The third-order aberrations of magnetic sector analyzers

To achieve higher performance of energy analyzers or mass spectrometers, the design of their core components, i.e., the magnetic sector analyzers, requires the analysis of the third-order aberrations. In this work, the successive approximation method is employed, and then the complete list of the integral formulas of the third-order aberration coefficients are derived and provided for magnetic sector analyzers. In particular, to fulfill the analysis and design of mass spectrometers, we extend the third-order chromatic aberration coefficients into those relating to energy and mass fluctuations. This is achieved by decomposing the momentum perturbation into energy and mass fluctuations. Finally, as a demonstration example, a magnetic sector is studied and analyzed. And the aberration coefficients up to the third-order are calculated using the derived integral formulas. An advantage of these derived formulas is that the fringing field of the magnetic sector analyzers is treated as a continuous function rather than certain approximations, such as sharp cutoff fringing field (SCOFF) and extended fringing field (EFF). The calculated third-order aberration coefficients are consistent with those calculated by the differential algebraic method. The results of this work would be beneficial to the system design and optimization of both electron and mass spectrometers.