Environmental Engineering Reference
In-Depth Information
ne
2
1
=
2
l
D
¼ð
k
B
Te
o
=
Þ
;
ð
3
:
71a
Þ
which is themaximumdistance over which two particles in the plasma experience the
Coulomb force. Beyond this distance, the small adjustments of positions of many
electrons screen away the direct Coulomb force. In this case, the ratio of the Debye
length to the classical turning point spacing
r
2
, which is called b in the plasma
literature, is important. Thus,
ð
2
l
D
ln
ðLÞ¼
ln
ð
2
l
D
=
b
Þ¼
d
r
=
r
:
ð
4
:
40
Þ
b
Taking
l
D
¼
84.5
m
and
r
2
¼
111.3 f, we
find ln(
L
)
¼
21.1, for the DT Tokamak
plasma at 150 million K.
This means that the plasma resistivity and resistance values are too small by a
factor 21.1, the electron mean free path reduced to 12.18 km, and the plasma
resistivity becomes 3.0
10
10
m. The voltage to produce the desired 10MW
heating rate has to be increased by a factor (21.1)
1/2
V
4.6. So the needed d
B
/d
t
in the
example above must be increased from 14.3mT/s to 65.8mT/s.
The design for ITER actually employs larger magnetic
field values (http://en.
wikipedia.org/wiki/ITER), 11.5 T for the toroidal
field, leading to a maximum stored
magnetic energy 41 GJ, a volume of 840m
3
and a central solenoid
field up to 13.5 T
(see Figure 4.10), which would limit the time of inductive heating at 10MW to 13.5 T/
65.8mT/s
¼
3.4min, assuming the central solenoid radius of 1m.
Beyond this, there are several technical issues that in practice are important. The
stability of the plasma has been assumed, which is a simpli
cation. The toroidal
magnetic
eld is approximately constant across the cross section, but more accurately
decreases from the inner to outer walls of the torus. The induced current in the torus
produces the usual circling magnetic field around the current, which is termed a
poloidal eld. In fact, an additional magnet, the poloidal magnet, produces a
vertical magnetic field needed to keep the plasma from expanding outward in radius.
In Figure 4.9, we see that the high-temperature part of the plasma occupies a cross
section less than the full vacuumvessel cross section,
pb
2
, but let us assume
b
0
¼
b
is
the radius of the current density when the ohmic heating is being applied. (The
plasma is actually diffuse and somewhat free tomove in themechanical cross section,
and could only roughly be described as a torus of major radius
a
0
andminor radius
b
0
.)
The resistance of the plasma
R
p
(4.36) when corrected for the small-angle scattering
factor ln(
L
)
¼
21.1 is raised from 0.204 n
V
to 4.30 n
V
. At the chosen heating power
10MW, the plasma current
I
p
must satisfy
I
p
R
p
¼
10 MW
;
ð
4
:
41
Þ
which gives
I
p
¼
48.2MA.
One aspect of the plasma equilibrium may be suggested by estimating the
magnetic
field produced by the plasma current
I
p
itself. If the current were
flowing
in a straight solenoid of radius
b
, the magnetic
field
B
p
(
b
) at its radius can be gotten
from Amperes law,
