79 300781172_002_C0 - 01/2019 - © Leybold
Appendix
the collector, but the quadrupole spectrometer uses an electric field to feed them to
the filter section with an energy of about 10 eV.
13.2.2 Filter section (Q-pole)
In the filter section, four columnar electrodes are arranged parallel to each other.
This is why the filter is called quadrupole and is referred to as mass filter.
As shown in on page 80, these opposing electrodes are connected with each other
and d.c. and a.c. voltages of (U + Vcoswt) overlapped are applied with reverse
polarity respectively. Here, the equation of motion of the ions incident on the filter
section are expressed by equation (1) with respect to the x, y and z axis shown in
on page 80.
As shown by equation (1), ions incident on the filter section are subjected to periodic
force in the x-axis direction and y-axis direction and oscillate.
Substituting equation (1) as shown in equation (2), we obtain Maschew's differential
equation, which is equation (3).
0
0)cos(2
0)cos(2
2
2
2
0
2
2
2
0
2
2
dt
zd
m
r
y
tVUe
dt
yd
m
r
x
tVUe
dt
xd
m
0)2cos2(
0)2cos2(
4
8eU
2
2
2
2
2
2
2
0
2
2
0
yqa
d
yd
xqa
d
xd
mr
eV
q
mr
a
t