AAWSAP DIRD, Advanced Nuclear Propulsion for Manned Deep Space Missions, March 2010

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From the burning plasma behind the detonation front, energy flows into all spatial
directions. Part is by bremsstrahlung and part by electronic heat conduction. Roughly
half of the energy flows into the liner, one-quarter into the still unburned fuel ahead of
the wave, and one-quarter into the opposite direction. The bremsstrahlung emission
rate is given by
(28)
For T = 109 K, one has &, ;::: 3.2 x 10-23 n2 [erg/cm 3s]. The flux of the bremsstrahlung
that goes into the liner is &,r/2, where r is the radius of the deuterium rod just behind
the detonation front. About one-half of this radiation runs ahead of the detonation
front, where it precompresses the deuterium. Its intensity is:
E r
23
'
- '-::::10- n·r [erg/cm 2s]
(29)
4
with nr;::: 3x 1024cm·2 (corresponding pr;::: 10 g/cm 2), one has
Er
- '-
:a:: 30n[erg/cm 2s]
(30)
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We are aiming at a density where the neutrons are absorbed in the burning plasma
cylinder of radius r. If the neutron-deuteron collision cross section is a, then the
neutron path length An must be smaller than r:
1
(31)
l,,=-<;;,r
nc,
or
1
nr ~ ­
c,
(32)
One typically has a;::: 10·24 cm 2, hence
nr ~ 1024 cm 2
(33)
If r = 0.01 cm, then n ~ 1026 cm·3 = 5 x 103 no, where no = 5 x 1022 cm·3, the particle
number density of liquid deuterium. With n=1026 cm·3, one finds that
s,.r/4 :a:: 3x l027 erg/cm 2s. The flux on a deuterium tube of radius rand length z, where
for the burn zoner ;::: z, one obtains onto its surface (s,. /4)2nrz :a:: 1024 erg/s = 1017 watts
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