Impedance Matching and PSpice R Simulation of One Atmosphere Uniform Glow Discharge Plasma (OAUGDP ) Reactor/Actuator Systems

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1 University of Tennessee, Knoxville Trace: Tennessee esearch and reative Exchange Masters Theses Graduate School 1-7 Imedance Matching and PSice Simulation of One Atmoshere Uniform Glow Discharge Plasma (OAUGDP ) eactor/actuator Systems Zhiyu hen University of Tennessee - Knoxville ecommended itation hen, Zhiyu, "Imedance Matching and PSice Simulation of One Atmoshere Uniform Glow Discharge Plasma (OAUGDP ) eactor/actuator Systems. " Master's Thesis, University of Tennessee, 7. htt://trace.tennessee.edu/utk_gradthes/69 This Thesis is brought to you for free and oen access by the Graduate School at Trace: Tennessee esearch and reative Exchange. It has been acceted for inclusion in Masters Theses by an authorized administrator of Trace: Tennessee esearch and reative Exchange. For more information, lease contact trace@utk.edu.

2 To the Graduate ouncil: I am submitting herewith a thesis written by Zhiyu hen entitled "Imedance Matching and PSice Simulation of One Atmoshere Uniform Glow Discharge Plasma (OAUGDP ) eactor/actuator Systems." I have examined the final electronic coy of this thesis for form and content and recommend that it be acceted in artial fulfillment of the requirements for the degree of Master of Science, with a major in Electrical Engineering. We have read this thesis and recommend its accetance: eon M. Tolbert, Peter Ping-Yi Tsai (Original signatures are on file with official student records.) J. eece oth, Major Professor Acceted for the ouncil: arolyn. Hodges Vice Provost and Dean of the Graduate School

3 To the Graduate ouncil: I am submitting herewith a thesis written by Zhiyu hen entitled Imedance Matching and PSice Simulation of One Atmoshere Uniform Glow Discharge Plasma (OAUGDP ) eactor/actuator Systems. I have examined the final electronic coy of this dissertation for form and content and recommend that it be acceted in artial fulfillment of the requirements for the degree of Master of Science, with a major in Electrical Engineering. J. eece oth, Major Professor We have read this thesis and recommend its accetance: eon M. Tolbert Peter Ping-Yi Tsai Acceted for the ouncil: arolyn. Hodges Vice Provost and Dean of the Graduate School (Original signatures are on file with official student records.)

4 Imedance Matching and PSice Simulation of One Atmoshere Uniform Glow Discharge Plasma (OAUGDP ) eactor/actuator Systems A Thesis Presented for The Master of Science Degree The University of Tennessee, Knoxville Zhiyu hen December 7

5 DEDIATION ii I would like to dedicate this thesis to my arents, who were research nuclear engineers and devoted most of their rofessional life to the thermal lasma nuclear fusion research rogram of hina. I would like to thank my arents for giving me the gifted talent in science and technology and their influences on me in those fields, and their unconditional suort for my own decision on choosing my life ath.

6 AKNOWEDGMENTS iii I would like to thank Prof. J. eece oth for teaching, mentoring me in the research field of industrial lasma engineering and lasma science and enduring suort for so many years. I would also like to thank all my committee members, including Dr. Peter Ping-Yi Tsai and Dr. eon M. Tolbert, for their advices on and suort of my research rogram. And I would also like to thank all the funding agencies that suorted my research work in the ast years, including UTK enter for Materials Processing (MP), UT Textiles and Nonwovens Develoment enter (TANDE), and the United States Air Force under ontract AF F (OTH), Dr. J. Schmisseur, Program Manager.

