We present advances in the photoemission and secondary emission models and implementations in the MICHELLE charged particle beam optics code. MICHELLE has been developed to include a wide variety of emission models designed to suit a robust set of applications and be customizable to use cases by institutions and groups. In the case of photoemission, there are upgrades to our computational methods to evaluate the Moments model for enhanced computational efficiency. In the case of secondary emission, MICHELLE employs a table-lookup approach that captures the moments of the secondary emission. Upgrades includes not only a more robust secondary particle distribution but a methodology employing the Sandia ITS suite to populate secondary emission tables for materials of interest. The paper highlights these models and features that have evolved over time and identifies cases where they can be applied to improve simulation fidelity or enable new problems to be approached.

We present progress on the application of an adjoint approach to determine sensitivity functions for the design of charged particle optics in the presence of both electric and magnetic static fields. The methodology is applied by implementing techniques in the MICHELLE beam optics code whereby a minimal number of time-reversed simulations enables the determination of a variety of figures of merit resulting from small, but arbitrary, property changes. Such changes may include geometric electrode shapes, magnetic field patterns, electrode voltages, emission properties, etc. The use of these sensitivity functions to determine manufacturing alignment and assembly tolerances to maximize production yield as well as in optimization algorithms will be discussed. Applications to beam transport in magnetic fields will be presented.

We present new capabilities in the Neptune electromagnetic particle-in-cell (EM-PIC) simulation code and design environment that support geometry-based design of vacuum electronic and HPM devices. New features of the EM-PIC model include a fully 3D, omnidirectional implementation of the perfectly-matched layer (PML) method that efficiently absorbs outgoing waves, a waveguide port model with time-dependent mode-decomposition diagnostics, and a model for space-charge limited emission from curved (cut-cell) interior surfaces that exhibits second-order convergence of the emitted current density with respect to the grid cell size. Collectively, these capabilities have enabled Neptune to perform 3D simulations of advanced HPM sources. We will summarize the new capabilities and present examples of applications to high power microwave sources.

We present advances, key features, and advanced capability in the MICHELLE charged particle beam optics code. Although the MICHELLE code was originally developed to support the vacuum electronics and accelerator physics communities, over the years it has had some significant developments that make it a truly general purpose charged particle beam optics code with many advanced models and features. This paper discusses some of the advanced models and features that we find useful in modern design and optimization workflow. These include capability for multi-faceted meshing (2D, 3D, unstructured, structured-multiblock, hybrid, all element shapes), various solution algorithms (steady-state, time-domain, Boltzmann electron, circuit model), latest advances in emission physics (generalized thermionic, general thermal-field with self-consistent heating effects, photoemission, secondary emission), thermal beam models, adjoint analysis integration, multi-physics analysis environments (CAD, meshing, solution, post-processing, pipelining, optimization, sensitivity), inter-code operability within user workflows, resolving highly-disparate feature scales and sizes, and computer platform support (laptop-to-HPC). The paper highlights these models and features that have evolved over time and identifies cases where they can be applied to improve simulation fidelity or enable new problems to be approached.

A W-band electron gun design under development has been modified for improved beam optics and reduced electric field stress. This design is based on a design presented by Nguyen et al. [1]. The main effort has been focused on designing magnet pole pieces that would provide an optimum magnetic field transition with sufficient distance from the cathode for the placement of focusing electrodes. Variations of the magnet pole pieces were tested with Poisson and MICHELLE [2], [3] to find a configuration that would focus the beam without requiring extensive changes to the electrode geometry; an effort was also made to avoid saturation of the magnetic field inside the pole piece and to avoid excessive electric field strength at the electrodes.

The status of first principles modeling and simulation tools for vacuum electronics (VEs) is presented. These tools, when combined with parametric beam-wave interaction tools, comprise the suite of tools that enable the design and optimization of VE devices, such as RF amplifiers. Although many basic algorithms discussed in the article have been around for decades, the advances in electromagnetic and electrostatic particle-in-cell and meshless beam codes have revolutionized the VE device development process where first-pass design has become the standard. These include advances in emission physics, disparate-mesh geometry resolution, advanced boundary conditions, intercode operability, multimodule simulation pipelines, exploitation of computer hardware, optimization and sensitivity analysis, and advanced user simulation environments with multimodule pipelines. The article presents these advances.

