Biology Reference
In-Depth Information
detect axial, magnetron, and cyclotron resonances. This technique
was also used for high precision measurement of the magnetic
moment of the electron. For their work on ion trapping Paul and
Dehmelt shared the 1989 Nobel Prize in Physics.
The transmission quadrupole mass filter consists of four parallel
metal rods. Opposing rods are connected electrically with a fixed
direct current (DC) and an alternating radio frequency (RF) volt-
age is applied between one pair of rods and the other. Superimposed
DC and RF potentials on the quadrupole rods can be set to let only
selected mass-to-charge ratio ions travel down the quadrupole. All
other ions do not have a stable trajectory through the quadrupole
mass analyzer and will collide with the quadrupole rods, never
reaching the detector. This permits selection of an ion with a par-
ticular
m
/
z
or allows scanning for a range of
m
/
z
values by con-
tinuously varying the applied voltage. Stable trajectories of ions
through the quadrupole are achieved by combinations of DC and
RF electric fields that define the stability diagram [
12
,
13
]. A deri-
vation of the working equations for a quadrupole mass analyzer is
beyond the scope of this discussion, but it is based upon a bounded
solution to the Mathieu functions originally derived in 1868 by the
French mathematician Émile Léonard Mathieu [
12
,
13
] (
http://
=− =
4
qU
mr
a
a
x
y
2
2
0
=− =
2
qV
mr
q
q
x
y
2
2
0
where
a
and
q
values are respectively related to the magnitude of
the applied DC potential (
U
) and the applied RF signal (
V
) that
correspond to stable trajectories in the quadrupole mass filter sta-
bility diagram (Fig.
1
), and
r
0
is the distance to the central (
z
) axis
of the quadrupole.
In a transmission quadrupole mass filter ions oscillate in the
x
-
y
plane with frequencies which depend on their
m
/
z
values. On
the other hand, the quadrupole ion trap, is the three dimensional
analogue of the linear quadrupole mass filter. In this device too,
ions are subjected to forces applied by an RF field but the forces
occur in all three (
x
,
y
,
z
), instead of just two dimensions, which
can result in ions being trapped in the field. In the 3D ion trap ions
experience restoring forces that drive them back toward the center
of the trap confining them in the small volume between a ring
electrode and two end-cap electrodes by appropriately oscillating
electric fields. Stability diagrams can be constructed from the inter-
dependence of the stable trajectories of the ions within the ion trap
and the field conditions plotted in Matthieu (
a
,
q
) space. The values
of
a
and
q
from the Matthieu equations depend on the dimensions
of the trap according to the following relationships (Fig.
1
):
