The method of power series tracking for the mathematical description of beam dynamics

Abstract A new method to compute the properties of charged particle optics systems is presented. It is based on the application of operators and functions to a power series algebra instead of real numbers. The method is as versatile as numerical integration methods and comparable to matrix methods in speed and accuracy thus combining the advantages of both strategies. The method has been implemented through fifth order in the code POWERTRACK. Due to the generality of the method, the order can be increased with very little programming effort.