3 - 7
Transpector MPS Operating Manual
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, and
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)
between the source exit aperture and the quadrupole. Imbalances in the amplitude
of the two phases of RF applied to the rod pairs, and of the DC voltages also
applied, result in a further modification of the ion energy.
The mass of the ions passed by the filter is determined by the RF amplitude, the
RF frequency, and the quadrupole radius, as shown by the following equation:
[3]
where
V
is the peak-to-peak RF amplitude in Volts,
M
the mass of the ion in
atomic mass units (AMU) per electron charge,
f
the RF frequency in
megahertz, and
r
0
the quadrupole radius in centimeters.
For example, a 200 AMU singly charged ion would pass through a quadrupole with
nominal 1/4 in. diameter rods (an
r
0
of 0.277 cm), operating at 1.78 MHz, at a
peak-to-peak RF amplitude of approximately 700 Volts.
X
V
2
ft
cos
U PZ
+
+
=
Y
V
–
2
ft
+
cos
U
–
PZ
+
=
V
14.438Mf
2
r
0
2
=
