Abstract: A simple method to calculate electrostatic fields of ion optical system and trajectories of ions in the field is discussed.The optimization methods to save disk space and accelerate the calculation process are given under condition of maintaining the calculation precision.A feasible method for searching the over-relaxation factor is present.The calculation method is applied to the calculation of a design of gridless high-resolution reflectron time-of-flight mass spectrometer.The results of the distribution of electrostatic fields,the ion trajectories and the best conditions of the fields are present.The system is adjusted to its fairly good working condition based upon these results,and mass spectra with much higher resolution are observed.

Key words: ion optics, numerical solution, reflectron time-of-flight mass spectrometer