Calculation of the shape of the mass peaks of hyperboloid mass spectrometers with one-dimensional unipolar sorting of the ions

The properties of the particular solutions of the Hill equation are used to obtain expressions for the envelopes of charged-particle trajectories in a hyperboloid analyzer with ion sorting along one coordinate in its positive range. Analytical relations for calculating the shape of the mass peaks are obtained on the basis of these expressions. The results of analytical calculations are compared with a computer simulation. The parameters for calculating the sensitivity and resolution of the one-dimensional analyzer are determined according to the mass peaks.