Theoretical Approach to Ion Separation

FIGURE 4.5 Quadrupole trunk under sagittal sectioning. 

The equations of the ion movanent within the field (established from the fundamental relation of the dynamics) in each of the x,y,z directions are the following  

The point here is not to resolve this equation in an algebraic manner. This equation admits two kinds of solutions (1) those referred to as stable, corresponding to trajectories allowing the ions to go through the quadrupole and reach the detector and (2) unstable solutions corresponding to trajectories allowing the ions to exit the field and thus the quadrupole before reaching the detector. In this last case, the ions are obviously not detected. 

When changing variables in order to make the parameters a and q appear, the movement of the ion within the quadrupole field is described by the following 

The a and q are called stability parameters a is directly proportional to U and q is proportional to V. The stability of an ion of a given m/z ratio in the quadrupolar field depends on these two parameters. 

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