A computer modelling and its partial experimental

Pramana – J. Phys. (2022) 96:1 © Indian Academy of Scienceshttps://doi.org/10.1007/s12043-021-02243-5

A computer modelling and its partial experimental validation tostudy the attenuation of electromagnetic waves in plasma usingCST MICROWAVE STUDIO®

HIRAL B JOSHI1,2 ,∗, N RAJAN BABU1, AGRAJIT GAHLAUT1, RAJESH KUMAR1 andASHISH R TANNA2

1Institute for Plasma Research, Gandhinagar 382 428, India2School of Science, RK University, Rajkot 360 020, India∗Corresponding author. E-mail: [email protected]

MS received 10 August 2020; revised 10 July 2021; accepted 9 August 2021

Abstract. There is a huge interest among the scientific fraternity to generate plasma that can selectively absorbor reflect the incident microwaves. Simulations have been carried out to study the absorption of microwaves inplasma using plane wave as a source. In real experiments, the source of microwaves is not always a plane waveand hence the exact simulated replication of the experiment cannot be done using a plane wave source. In order togenerate the exact experimental conditions, a horn antenna has been designed and used as a source. A computermodel to study the attenuation of X-band (8–12) microwaves in a plasma medium is prepared and partially validatedusing suitable initial experiments. The study can be extended to any target microwave frequency band. The presentwork discusses the preliminary simulations that are carried out to study the effect of plasma frequency (ωp) andcollisional frequency (υc) on attenuation of microwaves (MW) of 8–12 GHz using CST®MWS®. The plasma istreated as a Drude dispersive material whose properties are governed by two plasma parameters, namely plasmafrequency (ωp) and collisional frequency (υc). The simulation is carried out on an array of plasma tubes enclosedin a housing made of teflon. This chamber is then illuminated with microwaves using a horn antenna unlike othersimulations where the source of the signal is a plane wave. Using a horn antenna as the transmitter and receiverallows exact simulation of the experimental conditions in the laboratory. The amount of attenuation is measuredby considering the difference in return losses with and without plasma. The attenuation of incident microwave isstudied by varying plasma frequency from 0.02 GHz to 3 GHz at a fixed collisional frequency of 1010 S−1. Thesimulation is also carried out by varying υc from 108 to 1011 S−1 at a constant ωp. An experiment to validate thesimulation is designed to validate the simulation results. For experimental purpose, fluorescent tube array (FTA),which is a series connection of commercially available tubes is excited using a high-frequency power supply ofsuitable voltage. The simulation and initial experimental results are compared and are in good agreement with eachother. This model serves as a tool to study the attenuation of MW in plasma with given ωp and υc well before theexperiment is carried out. This can also be used to select optimum working points for further experiments.

Keywords. Electromagnetic wave absorption; Drude model; computer simulation technology; plasma.

PACS Nos 02.70.–c; 52.25.–b; 52.40.Fd; 52.77.–j

1. Introduction

It is interesting to the study the interaction of plasma andelectromagnetic waves, as the plasma can be an absorberof electromagnetic waves under certain plasma condi-tions [1,2]. In the study of the reflection and absorptioncharacteristics of EM wave in atmospheric plasma,Vidmar suggested that tenuous plasmas in the Earth’satmosphere from sea level to 100 km can be modelled

as cold collisional plasma [2]. The plasma is capableof reflecting or absorbing microwaves if the density fol-lows an Epstein profile [2]. The magnitude of absorptiondepends upon plasma parameters such as plasma den-sity and temperature. The interaction of microwaves hasa functional dependence on the electron number densityne, collisional frequency fc and angle of incidences.Vidmar further stated that a low density, collisionalplasma is less reflective of microwaves [2].

