Environmental Engineering Reference
In-Depth Information
out a radius
R
ion
¼
from the tip, and the area of the
ionizing hemisphere facing the target is 2
pR
ion
. The rate of ion formation is the
product of this area times
nv
/4, which is the rate, units 1/m
2
is at which gas molecules
cross unit area. Here,
n
is the density of deuteriummolecules, of thermal velocity
v
,
with another factor of 2 because each molecule releases two deuterons. The ion
current
I
i
is then
100
[0.8
10
3
/25]
1/2
¼
0.565
m
2
p R
ion
ð
I
i
¼
nv
=
4
Þ
2
e
:
ð
4
:
1
Þ
The ambient gas D
2
is dilute, such that themean free path
l
exceeds the dimension
of the chamber, so that theD
þ
ions fall down the potential gradient without collisions
and impact the (deuterated) target at 80 keVenergy. This energy is enough to drive the
nuclear fusion reaction
D
þ
þ
D
þ
!
3
He
2
þ
ð
820 keV
Þþ
n
ð
2
:
45 MeV
Þ;
(where D is the deuteron, the nucleus of deuterium,
2
H).
In the compact device shown in Figure 4.1 [45], no external high voltages are
needed. In this case, heating the LiTaO
3
crystal from 240 to 265 K, using a 2Wheater,
is stated to increase the surface charge density
s
by 0.0037 Cm
2
. This should
correspond to a surface electric
10
3
/(2
10
12
)
eld
E
¼s
/2
e
o
¼
3.7
8.85
¼
0.209 V/nm. The authors state that in the device geometry (see Figure 4.1) this
gives a potential of 100 kV. The observations, summarized in Figure 4.2, con
rm
D
-
D fusion, based on the observation of neutrons.
In Figure 4.2a, we see that a linear increase in temperature with time from240 K to
280 K leads to crystal potential rising fromzero to about 80 kVat
t
230 s. Figure 4.2b
shows onset of the X-rays that come as electrons released from the ionization events
fall onto the positively charged copper plate encasing the tantalate pyroelectric crystal.
The X-ray energies, observed up to about 100 keV, can come only from a tip potential
of the same order, which produces a local electric field sufficient to strip electrons
fromthe deuteriumgas. Figure 4.2c records the ionic current, presumably the sumof
electron current into the copper and positive ion current into the right hand electrode,
adding to 4 nA maximum. This number can be checked by elementary considera-
tions involving the radius and surface area around the tip leading to certain
ionization, the density of the gas at the stated pressure, and the number of deuterium
molecules in random gas diffusion that would cross that surface per unit time,
indicated in Equation 4.1. Finally, Figure 4.2d shows the measured number of
neutrons per second. The satisfactory coincidence of the peaking of the several
indicators at about 230 s makes it clear that fusion has occurred.
Let us look at these results from the simpli
ed theoretical model developed in
Chapter 2, leading to Equation 2.21. The tunneling transmission probability of the D
through the Coulomb barrier (see Figure 2.3) at 40 keV is now estimated as
¼
T
¼
exp
ð
2
cÞ;
ð
2
:
21
Þ
