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Model-order reduction is an important tool in the computational exploration of complex physical phenomena, such as kinetic plasmas. A popular strategy to achieve model reduction is the so- called projection methods, such as the proper orthogonal decomposition (POD), where the dynamics of interest are decomposed into a set of global modes and the problem is then projected onto those modes. While very successful, in general, the conventional POD technique is not suited for certain advection-dominated problems or “transport” problems where moving localized features cannot be well represented by global modes. In this work, we apply an extension of the POD technique to obtain an efficient reduced-order model of advection-dominated kinetic plasma problems from finite-element particle-in-cell (PIC) simulations. The results obtained showcase the efficacy of this strategy for obtaining a parsimonious representation of the degrees of freedom of the problem that serves to both reduce simulation costs and provide added physical insight into the problem.

We review progress in kinetic plasma modeling by electromagnetic particle-in-cell (EM-PIC) algorithms on unstructured grids. These algorithms are implemented in modular CONPIC and BORPIC C++ codes that integrate a matrix-free explicit finite-element (FE) Maxwell solver based on a parallel sparse-approximate inverse (SPAI) algorithm and a first-principles charge-conserving scatter algorithm to transfer the charged particle information into dynamic variables on the grid. The Maxwell solver of the EM-PIC algorithm utilizes a mixed FE basis and discretizes the time-dependent coupled first-order Maxwell’s system explicitly. The explicit solver approximates the inverse FE system matrix (“mass” matrix) using hierarchical sparsity patterns based on the sparsity pattern of the original matrix. The resulting algorithm effectively accounts for multiscale plasma phenomena. We discuss the application of the developed EM-PIC algorithm to the analysis of laboratory plasmas, vacuum electronic devices for generation of high-power microwave signals, and RF electronics multipactor effects and apply the algorithm to the analysis of multipactor effects and its mitigation in coaxial cables.

The proper orthogonal decomposition technique is applied to a finite-element time-domain particle-in-cell (PIC) algorithm for the simulation of kinetic plasmas, resulting in a reduced-order system. The reduced model is tested with representative examples involving an accelerated electron beam and a plasma ball expansion and compared with full-order simulations. The strengths and weakness of this type of model order reduction when applied to PIC algorithms are discussed through the analysis of the results. In particular, the method allows for a major reduction in the field degrees of freedom necessary to capture the relevant physics, but it can also lead to spurious results if proper care is not taken when assembling the reduced-order system.

The Proper Orthogonal Decomposition (POD) is a mode decomposition technique that can be used for the creation of reduced order models or for analysis of complex dynamic systems. In this work, we apply the POD to analyze the characteristics of the oscillations present in an electron beam with formation of an oscillating virtual cathode.

The scattering of time-harmonic plane waves by a perfectly electrically conducting (PEC) half-plane (H-P) in relativistic uniform motion is discussed. The problem is formulated using the special theory of relativity by means of the Lorentz transformation applied to the classic Sommerfeld solution. Exact fields are obtained for the 3-D vector problem of scattering of an obliquely incident and arbitrarily polarized plane wave by a PEC H-P in relativistic translational motion. The total fields are then presented as the relativistic analog of their motionless counterparts and an association with the uniform asymptotic theory of diffraction framework is inferred. In addition to recovering known features such as the relativistic Doppler effect and shadow boundary shifts, it is herein depicted a polarization coupling effect due to motion that can give rise to a 3-D scattered field with all components present even for a linearly polarized incident wave. Validating results and illustrative examples are also presented.

Particle-in-cell simulations are widely utilized for the analysis and design of state-of-the-art plasma-based devices. However, detrimental artifacts present in relativistic PIC simulations exist, called numerical Cherenkov instabilities. These instabilities are caused by grid dispersion and beam aliasing effects. Here, we analyze Numerical Cherenkov instabilities in finite-element-based PIC algorithms on unstructured grids and compare against results from conventional finite-difference-based PIC algorithms on structured grids. We assess the conditions for the onset of numerical Cherenkov instabilities by performing a complete grid dispersion analysis of finite-element field-solvers for various mesh layouts. The analytic predictions are validated against PIC simulations of relativistic plasma beams. We observe that highly irregular meshes alter the beam physics the least among different mesh layouts, preventing coherent spurious wave-particle interactions.

Particle-in-Cell (PIC) simulations are an useful tool for the analysis of kinetic collisionless plasmas such as those found in high power microwave devices, vacuum electronics, directed energy devices, among others. However, PIC simulations remain computationally costly, and model order reduction strategies such as the Proper Orthogonal Decomposition (POD) can be instrumental in reducing some of these costs. The efficacy of the reduced-order model resulting from application of POD depends on several factors, among them the strategy employed to sample field values when constructing the reduced order model. In this work we analyze and compare several such field sampling strategies.

We review progress in kinetic plasma modeling by electromagnetic particle-in-cell (EM-PIC) algorithms on unstructured grids. These algorithms are implemented in modular CONPIC and BORPIC C++ codes which integrate a matrix-free explicit finite-element (FE) Maxwell solver based on a parallel sparse-approximate inverse (SPAI) algorithm and a first-principles charge-conserving scatter algorithm to transfer charged particle information into dynamic variables on the grid. The Maxwell solver of the EM-PIC algorithm utilizes a mixed FE basis and discretizes the time-dependent coupled first-order Maxwell's system explicitly. The explicit solver approximates the inverse FE system matrix (“mass” matrix) using hierarchical sparsity patterns based on the sparsity pattern of the original matrix. The resulting algorithm effectively accounts for multiscale plasma phenomena. We discuss the application of the developed EM-PIC algorithm to the analysis of laboratory plasmas, vacuum electronic devices for generation of high power microwave signals, and RF electronics multipactor effects in harsh space environments.

