On Mar 18, 11:58 am, jdnic...@[EMAIL PROTECTED]
(James Nicoll) wrote:
> In article
<c5edc0c1-efe7-47ca-9abd-400864338...@[EMAIL PROTECTED]
>,
>
>
>
> <sigidu...@[EMAIL PROTECTED]
> wrote:
> >On Mar 18, 7:01 pm, jdnic...@[EMAIL PROTECTED]
(James Nicoll) wrote:
>
> >> might have a peak power output of 5^16 Watts (plus whatever
> >> for ineffeciencies).
>
> >> Could we spot this at 4.3 LY? Would we recognize it
> >> for what it was?
>
> >Cheap dumb answer: the power output of the Sun is 4 x 10^26 watts.
> >So, this is about 10^-10 as bright as the Sun.
>
> >One way to phrase the question: can we detect a one-ten billionth
> >change in luminosity?
>
> >As for absolute magnitude, Alpha Centauri is about as bright as the
> >Sun (it's a bit brighter actually, but this is BOTE). Its visual
> >magnitude is just about 0.0. So, your Centuarian torch****p would have
> >an absolute magnitude of about +25.
>
> >I'm thinking no, we wouldn't see it.
>
> OK, this probably has a flaw in it somewhere: The shuttle
> jet is what, 3000K? And ISP scales as the square root of temperature,
> so if the ISP in this case is 500,000 or about 1000 times greater
> than the shuttle's ISP, then the temperature should be somewhere
> around 3 billion degrees.
>
> If I run that through Wein's law, I get a peak at about
> 10^-12 m. That's gamma radiation, right?
The optimum temperature for igniting a D-T fuel mixture is 1.6E8 K,
which corresponds to 13.6 keV. This means the radiated
electromagnetic radiation will peak at 2.82 x 13.6 keV = 38.4 keV,
which is in the x-ray part of the spectrum.
However, fusioning gas in a reactor or pulse drive will be optically
thin for pretty much any kind of engineering you can imagine. This
means it will not be in thermal equilibrium with its electromagnetic
radiation field and thus will not emit any kind of blackbody
spectrum. The primary radiation will be x-ray bremsstrahlung, with
energies roughly of the same order as the temperature (so between
about 10 to 30 keV for D-T fusion). The bremsstrahlung power per unit
volume goes as the ion density times the electron density. Thus the
fusion exhaust plume will radiate the most energy while it is still
relatively dense. If it has not radiated most of its energy by the
time it has expanded significantly, it may well essentially stop
radiating, except from collisions between the particles in the plume
and the solar wind (or ISM, as the case may be). In addition, the
process of allowing the hot propellant to expand against a magnetic
nozzle will cool the exhaust, exchanging thermal energy for kinetic
energy of the bulk flow, which will also reduce the radiation
emitted. On the other hand, the rocket exhaust signature would not
now be near the peak of the solar emission spectrum - stars emit far
fewer x-rays than they do visible or IR or near UV photons. This will
greatly reduce the background for detection.
For other fusion fuels, the fuel temperature during fusion will more
likely be set by the requirement of maximizing fusion energy delivered
to the fuel compared to the bremsstrahlung losses from the fuel. For
D-D, this will put the fuel temperature at around 500 keV, or 5.8E9 K,
and for D-3He at 100 keV, or 1.2E9 K. Again, the radiated photons
will be x-rays, although a bit harder x-rays.
Other kinds of fusion reactions will always lose more energy to
bremsstrahlung than they gain due to fusion, so these kinds of fusion
reactions cannot take place in a fuel that has a well defined
temperature. You can get around this by using techniques that keep
the ions with a significantly larger energy than the electrons, such
as polywell fusors. In this case, the maximum exhaust velocity will
be given by the energy of the fast fusion products as they exit the
reaction volume - an average of 2.9 MeV for the alphas from p-11B
fusion (12E6 m/s), or a 3.6 MeV alpha particle (13E6 m/s) and 14.7 MeV
proton (53E6 m/s) for D-3He fusion. It is unclear what the actual
temperature of such an exhaust plume would be, if it exists at all,
since although the particles would have a high energy they might be
nearly non-interacting and in a highly non-thermal distribution, and
might have a rather small distribution of energies from each other.
It could the radiated energy is mostly diffuse bremsstrahlung gamma
rays from the plume interactions with the solar wind. Since stars put
out relatively few gamma rays, this gamma ray emission from the plume
might be fairly detectable.
Luke
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