Re: Thermal rocket, magnetic nozzle, heat management

On Jan 6, 4:47 pm, IsaacKuo <mech...@xxxxxxxxx> wrote:

Since your magnetic field strength is limited to a particular
Tesla value, the way to get more energy is to make the field
bigger.  

The tension on the current carrying loops that generate the field due
to the self interaction of the current with the field it generates is
proportional to the loop circumference times the current times the
field. Idealizing the magnetic nozzle as a solenoid, the field
strength is independent of the loop radius, and is linearly
proportional to the current. Thus, the tension on the loop increases
as the field gets bigger until at a maximum size for a given field,
the structure holding the loop together can no longer withstand the
tension and the loop breaks. This indicates that for a desired field,
the maximum radius is proportional to 1/B^2, where B is the magnetic
field magnitude. Thus, you can't always just make the field bigger.
At the very least, you will need to add a bunch of extra support to
make the loops stronger.

There are other constraints, such as the critical magnetic field at
which superconductors stop carrying a supercurrent, which is
independent of the size of the nozzle, if you want to use
superconductors - this limit tends to be in the realm of 10 Tesla for
modern superconductors, which is a couple orders of magnitude higher
than the back of the envelope estimate of the required field for a 10
TW fusion torch drive in my previous estimate. I suspect that the
tension will be the limiting factor on the field strength in this
application.

Other than that, the rest of your analysis looks good.

2. The particles may not come in contact with the frame, but they
should still radiate heat. This could turn out to be a problem for the
power regions I'm looking at (if possible, Terawatt range, because I
like brawny ships).
Ideally, the plasma would not radiate any heat at all.  All the energy
would then go into the exhaust and be usable for propulsion.

Any ideas on how to convince the exhaust plasma to do this?

You could try a non-equilibrium fusor, like a polywell. Since the
electrons are kept cold, you limit the bremsstrahlung. With the
aneutronic proton-boron fusion reaction, you nearly get rid of the
neutron radiation. I have serious doubts that this could handle TW
power levels, since you need significant equipment around the reaction
volume which will absorb any radiation that does come off, but GW
power levels may be achievable.

As mentioned, if you can find a baryon decay catalyst and an isotope
that greatly limits the amount of pion and neutron radiation (Ar 36,
perhaps? It is heavy to limit the number of pions escaping, and has
equal numbers of protons and neutrons to limit the neutronicity), then
you can reduce the density of the plasma to reduce the bremsstrahlung
intensity.

I have been thinking about how to shield the magnetic loops from the
radiation produced by D-3He fusion. A thin *** of tungsten, perhaps
2 mm thick, is pointed to within 0.3 degrees of the fusion x-ray
source. This acts as a grazing incidence mirror to shadow the
supercurrent-carrying wire, coolant, and neutron shields. At 0.3
degrees, the *** should reflect at least 99% of the incident x-
rays. 0.3 degrees is a 200:1 slope, so if we want to shield a 2 cm
wide pipe, this either requires a 4 meter long ***, or two 2 meter
long sheets formed into a very sharp wedge shape. The single 4 meter
long *** has the advantage of being able to radiate from both sides,
so I will consider that configuration.

At 200:1 slope, a 2 mm thick *** will present 40 cm of thickness to
any incoming neutrons. Neutrons are primarily generated by the D-D
fusion side reaction, which have an energy of 2.5 MeV. At 2.5 MeV,
the elastic mean free path of a neutron in tungsten is 2.6 cm, which
gives us a bit over 15 interaction lengths. Neutrons interacting with
a tungsten nucleus will scatter, depositing on average about 1% of
their energy in the kinetic energy of the tungsten nucleus and the
remaining 99% stays with the scattered neutron. Since the *** is so
thin, scattered neutrons will simply scatter out of the tungsten and
will have very little chance of interacting a second time. Thus,
nearly all of the neutrons will be scattered away with 1% of the
energy deposited in the tungsten.

Tungsten melts at 3695 K, but sublimation rates will likely be too
high above 3000 K. At 3000 K, the tungsten will be radiating 4.6 MW/
m^2 as light and other forms of electromagnetic energy (IR, mostly,
although this is about the temperature of the tungsten filament of an
incandescent bulb, so it will be as bright per unit area). A 1 meter
section along the circumference of the loop will have a radiating area
of 4 m^2 from the tungsten ***. Thus, the *** can withstand
absorbing up to 18 MW per meter of circumference. With 2 cm cross
section exposed to the radiation source, and absorbing only 1% of the
radiation, the *** could withstand a total intensity of 90 GW/m^2.

D-3He fusion throws off about 25% of its energy as radiation (20% x-
rays, 5% neutrons) at its optimal temperature. A 10 TW D-3He torch
will thus put out 2.5 TW of radiation. Solving for the minimum
radius, I get that the tungsten *** could extend an astonishing 1.5
meters from the fusion "torch flame". Of course, the field coils must
be at least 4 meters further away, and if you use multiple field
coils, you will want large spacings between them to limit the EM
radiation emitted or neutron radiation scattered onto adjacent
tungsten shields.

Behind the tungsten shield, place a ring of graphite several tens of
cm thick to intercept and scatter away those neutrons that scatter off
the tungsten shield in the direction of the field coil (graphite
absorbs about 14% of the neutron energy it scatters, assuming each
neutron only scatters once and escapes - since the mean free path of
2.5 MeV neutrons in graphite is about 6 cm, this should hold as long
as the graphite is significantly less than 6 cm thick. Graphite can
be heated to about 4000 K before sublimating - the only material
better than tungsten - so we should be safe). A polished mirror
between the graphite neutron shield and the field coil helps keep
stuff in the shield's shadow cool from the thermal radiation. A ring
of berylium doped PET plastic then thermalizes and absorbs any
neutrons that get past the graphite. The PET may need to be actively
cooled with water coolant (water will also help to thermalize
neutrons). Next come the pipes of cryogenic coolant to keep your
superconductor superconducting, with the superconducting wire inside.
The wire is backed by some material with a very high tensile strength
(one of those novel nanostructured forms of carbon, perhaps?) to
provide structural support for the wire due to the field/current self
interaction.

Similar sheets can shield any structural elements needed to hold the
magnetic coils in place and transmit thrust to the spacecraft.
Mirrors for reflecting the laser pulses to initiate fusion would need
to be located some distance away from the nozzle and fusion flame,
since they could not be protected by the tungsten sheets while still
allowing laser light to reach the fusion fuel pellet.

Luke
.

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