12.7 The Penning trap and the Paul trap 27112.7 The Penning trap and the Paul trap
For experiments with several ions the linear Paul trap has the advantage
that the ions lie like a string of beads along the trap axis, with little mi-
cromotion. However, most of the pioneering experiments on ion traps
used the electrode configuration shown in Fig. 12.7. The cylindrical
symmetry of these electrodes imposes boundary conditions on the elec-
trostatic potential, as in Section 12.3.3. Solutions of Laplace’s equation
that satisfy these conditions have the form
φ=φ 0 +a 2(
z^2 −x^2 +y^2
2)
. (12.23)
The surfaces of constant potential have a hyperbolic cross-section in
any radial plane, e.g.y= 0; in many experiments the electrodes match
the shape of these equipotentials so that the potential corresponds to
eqn 12.23 right out to the electrode surfaces, but any cylindrically-
End capEnd capz 0
Ring r 0
(a)(b) Fig. 12.7The electrode configuration
of (a) the Paul trap and (b) the Penning
trap, shown in cross-section. The lines
between the end caps and ring elec-
trode indicate the electric field lines;
the Paul trap has an oscillating elec-
tric field but the Penning trap has static
electric and magnetic fields. The elec-
trodes shown have a hyberbolic shape
(hyperbolae rotated about thez-axis),
but for a small cloud of ions con-
fined near to the centre any reason-
able shape with cylindrical symmetry
will do. Small ion traps with di-
mensions∼1 mm generally have sim-
ple electrodes with cylindrical or spher-
ical surfaces (cf. Fig. 12.3). Courtesy of
Michael Nasse.