starship-design: Relativistic Electric Thrusters

[wharton@physics.ucla.edu (Ken Wharton)]

Greetings to all!

IÕm new here... NameÕs Ken Wharton, IÕm a 5th year physics 
graduate student at UCLA, currently living up in Northern 
California and doing research at Lawrence Livermore National 
Labs.  IÕm currently working on experiments with a short-
pulse 100 TeraWatt laser, looking into a novel Laser Fusion 
concept.  (ThatÕll probably fit in well to at least some of 
the discussions)
	
For now, though, the questions on relativistic thrusters by 
Rex Finke are more related to the work I did at UCLA on 
laser-plasma accelerators.  The big advantage they have over 
conventional accelerators is that theyÕre much smaller, and 
therefore would be ideal on a spaceship.  Conventional 
accelerators are limited by how strong an electric field they 
can produce; too strong and it starts to rip the apparatus 
apart.  A plasma, on the other hand, is already ripped apart; 
it can handle much, much stronger E-fields.  A conventional 
accelerator is limited to roughly 10 MeV/meter; the beatwave 
plasma accelerator at UCLA has already achieved 3 GeV/m (over 
1cm), and other laser-plasma accelerators at Rutherford, UK 
and elsewhere have pushed that to 60 GeV/m (over 1mm); the 
ultimate limit it given only by the density of the plasma 
where you can create the coherent E-field, and the length of 
the interaction region.  So, keeping plasma accelerators in 
mind IÕll make a first pass at RexÕs questions...

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.  Assuming that the final 
energy of the particles will be large compared to the rest 
mass, the above equation simplifies to P = E/c; the rest mass 
becomes irrelevant to the momentum (but still important to 
the ÔlspÕ)

The Big Problem, of course, is keeping the ship neutral.  
Assuming we donÕt have positrons handy (if we did, the engine 
design would be much easier!) we need one proton per 
electron, which will severely hurt the ÔlspÕ.

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!  
Of course this also depends on what youÕre using to drive the 
plasma wave, (lasers, I would guess) so IÕll get back to this 
later.

Fortunately, you might only need one plasma accelerator to 
accelerate both electrons and protons.  The actual 
accelerating mechanism is an electron plasma wave that 
travels through the plasma with a phase velocity close to the 
speed of light.  Half of the wave will accelerate electrons 
and the other half will accelerate protons; an electron wonÕt 
slip to the ÔwrongÕ half of the wave because everythingÕs 
moving at near the speed of light; the correct E-field 
(ideally) follows the electron or proton as it is 
accelerated.

I say ÔideallyÕ here, because while everything is moving at 
nearly the speed of light, small differences in velocities 
will cause the particles to slip back to the wrong phase of 
the accelerating wave. It might be possible to change the 
phase velocity of the wave as a function of space, allowing 
it to Ôkeep upÕ with the electrons and protons better, but 
this would be a big problem if we were trying to accelerate 
both at once; the electrons would speed up much faster than 
the protons, so the wave would eventually lose resonance with 
one of the species.  Perhaps two accelerators would be the 
way to go after all.  The you have huge magnetic fields, 
leading to the next question... 

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.  If youÕre 
trying to shoot out fuel ahead of you, youÕre leaving 
yourself wide open to near-lightspeed chunks of matter coming 
in where the fuel comes out!  The only possible way around 
this that I can think of is to shoot out the fuel into a wide 
cone angle, leaving the back of the ship protected by major 
shielding. This decreases the thrust, perhaps significantly, 
but maybe it could be made up for by applying large external 
magnetic fields to steer the angled beams of 
electrons/protons into a more normal trajectory.  This, of 
course, assumes you have near-monoenergetic beams, which 
would be another tough constraint.  Plus you might direct 
interstellar particles back into the accelerators!  All in 
all, probably not a good solution...
	
As for the other points:

a) IÕll 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.  
b) True; the protons (or electrons!) could just be dumped at 
zero velocity, but given how tight our fuel will be I imagine 
weÕd want to try to accelerate both species.
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!
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...
e)  The only issue I can see with steering the ship by 
deflecting the electron beam is this:  ALL of the force has 
to be taken up by the electrodes before itÕs transferred to 
the rest of the ship.  YouÕd need some pretty strong 
electrodes to make any difference.  I donÕt think steering is 
going to be a big issue.
f)  Using the interstellar protons to augment the beam is an 
interesting idea, at least for the acceleration phase.  Beams 
of particles can drive plasma waves, so if the protons were 
directed into the plasma accelerator at the front of the 
ship, and channeled out the back, it might save significantly 
on energy and fuel constraints.  This of course would fail 
miserably for the decelerating portion, though...
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.

Some particular issues w/ plasma accelerators:

Efficiency???  This point could be the killer.  For a given 
accelerating structure, it is possible to Ôfill the bucketÕ 
with particles, preventing any additional particles from 
being accelerated.  This is a problem with all accelerators, 
but I think itÕs worse in a plasma.  Plus, you need energy to 
create and maintain the plasma in the first place, and that 
will hurt the efficiency as well.  I like the idea of using 
interstellar matter to help out in the acceleration phase, as 
I mentioned above.

How to best drive the plasma wave?  The most successful 
experiments to date have all been done with lasers, although 
particle beams may also drive a plasma wave.  The good thing 
about relying on lasers is that, like computers, they have 
improved exponentially in the past and may very well continue 
to do so in the future.  Very short-pulse, high-power lasers 
might be ideal because they can drive strong waves with 
relatively little energy.  The waves damp away pretty 
quickly, though, so youÕd need a high rep-rate, something 
that current high-power lasers donÕt have.

How long an accelerator is feasible?  So far the longest 
coherent accelerating structure in a plasma is 1 cm (at 
UCLA); a 6cm version should be working in 2 years. The limit 
is the focal distance of the laser we use to drive the plasma 
wave.  Obviously, we want meters, not centimeters, so how 
will this work?  One promising fact is that high power lasers 
self-focus and self-channel in plasmas; it is not 
inconceivable that a high-enough power laser will maintain a 
narrow focus over large distances.  Ideally, of course, the 
laser will be powerful enough that we wonÕt NEED to focus it; 
that way the size of the accelerator will be bigger, and we 
could get more thrust.  That will require many orders of 
magnitude improvement over todayÕs lasers, though.  Here at 
LLNL, the worldÕs most powerful laser, the PetaWatt, is about 
to go into operation.  It has 600 Joules of energy in 450 
femtoseconds, and is the result of pushing current technology 
as far as it will go.  Any additional improvement is hard to 
imagine at this time, but there are enough people working on 
the problem that ExoWatt lasers probably arenÕt more than a 
generation away...

Enough rambling for now.  More later.

Ken