy replies to Ken Wharton's 1/27 letter:

>I'm currently working on experiments with a short-
>pulse 100 TeraWatt laser, looking into a novel Laser Fusion 
>concept.

Sounds interesting, we need (continuous) power outputs somewhere around 1E17
Watt (give or take an order of magnitude).

>1) and 2)  In deciding the best exhaust particle, the only 
>equation you need is E^2 = P^2 c^2 + (m c^2)^2:  And 
>everything points to low mass particles being the best.  Not 
>only do they give a higher Momentum/Energy ratio, but a 
>higher Momentum/Mass ratio as well.

Sorry if I have to be picky, but the momentum/energy ratio does not depend
on mass, but only on velocity.
Therefore I assume that you mean that since particles with high charge/mass
ratios (like electrons) will be easier to accelerate and thus achieve higher
final velocities and are thus better.
However high velocities do NOT mean a higher momentum/energy ratio:

momentum: p=gamma m v
Energy  : E=m c^2 (gamma-1)

p/E=1/c {v/(c-Sqrt[c^2-v^2])}

For v->c it goes to 1, for v->0 it goes to infinity, so higher velocities
have a LOWERr momentum/energy ratio.

>3) In terms of size, it really depends on the plasma 
>accelerator.  Perhaps we can assume we might get 100 GeV in 
>acceleration per meter of accelerator.  Would there be an 
>optimal length?  I would guess no:  you want the device as 
>long as possible; the entire length of the ship, I suppose.  

>Doubling the length will not double the mass of your entire 
>ship, but it will double the amount of thrust you can get!  

Previous calculations have shown that optimal exhaust velocity depends
(among other things) on the final velocity of the starship. Just creating
the highest exhaust velocity is therefore not the main goal.
(Several of these calculations are available at
 http://www1.tip.nl/users/t596675/sd/sd.html)

>4)  Disadvantages to the moving charges.  
>
>In my mind, the #1 problem to any spaceship propulsion scheme 
>was not mentioned here.  There are bound to be some stray 
>macroscopic pieces of matter in interstellar space.  This is 
>less of a problem for the accelerating half of the journey, 
>assuming one has adequate shielding in front.  But what about 
>the decelerating portion???  All of a sudden you have the 
>engine, the most critical portion of the ship, exposed to 
>whatever might be speeding in your direction....

Good point, I can't remember that we ever wrote about this before in this
mailing list.
However it is likely that the exhaust particles will either burn or push
away everything that is in the path of the ship. It may be a very effective
shield.

>As for the other points:
>
>a) I'll assume we wonÕt want to charge up the ship much.  Of 
>the things that could be adversely affected by this, 
>computers would probably be at the top of the list.  If we 
>ground all the computers, that leaves us with dangerous 
>potential differences.

Or worse, assuming the charge isn't static, the enormous currents would melt
away the ship's hull.
  
>b) True; the protons (or electrons!) could just be dumped at 
>zero velocity, but given how tight our fuel will be I imagine 
>we'd want to try to accelerate both species.

Yes, unless the added complexity of the engine (and weight of the engine)
make the whole thing less attractive

>c) I think the magnetic field produced by a beam might help 
>deflect incoming charged particles at low velocities, but 
>eventually the incoming protons/electrons would be energetic 
>enough to blast right on through.  Also, accelerating charges 
>produces radiation; this might actually require more 
>shielding, as IÕd think the relativistic particles would 
>produce x-rays as theyÕre steered around the ship!

True, I think the best way would be to push the particles asside by use of
EM-radiation (laser).
And what about the accelerating of charge in the engine of the ship, won't
that generate even more dangerous radiation?

>d)  I donÕt think youÕd want to charge up the whole ship just 
>to deflect protons; if this might work itÕd be easier to just 
>charge up the nose cone.  Plus, of course, youÕd attract 
>electrons.  Still, I like the idea; protons are obviously 
>much worse...

I think Rex meant to charge the cone (actually even better a tip far in
front of the cone).

>f)  Using the interstellar protons to augment the beam is an 
>interesting idea, at least for the acceleration phase.

Actually I would think it is of more use during the deceleration phase. (see
my relpy to Rex)

>g)  We donÕt have to worry about the particle beam damaging 
>anything far away; the beam will spread out in space as it 
>travels.  As for whether it would blast apart an incoming 
>meteor; that would be an important question.

It certainly could do that, if the beam would still be concentrated enough.
The energy transfer would ionize everything inside the beam.

>Some particular issues w/ plasma accelerators:
>
>Efficiency???  This point could be the killer.

Keep in mind that bad efficiencies produce a lot of heat when you are
talking about 1E17 Watt.

>Enough rambling for now.  More later.

Keep rambling, it sounds very interesting,

Tim