High Power Microwave Breakdown Research Articles

Transient Analysis of High-Power Microwave Air Breakdown under External DC Magnetic Field

This article concentrates on the high-power microwave (HPM) breakdown process and behaviors in air-filled rectangular waveguide under the external dc magnetic field. To solve the persuasive issue, a three-dimensional (3-D) multiphysics model coupling full-wave Maxwell’s equations with plasma fluid equations is established and solved by the spectral-element time-domain (SETD) method. In our simulation, the Galerkin’s method is employed for the space discretization and the central difference scheme is used for the temporal discretization during the SETD process. The numerical results reveal that the external dc magnetic field applied in breakdown volume can significantly enhance the breakdown threshold to suppress the HPM breakdown, which is beneficial for the propagation of HPM pulse in air-filled waveguide. Our research provides theoretical guidance for suppressing the impact of HPM breakdown for HPM devices protection.

Space and time evolution of high-power microwave breakdown on the atmosphere side of the dielectric surface

The high-power microwave breakdown on the atmosphere side of the dielectric surface leads to the formation of the thin plasma layer. A two-dimensional model coupling Maxwell’s equations with quasi-neutral plasma fluid equations is used to study the breakdown evolution. We concentrate on the breakdown caused by the incident electric field parallel to the dielectric surface. The results show that the electric field enhancement at the tips of plasmoid in the direction parallel to the dielectric surface accelerates the propagation of the plasma front, while the propagation speed in the perpendicular direction decreases in time since the upstream plasma collapses the local electric field. The difference between the two speeds is responsible for the formation of the thin plasma layer. The effect of air pressure on the breakdown evolution is discussed. The breakdown delay time from simulations as a function of pressure shows the same trend as the experiment.

Accelerated simulation of microwave breakdown in gases on Xeon Phi based cluster-application to self-organized plasma pattern formation

Modeling and simulation of high power microwave (HPM) breakdown, involving complex coupling between high frequency electromagnetic wave and plasma, is a computationally challenging and expensive problem due to the stringent numerical criteria. In this article, efficient parallelization and optimization strategies for two dimensional fluid simulation of microwave breakdown phenomena in air/gas on Intel’s Xeon Phi Many Integrated Core (MIC) data parallel architecture are being presented. The numerical model used for this study is based on Finite Difference Time Domain solutions of Maxwell Equation coupled with the plasma fluid Continuity Equation (Boeuf et al., 2010). The optimized parallel version of this algorithm using OpenMP on Xeon Phi co-processors achieves a speedup of around 5–138 times (on Knights Corner and Knights Landing for different problem sizes) compared to a serial version (on Intel i7-4790 processor) in a much more energy efficient way. Moreover, a hybrid strategy based on OpenMP and MPI, involving a three-level parallelization (instruction level within SIMD VPUs, thread-level over many cores and accelerator level across a cluster of Xeon Phi processors), achieves a speedup of around 1400 (compared to a serial version on xeon-phi 7250 processor) on an HPC cluster with 24 Xeon-Phi co-processors. Several fast and accurate numerical experiments have been performed on the Xeon-Phi based system, and the results are illustrated with the example of the formation of a self-organized fishbone like plasma structure during breakdown similar to the images obtained from high power microwave experiments in air (Hidaka et al., 2008). Numerical experiments show that a good resource utilization can be achieved by proper code design, cache optimization and good programming practices, and opens up many possibilities for HPM breakdown research which require resource intensive EM-fluid simulations as a precursor at a relatively cheap cost.

Interaction of high-power microwave with air breakdown plasma at low pressure

The high-power microwave breakdown at the low air pressure (about 0.01 atm) is simulated numerically using the one-dimensional model coupling Maxwell's equations with plasma fluid equations. The accuracy of the model is validated by comparing the breakdown prediction with the experimental data. We find that a diffuse plasma with a stationary front profile forms due to the large electron diffusion. Most of the incident wave energy is absorbed and reflected by the plasma when the plasma front achieves a stationary profile. The front propagation velocity remains almost unchanged with time and increases when the incident wave amplitude increases or the incident wave frequency decreases. With the incident wave frequency increasing, the maximum density of the stationary plasma front increases, while the ratio of the reflected wave power to the incident wave power remains almost unchanged. At a higher incident wave amplitude, the maximum density and reflectance become large.

