The Mathieu parameters a and q

[Ricardinio]

I read that the Mathieu parameters a and q are indicative of the stability and motion of an ion in the quadrupole field. Can any body give me a better (clear) idea/representation of these parameters?

[JI2002]

If I remember this right, for quadrupole ion trap MS, a and q are indicative of ion stability as we see in Mathieu stability diagram, but not indicative of motion of an ion. The trejectory of an ion is described by Mathieu second differential equation, the solution to that equation which is the relationship between time and coordinates of an ion in the ion trap is indicative of motion of ions. However, our main concern is if an ion is stable in the ion trap, this is where a and q come into play. These two parameters are calculated from DC voltage, rf volatage, rf frequency, geometry of the trap, and m/z ratio of the ion. An ion needs to be stable in both radial direction(r) and axial direction(z) for it to stay in the trap. Because ions are ejected from the trap in z direction, what we usually see is Methieu stability diagram of az and qz.