Environmental Engineering Reference
In-Depth Information
Figure 4.4 Ground-state potential V(r) and lowest vibrational wavefunction sketched for DD
m
or
DT
ion. The large extent of the vibrational wavefunction suggests a chance for fusion, related to a
nonzero probability of nuclear spacing near zero [47].
m
function (Maxwell
-
Boltzmann) and the quantum mechanical tunneling function
through the Coulomb barrier are small for the overlap region, the convolution of the
two functions results in a peak (the Gamow peak) near the energy
E
o
, giving a
sufficient probability to allow a significant number of reactions to occur. The energy
of the Gamow peak is generally larger than
k
B
T
. In the compact device of Figure 4.1,
the energy is fixed by the accelerating potential, so the thermal distribution of
energies in Figure 4.4 is replaced by a single energy.
Returning to the results (Figure 4.3) from the compact fusion device, we can
nd
the experimental probability
P
f
per incoming D of fusion. The result in the
experiment, since the measured 4.4 nA corresponds to a deuteron
flux of
10
9
/(1.6
10
19
)
10
10
D/s, is
4.4
¼
2.75
P
f
¼
130
=ð
2
:
75
10
10
Þ¼
4
:
72
10
9
ð
4
:
3
Þ
at accelerator voltage 115 kV.
We can estimate the density of deuterons in the ErD
2
target as
n
D
¼
10
28
m
3
.
6
The mean free path for fusion then is
0.061m. However, the deuterons
rapidly get slowed down, and do not in fact penetrate more than a few atomic layers.
The energy loss d
E
/d
x
L¼
1/
n
D
s ¼
¼a
that comes from electron excitation as the energetic
incoming ion proceeds into the target is on the order of 200MeV/mm. We can
estimate the distance of penetration as
x
0.5
E
in
/
a
. Taking
E
in
¼
115 keV, we
nd
10
7
. If fusion occurs certainly for 0.61m, then in distance
x
the chance of
x
¼
2.8
fusion is
10
6
P
f
ð
x
Þ¼
x
=
0
:
061
¼
4
:
7
:
ð
4
:
3a
Þ
