# starship-design: Relativistic Electric Thrusters

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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,

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,
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

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