Modeling of Plasma Formation During High-Power Microwave Breakdown in Air Using the Discontinuous Galerkin Time-Domain Method

Rapid plasma formation and evolution during high-power microwave (HPM) air breakdown in an HPM device produce a macroscopic plasma shield to the microwave transmission, which can severely limit the performance of the device. In this paper, the electromagnetic (EM)–plasma interaction and the HPM breakdown in air are modeled by a nonlinearly coupled full-wave Maxwell and plasma fluid system under conditions of high pressure and high collision frequency. The resulting multiphysics and multiscale system is solved by a nodal discontinuous Galerkin time-domain (DGTD) method, which is uniformly high order in both space and time. To demonstrate the capability of the DGTD method in the modeling of the HPM breakdown problems, the air breakdown and plasma formation in a metallic aperture are simulated, from which the underlining physical process can be interpreted and better understood.

Theory of Nanosecond High-Power Microwave Breakdown on the Atmosphere Side of the Dielectric Window

This paper deals with the theory of plasma development in the nanosecond high-power microwave breakdown at the dielectric/air interface. Utilizing the Poisson and Boltzmann equations, the basic physics are explored and investigated. Corresponding to the incident electric field, electrons moving back and forth bring about the negative charge accumulation at the interface. This process generates an extra electric field, strengthening the total amplitude. Simultaneously, deviations of electrons and ions lead to a sheath region providing a space charge field. Secondary electrons are strongly accelerated in the sheath region, eventually leading to an ionization avalanche in a very short time. Both the densities and energies of particles reach the maximums near the sheath region, and that is why the illumination is most significant near the interface. The theory is in good accordance with an experiment conducted under the same conditions.

Short-pulse high-power microwave breakdown at high pressures**Project supported by the National Basic Research Program of China (Grant No. 2013CB328904), the NSAF of China (Grant No. U1330109), and 2012 Doctoral Innovation Funds of Southwest Jiaotong University.

The fluid model is proposed to investigate the gas breakdown driven by a short-pulse (such as a Gaussian pulse) high-power microwave at high pressures. However, the fluid model requires specification of the electron energy distribution function (EEDF); the common assumption of a Maxwellian EEDF can result in the inaccurate breakdown prediction when the electrons are not in equilibrium. We confirm that the influence of the incident pulse shape on the EEDF is tiny at high pressures by using the particle-in-cell Monte Carlo collision (PIC-MCC) model. As a result, the EEDF for a rectangular microwave pulse directly derived from the Boltzmann equation solver Bolsig+ is introduced into the fluid model for predicting the breakdown threshold of the non-rectangular pulse over a wide range of pressures, and the obtained results are very well matched with those of the PIC-MCC simulations. The time evolution of a non-rectangular pulse breakdown in gas, obtained by the fluid model with the EEDF from Bolsig+, is presented and analyzed at different pressures. In addition, the effect of the incident pulse shape on the gas breakdown is discussed.

Validity of the two-term Boltzmann approximation employed in the fluid model for high-power microwave breakdown in gas

The electron energy distribution function (EEDF), predicted by the Boltzmann equation solver BOLSIG+ based on the two-term approximation, is introduced into the fluid model for simulating the high-power microwave (HPM) breakdown in argon, nitrogen, and air, and its validity is examined by comparing with the results of particle-in-cell Monte Carlo collision (PIC/MCC) simulations as well as the experimental data. Numerical results show that, the breakdown time of the fluid model with the Maxwellian EEDF matches that of the PIC/MCC simulations in nitrogen; however, in argon under high pressures, the results from the Maxwellian EEDF were poor. This is due to an overestimation of the energy tail of the Maxwellian EEDF in argon breakdown. The prediction of the fluid model with the BOLSIG+ EEDF, however, agrees very well with the PIC/MCC prediction in nitrogen and argon over a wide range of pressures. The accuracy of the fluid model with the BOLSIG+ EEDF is also verified by the experimental results of the air breakdown.