7 ABSTAT iv This thesis addresses two imortant issues relevant to One Atmoshere Uniform Glow Discharge Plasma (OAUGDP ) reactors and actuators imedance matching and PSice simulation. An OAUGDP reactor/actuator with the lasma energized can be modeled as a caacitor in arallel with a resistor. In addition, the non-ideality of the transformer between the F ower suly and the lasma reactor/actuator introduces an imaginary comonent in its imedance. Thus, the load of the F ower suly, as seen by its outut terminals, is highly reactive. An imedance mismatch resulting from the absence of a matching network will cause a large reflected ower from the lasma reactor back to the ower suly that does not contribute to lasma formation, but requires an exensive, over-rated ower suly. All the imedance matching networks in the existing literature are for much higher F or microwave lasma alications at low ressures, and they cannot readily be adated to OAUGDP alications, which are normally oerated at lower frequencies and higher voltages. In this thesis, the design, theory, and exerimental erformance of two tyes of low F imedance matching circuits are resented, that match OAUGDP reactors/actuators to their ower sulies. This thesis also considers PSice simulation of the electrical characteristics of OAUGDP reactor/actuator systems. An OAUGDP reactor/actuator system normally includes a ower suly, a transformer, an imedance matching network, and the lasma reactor/actuator. The rincial task in simulation is to develo a comrehensive PSice model for the lasma discharge in an OAUGDP reactor/actuator. In an OAUGDP, at least one electrode is covered with a dielectric, which can be modeled as a caacitor, as can the ga containing the lasma. The lasma discharge itself is modeled as a voltagecontrolled current source that is switched on when the voltage across the ga exceeds the lasma initiation voltage. The outut current follows a ower law of the alied voltage,

8 v an observed henomenological characteristic of the voltage-current behavior of normal glow discharges. Simulation results agree qualitatively and quantitatively with exerimental data from actual reactors/actuators. In addition to simulation of the lasma discharge in OAUGDP reactors/actuators, the modeling of the whole OAUGDP reactor/actuator system including a non-ideal transformer and imedance matching network can hel engineers to imrove the design of actual OAUGDP reactor/actuator systems.

9 TABE OF ONTENTS vi hater Page hater 1 Introduction Motivation ontributions Organization of Text... 6 hater iterature eview Imedance Matching omutational Simulation of Plasma eactors... 8 hater 3 Imedance Matching of OAUGDP eactor/actuator Systems Introduction Secondary-Side Imedance Matching ircuit Definition of Imedance Matching Electrical ircuit Model of OAUGDP eactor with Plasma Initiated Basic Imedance Matching Theory efined Imedance Matching Theory equirement on the Magnitude of the Matching Network Imedance Primary-Side Imedance Matching ircuit Exerimental esults and Discussion... 4 hater 4 PSice Simulation of OAUGDP eactor/actuator Systems Introduction A PSice Model for Parallel-Plate OAUGDP eactors A PSice Model for o-planar OAUGDP Actuators omuter Simulation and omarison with Exerimental esults Discussion and onclusions hater 5 Summary and Discussions ist of eferences Vita... 77

10 IST OF TABES vii Table Table 3.1. Table 4.1. Page Maximum lasma ower with different combinations of inductance and caacitance in the secondary-side matching circuit haracteristic values of the lasma arameters of a arallel-late OAUGDP reactor Table 4.. PSice Simulation Parameters of a Parallel-Plate OAUGDP eactor Table 4.3. PSice Simulation Parameters of a o-lanar Plasma Actuator Panel Table 4.4. PSice Simulation Parameters of a Single Plasma Actuator Stri... 69

11 IST OF FIGUES viii Figure Page Figure 1.1. Schematic of the MOD IV OAUGDP arallel late reactor system... Figure 1.. Photograh of the MOD IV OAUDGP arallel late reactor in oeration. 3 Figure 1.3. Schematic of a symmetric lasma anel to generate a flat layer of OAUGDP lasma... 4 Figure 3.1. Electrical Model of OAUGDP eactor with Plasma Initiated Figure 3.. An OAUGDP system with secondary-side imedance matching circuit.. 13 Figure 3.3. Equivalent ircuit of a Non-ideal Transformer Figure 3.4. Equivalent circuit of the OAUGDP system with secondary-side imedance matching circuit Figure 3.5. An OAUGDP system with rimary-side imedance matching circuit... Figure 3.6. Equivalent circuit of an OAUGDP system with rimary-side imedance matching circuit... Figure 3.7. Simlified equivalent circuit of OAUGDP system with rimary-side imedance matching circuit... 3 Figure 3.8. Exerimentally-obtained voltage (sinusoidal waveform) and current waveforms without imedance matching... 7 Figure 3.9. Time variation over 3 cycles of half the alied voltage (sinusoidal waveform) and the discharge current in the imedance matched MOD V emote Exosure eactor with 11 anels energized (The waveforms were exerimentally-obtained)... 9 Figure 3.1. Time variation over 3 cycles of half the alied voltage (sinusoidal waveform) and the discharge current in the imedance matched MOD V emote Exosure eactor with 11 anels energized (The waveforms were exerimentally-obtained)... 3 Figure Exerimentally-obtained waveforms of the measured ower suly outut voltage and current before the rimary-side matching circuit and the transformer, and the measured discharge current of the rimary-side imedance matched MOD IV OAUGDP arallel late reactor... 31

