Environmental Engineering Reference
In-Depth Information
Figure 4.8 Sketch indicating radio frequency
(microwave) and neutral beam injection
heating, in addition to ohmic heating of gas
mixture to reach the plasma operating
temperature. Assuming the toroidal magnetic
field 5 T, the electron cyclotron resonance
frequency was found in the text to be 140 GHz
(http://www-fusion-magnetique.cea.fr/gb/
fusion/principes/principes05.htm).
through the hole of the donut and its magnetic
field is ramped to produce an EMF
round the loop.
4.3.1
Electrical Heating of the Plasma
I
2
R
is provided by Faradays law of
induction of heating current from changing magnetic
ux
d
/d
t
(BA)
Conventional electric plasma heating
P
¼
IR
.
Fusion occurs at temperatures near 150 million K. When fusion occurs, released
energy is collected from the energetic neutron emissions, in a surrounding
blanket and heat exchanger (not shown, see below), while the charged reaction
products are retained in the plasma by the magnetic con
nement, and further
heat the plasma.
We will model a simpli
ed Tokamak, assuming a pure deuteron
-
electron plasma
at density
n
¼e ¼
10
6
K (10 times higher than the suns core).
Consider a torus of volume 489.5m
3
(about 500) and this has major radius 6.2m
and minor radius 2m. Think of this as a cylinder of length 2
p
6.2m and cross-
sectional area
p
2
2
. Using the formula for the resistance
R
of a length
L
with cross
section
A
,
R
10
20
,
T
¼
¼
150
¼rL
/
A
, the resistance around this torus, containing the plasma as
described, is
R
¼r
2
p
6.2/
p
2
2
3.1
r
ohms.
We have described in Chapter 2 the power density from fusion in the sun, at some
length. Our approach here will be to scale the analysis from the sun to the situation of
the model Tokamak plasma. Scaling is an attractive approach with the assumption
that a successful analysis allows extrapolation to a similar situation with modi
¼
ed
parameters.
