Neustock Lars Thorben, Hansen Paul C, Russell Zachary E, Hesselink Lambertus
Stanford University, Department of Electrical Engineering, 226 Serra Mall, Stanford, 94305, CA, USA.
Ion Innovations, 3815 Courtside Terrace, Norcross, 30092, Georgia, USA.
Sci Rep. 2019 Jul 30;9(1):11031. doi: 10.1038/s41598-019-47408-w.
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.
我们展示了一种使用伴随变量法的离子光学器件计算机辅助设计工具。数值方法对于电子显微镜和质谱仪等离子光学器件的发展至关重要。然而，由于带电粒子光学的控制方程无法以封闭形式求解，离子光学器件的详细计算分析和优化仍然很繁琐。在此，我们展示了如何将伴随变量法应用于静电带电粒子器件的有限元法和斯托默 - 维尔特法。该方法允许对离子光学器件进行全面的灵敏度分析，以相对于参数数量近乎恒定的计算成本，提供设计参数对器件性能影响的定量度量。为了证明这一点，我们对不同的自由形式N元单透镜系统进行了这样的灵敏度分析，包括具有超过13000个参数的设计。我们还展示了使用基于梯度的方法结合伴随变量法对这种透镜的光斑尺寸进行优化。该方法的计算效率有助于优化器件所有表面的形状和施加电压。
