Environmental Engineering Reference
In-Depth Information
Since a Pascal is 1 N/m
2
, and one atmosphere (1 bar) is 101 kPa, the pressure is 98.4
atmospheres. So the magnetic vessel has to be very strong indeed.
The production of the
field can be understood from the formula for the
B
field in a
long solenoid,
B
¼m
0
nI
, where
n
is the number of turns of wire per meter and
I
is
current. Once established, the
field has no further energy cost because the current is
maintained in a superconducting magnet.
The result of D-T
-
T fusion as we have seen is an alpha particle of energy
1
/
2
4
m
p
V
2
. The velocity of the alpha is thus
V
K
¼
0.2
17.6MeV
¼
3.52MeV
¼
¼
(2
K
/4
m
p
)
1/2
10
7
m/s. The basic force
¼
1.3
F ¼ qV B ¼ ma
ð
:
Þ
4
27
with
m
is the mass. The acceleration
V
t
=
a
¼
R
ð
4
:
28
Þ
for a circular orbit of radius
R
, with
V
t
the component of the velocity transverse to the
B
field, gives us
1
=
2
R
¼
mV
t
=
qB
¼ð
2
mK
Þ
=
qB
ð
:
Þ
4
28a
for the radius
R
of the circular orbit, at kinetic energy
K
, around the
B
field lines. The
path of the charged particle is a spiral, whose orbital radius depends on the angle of
the velocity vector relative to the magnetic
eld
B
. Aparticle moving perpendicular to
the
field has the largest orbital radius. The frequency of the orbital motion is
v
L
¼
qB
=
m
;
ð
4
:
29
Þ
which is called the Larmor frequency. For the alpha particle
4
He
2
þ
released in theDT
reaction at 5 Tesla, we
find for the maximum radius,
10
27
10
7
10
19
R
¼ð
4
1
:
67
1
:
3
Þ=ð
2
1
:
6
5
Þ¼
0
:
054 m
:
ð
4
:
30
Þ
This means that the alpha particle, charge 2
e
and mass 4
m
p
, created in the plasma
will at most move 0.054m toward the wall of the toroidal container. Only those alpha
particles created within 5.4 cm of the wall, and moving speci
cally in the radial
direction, will have a chance of colliding with the wall. Since the emission directions
of the alphas are randomly distributed, an even smaller probability of wall collisions
will occur. This is the basis of the con
nement.
The Larmor frequency for the electrons is of interest in regard to heating the
plasma. It is
10
19
10
31
rad
v
L
¼
qB
=
m
¼
1
:
6
5
=
9
:
1
=
s
10
11
rad
¼
8
:
79
=
s
¼
140 GHz
;
ð
4
:
31
Þ
corresponding to radiation wavelength
l¼
c
/
f
¼
2.14mm. This corresponds to F- or
D-band microwave radiation.
