Environmental Engineering Reference
In-Depth Information
One can see that the resonant absorbed power is less than half of what is absorbed
in a constant electric field. That the same order of magnitude is obtained for these
values is explained by the related character of the electron motion in these cases.
4.5.4
Motion of Charged Particles in a NonuniformMagnetic Field
We now analyze the behavior of a charged particle in a weakly nonuniform mag-
netic field. We consider a magnetic trap of axial symmetry with a higher magnetic
field strength near its ends, as shown in Figure 4.23. In this case a charged particle
may be reflected from the ends with a higher magnetic field and become locked in
the trap. A weak nonuniformity of the magnetic field is governed by the criterion
r
L
@
ln
H
z
@
r
L
@
ln
H
@
1,
1 .
(4.146)
z
A charged particle is moving along a helical trajectory near the axis. In addition,
we assume that the presence of charged particles does not influence the character
of the magnetic field because of their small density, and the spatial variation of the
magnetic field is subjected to the Maxwell equation div
H
D
0. Because of the axial
symmetry, div
H
D
0 can be written as
H
C
@
1
@
@
H
z
@
z
D
0 ,
(4.147)
where
H
D
0 at the axis. Near the axis, (4.146) gives
@
H
D
2
H
z
@
.
z
D
0
Figure 4.23
Magnetic lines of force in a simple magnetic trap with axial symmetry. Charged
particles may be locked in this trap.
