Environmental Engineering Reference
In-Depth Information
ð
B
dl
¼ m
0
I
p
:
ð
4
:
42
Þ
1m.If
we imagine bending the solenoid to
t themajor radius
a
, then the
eld
B
will become
smaller on the outside and bigger on the inside and the relevant factor will be
approximately (
a
In this situation then, we estimate
B
p
(
b
)
¼m
0
I
p
/2
pb
¼
9.64 T, choosing
b
¼
b
)/
a
. The difference in the plasma-current-induced magnetic
elds
B
p
on the inside versus the outside is then
D
B
(2
b
/
a
)
B
p
(
b
). If a vertical
eld
B
z
(
b
/
a
)
B
p
(
b
) is added (to increase the
field on the outside), the current
I
p
will tend
to be stabilized, with sum vertical fields equal on the inside and the outside. The
required vertical field, in our rough analysis that neglects an outward force from the
plasma pressure, is then
¼
B
z
¼ m
0
I
p
=
2
pa ¼
1
:
56
T ð
for
a ¼
6
:
2
m; I
p
¼
48
:
2MA
Þ:
ð
4
:
43
Þ
The vector sum of this circling poloidal
field and the toroidal
field is then a helical
field, which is the
field that the ions and electrons in the plasma will follow,
depending on
I
p
.
This situation is sketched inFigure 4.10. On the left, themagnetic
eld lines shown
on a cut through the torus are distorted, stronger on the inside and weaker on the
outside, estimated as
B
above. The uniform vertical
eld
B
z
is shown added in the
sense to strengthen the
field on the outside of the torus. On the right, the resultant
field is nearly symmetric as would occur for a straight solenoid. The detailed force
balance has to include a component of the plasma pressure to the outside, which
arises due to the curvature.
The difference
D
B
is the origin of the tendency of the plasma to expand outward,
which is corrected by the poloidal coil system. The vertical
eld
B
z
, estimated in
Equation 4.43, should be applied to maintain the plasma centered in the physical
cross section of the torus. A more accurate analysis, which includes the plasma
pressure, gives
D
B
z
¼ðm
0
I
p
=
4
pa
Þ½
ln
ð
8
a
=
b
Þþ
p
plasma
=
p
magnetic
þd;
ð
4
:
43a
Þ
where the correction
d<
0 is given by Miyamoto [52]. Here pressure
10
20
10
3
10
19
p
plasma
¼
2
Nk
B
T
¼
2
12
:
93
1
:
6
¼
0
:
414 MPa
¼
4
:
1 bar
;
ð
4
:
44
Þ
and
p
magnetic
is of the form (
B
0
)
2
/2
0
. If we interpret
B
0
¼D
m
B
as de
ned above, then
B
)
2
/2
p
magnetic
3.84MPa. It appears that our rough estimate is within a factor
of two of the correct form (4.43a). A full analysis of the equilibrium is given in Section
6.3 of Miyamoto [52].
A variety of undesirable modes have been found to occur and to reduce power. The
underlying nanophysics of the fusion power generation is quite clear, but the
engineering design of a practical reactor to avoid the plasma instabilities is dif
cult.
Furthermore, there are material degradation problems. We mentioned above the
power loss from the plasma if highly charged nuclei such as tungsten are eroded into
¼
(
D
m
¼
0
