The described method easily integrates into the design process for ion optical systems, because it uses the discrete adjoint approach and is based on established simulation models 4. In this work, we describe how the computational efficiency of the method allows us to not only analyze and optimize the key dimensions but also the shape and applied voltages of all surfaces of a design. This is, to the best of our knowledge, the first application of AVM to ion optical device optimization and the first derivation of a discrete adjoint system for charged particle devices. We present the application of AVM for the optimization of electrostatic ion optical, or more generally charged particle optical, systems.
It helps visualizing how design parameters, such as each point on a surface, should be perturbed to enhance device performance. Quantitative knowledge of the design sensitivities not only enables local optimization of devices, but also aids physical understanding. These effects are called design sensitivities and can be calculated efficiently using the adjoint variable method (AVM).
To avoid the effort of such an extensive analysis, the method introduced here computes the effects a design parameter variation, such as device dimensions or applied voltages, has on the physical behavior of ion optical devices. To optimize a device, most commonly used approaches must analyze an extensive number of devices, which can be prohibitively slow. Instead, engineers and physicists rely on numerical modeling to understand and design ion optical devices 3. Neither equation can be solved in closed form for any but the simplest devices. The (nonrelativistic) motion of charged particles obeys a nonlinear coupled system of equations, composed of the Laplace equation for the electrostatic potential and a combination of Newton’s and Coulomb’s laws for the equation of motion. The computational efficiency of the method facilitates the optimization of shapes and applied voltages of all surfaces of the device.Įlectromagnetic fields have been applied to accelerate, guide and focus ions and electrons for over 100 years, with applications as far-ranging as vacuum tubes, electron microscopes, terahertz emitters, mass spectrometers and high-energy particle accelerators 1, 2. We further show the optimization of the spot size of such lenses using a gradient-based method in combination with the adjoint variable method. To demonstrate this, we perform such a sensitivity analysis for different freeform N-element Einzel lens systems including designs with over 13,000 parameters.
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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.
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Here, we show how to employ the adjoint variable method on the finite-element method and Störmer-Verlet method for electrostatic charged particle devices. 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. Numerical methods have been essential for the development of ion optical devices such as electron microscopes and mass spectrometers. We present a computer-aided design tool for ion optical devices using the adjoint variable method.
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