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1 Page 2 of 8 Pramana – J. Phys. (2022) 96:1

Interaction of microwaves with inhomogeneous plasmacolumn has been extensively studied using numericalmethods. The parabolic plasma density profile assumedfor the numerical computations closely approximatesthe actual profile encountered in the discharge tube [3].The attenuation of EM waves of 7–12 GHz was studiedtheoretically for capacitively-coupled plasma by usingthe plasma parameters obtained from the preliminaryexperiments [4]. It showed that transmission attenua-tion of −4.5 dB was obtained. A similar measurementwas done experimentally to measure the transmissionattenuation in an anechoic chamber. Yeh and Ruschstudied the interaction of microwaves with inhomoge-neous and anisotropic plasma column by assuming aparabolic density profile for the numerical calculation[3]. Zhang et al studied the scattering of microwavesby underdense inhomogeneous plasma column [5]. Thesimulation was carried out using the finite differencetime domain (FDTD). The results show that a parabolicdistribution of electron density in the plasma columnis relatively more effective for scattering of MWs [5].There have been several studies [1,2,4] on plasma as themicrowave reflector or the absorber based on its appli-cation in the field of RADAR communication. Shen etal observed that plasma with density above n ≥ 1.2× 1018 m−3, produced by using low ionisation energyorganic gas microwaves of X-band can be absorbed [6].A similar study has been carried out by Zhang andScharer, where plasma was generated using low ion-isation potential gas such as tetrakis (dimethylamino)ethylene (TMAE) [7,8]. The peak density observed inthis study was ne = 5×1013 cm−3 and the peak electrontemperature was 1 eV. An investigation has been madeby Klein et al of the interaction of MW radiation witha non-uniform plasma for both normal and non-normalincidence of radiation [9]. The results show that for alarge range of collisional frequencies, a major fractionof the incident radiation is absorbed by plasmas. Theabsorption coefficients remain large over a wide rangeof angles of incidence but goes down rapidly beyond 45degrees [9]. Takeda et al experimentally examined thereflected power of X-band microwaves from the plasmaslab with a metal wall at its back side by carrying out anexperiment using the repeated pulses of high DC voltage[10]. A similar study was done by Srivastava et al usingthe helium glow discharge at atmospheric pressure. Heretoo microwave of 10 GHz was launched into the plasmaand the attenuation was measured as a function of elec-tron plasma density [11]. Yeh studied the reflection andtransmission of EM waves in a moving plasma column[12,13]. Bo et al experimentally studied the interactionof microwaves with collisional combustion plasma [14].They found that the density from 1017 m−3 to 1019 m−3

and collisional frequency of about 5× 1010 s−1 gave an

attenuation more than 18 dB. The simulations carriedout so far used plane wave or an ideal source of elec-tromagnetic waves. In real experiments however, hornis used for such measurements.

A simulation is carried out to study the absorption ofmicrowaves before the experiment is carried out usingCST MWS. The present simulation is carried out usingthe Drude dispersion model which explains the prop-agation of electromagnetic waves in cold collisionalplasma. According to this model, the plasma is treatedas a stationary medium with a fixed permittivity. Thepermittivity of a Drude material is dependent on twoplasma parameters, namely electron plasma frequencyωp and electron neutral collisional frequency υc. Interms of electromagnetic properties, one may defineplasma as a non-homogeneous, non-linear and disper-sive medium. Unlike other simulations, the source usedhere for launching the microwaves is a horn antennawhose dimensions are similar to that of a commercialantenna. This ensures the exact simulation of the exper-imental set-up with all errors. The aim of this study is toproduce a simple simulation model to study the absorp-tion of microwaves in plasma of various densities andtemperature. This will be a useful tool for further exper-iments in similar configurations.

The paper is organised as follows. A model to studythe microwave absorption is discussed in §2. Procedurefor carrying out simulation is discussed in §3. Initialexperimental set-up is discussed in §4. Section 5 dis-cusses the simulation and experimental results and §6presents the conclusion and future scope of the study.

2. Model and validation

The model to study the attenuation is based on the free-space measurement method known as the radar cross-section reduction (RCS) method. Here, the antenna usedfor transmitting and receiving the microwaves is thesame. Plasma is placed between the metallic plate andthe antenna. The signal is received at the same antennaafter passing through the plasma medium and gettingreflected from the metallic back plates. The details ofeach sub-part of the model are given as follows.

2.1 Modelling of horn antenna

A horn antenna is modelled as shown in figure 1 whosedimensions are the same as that of the antenna used formicrowave absorption experiments. The dimensions ofthe flare of the horn antenna are 103 mm × 130 mm. TheS11 parameter and gain of the antenna are obtained usingthe simulation and are compared with the datasheetprovided by the manufacturer (Vector Telecom) of theantenna.

