Study on time of flight property of electron optical systems by differential algebraic method

Differential algebraic method is a powerful and promising technique in computer numerical analysis. When applied to nonlinear dynamics systems, the arbitrary high-order transfer properties of the systems can be computed directly with high precision. In this paper, the principle of differential algebra is applied to study on the time of flight (TOF) property of electron optical systems and their arbitrary order TOF transfer properties can be numerically calculated out. As an example, TOF transfer properties of a uniform magnetic sector field analyzer have been studied by differential algebraic method. Relative errors of the first-order and second-order TOF transfer coefficients of the magnetic sector field analyzer are of the order 10(-11) or smaller compared with the analytic solutions. It is proved that differential algebraic TOF method is of high accuracy and very helpful for high-order TOF transfer property analysis of electron optical systems.