New trends in physics teaching, v.4; The ... - unesdoc - Unesco

New Trends in Physics Teaching IV
magnetohydrodynamics is not the sort of thing that is considered fit for simple illustration. On
the other hand we were pleased to discover that it offers some nice applications of introductory
electromagnetism, on a semi-quantitative basis. It may be of interest to look at some examples.
In the usual physics course, students discuss the motion of a charged particle in a uniform
magnetic field. The discussion of plasma confinement requires them to consider a non-uniform
field.
We consider two possibilities: field intensity may either vary across the magnetic field lines,
or along them.
The first case occurs in such toroidal devices as Tokamaks, as simple reasoning based on the
circuital law shows at once (figure 4(a). Let us consider an electron moving in a plane normal
to the field lines (in figure 4(b) B lines cross the page at points indicated by dots). The field B
is normal to the paper, directed away from the reader, and it is stronger in the lower part of the
diagram. The electron path wil have two different radii of curvature, and it is apparent from the
diagram that this wil lead to an open trajectory, drifting towards the right. This is the main
reason why a simple toroidal field cannot provide plasma confinement. Another field must be
superposed on it.
TOROID‘AL FIELD: internal fieldlines
being shorter, must correspond to
higher B values.
t b3
.........
.........
I C3
___)
... vdrift
.................
.................
‘current
Figure 4.
The second case is typical of ‘mirror’ devices, (figure 4c) where the field lines converge at the
two ends of the device. Let us consider a charged particle arriving from the left, spiralling along
the magnetic field line. It can be considered as a current loop, travelling towards a region of
increasing magnetic field. As the number of the magnetic field lines crossing the loop increases,
an e.m.f. increases the current in the loop which generates a current that slows down the loop
and eventually reflects it back. This is a very well known fact (eddy currents in a moving conductor)
and every physics laboratory has devices to illustrate it.
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