New advances in the application of adjoint methods [1] to determine beam transport sensitivities to device parameters using the MICHELLE [2] , [3] code are presented. Such sensitivities are due to manufacturing assembly tolerances, field errors from components, including how both may vary over the lifetime of a device. Understanding the sensitivities to alignments, for example, informs the assembly process of the effect of misalignments. The methodology is applied by implementing techniques in the MICHELLE beam optics code whereby a minimal number of time-reversed simulations enables the determination of a wide variety of figures of merit resulting from small, but arbitrary property changes. Such changes may include geometric electrode shapes, magnetic field patterns, electrode voltages, emission properties, etc. Each of the adjoint method simulations are made on the original geometry and computational mesh, and replaces multiple such direct simulations where geometries may be changed and the resultant mesh changed. Not changing the mesh using the adjoint method improves the sensitivity of the simulation differences and improves result fidelity. The development and use of these sensitivity functions to determine manufacturing alignment and assembly tolerances to maximize production yield as well as in optimization algorithms will be discussed. Applications to beam transport in magnetic fields will be presented to illustrate the effectiveness of the technique.

We report on a new process under development in recent years that enables bringing the effects of detailed meso-scale thermionic emission properties to inform full-scale electron gun simulations. Specifically, detailed material properties and electrical properties of emitter samples are measured and processed, leading to a mapping of the work function across the emitter surface patch that is statistically applicable to the larger surface areas existing in a gun simulation. The measurements and processing subsequently leads to the development of Miram and IV curves for the material, as well as a prediction of the particle energy distribution and intrinsic emittance. Having this, we can then use these properties in simulations for high fidelity gun modeling for design applications. The process includes EBSD measurements, DFT simulations, then fast simulations using new 2-1/2D models from U. Wisconsin and U. Michigan 3D in collaboration with “first-principles” MICHELLE simulations, and will be presented.

We present new advances in the MICHELLE charged particle beam optics code in area of advancing emission models and algorithms that capture more electron emission physics. The new capability covered in this paper concerns the implementation of a new general thermal field (GTF) model that predicts current density in the transition region between temperature limited emission and field emission. In the case of electron thermionic emission where the effective AK gap is not large compared with the potential minimum distance that forms in front of the cathode, we employed a modified and improved thermionic emission model Coupled to these models are a new thermal beam model that better control macro-particle count while maintaining simulation fidelity, as well as new meshing methodologies that improve emission fidelity in the regime of disparate spatial scales, especially useful for field emitter fibers. Lastly, also for field emission fibers, we will present results from the implementation of a self-consistent thermal model. To support such widely ranging spatial scales, effort has been put into disparate meshing capabilities. The presentation provides an overview of the new capabilities that has been achieved.

Compass [1] is a new design environment for rapid prototyping. It marries rapid geometry modeling, using SolidWorks, with geometry based simulation software. Compass packages any command line based simulation software into a Compass module. Each module interacts with other modules and is reusable in other design flows.

New advanced models and applications of the MICHELLE electrostatic particle-in-cell code are presented. MICHELLE continues to follow a strong development plan, advancing the level of physics-based models to improve simulation fidelity in more complex regimes. As a charged particle beam optics code MICHELLE [1] now includes a new model for thermionic emission that more accurately transitions through the knee of the Miram curve as a cathode crosses from temperature-limited to fully space-charge limited emission. This is fortified by a new thermal beam model to greatly reduce computation resources in the transition regime. The model correctly treats small scale geometries where the potential minimum is resolved as well as the large, cm-scale diodes. Another area that has undergone much development is MICHELLE's ability to mesh with various user design environments, including the state-of-the-art Cadence Analyst-MP [2] toolset as well as the new COMPASS II environment that enables the stitching together of native and third-party simulation tools and utility tools, all supporting UNIX & Windows, up through Windows 10. These environments and tool sets work together with the NRL Vacuum Electronics tools, including CHRISTINE-Z, TESLA-Z [3] and NEPTUNE [4] large signal and first principle codes, respectively. Lastly, high energy beam sources require high-fidelity self-magnetic fields to be calculated. Several examples and applications that stress codes such as MICHELLE will be presented, illustrating how the new capability can be used by the device designer.

Carbon fibers passing current are subject to resistive heating. When failure occurs, this is related to their local temperature. The failure temperature and its location are estimated. The temperature variation is calculated using analytical models for electrical and thermal conductivities based on the temperature dependent electron–phonon relaxation time. In the absence of radiative heat loss, an analytic expression of temperature along the fiber is given from which a maximum possible emission current is derived and is governed by a single introduced parameter ωo. A method of treating the radiative heat loss is developed and is governed by a second parameter γ, which allows a rapid numerical means to calculate the correction to the analytic form. Heat variation along a thick carbon fiber is contrasted to that along a multi-walled carbon nanotube (MWNT): it is shown that the relative magnitude of ωo compared to γ determines that the analytical formula is a good approximation for MWNTs but requires numerical correction for fibers. Furthermore, it is shown that the analytical form of ωo specified a maximum current beyond which the carbon emitter fails due to thermal runaway. The theoretical models are used to interpret observed behavior of field emission from carbon fibers and the resulting damage they endure when the extracted field-emission current is high. Results from implementing the developed temperature variation model into the MICHELLE beam optics simulation code are presented, with an example application predicting the conditions for stable equilibrium operation as well as for the onset of fiber failure.