Pramana – J. Phys. (2022) 96:1 Page 3 of 8 1

Figure 1. Model of the horn antenna.

Figure 2. Gain vs. frequency plot (simulation).

Figure 2 shows the gain of the horn antenna simulatedfor the X-band. It can be seen that the gain of the simu-lated horn antenna is above 19 dB over the entire rangeof frequency. A similar result is seen in figure 3 which isthe gain vs. frequency plot from the datasheet providedby the manufacturer of the commercial antenna. A com-parison of figures 2 and 3 show good agreement betweenthe results. This ensures that further simulations carriedout with this antenna is comparable to the exact exper-imental conditions. For carrying out further studies, amaterial has to be selected that can hold plasma and isalso transparent to microwaves.

2.2 Study of transmission property of teflon

The simulation was carried out to study whether teflonis a suitable candidate for making the plasma chamber.The aim of this simulation is to find out which material istransparent to microwave and can also be machined into

Figure 3. Gain vs. frequency plot (datasheet).

Figure 4. Simulation configuration.

vacuum vessel that will hold the plasma. Two antennaswere placed on either side of the material in the near-field region of the antenna as shown in figure 4. Thereceived MW power, after passing through the mate-rial, was measured with respect to the power radiatedthrough the transmitting antenna. The dimension of theteflon block is 30 cm × 30 cm × 5 cm (L × B × H ).The S21 parameter was obtained to find out the trans-mission capability of the material to hold plasma. Thetransmitting and receiving horns were placed on eitherside of the material under test, i.e., teflon (PTFE - polyte-trafluoroethylene). The transmission properties of teflonwere compared with that of a metallic plate of the samedimension.

A similar experiment was carried out to validate theresults. The experiments were carried out in the near-field region. The dimensions of the teflon block andthe experimental configuration were exactly like thatin the simulation. Figure 6 shows the experimental con-figuration. A Keysight make N9926A Vector NetworkAnalyzer (VNA) is used to transmit the MW signal fromport 1 to port 2. Scattering parameter S21 was measuredto get the transmission coefficient of the medium.


Figure 5. Simulation result.

Figure 6. Experimental configuration.

Figure 7. Experimental result.

Figures 5 and 7 show the results obtained in simulationand experiment respectively. After the experimental andsimulation study, teflon is chosen as the material for fur-ther studies. After deciding the material to make plasmachamber, a model of plasma is made which can facilitatethe study.

2.3 The plasma model

The plasma model presented here is constructed assum-ing plasma to be Drude material. According to thisassumption, the plasma is treated as a stationary mediumwith a given permitivity which is also known as coldplasma approximation. The relative permitivity (εp) ofcollisional, unmagnetised cold plasma is given by theequation

εp =(

1 − ω2p

ω2 + υ2c

)− i

υc

ω

(1 − ω2

p

ω2 + υ2c

)

where

ωp =√

ne e2

me ε0

is the plasma frequency in rad/s, ω is the angularfrequency of the incident microwaves and υc is the col-lisional frequency. From the equation it is clear thatthe permitivity is dependent on two key parameters ofplasma, i.e. plasma frequency and collisional frequency.The model is suitable as the interest of this study liesin the propagation of MW through a plasma mediumand not in the evolution of plasma or its production.This model of plasma takes care of the interaction ofmicrowaves with the plasma. It must be noted here thatthe model treats plasma as a stationery medium witha specified permitivity. This does not account for thetransient changes in the plasma parameters. With thismodel, further simulations were carried out to obtainthe S-parameters.

3. The simulation methodology

A teflon block of 70 mm thickness, 560 mm length and350 mm height is modelled to house the plasma as shownin figure 8 making a fluorescent tube array (FTA). Cylin-drical Drude material of 40 mm diameter and 550 mmlength is modelled as the plasma inside the teflon blockas shown in the figure. The FTA is placed just before ametal plate which is our device under test (DUT). Twohorn antennas are placed at a far field distance from themetal plate, one as the transmitter and the other as thereceiver.

