Vacuum Technology Know How - Triumf

Formula 4-2
Stability parameter a
Formula 4-3
Stability parameter q
Ideal quadrupole fields require rods that have a hyperbolic profile. In actual practice, however,
round rods are used, with the rod radius being equal to 1.144 times the field radius r . 0
An electrical quadrupole field is formed between the rods. Ions of varying mass are shot
axially into the rod system at approximately equal energy and move through the rod system
at uniform velocity. The applied quadrupole field deflects the ions in the X and Y directions,
causing them to describe helical trajectories through the mass filter. To solve the movement
equations, the dimensionless variables
and
www.pfeiffer-vacuum.net
Ions created through
electron bombardment
in the ion source
Ion Optics
Cathode
Formation
Area
Ions separated by the m / e
ratio in the rod system
Figure 4.4: Operating principle of a quadrupole mass spectrometer
a =
q =
8 . e . U
m . 2 r . � 0
2
4 . e . V
m . 2
r0 . � 2
are introduced to obtain Mathieu‘s differential equations. Their solutions yield the stable area
with oscillation amplitudes of less than r beneath the triangle formed by the two solubility
0
curves in Figure 4.5. The values a = 0.23699 and q = 0.706 apply for the apex of the triangle.
p p
All solutions outside result in increasing oscillation amplitudes and thus in neutralization of
the ions on the rods of the quadrupole filter.
Dividing the two equations by one another yields:
a U
= 2 .
q V
This is the pitch of the so-called load line of the mass filter.
Ions detected in the
ion detector
Page 89
Vacuum
Technology