Differential algebraic method for arbitrary-order aberration analysis of combined electron beam focusing-deflection systems

A novel numerical method based on non-standard analysis, differential algebraic (DA) method, is introduced into aberration analysis of combined electron beam focusing-deflection system. The principle of this method for combined system is studied. It requires only tracing one main ray in a special algebra and the fields are expressed by superposition of different field harmonic functions. Aberrations up to n-th order of the combined system, are given simultaneously with the Gaussian properties from the results of the DA method with very high accuracy. The aberrations are classified into three categories and subdivided into different types by a similar way as in lens or deflectors. As an example, aberrations up to 7th order for an in-lens deflection system are calculated using the DA method. It is shown that in this case the relative errors for Gaussian properties are on the scale of 10-8-10-10 comparing with the (quasi-) analytic solutions. The patterns of 5th-7th order aberrations of the combined system are studied. There are significant differences between these patterns and the counterparts in pure deflection system.