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Transpector XPR 3+ Operating Manual
closest rod surface is known as the quadrupole radius, with the symbol r
0
. Ideally,
the rod should have a hyperbolic shape (towards the center of the assembly) rather
than round. The Transpector XPR 3+ quadrupole is machined to have the
hyperbolic shape and thus has an optimum electric field for mass filtering ions.
Opposite rods are electrically connected together. The ions are directed into the
space between the poles, in a direction nominally parallel to the length of the rods.
There the ions are separated according to their mass-to-charge ratios by the lateral
forces resulting from the potentials applied to the poles.
The applied potentials consist of an RF component and a DC component. The RF
potential on one set of rods is out of phase by 180° with respect to the RF potential
on the other set of rods, but of the same amplitude. For one pair of rods, the “X”
pair, the DC potential is positive. For the other, the “Y” pair, the DC potential is of
the same magnitude but negative. The DC and RF potentials are referenced to a
“center voltage” (sometimes called the “pole zero”). The following equations
summarize the potentials applied to the rods:
[1]
[2]
where:
V
is the RF amplitude,
f
is the RF frequency,
t
is time,
U
is the DC potential,
PZ
is the pole zero.
The RF component removes the low-mass ions from the beam. Ions of sufficiently
low mass have their motions remain in phase with that of the applied RF. These
ions will gain energy from the field and oscillate with increasingly large amplitudes.
Eventually, as they travel along the length of the rods, they will strike one of the
rods and be neutralized. On the other hand, high-mass ions are focused by the RF
component to an area close to the quadrupole’s long axis, the “Z” axis.
The DC component is superimposed on the RF to remove high-mass ions from the
beam. The DC field deflects the high-mass ions toward the negative poles,
opposing the focusing effects of the RF field. Eventually, these high-mass ions
strike the negative rods and are neutralized. By a suitable choice of DC-to-RF ratio,
the mass filter can be made to discriminate against both high and low-mass ions to
the desired degree.
The kinetic energy directed along the Z axis of the mass filter (usually called the ion
energy) is primarily dependent on the difference between the potential at which the
ions were formed (approximately the anode voltage), and the pole zero. The ion
energy is usually only slightly modified by the electric field (the “fringing” field)
X
V
2
ft
cos
U PZ
+
+
=
Y
V
2
ft
+
cos
U
–
PZ
+
=