High power microwave breakdown in gas using the fluid model with non-equilibrium electron energy distribution function

The electron energy distribution function (EEDF) is usually assumed to be of the Maxwellian distribution in the fluid model in the simulation of high power microwave breakdown in gas. However, this assumption may lead to some large errors in the simulations. In this paper we compute the non-equilibrium EEDF via solving the Boltzmann equation directly, and incorporate it into the fluid model for argon breakdown. Numerical simulations show that the breakdown time obtained by the fluid model with the non-equilibrium EEDF accords well with the Particle-in-cell-Monte Carlo collision simulation result, while the Maxwellian EEDF has higher energy tail and results in faster breakdown time at low mean electron energy. Based on the non-equilibrium EEDF, the dependence of the breakdown threshold on the pressure predicted by the fluid model accord well with the argon breakdown experimental result.

Imaging of Pressure-Dependent High-Power Microwave Surface Flashover

Open-shutter and intensified charge-coupled device images of high-power microwave breakdown were taken in an effort to characterize the pressure dependence of plasma development. These images were taken with a Nikon D200 and Andor iStar DH734-25U-03, respectively. With the pressures increasing from 200 mtorr to 155 torr, the plasma changes from a diffuse discharge encompassing a large volume to a multichannel structure following the electric field lines.

Numerical studies of the high power microwave breakdown in gas using the fluid model with a modified electron energy distribution function

A modified electron energy distribution function (EEDF) is introduced into the fluid model and its effects on the high power microwave (HPM) breakdown in air and argon are investigated. A proper numerical scheme for the finite-difference time-domain method is employed to solve the fluid model. Numerical simulations show that the HPM breakdown time in argon predicted by the fluid model with the modified EEDF agrees well with the results of Particle-in-cell-Monte Carlo collision simulations, while the Maxwellian EEDF results in faster HPM breakdown when the mean electron energy is less than 20 eV. We also confirm that the Maxwellian EEDF can be used in the fluid model for simulating the air breakdown at the low frequencies based on the reported experiments.

Modeling statistical variations in high power microwave breakdown

Flashover of high power microwave (HPM) vacuum isolation windows presents a serious design limitation of megawatt class HPM systems. The delay time from HPM radiation incident on the window to flashover development on the atmospheric side is critical. Previously developed modeling efforts have yielded reasonable correlation with experimentally observed average delay times while failing to capture any statistical variations. Simply preseeding the volume with an initial electron density is identified as inadequate to describe the source of initiatory electrons. The process of field assisted electron detachment is examined and shown to be a probable candidate for the initiatory electron generation.

Review of recent theories and experiments for improving high-power microwave window breakdown thresholds

Dielectric window breakdown is a serious challenge in high-power microwave (HPM) transmission and radiation. Breakdown at the vacuum/dielectric interface is triggered by multipactor and finally realized by plasma avalanche in the ambient desorbed or evaporated gas layer above the dielectric. Methods of improving breakdown thresholds are key challenges in HPM systems. First, the main theoretical and experimental progress is reviewed. Next, the mechanisms of multipactor suppression for periodic rectangular and triangular surface profiles by dynamic analysis and particle-in-cell simulations are surveyed. Improved HPM breakdown thresholds are demonstrated by proof-of-principle and multigigawatt experiments. The current theories and experiments of using dc magnetic field to resonantly accelerate electrons to suppress multipactor are also synthesized. These methods of periodic profiles and magnetic field may solve the key issues of HPM vacuum dielectric breakdown.

