Quadrupole mass analyzers (2D and 3D) are the overwhelming choice as mass analyzers for researchers developing portable mass spectrometry systems. And as the analyzer dimensions decrease in size, an increased reliance on the fundamental mathematical underpinnings of these devices is required to correct for field imperfections introduced by compromises in the machining or degradation in the accuracy of the fields formed by intentionally approximating or compromising ‘ideal’ electrodes geometries. Fortunately, researchers developing these miniature devices can rely on the theoretical trapping stability and field equations that were co-developed with the the devices in the 1950’s. Toroidal ion traps are another novel approach to reduced size mass analyzers. And while the conception of the toroidal mass analyzer proceeded from quadrupole devices, they cannot be described by the quadrupole device fundamental mathematical equations. This barrier originates from the fact that 2D/3D quadrupole device fields can be described in Cartesian (or cylindrical) coordinates while the toroidal trapping field cannot. For example, the sublinear even-order (mostly octapole) contribution to the trapping field added by opening slits in the original Finnigan ion trap was compensated by a adding a positive octapole component (stretching the endcap electrode distance). There currently is no analog process known in the toroidal coordinate system.
We have recently begun an effort to develop the field description and analysis tools needed to describe, analyze and optimize trapping fields in the toroidal coordinate system. For example, we have solved the Laplace equations for the first 10 ‘poles’ in a toroidal coordinate system and have used these solutions in an attempt to describe the current PerkinElmer TRIDION mass analyzer trapping field. This example is part of a multifaceted approach using fundamental/theoretical, computational and empirical methods which will be presented. |