12 Figure 4.1. A PSice Model for arallel-late OAUGDP reactors Figure 4.. Universal voltage-current characteristic of the D electrical discharge tube [1, Fig. 1.1]. The normal glow discharge regime is between F and G on the diagram Figure 4.3. Schematic of a arallel-late OAUGDP reactor system for PSice simulation... 4 Figure 4.4. Schematic of a flat layer of OAUGDP lasma on a lasma actuator anel 43 Figure 4.5. Photograhs of an OAUGDP actuator anel Figure 4.6. ross section of a flat anel lasma actuator with lasma energized on both sides Figure 4.7. A comrehensive PSice model for a co-lanar OAUGDP actuator anel 46 Figure 4.8. omarison of the actual discharge current with the simulated discharge current for a arallel-late OAUGDP reactor ( Frequency f = 648 Hz, Amlitude of inut voltage at the transformer rimary side V = 4 V, Plasma caacitance [ V ) 1] 3 g V ( i =.5 g nf, Power law of the discharge current: I =, Power-law exonent α = 3) Figure 4.9. omarison of the actual discharge current with the simulated discharge current for a arallel-late OAUGDP reactor ( Frequency f = 63 Hz, Amlitude of inut voltage at the transformer rimary side V = 465 V, Plasma caacitance [ V ) 1] 3 g V ( i =.3 g nf, Power law of the discharge current: I =, Power-law exonent α = 3)... 5 Figure 4.1. omarison of the actual discharge current with the simulated discharge current for a arallel-late OAUGDP reactor ( Frequency f = 618 Hz, Amlitude of inut voltage at the transformer rimary side V = 48 V, Plasma caacitance =.3 g nf, Power law of the discharge current: I = V g V ) 1, Power-law exonent α = 1) ( i Figure Effect of the ower-law exonent α on the shae of discharge current waveforms (All the simulation arameters excet α are the same as those in Fig. 4.8) i i i ix

13 Figure 4.1. omarison of the actual discharge current with the simulated discharge current for a arallel-late OAUGDP reactor ( Matching inductor = 19 mh, Matching caacitor =, Frequency f = 65 Hz, Amlitude of inut voltage at the transformer rimary side V = 84 V, Plasma caacitance =.13 g nf, Power law of the discharge current: I = V g V ) 1, Power-law exonent α = 1) ( i Figure Effect of the caacitor in the imedance matching network [8] on the shae of discharge current waveforms of a arallel-late OAUGDP reactor (All the simulation arameters excet are the same as those in Fig. 4.1) Figure Effect of the inductor in the imedance matching network on the shae of discharge current waveforms of a arallel-late OAUGDP reactor (All the simulation arameters excet are the same as those in Fig. 4.1) Figure Effect of the resistor in the imedance matching network on the shae of discharge current waveforms of a arallel-late OAUGDP reactor (All the simulation arameters excet are the same as those in Fig. 4.1) Figure The simulated discharge current in a arallel-late OAUGDP reactor driven by a ulsed ower suly ( Internal resistance of the ulsed ower suly s = 5 kω, Plasma caacitance =.5 g nf, Power law of the discharge current: I [ V ) 1] 3 g V ( i i =, Power-law exonent α = 3) Figure omarison of the actual discharge current with the simulated discharge current for a co-lanar lasma actuator anel ( Frequency f =1741Hz, Amlitude of inut voltage at the transformer secondary side V = 46 V, Plasma caacitance = 1.4 g nf, dielectric caacitance =.3 d nf, Power law of the discharge current: I = V g V ) 1, Power-law exonent ( i α = 1)... 6 Figure omarison of the actual discharge current with the simulated discharge current for a co-lanar lasma actuator anel ( Frequency f =1741Hz, Amlitude of inut voltage at the transformer secondary side V = 49 V, Plasma caacitance = 1.7 g nf, dielectric caacitance =.7 d nf, Power law of the discharge current: I = V g V ) 1, Power-law exonent ( i α = 1) Figure omarison of the actual discharge current with the simulated discharge current for a co-lanar lasma actuator anel ( Frequency f =1741Hz, o o x