Investigation of the delay time distribution of high power microwave surface flashover

Characterizing and modeling the statistics associated with the initiation of gas breakdown has proven to be difficult due to a variety of rather unexplored phenomena involved. Experimental conditions for high power microwave window breakdown for pressures on the order of 100 to several 100 torr are complex: there are little to no naturally occurring free electrons in the breakdown region. The initial electron generation rate, from an external source, for example, is time dependent and so is the charge carrier amplification in the increasing radio frequency (RF) field amplitude with a rise time of 50 ns, which can be on the same order as the breakdown delay time. The probability of reaching a critical electron density within a given time period is composed of the statistical waiting time for the appearance of initiating electrons in the high-field region and the build-up of an avalanche with an inherent statistical distribution of the electron number. High power microwave breakdown and its delay time is of critical importance, since it limits the transmission through necessary windows, especially for high power, high altitude, low pressure applications. The delay time distribution of pulsed high power microwave surface flashover has been examined for nitrogen and argon as test gases for pressures ranging from 60 to 400 torr, with and without external UV illumination. A model has been developed for predicting the discharge delay time for these conditions. The results provide indications that field induced electron generation, other than standard field emission, plays a dominant role, which might be valid for other gas discharge types as well.

Computational Studies of Filamentary Pattern Formation in a High Power Microwave Breakdown Generated Air Plasma

Simulations of the dynamics of high power microwave breakdown of air at atmospheric pressure and 110 GHz are presented. The model reproduces well the formation and motion of filamentary plasma arrays observed experimentally with fast camera imaging. The numerical model is based on finite-difference time domain solutions of Maxwell equations coupled with a simple fluid description of the plasma growth and diffusion. The computational procedure is discussed in details along with numerical experiments, to show the sensitivity of the results to different numerical parameters.

Single and repetitive short-pulse high-power microwave window breakdown

The mechanisms of high-power microwave breakdown for single and repetitive short pulses are analyzed. By calculation, multipactor saturation with electron density much higher than the critical plasma density is found not to result in microwave cutoff. It is local high pressure about Torr class that rapid plasma avalanche and final breakdown are realized in a 10–20 ns short pulse. It is found by calculation that the power deposited by saturated multipactor and the rf loss of protrusions are sufficient to induce vaporizing surface material and enhancing the ambient pressure in a single short pulse. For repetitive pulses, the accumulation of heat and plasma may respectively carbonize the surface material and lower the repetitive breakdown threshold.

Theory and Modeling of Self-Organization and Propagation of Filamentary Plasma Arrays in Microwave Breakdown at Atmospheric Pressure

High power microwave breakdown at atmospheric pressure leads to the formation of filamentary plasma arrays that propagate toward the source. A two-dimensional model coupling Maxwell equations with plasma fluid equations is used to describe the formation of patterns under conditions similar to recent experiments and for a wave electric field perpendicular to the simulation domain or in the simulation domain. The calculated patterns are in excellent qualitative agreement with the experiments, with good quantitative agreement of the propagation speed of the filaments. The propagation of the plasma filaments is due to the combination of diffusion and ionization. Emphasis is put on the fact that free electron diffusion (and not ambipolar diffusion) associated with ionization is responsible for the propagation of the front.

不同气压下介质表面高功率微波击穿的数值模拟

不同气压下介质表面高功率微波击穿的数值模拟

Global model for high power microwave breakdown at high pressure in air

Global models (GM) have proven a key tool for modeling low temperature plasmas for materials processing due to simplicity and speed. However, a GM requires specification of the electron energy distribution function (EEDF). The assumption of a Maxwellian EEDF leads to inaccurate power absorption and reaction rate coefficients and results in errors in plasma parameter prediction in high power microwave (HPM) driven discharges. In this work, a GM was developed with a pressure-independent enhanced EEDF and enhanced power absorption model to improve fidelity for modeling HPM breakdown, and extended to two decades in applied frequency. The GM is applied to HPM breakdown in air at high pressure and over a wide frequency range, and results compared well with PIC-MCC simulations as well as experimental data.

Effect of microwave frequency on breakdown and electron energy distribution function using a global model

Global models (GMs) have proven a key modeling tool for the plasma processing field due to simplicity and speed. However, a GM requires specification of the electron energy distribution function (EEDF). The assumption of a Maxwellian EEDF leads to inaccurate reaction rate coefficients and results in error in plasma parameter prediction in high power microwave (HPM) driven discharges. Recently, a GM was developed with a pressure-independent enhanced EEDF to improve fidelity for modeling HPM breakdown. In this work, the GM is extended to 2 decades in frequency, and the frequency effect on HPM breakdown and the EEDF is investigated.