IRadius optimization
The quadrupole design in SIMION® is done with a 0.25mm grid unit. That value implies a 0.45mm radius r0 between quadrupole rods. In order to optimize the r
0
parameter for better ion selectivity in the quadrupole, we made a comparison between several values. The figure 1 present three values for the radius r
0
: 0.44, 0.445 and 0.45mm. For this study, we chose positively charged ions with a 1000 atomic mass unit mass. In order to verify the selectivity of the simulated quadrupole, we changed the m/z ratio to check the number of ions flying through the quadrupole. The measure was done at the exit end of the quadrupole. The dashed blue curve present the selectivity for a radius r
0
=0.45 mm, the solid red curve present r
0
=0.445mm and the dotted green curve the r
0
=0.44mm radius.
Figure 1 : comparison between 3 radii for 1000 amu ions selectivity in the quadrupole in SIMION®
The results presented on the fig 1 show that the ion selectivity is optimized for a r
0
radius of
0.445mm. In fact the half height width is smallest with that optimized value.

IIEnergy measurement in SIMION: kinetic energy in a XY plane and translational kinetic energy at the exit end of Q3 quadrupole.
SIMION® provides a measurement of the kinetic energy at the end of the quadrupole in the
XY plane (fig 2 dotted blue curve). That measurement shows a high energy tail up to 1500eV.
The solid red curve present the calculation of the translational kinetic energy along the ion beam propagation axis z. SIMION® allows the measurement of the speed Vz for each ions flying in the quadrupole. The distribution of the translational kinetic energy has the same profile as the kinetic energy and shows a high energy tail up to 1200eV.
Figure 2 : Kinetic energy histogram in the XY plane (dotted blue curve) and translational kinetic energy along z axis (solid red curve) at the end of the quadrupole
IIIEffects of the triplet of lenses for several polarizations on ions energy at the exit end of the quadrupole Q3
The triplet of lenses acts as a collimation device concerning the exit angle of the ion beam.
We studied the effect of the polarization of the triplet on the high energy tail. On the figure 3 is plotted energy measurements at the end of the quadrupole for different polarization of the lenses. We can see on that figure that for all polarization the high energy tail is still visible but less high. In fact the tail is up to 500eV.

Figure 3 : Effects of the triplet of lenses polarization on the high energy tail.
IVScreens description
During our initial study of the device design, the electrostatic sector had a 15 mm width. Ions enter the electrostatic sector through the entrance diaphragm with an angle α. That angle α is linked to the way ions exit the lenses triplet. The first simulations showed that a large proportion of ions was picked up by the electrostatic sector electrodes and containment screens. Ions picked up by the electrodes are ions whose kinetic energy deviates too much from the energy corresponding to the applied voltage Vs. Ions captured by the screens are those with a too elevated angle β . Angle β must be reduced to sort a maximum of ions. To confine the ions in the center of the path, we installed two polarizable containment screens on the sides of the electrostatic sector shown in Figure 4.

Figure 4 : (left) 15 mm width electrostatic sector design in SIMION® and (right) side view XY of 5000 ions trajectories in the electrostatic sector ( mass 1000 amu and charge +1)
Then we studied the influence of the polarization of these screens on the potential felt by the ions. SIMION® allows to view the electrostatic sector potential lines as a function of the applied voltage on the screens. This study was performed for ions with a 200 amu mass and a charge +1. For this mass, the energy peak is located at 8.9 eV, the voltage applied to the electrodes of the electrostatic sector is Vs = ± 3 V in accordance with the equation below.
During ions flight through the electrostatic sector, we have seen that ions were, for the most part, captured by the screens. Figure 5 shows the iso-potential lines induced by the polarization of the electrostatic sector electrodes when screens are at a zero potential.
Gradually polarizing the screens, the electrostatic sector potential lines are evolving. We assigned the screens containment VEC tensions ranging from 0 to 70 V to see this evolution of potential lines of electrodes of the electrostatic sector (Figure 5).

Figure 5 : Iso potential lines evolution with the screen polarization from 0 to 70V in a 15mm width electrostatic sector (Sector polarization = ± 3 V)
By polarizing positively the screens in order to tighten the trajectory of positive ions in the electrostatic sector, potential lines are localized on the sector negatively polarized electrode, which greatly affects the filtering function of the analyzer. One of the solutions we proposed to reduce the influence of the screens, without affecting the efficiency of the electrostatic sector, was to expand the electrostatic sector width. We chose a 40 mm width. We tested the impact of that enlargement on the iso-potential evolution under the same conditions as above.
By gradually polarizing the screens, we can see that the potential at the center of the sector is not affected by the polarization on the screens (Figure 6). Up to 100 V applied on the screens, the electrostatic field at the center of the sector remains undisturbed. The expansion of the electrostatic sector allows to apply a voltage on screens without disturbing the field created by the low polarization of the electrostatic sector.

Figure 6 : Iso potential lines evolution with the screen polarization from 0 to 500V in a 40mm width electrostatic sector (Sector polarization = ± 3 V)
Finally, we verified that the polarization on screens allow lateral containment to tighten the ion trajectories in the electrostatic sector. Figure 7 shows the sectional view XY of the electrostatic sector. The applied bias tightens ion trajectory in the center of the electrostatic sector in order to collect more ions.
Figure 7 : Comparison of ions trajectories in the electrostatic sector (m=1000 amu and +1 charge) for three polarizations applied on screens (Electrostatic sector XY view).

VHigh-energy tail observation using Q1 quadrupole
Energy experimental measurement of the 219 amu ions by sorting with Q1 quadrupole.
Figure 8: Ion current Iions (dashed blue curve) and negative derivative -dIions/dVgrid (solid red curve) as a function of the grid voltage Vgrid, obtained for ions C3F9+ of m/z=219 at the Q1 output.
VI-
Energy measurement in SIMION® for m219 amu ions

Figure 9: (left) Semi log energy histogram H(Eions) for 219amu ions (solid red curve) and the percentage of ions having an energy higher than Eions R(Eions) (dotted blue curve) (right )Zoom in.
Energy measurement in SIMION® for m69 amu ions
Figure 10 : left) Semi log energy histogram H(Eions) for 69amu ions (solid red curve) and the percentage of ions having an energy higher than Eions R(Eions) (dotted blue curve) (right )Zoom in.