The scattering of time-harmonic plane waves by a perfectly electrically conducting half-plane in relativistic uniform motion has been previously shown to give rise to polarization effects when the line of motion is along an arbitrary direction. A physical interpretation for the observation of these polarization effects is herein presented, based on an analysis of the geometric properties of the scatterer under Lorentz transformations.

The Proper Orthogonal Decomposition technique for model order reduction is applied to electromagnetic particle-in-cell algorithms. The resulting low-dimensional model can be used to achieve solutions with acceptable accuracy and reduced computational costs in problems with charged particle beams.

The study of fast-moving scatterers has received much attention due to its fundamental applications for modern radio astronomy and radar problems. This kind of problem relies on solving complicated time-dependent boundary conditions and only the wave phenomena associated with simplified scattering scenarios are today completely deep-seated. In this paper, a novel solution for the scattering of plane waves by a perfectly electrically conducting (PEC) wedge in motion is introduced on the grounds of Einstein's special theory of relativity. The exact solution for the 3D vector problem of an arbitrarily polarized time-harmonic plane wave excitation is obtained in closed form. In addition, a solution based on the uniform asymptotic theory (UAT) ansatz is obtained, rendering this approach a promising framework for modeling several relativistic effects of other complex-shaped and fast-moving objects.

In a recent paper [1] , there was a typo in (13), which should read as a scalar equation for the $ {z}$ -component of $\tilde {\mathbf {E}}\{\tilde {\mathbf {H}}\}$ in the form \begin{equation*} \tilde {E}_{ {z}} \{\tilde {H}_{ {z}}\} = F(\tilde {\xi }^{i}) \, \tilde {E}_{ {z}}^{i} \{\tilde {H}_{ {z}}^{i}\} + F(\tilde {\xi }^{r}) \tilde {E}_{ {z}}^{r} \{\tilde {H}_{ {z}}^{r}\} \end{equation*} from which the remaining field components may be obtained. The full vector equation for the electric field is then given by \begin{align*} \tilde {\mathbf {E}}=&F(\tilde {\xi }^{i}) \tilde {\mathbf {E}}^{i} + F(\tilde {\xi }^{r}) \tilde {\mathbf {E}}^{r} + \frac {e^{i \pi /4}}{\sqrt { 2 \pi \tilde {k} \tilde {\rho } \sin \tilde {\theta }_{0} }} e^{i \tilde {k} (\tilde {\rho } \sin \tilde {\theta }_{0} -\tilde { {z}} \cos \tilde {\theta }_{0})} \\[3pt]&\times \bigg \{ \cos \frac {\tilde {\phi }-\tilde {\phi }_{0}}{2} \left [{ \left ({ \tilde {\mathbf {E}}^{i}_{0} \cdot \hat {\tilde { {z}}} }\right) \hat {\tilde { {z}}} - \tilde {\mathbf {E}}^{i}_{0} }\right ] +\sin \frac {\tilde {\phi }-\tilde {\phi }_{0}}{2} \, \hat {\tilde { {z}}} \times \tilde {\mathbf {E}}^{i}_{0} \\[4pt]&+\,\cos \frac {\tilde {\phi }+\tilde {\phi }_{0}}{2} \left [{ \left ({ \tilde {\mathbf {E}}^{r}_{0} \cdot \hat {\tilde { {z}}} }\right) \hat {\tilde { {z}}} - \tilde {\mathbf {E}}^{r}_{0} }\right ] +\sin \frac {\tilde {\phi }+\tilde {\phi }_{0}}{2} \, \hat {\tilde { {z}}} \times \tilde {\mathbf {E}}^{r}_{0} \bigg \} \end{align*} where $\tilde {\mathbf {E}}^{i,r}_{0}$ denotes the incident (reflected) electric field amplitude at the edge of the half-plane in frame $\tilde {S}$ . In addition, $Z \tilde {B}_{h}$ in (24) should read as $\tilde {B}_{h}$ , yielding \begin{align*} \tilde {\bar {\bar {F}}}_{re}=&\dfrac {\tilde {Q}}{c} \\&\times \! \begin{bmatrix}\! 0 \!&\quad \! -\!\tilde {B}_{e} \sin \dfrac {\tilde {\phi }}{2} \!&\quad \! \tilde {B}_{e} \cos \dfrac {\tilde {\phi }}{2} \!&\quad \! 0 \\ \tilde {B}_{e} \sin \dfrac {\tilde {\phi }}{2} \!&\quad \! 0 \!&\quad \! 0 \!&\quad \! -\tilde {B}_{h} \sin \dfrac {\tilde {\phi }}{2} \\ -\tilde {B}_{e} \cos \dfrac {\tilde {\phi }}{2} \!&\quad \! 0 \!&\quad \! 0 \!&\quad \! \tilde {B}_{h} \cos \dfrac {\tilde {\phi }}{2} \\ 0 \!&\quad \! \tilde {B}_{h} \sin \dfrac {\tilde {\phi }}{2} \!&\quad \! -\tilde {B}_{h} \cos \dfrac {\tilde {\phi }}{2} \!&\quad \! 0 \end{bmatrix}\!. \end{align*} None of the above-mentioned remarks affect the calculations and results presented in [1] .

In this paper, a simple and accurate technique for the measurement of the S-Parameters of a two-port network from time domain data is presented, based on Fourier theory and techniques. This method is proposed to circumvent the need of a network analyser when studying an unknown device, as no additional measurements other than the time domain data are required. An excellent correspondence between this technique's results and regular network analyser measurements is achieved for the entire operational band of the devices tested.