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Solving real-world nonlinear semiconductor device problems modeled by the drift-diffusion equations coupled with the Poisson equation (also known as the Poisson-Nernst-Planck equations) necessitates an accurate and efficient numerical scheme which can avoid non-physical oscillations even for problems with extremely sharp doping profiles. In this paper, we propose a flexible and high-order hybridizable discontinuous Galerkin (HDG) scheme with harmonic averaging (HA) technique to tackle these challenges. The proposed HDG-HA scheme combines the robustness of finite volume Scharfetter-Gummel (FVSG) method with the high-order accuracy and $hp$-flexibility offered by the locally conservative HDG scheme. The coupled Poisson equation and two drift-diffusion equations are simultaneously solved by the Newton method. Indicators based on the gradient of net doping $N$ and solution variables are proposed to switch between cells with HA technique and high-order conventional HDG cells, utilizing the flexibility of HDG scheme. Numerical results suggest that the proposed scheme does not exhibit oscillations or convergence issues, even when applied to heavily doped and sharp PN-junctions. Devices with circular junctions and realistic doping profiles are simulated in two dimensions, qualifying this scheme for practical simulation of real-world semiconductor devices.

Integrated optical electric field sensors (IOES) play a crucial role in electric field measurement. This paper introduces the principles of the IOES and quantitatively evaluates the impact of humidity on measurement accuracy. Sensors with different levels of hydrophobicity coatings and hygroscopicity shells are fabricated and tested across the relative humidity (RH) range of 25% to 95%. Results reveal that humidity stability is primarily influenced by water vapor absorption through the sensor shell, which increases its conductivity. This further results in amplitude deviation and phase shift of the sensor output. To address this, an optimal humidity-stable packaging scheme is proposed, which involves using PEEK shell with room temperature vulcanized fluorinated silicone rubber coating. Compared with uncoated ceramic shell, the phase shift of the IOES reduces from 90$^\circ$ to 1$^\circ$ under a RH of 90%. The amplitude deviation of electric field measurement decreases from 20% to nearly zero after a 20-hour humidity experiment conducted under RH of 90% at 30 $^\circ$C. The proposed packaging scheme could be used to improve the humidity stability of the sensors deployed in outdoor environments, especially on ships and coastal areas.

As the capacity of power systems grows, the need for quick and precise short-circuit fault location becomes increasingly vital for ensuring the safe and continuous supply of power. In this paper, we propose a fault location method that utilizes electromagnetic transient convolution (EMTC). We assess the performance of a naive EMTC implementation in multi-phase power lines by using frequency-dependent parameters in real fault simulation, while using constant parameters in pre-calculation. Our results show that the location error increases as the distance between the fault location and the measurement location increases. Therefore, we adopt the aerial mode transients after phase-mode transformation to perform the convolution, which reduces the influence of frequency-dependence and ground loss. We conduct numerical experiments in a 3-phase 100-km transmission line, a radial distribution network and IEEE 9-bus system under different fault conditions. Our results show that the proposed method achieves tolerable location errors and operates efficiently through direct convolution of the real fault-generated transient signals and the pre-stored calculated transient signals.

Recently, a new framework to compute the photoionization rate in streamer discharges accurately and efficiently using the integral form and the fast multipole method (FMM) was presented. This paper further improves the efficiency of this framework with adaptive strategies. The adaptive strategies are based on the magnitude of radiation and the electric field during the streamer propagation, and are applied to the selection of the source and target points. The accuracy and efficiency of this adaptive FMM are studied quantitatively for different domain sizes, pressures and adaptive criteria, in comparison with some existing efficient approaches to compute the photoionization. It is shown that appropriate adaptive strategies reduce the calculation time of the FMM greatly, and maintain the high accuracy that the numerical error is still much smaller than other models based on partial differential equations. The performance of the proposed adaptive method is also studied for a three-dimensional positive streamer interacting problem with a plasma cloud.

It is very important to locate the short-circuit fault in a power system quickly and accurately. Electromagnetic time reversal (EMTR) has drawn increasing attention because of its clear physical background and excellent performance. This paper studies the EMTR method for locating the short-circuit fault of transmission and distribution lines with or without branches, and introduces a simulated annealing algorithm to accelerate the calculation of an EMTR fault location. This algorithm is different from the traditional exhaustive method in that it solves the corresponding optimization problem, thus improving the location speed by up to an order of magnitude. With the help of graph theory, a method is proposed that automatically splits a complex line topology with branches into several one-dimensional lines. The problem of short-circuit fault location in the branching lines is then transformed into several one-dimensional optimization problems, which are then solved by the optimization algorithm. This solves the problem of realizing rapid location in a power network with branches. Numerical experiments are carried out in a distribution network model to demonstrate the effectiveness of the method. Results under different conditions show the method works reliably and efficiently.

