A
magnetic lens consists of a coil of copper wires inside the
iron pole pieces. A current through the coils creates a magnetic
field
(symbolized by red lines) in the bore of the pole pieces. The
rotationally symmetric magnetic field is inhomogeneous in
such a way that it is weak in the center of the gap and becomes
stronger
close to the bore. Electrons close to the center are less strongly
deflected than those passing the lens far from the axis. The
overall effect is that a beam of parallel electrons is focused
into a spot (so-called cross-over).
In
a magnetic field, an electron experiences the Lorentz force
F:
F = -e (E + v x B)
|F| = evBsin(v,B)
E: strength of electric field
B: strength of magnetic field
e/v: charge/velocity of electrons
The
focusing effect of a magnetic lens therefore increases with
the magnetic field B, which can be controlled
via the current
flowing through the coils. As it follows from the vector
product, the resulting force F is
perpendicular to v and to
B. This leads to a helical trajectory
of the
electrons
and
to
the
magnetic
rotation (image
is rotated in respect of the object). |