The microwave signal from the horn antenna passesthrough the plasma chamber and hits the metal platefrom which it gets reflected. The S21 parameter givesthe ratio of power received at the receiver horn to thattransmitted from the transmitter. The S21 parameter ismeasured with and without plasma. The absorption ismeasured by taking the difference of S21 parameter inboth the cases. The plasma frequency and the collisional


Figure 8. Simulation configuration.

Figure 9. Model of plasma tubes embedded in an elliptical cylinder.

frequency are the two parameters that govern the atten-uation of MW inside the plasma. The initial results ofsimulations showed that the sharp edges of the teflonblock gave reflections and as a result the model wasupdated by giving a smooth elliptical cylinder with amajor radius of 180 mm and a minor radius of 45 mm asshown figure 9.

The plasma frequency is varied from 108 rad/s to1011 rad/s at a fixed collisional frequency of 5×1010 s−1.The input for the range of plasma frequency and colli-sional frequency was adapted from the literature survey[2,14–18]. The absorption of MW at various plasma fre-quencies is studied for 8–12 GHz incident frequency.The results of the simulation are discussed in §5.

4. Experimental configuration

Whenever one talk about man-made plasma, the firstcommon example that comes to mind is the commer-cial fluorescent tubes used in our homes. These tubesare filled with argon at 2 Torr pressure with a traceamount of mercury. A teflon block of 70 mm thickness,550 mm length and 350 mm height is used to house aseries connection of seven tubes making an FTA. Fig-ure 10 shows the experimental set-up of the FTA in theanechoic corner. Teflon is used as a holding structure as it

Figure 10. Experimental configuration.

is a microwave-friendly material. Previous experimentswith teflon have shown that not only does it allow thetransmission of microwave through it but also partiallyabsorbs the same at some microwave frequencies. Thisplasma panel is placed inside an anechoic chamber forcharacterisation using the NRL Arch method developedby naval research laboratory that tests the absorptionperformance of the absorber. In this case, two antennas


Figure 11. Experimental set-up inside the anechoic cham-ber.

(transmitter and receiver) are placed on an imaginaryarch of constant radius around the absorber.

The reflection from the absorber is compared to thatfrom a flat metal surface behind it. The angle betweenthe two antennas at the absorber can be 90◦ to 10◦.The radius of the arch must be greater than half of thefar-field distance for that frequency range. The measure-ment is carried out using a signal generator, spectrumanalyser, plasma chamber and two antennas. As shownin figure 11, two antennas are placed in an arch andare connected to the microwave signal generator (Anir-itsu make MG3692C) and as spectrum analyser (Agilentmake N9030A) to transmit and receive the microwavesignals respectively. A wooden fixture for holding thetwo antennas in the arch is fabricated precisely.

To study the absorption of microwaves in the plasmapanel, it is placed at an elevated platform before themetallic target. The metallic target acts as a reflectorof the microwaves. X-band microwaves are transmittedusing a standard gain (20 dB) horn antenna. This trans-mitting antenna is connected to the MW source. Now thereflected signal from the metallic target is received usinganother similar horn antenna. This receiver antenna isconnected to the spectrum analyser. Both the antennasare placed on the arch in such a way that they sub-tend various angles at the centre of the plasma panel.The received microwave power is measured at variousangles over the arch. The minimum angle of measure-ment is 20◦ and the maximum is 60◦. The difference inthe received power with and without plasma is under-stood as the absorption.

Figure 12. Simulation result of absorption in plasma at con-stant collisional frequency.

Figure 13. Simulation result of absorption in plasma at con-stant plasma frequency.

5. Results and discussion

5.1 Simulation results

Figure 12 shows the absorption of microwaves at variousplasma frequencies at a constant collisional frequencyof 5× 1010 Hz.

The absorption of microwaves is observed after aplasma frequency of the order of 1010 rad/s (~2 GHz)which corresponds to an approximate plasma density ofthe order of 1011 cm−3. So, this is the cut-off frequencyof the microwaves. So, any wave with frequency higherthan that can enter the plasma and further the collisionalfrequency takes care of the absorption. This means aminimum plasma frequency is required for the wave tointeract with plasma and absorbed.