14 Amlitude of inut voltage at the transformer secondary side V = 4 V, Plasma caacitance = 1.5 g nf, dielectric caacitance =. d nf, Power law of the discharge current: I [ V ) 1] 3 g V =, Power-law exonent ( i α = 3) Figure 4.. Transformer outut voltage and lasma actuator anel discharge current observed when the imedance matching circuit was disconnected from the OAUGDP lasma actuator system Figure 4.1. Transformer outut voltage and lasma actuator anel discharge current observed when the imedance matching circuit was disconnected from the OAUGDP lasma actuator system Figure 4.. omarison of the actual discharge current with the simulated discharge current for a single lasma actuator stri ( Frequency f = 1735 Hz, Amlitude of inut voltage at the transformer secondary side V = 56 V, Plasma caacitance =.3 g nf, dielectric caacitance =. d nf, Power law of the discharge current: I [ V ] 3 g V = ) 1, Power-law ( i exonent α = 3) Figure 4.3. Actual discharge current of a single lasma actuator stri oerating in the filamentary mode... 7 o o xi

15 1 hater 1 Introduction 1.1 Motivation The One Atmoshere Uniform Glow Discharge Plasma (OAUGDP ) investigated at the Plasma Sciences aboratory of the University of Tennessee (UT) [1], [] can be oerated in a wide range of geometrical configurations, ranging from a slab lasma between arallel lates [1], to a surface layer of lasma on flat anels [3], all of which are caacitively-couled. The OAUGDP is caable of oerating at one atmoshere in air and other gases, and its active secies can be used, among other things, to sterilize and decontaminate surfaces, or to modify surface characteristics. The OAUGDP generated by a lasma actuator is also caable of accelerating aerodynamic flows [4] and/or imroving aerodynamic flow control [5], [6]. An OAUGDP reactor/actuator characteristically requires a ower suly caable of delivering a few kilowatts at a frequency of 1 1 kilohertz, and an MS voltage of u to kilovolts. Fig. 1.1 shows a schematic of the MOD IV OAUGDP arallel late reactor and Fig. 1. shows a hotograh of it in oeration. Fig. 1.3 shows a schematic of a symmetric lasma anel used to generate a flat layer of OAUGDP lasma. All were develoed at the UT Plasma Sciences aboratory [6] [9]. An OAUGDP reactor/actuator is mainly a caacitive load seen by the ower suly and the secondary side of the transformer. The OAUGDP reactor with lasma energized can be modeled as a caacitor in arallel with a resistor. The transformer converts the low voltage outut of the ower suly to a high voltage for lasma formation. The caacitive lasma reactor can reflect a large art of inut ower back to the ower suly, and in this circumstance, only a small art of the ower suly outut ower is delivered to the lasma, i.e. the lasma reactor is not imedance matched to the

16 HIED WATE POWE SUPPY GAS EXHAUST DIEETI GAS FOW IMPEDANE MATHING NETWOK EETODE SAMPE GAS INET HIED WATE Figure 1.1. Schematic of the MOD IV OAUGDP arallel late reactor system

17 3 Figure 1.. Photograh of the MOD IV OAUDGP arallel late reactor in oeration ower suly. The reflected ower does not contribute to lasma formation, but requires an exensive over-rated ower suly. In addition, the non-ideality of the transformer between the F ower suly and the lasma reactor also contributes an imaginary art to its imedance. Thus, the whole load for the ower suly, seen by its outut terminals, is highly reactive. The imedance of the load seen by the ower suly should be otimized in order that the maximum ower is delivered to the lasma. However, the equivalent imedance of the lasma is strongly deendent on the ower dissiated in it. By changing the arameters of the matching network, the imedance match to the load can be otimized. For otimum erformance, an imedance matching circuit must be inserted between the ower suly and the lasma reactor in order to efficiently generate a high ower OAUGDP. The characteristics of many electrical systems can be simulated with rorietary comutational tools such as PSice. Devices emloying lasmas are embedded in electrical systems and in many situations, it is advantageous to simulate the comlete system, including the lasma, with such commercial software. The One Atmoshere

18 4 HIGH VOTAGE POWE SUPPY UPPE EETODE PASMA DIEETI OWE EETODE Figure 1.3. Schematic of a symmetric lasma anel to generate a flat layer of OAUGDP lasma

