Geometric Aspects of Optimizing the Acceptance of a Static Mass Analyzer

The axial aberration of the ion-optical system of a static mass analyzer is one of the main factors limiting the transmission and sensitivity of the instrument. We described an algorithm for selecting the optimal collimating system for a mass analyzer, which makes it possible to decrease this aberration effectively, with minimal loss in the intensity of the mass spectral lines. The algorithm is based on the representation of the considered aberration in the phase space as an ellipse and the optimal approximation of this aberration ellipse by a polygon with a given number of vertices. In the absence of constraints, the solution of the corresponding optimization problems is in phase polygons generated by regular polygons inscribed in a unit circle or circumscribed around a unit circle with the same number of vertices. After that, the unit circle along with the polygons is "stretched" to the size of the specified aberration ellipse along its main axes. Additional freedom of the rotation of the original polygon around the center of the unit circle can be used to position auxiliary slits of the collimating system more conveniently.