Figure 13 shows the absorption pattern with varyingcollisional frequency at a fixed plasma frequency of 5×1010 rad/s.


Figure 14. Comparison of absorption in a rectangular staband elliptical cylinder (simulation).

One may see that maximum absorption is observed ata collisional frequency of the order of 1010 Hz. It shouldalso be noted here that lesser or more frequency than aparticular order reduces the absorption.

A similar study was done by changing the housing ofthe FTA into elliptical shape to reduce the sharp bound-aries. Here the plasma frequency was of the order of afew GHz and collisional frequency was of the order of afew tens of GHz. The comparison of absorption in boththe cases is shown in figure 14.

There is a clear difference in the absorption pattern inboth the cases. The smooth boundaries in the ellipticalcylinder have greatly improved the absorption.

5.2 Experimental results

The initial experimental results of absorption are givennow. Here a metallic target is kept behind the FTA andthe return losses are compared with and without the FTA.

Figure 15 shows the reduction in the RCS of the givenmetallic target in 8–12 GHz. It can be observed that thereis 30 to 90% reduction in the received power by placingthe plasma panel in front the metallic target. This showsthat the plasma panel has a potential capability to reducethe RCS of the given object. The preliminary resultsshow a promising way for RCS reduction and it can befurther modified to enhance the results.

After carrying out extensive literature survey, it isfound that the typical values of plasma frequency andcollisional frequency are 1010–1011 rad/s and 109–1010 Hz respectively [16–19]. The simulations pre-sented here were carried out using the same parameters.A comparison of simulation and experimental resultsfor rectangular teflon-enclosed FTA can be seen infigure 16.

Figure 15. Experimental results of absorption of X-bandmicrowaves in plasma.

Figure 16. Comparison of simulation and experimentalresults of rectangular teflon-enclosed FTA.

It can be seen from figure 16 that a large portion onmicrowave power is absorbed in the frequency range ofthe X-band. However, there is some reflection at twofrequencies around 9.5 GHz. Moreover, the experimen-tal results show less absorption in the X-band but is asignature of potential capability of simulation and exper-imental comparison.

It is seen that in the absorption pattern in figures 14–16, there are sharp variations at different frequencies.A similar kind of result is observed in the past works[5,20,21] where the absorber of microwave is testedusing free space techniques. There are several mediumsin the path of the incident electromagnetic waves, beforeit hits the target and also same mediums are crossed afterreflection from the target to reach the receiver. When theEM waves pass through these mediums, they experiencemultiple reflections at every boundary. For instance, at


teflon–glass boundary, a part of EM waves will be trans-mitted and some will be reflected back to the receiveror will be scattered in the anechoic environment whichwe believe will be absorbed by the absorbers. A simi-lar reflection–transmission will occur at every boundary.The return loss which we observe is the collective resultof these phenomena which is obviously different forevery frequency in the X-band. Hence, there are sharpvariations in the absorption.

6. Conclusion and future work

Simulation model to study the absorption of microwavein the plasma was prepared using the Drude model forcold plasma. This model is capable of simulating theactual experimental set-up as the source of microwaveis a horn antenna. The model was validated by suitableexperiments carried out in the laboratory. For attenua-tion of microwaves of 8–12 GHz frequency, an operatingrange of plasma frequency and collisional frequency isidentified. Experimental validation of the model wasdone by studying the absorption of X-band microwavesin FTA with teflon enclosure. Future work includes fur-ther experiments by varying plasma parameter whichwas not possible in the FTA. Further experiments tostudy the attenuation of microwaves can be easily car-ried out on the basis of this model. One can estimate theattenuation of microwaves in plasma just by knowingthe shape, density and temperature of the plasma. Thework described in the paper is based on the assumptionthat the plasma has a uniform density. Similar study witha density profile will be carried out in future.

Acknowledgements

The authors are thankful to Mr. Yogesh Jain for hisextended help during the simulation. The authors thankthe director IPR for the constant support and inputs dur-ing the work. The simulations for the work described inthis paper were performed on ANTYA, an IPR Linux

cluster. The authors are also thankful to Mr PrashantKumar for his help in using the HPC, ANTYA.

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A computer modelling and its partial experimental