This article discusses the properties of a time-of-flight mass spectrometer, the ion-optical path of which contains a pulsed annular ion source and an electrostatic deflector with electrodes in the form of cylinders of equal diameter with a common axis. The high efficiency of wedge-shaped mirrors with a two-dimensional field is due to the fact that the rear electrode of the mirror is made in the form of a concave cylinder and the focusing properties of the mirror can be changed by changing the curvature of the electrode. There are two modes of space-time-of-flight focusing: “ring-axis” and “axis-ring”. The potential distribution in such a system is presented in a simple analytical form. To find the trajectories and time of flight of charged particles in the electrostatic field of the deflector, the
dimensionless Newton equations are used, which are integrated by the Adams method with an automatic choice of the integration step. The accelerating points were found by the method of successive approaches of Krylov. The relative accuracy of integration was chosen equal to10⁻⁹. The spatial focusing and the time of arrival of particles to the detector plane were calculated by the Monte Carlo method with a normal distribution of events in a given interval of initial parameters. Calculations have shown that the resolution of a TOF mass spectrometer can be increased to 5000 (at the level of 50% of the peak heights).

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