Electromagnetic time reversal (EMTR) is drawing increasing interest in short-circuit fault location. In this letter, we investigate the classic EMTR fault location methods and find that it is not necessary to reverse the obtained signal in time which is a standard operation in these methods before injecting it into the network. The effectiveness of EMTR fault location method results from the specific similarity of the transfer functions in the forward and reverse processes. Therefore, we can inject an arbitrary type and length of source in the reverse process to locate the fault. Based on this observation, we propose a new EMTR fault location method using direct convolution. This method is different from the traditional methods, and it only needs to pre-calculate the assumed fault transients for a given network, which can be stored in embedded hardware. The faults can be located efficiently via direct convolution of the signal collected from a fault and the pre-stored calculated transients, even using a fraction of the fault signal.

This paper focuses on the three-dimensional simulation of the photoionization in streamer discharges, and provides a general framework to efficiently and accurately calculate the photoionization model using the integral form. The simulation is based on the kernel-independent fast multipole method. The accuracy of this method is studied quantitatively for different domains and various pressures in comparison with other existing models based on partial differential equations (PDEs). The comparison indicates the numerical error of the fast multipole method is much smaller than those of other PDE-based methods, with the reference solution given by direct numerical integration. Such accuracy can be achieved with affordable computational cost, and its performance in both efficiency and accuracy is quite stable for different domains and pressures. Meanwhile, the simulation accelerated by the fast multipole method exhibits good scalability using up to 1280 cores, which shows its capability of three-dimensional simulations using parallel (distributed) computing. The difference of the proposed method and other efficient approximations are also studied in a three-dimensional dynamic problem where two streamers interact.

This paper summarizes the electromagnetic time reversal (EMTR) technique for fault location, and further numerically validates its effectiveness when the fault impedance is negligible. In addition, a specific EMTR model considering the fault impedance is derived, and the correctness of the model derivation is verified by various calculation methods. Based on this, we found that when the fault impedance is large, the existing EMTR methods might fail to accurately locate the fault. We propose an EMTR method that improves the location effect of high-impedance faults by injecting double-ended signals simultaneously. Theoretical calculations show that this method can achieve accurate location for high-impedance faults. To further illustrate the effectiveness, the proposed method is compared with the existing EMTR methods and the most commonly used traveling wave-based method using wavelet transform. The simulation results show that the proposed double-ended EMTR method can effectively locate high-impedance faults, and it is more robust against synchronization errors compared to the traveling wave method. In addition, the proposed method does not require the knowledge or the a priori guess of the unknown fault impedance.

Electric field distribution is critically important for quantitative insights into the physics of non-equilibrium plasma like corona. To analyze the electric field as well as the ion flow (space charge) distribution under DC corona discharges, the ion flow model has been widely adopted; Kaptzov's assumption, which states the {steady state} electric field at the conductor surface remains at the corona onset value, serves as a boundary condition. In this letter, we investigate the electric field distribution under DC corona discharges between coaxial cylindrical electrodes in ambient air by electric field induced second harmonic generation with nano-second pulse laser beams. The electric field distribution (with or without corona discharge) is obtained. By comparing the measurements with the results predicted by the ion flow model for negative corona discharge, it is found that the electric field at the conductor surface is proportional to the current density of the corona discharge with a negative constant of proportionality. Therefore, for negative corona discharges, Kaptzov's assumption is valid only when the discharge current approaches zero or is small., Comment: 5 pages

In this paper, we propose an efficient and accurate message-passing interface (MPI)-based parallel simulator for streamer discharges in three dimensions using the fluid model. First, we propose a new second-order semi-implicit scheme for the temporal discretization of the model that relaxes the dielectric relaxation time restriction. Moreover, it requires solving the Poisson-type equation only once at each time step, while the classical second-order explicit scheme typically needs to do twice. Second, we introduce a geometric multigrid preconditioned FGMRES solver that dramatically improves the efficiency of solving the Poisson-type equation with either constant or variable coefficients. We show numerically that no more than 4 iterations are required for the Poisson solver to converge to a relative residual of $10^{-8}$ during streamer simulations; the FGMRES solver is much faster than R&B SOR and other Krylov subspace solvers. Last but not least, all the methods are implemented using MPI. The parallel efficiency of the code and the fast algorithmic performances are demonstrated by a series of numerical experiments using up to 2560 cores on the Tianhe2-JK clusters. For applications, we study a double-headed streamer discharge as well as the interaction between two streamers, using up to 10.7 billion mesh cells.

