Environmental Engineering Reference
In-Depth Information
ions (deuterons plus tritons) as electrons, and each has average energy 12.93 keV.
Thus,
U
¼
2
ð
N
D
þ
N
T
Þ
k
B
T
ð
4
:
26
Þ
10
20
10
3
10
19
J
57.5 kWh. The mar-
ket cost of this energy, at 14c/kWh, the price of electricity in New York City, is $8.05.
This is small, and the key is the assumption that only the gas is heated, the
containment (to be described) allows the walls and the whole containment vessel
to remain cool.
We might next ask how long can the reactor run at 634MWbefore running low on
fuel? Arbitrarily, let us
nd
T
1/2
, when half the energy of the fusion reactions is
consumed, assuming the D-T
-
T reaction generating 634MW:
¼
2
500
12.93
1.6
¼
206.8MJ
¼
10
20
10
6
10
19
J
10
10
J
PT
1
=
2
¼
:
:
:
¼
:
;
0
5
500
17
6
1
6
7
04
so
10
10
J/634
10
6
T
1/2
111 s, not quite 2min.
So the reactor will de
nitely need a continuous feed of DTmixture. (In the planned
ITER device, the
T
(triton) generation is accomplished by feeding Li into system,
which generates
T
(tritium) by absorption of neutrons.)
We should confront an issue of how the fusion power is harvested. While the
reaction of DT produces 17.6MeV, this energy is shared between a neutron and an
alpha particle (
(first line in Table 4.1). In the frame of the fusion event, themomentum
of the particles will add to zero, so 4
V
¼
7.04
¼
v
, with
V
and
v
, respectively, the speeds of the
alpha (mass 4) and the neutron (mass 1). The kinetic energy of the neutron is
1
/
2
mv
2
and that of the alpha is
1
/
2
(4
m
)(
v
/4)
2
. On this basis, the neutron gets 0.8 of the kinetic
energy, which it carries out of the reaction zone into the containment structure. We
will mention next how the alpha particle is trapped into circling the magnetic
eld
lines, and thus returns its heat energy back into the plasma. The
4
He is a waste
product, termed ash in the literature of Tokamaks. The neutrons are equally
emitted in all spherical directions, and their motion is not at all impeded by the
magnetic
field.
Another aspect to be confronted is that we assume a uniform temperature
distribution in the full torus. The major and minor radii
a
,
b
and volume should
realistically be interpreted as the dimensions of the hot part of the plasma. Indeed, it
is essential to establish a large radial temperature gradient in the cross section of the
torus to keep the walls cool, except for the 14.1MeV fusion neutrons that carry the
fusion energy out of the reactor.
Another energy cost is the toroidal magnetic field; we assume it is 5 Tesla
uniformly in the cross section
pb
2
. The energy density of the 5 Tmagnetic
eld
B
,
¼
B
2
u
B
¼
=
2
m
0
ð
4
:
26a
Þ
10
6
J/m
3
, where
10
7
N/A
2
. Therefore, the energy of the whole
¼
9.94
m
0
¼
4
p
uniform magnetic
field is
U
B
¼
4.97GJ, with cost at $0.14/kWh of $193.42. The
pressure of themagnetic
eld on thewalls is
u
B
10
6
J/m
3
10
6
N/m
2
.
¼
9.94
¼
9.94
