Abstract
We present a computer-aided design tool for ion optical devices using the adjoint variable method. Numerical methods have been essential for the development of ion optical devices such as electron microscopes and mass spectrometers. Yet, the detailed computational analysis and optimization of ion optical devices is still onerous, since the governing equations of charged particle optics cannot be solved in closed form. Here, we show how to employ the adjoint variable method on the finite-element method and Störmer-Verlet method for electrostatic charged particle devices. This method allows for a full sensitivity analysis of ion optical devices, providing a quantitative measure of the effects of design parameters to device performance, at near constant computational cost with respect to the number of parameters. To demonstrate this, we perform such a sensitivity analysis for different freeform N-element Einzel lens systems including designs with over 13,000 parameters. We further show the optimization of the spot size of such lenses using a gradient-based method in combination with the adjoint variable method. The computational efficiency of the method facilitates the optimization of shapes and applied voltages of all surfaces of the device.
Highlights
The described method integrates into the design process for ion optical systems, because it uses the discrete adjoint approach and is based on established simulation models[4]
We further demonstrate the AVM method with the optimization of N-element freeform Einzel lens systems, an example of ion optical devices
Subtle changes in the geometry of such systems can have a significant effect on the electrostatic field distribution and ion trajectories, slightly inaccurate gradients would cause a diverging objective function during the optimization procedure
Summary
The described method integrates into the design process for ion optical systems, because it uses the discrete adjoint approach and is based on established simulation models[4]. With AVM, the design process contains numerical modelling of a device, and a sensitivity analysis. All design sensitivities of a device are computed. The geometry of a device is represented numerically first. A simulator based on the governing differential equation predicts the electromagnetic fields with a rigorous technique such as the finite element method (FEM)[5]. The equation of motion for the charged particles is solved, most commonly with a Runge-Kutta method or a Störmer-Verlet method (SVM)[6]. We can calculate the design sensitivities by solving another set of systems posed using AVM
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