Computational and Data Driven Approaches for Investigation of Microwave-Plasma Interaction

Abstract

Microwave-plasma interaction and High power microwave (HPM)breakdown involving plasma formation have been studied theoreticallyas well as experimentally since the 1950s for a wide variety of applications.Microwave plasma interaction can be classified into two broad categories,firstly involving low power non-ionizing waves and secondly high powerionizing waves leading toHPMbreakdown. Early studies onHPMbreakdownprimarily focused on the determination of the breakdown field as a functionof pressure, frequency and pulse duration. However, only recently, detailedexperimental investigations of the plasma dynamics during breakdownhave been possible with the use of sophisticated high-speed ICCD cameras.Particularly, in the past few years, several experiments and numericalsimulations using millimeter and sub-millimeter wave irradiation ( 100 GHz)at high pressures (ten to hundreds of Torr) have been carried out. The renewedinterest in this area is primarily because of two reasons. Firstly, the potentialapplications of such discharges to aerodynamic flow control, combustionignition, flame stabilization and to propulsion have been investigated veryrecently. Secondly, the dynamics of high frequency wave breakdown at highpressures leading to formation of complex plasma structures (spatio-temporalpropagation of plasma) such as self-organized plasma arrays is a subject ofgreat interest from scientific point of view.To completely understand the physics and properties of different types ofdischarges associated with microwave breakdown, it is crucial to furtherimprove our current understanding of the microwave-plasma interactionand plasma formation at high pressures. To fully utilize the potential of thispromising area of research, it is crucial to understand microwave-plasmainteractions, both in the context of low-power non-ionizing microwaves andwhen the power is sufficient to ionize the gaseous species and form plasma.Modeling and simulation of the strong coupling between the high frequencyEM waves and the plasma is still a challenging research problem due tothe different time and space scales involved in the process. Particularlyaccurate 2D/3D simulations are computationally very expensive and werequire new efficient computational approaches to investigate this problemfor real life applications. Most of the computational studies reported in theliterature till now (particularly recent 2D simulations) have focused only onthe wave scattering by the plasma and ionization-diffusion mechanism forplasma evolution (time scale of 100s of nanoseconds) due to computationalconstraints. Researchers have primarily studied this problem using asimple model wherein Maxwell�s equations have been coupled with plasmacontinuity equations and these models have been used to investigate theplasma dynamics in nanosecond timescales.As a first step, we have developed a comprehensive computational modelfor investigating microwave-plasma interaction and different kinds ofmillimeter wave breakdown at high pressures. An in-house 2D simulatorhas been implemented in C language and the validity of the code has beenestablished by directly comparing the simulation results with the experimentalobservations available in the literature. The computational tool consist ofthree computational solvers (EM wave solver, Plasma solver and Fluid solver)coupled with each other. The inputs to this computational tool are the fieldstrength of the EM wave, frequency of the wave, pressure and gas details. Theimportant output required for investigating the physics of plasma dynamicsare: plasma density, electric field distribution, electron temperature, gasdensity distribution etc.As a second step, to address the computational challenges associated withsuch simulations, a self-aware mesh refinement algorithm has been presentedthat uses a coarse mesh and a fine mesh that dynamically expands based on theplasma profile topology to resolve the sharp gradients in E-fields and plasmadensity in the breakdown region. The dynamic mesh refinement (DMR)technique is explained in detail, and its performance has been evaluatedusing two metrics, the accuracy and efficiency, on a standard benchmarkmicrowave breakdown problem. Different 2-D simulations are performed tocapture the front velocity and the filamentary pattern formation, and, resultsare compared for DMR (different refinement factors (r = 2, 4)) with the resultsobtained from uniform fine mesh. From the efficiency analysis, we observea speedup of 8 (of the order of O(r3), when the refinement factor (r) is 2)compared to a traditional single uniform fine mesh-based simulation. Thetechnique is scalable and performs better when the problem size increases.Two applications related to HPM breakdown have been explored usingour in-house 2D simulator, one associated with the protection of electroniccomponents and the second on HPM swtching. Breakdown thresholds, thefield strength and the initial plasma density that determines breakdowntime for such applications are reported. The dependence of cutoff time oninitial plasma as well as strength of microwave E-field are investigated. Thetransmission and rejection capability of plasma for certain frequencies areinvestigated. Additionally, effect of gas heating on the HPM breakdowninduced plasma and the cutoff time is studied for switching and limiter action.We propose a completely new machine learning based data driven approachfor investigation of microwave-plasma interaction. Complete deep learning(DL) based pipeline to train, validate and evaluate the model has beendiscussed in this thesis. A convolutional neural network (CNN)-based deeplearning model, inspired from UNet with series of encoder and decoder unitswith skip connections, for the simulation of microwave-plasma interactionhas been discussed. The microwave propagation characteristics in complexplasma medium pertaining to transmission, absorption and reflectionprimarily depends on the ratio of electromagnetic (EM) wave frequency andelectron plasma frequency, and the plasma density profile. The scattering ofa plane EM wave with fixed frequency (1 GHz) and amplitude incident ona plasma medium with different Gaussian density profiles (in the range of1 � 1017 ? 1 � 1022m?3) have been considered. The training data associatedwith microwave-plasma interaction has been generated using 2D-FDTD(Finite Difference Time Domain) based simulations. The trained deep learningmodel is then used to reproduce the scattered electric field values for the1GHz incident microwave on different plasma profiles with error margin ofless than 2%. We compare the results of the network, using various metricslike SSIM index, average percent error and mean square error, with thephysical data obtained from well-established FDTD based EM solvers. Theproposed deep learning technique is significantly fast as compared to theexisting computational techniques, and can be used as a new, prospectiveand alternative computational approach for investigating microwave-plasmainteraction in a real time scenario.Most of the plasma applications and research in the area of low-temperatureplasmas (LTPs) is based on accurate estimation of plasma density and plasmatemperature. The conventional methods for electron density measurementshave major disadvantages of operational range (not very wide), cumbersomeinstrumentation, and complicated data analysis procedures. To address suchpractical concerns, the thesis further proposes a novel machine learning(ML) assisted microwave-plasma interaction based strategy which is capableenough to determine the electron density profile within the plasma. Theelectric field pattern due to microwave scattering is measured to estimate thedensity profile. The proof of concept is tested for a simulated training data setcomprising a low-temperature, unmagnetized, collisional plasma. Differenttypes of Gaussian-shaped density profiles, in the range 1016 ? 1019m?3,addressing a range of experimental configurations have been considered inour study. The results obtained show promising performance in estimatingthe 2D radial profile of the density for the given linear plasma device.The performance of the proposed deep learning based approach has beenevaluated using three metrics- SSIM, RMSLE and MAPE. The favourableperformance affirms the potential of the proposed ML based approach inplasma diagnostics and in future to replace existing plasma diagnostics.In conclusion, the thesis presents new approaches for investigation ofmicrowave-plasma interaction and HPM breakdown, which are significantlyefficient compared to existing simulation techniques. To the best of ourknowledge, this is the first effort towards exploring a data-driven DL basedapproach for the simulation of complex microwave plasma interaction. Thesimulations presented in the thesis provide a better understanding of bothionizing and non-ionizing applications of microwave-plasma interaction.They contribute to the study of complex plasma dynamics associated withhigh-frequency HPM breakdown-induced plasma, with potential applicationssuch as switching/limiters, and plasma diagnostics.