A model of a thermionic cathode in a planar diode in which the Poisson and Vlasov equations are solved in 3-D assuming an infinite magnetic field is presented. We explore how 2-D work function variations across the cathode surface may affect the transition between temperature-limited and space-charge-limited flow, commonly known as the “knee” of the Miram curve. We study a variety of work function distributions, both realistic and idealized, and demonstrate how emission from the lowest work function regions dominates the total anode current even when such regions make up a relatively small fraction of cathode area. Our model also illustrates the ability of cathodes to reach the full Child-Langmuir current despite the presence of a sizeable nonemitting region. We find that as the length scale of these work function variations decreases, the Miram knee grows sharper, indicating improved cathode performance.

The Compass framework manages simulation pipelines. Any simulation software can be mapped into a Compass compatible module using Compass' module template. Once-developed modules can be reused for other simulation pipelines with little additional effort. The Compass module interface is designed so that modules can communicate data between each other with the only requirement being that the data transferred is of the same data type in both modules. The Compass framework is discussed. Application of the Compass framework to multidisciplinary problems is presented.

We present improved numerical algorithms for thermionic emission in the finite-element gun code MICHELLE. The improved algorithms employ newly implemented Child-Langmuir special functions and robust iterative solvers that quickly yield near double precision machine accuracy in analytic problems. The implementation in MICHELLE yields substantially improved current densities, reducing the 1% error observed in some cases to less than 0.25% error.

This paper reports recent developments of a semi-analytic 2-1/2D model which could provide a realistic description of the Miram curves. We solve the Vlasov and Poisson equations in 3-dimensions assuming an infinite magnetic field, but include electron thermal emission and non-uniform distribution of work function on the cathode surface. This 2-1/2 D theory will be compared with 3D MICHELLE runs.

Analysis of temperature-limited flow, space-charge-limited flow, and the transition between them using a simple planar diode with a thermionic cathode, in which the cathode surface has spatially nonuniform emission properties, is presented. Our theoretical results, which are derived from a model based on solutions to the Vlasov and Poisson equations, compare well with the results of particle-in-cell simulations. We find that the location and the shape of the knee in the anode current versus temperature characteristic (Miram or “rollover” curve) are significantly affected by non-uniformities in the space-charge density in the A-K gap, but are relatively unaffected by the electron motion parallel to the electrode surfaces. In particular, emission from an actively emitting region is strongly affected by the forces (or lack thereof) exerted by the space-charge of the electrons emitted by their neighbors. Perhaps, most remarkably, we find that the limiting current reaching the anode is approximately given by the classical 1-D Child-Langmuir law, even if a significant fraction of the cathode surface is non-emitting.

3D Electromagnetic Particle-in-Cell (EM-PIC) simulation has become a powerful computational tool for simulation-based design of modern vacuum electronic RF amplifiers and high-power RF sources. The performance and accessibility of 3D simulation tools has been driven by the growth in available computing power (both multi-core CPUs and many-core GPU accelerators) and the advancement of EM-PIC algorithm implementations that take full advantage of the available computational hardware.

We present new visualization tools for the recently developed High Performance Computing (HPC) capability for the MICHELLE code. New HPC support has been implemented in the MICHELLE code in support of rapid device design and optimization. The adoption of HPC tools and the porting of the code to HPC platforms allows for high -resolution, large-scale models and simulations of multiple beam devices, such as MBK guns and MB-IOTs. Visual analysis and postprocessing of simulation results from such large-scale models is a computational challenge that requires advanced scientific visualization tools such as Para View, which was chosen for our program due to its flexibility to plug-in customization. To enhance usability and efficiency for new and existing MICHELLE users, a GUI plug-in to ParaView with MICHELLE-specific tools has been developed using the Qt GUI toolkit and Python. Here we present a description of the Qt plug-in with example problems, and a review of some Para View capabilities. Also presented is real-world benchmarking of HPC visualization performance using Para View's in client-server mode.

The advancement of modern vacuum electronics into millimeter and sub-millimeter wavelengths places a growing demand on sensitivity analysis which in turn plays an increasingly important role in improving production yield. This results in higher computational demand on simulation software, often pushing it into the realm of High Performance Computing (HPC). Domain decomposition provides one means for increasing simulation resolution and/or decreasing simulation execution time by breaking the volumetric mesh into sub-domains (blocks) which can be distributed over memory and multiple processors.