Previous studies of streamer discharge branching mechanisms have mainly been generative other than predictive. To predict or even control branching, a reliable connection between experimental conditions and streamer branching needs to be established. As an important step toward the goal, in this work, a 2D deterministic model of negative streamers in air is numerically solved with the ionization seeds assumed as the superposition of Gaussians. The "indicative profiles approach" developed here can consistently relate the change in a quantitative measure of geometrical irregularity of the seed profiles with specific electron densities to the emergence of front splitting of streamer discharges under various voltages, seed characteristic sizes, and preionization levels. The results of this study could inform experiments to identify and clarify streamer branching mechanisms.

A leader is an electric discharge mechanism in long-air-gap discharges. In this work, we report the shock wave phenomenon in an air-gap leader discharge observed using a Mach-Zehnder interferometer with a time resolution of several microseconds. The continuous temporal evolution of the shock wave and the plasma channel was recorded and reproduced with a thermo-hydrodynamic model based on the measured current. The wave propagated at nearly the speed of sound, and the simulation results for the shock wave front positions and the plasma channel radius showed good consistency with the experimental measurements. Detailed thermal parameters obtained through the simulation showed that continuous energy injection by the current results in a temporary over-pressure process in the plasma channel and produces the shock wave.

The simulation of electrical discharges has been attracting a great deal of attention. In such simulations, the electric field computation dominates the computational time. In this paper, we propose a fast tree algorithm that helps to reduce the time complexity from $O(N^2)$ (from using direct summation) to $O(N\log N)$. The implementation details are discussed and the time complexity is analyzed. A rigorous error estimation shows the error of the tree algorithm decays exponentially with the number of truncation terms and can be controlled adaptively. Numerical examples are presented to validate the accuracy and efficiency of the algorithm.

In this work, we propose and compare four different strategies to simulate the fluid model for streamer propagation in one-dimension (1D) and quasi two-dimension (2D), which consists of a Poisson's equation for particle velocity and two continuity equations for particle transport. Each strategy involves of one method for solving Poisson's equation and the other for solving continuity equations, and a total variation diminishing three-stage Runge-Kutta method in temporal discretization. The numerical methods for Poisson's equation include finite volume method, discontinuous Galerkin methods, mixed finite element method and least-squared finite element method. The numerical method for continuity equations is chosen from the family of discontinuous Galerkin methods. The accuracy tests and comparisons show that all of these four strategies are suitable and competitive in streamer simulations from the aspects of accuracy and efficiency. Results show these methods are compatible. By applying any strategy in real simulations, we can study the dynamics of streamer propagations in both 1D and quasi 2D models.

Assumed having axial symmetry, the streamer discharge is often described by a fluid model in cylindrical coordinate system, which consists of convection dominated (diffusion) equations with source terms, coupled with a Poisson's equation. Without additional care for a stricter CFL condition or special treatment to the negative source term, popular methods used in streamer discharge simulations, e.g., FEM-FCT, FVM, cannot ensure the positivity of the particle densities for the cases in attaching gases. By introducing the positivity-preserving limiter proposed by Zhang and Shu \cite{ppl} and Strang operator splitting, this paper proposed a finite difference scheme with a provable positivity-preserving property in cylindrical coordinate system, for the numerical simulation of streamer discharges in non-attaching and attaching gases. Numerical examples in non-attaching gas (N$_2$) and attaching gas (SF$_6$) are given to illustrate the effectiveness of the scheme.

Streamer discharges are important both in theory and industry applications. This paper proposed a local discontinuous Galerkin method to simulate the convection dominated fluid model of streamer discharges. To simulate the rapid transient streamer discharge process, a method with high resolution and high order accuracy is highly desired. Combining the advantages of finite volume and finite element method, local discontinuous Galerkin method is such a choice. In this paper, a simulation of a double-headed streamer discharge in nitrogen was performed by using 1.5-dimensional fluid model. The preliminary results indicate the potential of extending the method to general streamer simulations in complex geometries.