19 5 Uniform Glow Discharge Plasma (OAUGDP ) [1], [] reactor/actuator system consists of a ower suly, a transformer, an imedance matching network, and the lasma reactor/actuator. This system is a candidate for simulation with such comutational tools. Simulation of the lasma discharge in OAUGDP reactors/actuators, and modeling of the whole OAUGDP reactor/actuator system, including the non-ideal transformer and imedance matching network, can hel engineers to imrove the design of actual OAUGDP reactor/actuator systems. 1. ontributions In this thesis work, two tyes of imedance matching circuits have been develoed to match OAUGDP reactors/actuators to their ower sulies. The two tyes of matching circuits are referred to as a secondary-side imedance matching circuit, and a rimary-side imedance matching circuit, resectively, according to the matching network s location relative to the transformer. The two imedance matching circuits are designed to satisfy the unique oeration requirements of OAUGDP systems low F frequency, high voltage, and high current. Besides imedance matching, in this thesis work, secific circuit models of One Atmoshere Uniform Glow Discharge Plasma (OAUGDP ) arallel-late reactor and co-lanar actuator systems have been formulated. In addition, simulations of the electrical characteristics of these OAUGDP reactor systems have been obtained with the rorietary circuit simulation software, PSice. Simulation results agree qualitatively and quantitatively with the exerimental data.

20 1.3 Organization of Text 6 hater is a literature review of imedance matching and comutational circuitry simulation of lasmas. hater 3 covers the design, theory, and exerimental results of two imedance matching circuits for OAUGDP reactor/actuator systems. hater 4 covers PSice models of OAUGDP reactor/actuator, simulation results, and comarison with actual discharge current data. hater 5 summarizes this thesis work and contributions.

21 7 hater iterature eview.1 Imedance Matching Imedance matching is a well-studied subject in the fields of F and microwave alications, and there are numerous books secifically devoted to this subject [1] [1]. There are also numerous articles ertaining to the issue of matching a lasma reactor to a ower suly in the literature [13] [17]. The classical Π-tye, T-tye and -tye matching networks [11], [13], [15] [17] should not be alied to the OAUGDP system, since their circuit leg in series with the OAUGDP reactor will share a significant art of the outut voltage of the transformer, and the generation of the OAUGDP needs a higher voltage (4 kv rms kv rms) than low-ressure glow discharge lasmas. Therefore, if a Π-tye, T-tye or -tye matching network is used, the available maximum voltage across the OAUGDP reactor will be significantly decreased and a more exensive transformer caable of generating higher voltages is necessary in order to generate a high ower OAUGDP. To the knowledge of the author, however, the imedance matching techniques and matching networks in the existing literature are for megahertz or microwave lasma alications at low ressures. They cannot readily be adated to alications of the OAUGDP, which is oerated at much lower frequencies (from 1 khz to 1 khz), and much higher voltages (from 4 kv rms to kv rms). Therefore, new imedance matching techniques are needed for OAUGDP alications. The characteristics of OAUGD lasmas can be found in [].

22 . omutational Simulation of Plasma eactors 8 Previous work regarding the comutational simulation of lasma reactors has been ublished [18] [3]. In these aers, simulation of low-ressure lasmas in gaseous discharge lams, ulsed, F and/or inductively couled electrical discharges were investigated. In Wu, et al. s [18] and Ben-Yaakov, et al. s [] aers, they develoed two similar comrehensive SPIE models for low-ressure gaseous discharges in fluorescent lams. The model is basically a voltage-controlled current source. In Shvartsas and Ben- Yaakov s aer [1], they used a behavioral deendent current source to model the high density discharge in gaseous discharge lams. In Howood s aer [3], an inductivelycouled lasma is modeled as a single current loo with an inductance and a resistance. Other aers rovide lasma circuit models caable of incororation into circuit simulations, although simulation was not reorted [4] [6]. In Ben Gadri s aer [7], the hysical rocesses in such a lasma were simulated by one-dimensional numerical methods. However, his simulation was not a comlete OAUGDP reactor/actuator system, and simulation of such a system has not been reorted by other researchers. In an OAUGDP system, the inductor and caacitors in the imedance matching network [8], the ower suly, and the transformer are ordinary electrical comonents and have well-develoed PSice models. However, there is no available electrical model in PSice for the lasma discharge in an OAUGDP reactor/actuator, so a rincial task in develoing such a simulation is to develo such a model.

23 9 hater 3 Imedance Matching of OAUGDP eactor/actuator Systems 3.1 Introduction An OAUGDP reactor/actuator is mainly a caacitive load seen by the ower suly and the secondary side of the transformer. The OAUGDP reactor with lasma energized can be modeled as a caacitor in arallel with a resistor. The transformer converts the low voltage outut of the ower suly to a high voltage for lasma formation. The caacitive lasma reactor can reflect a large art of inut ower back to the ower suly, and in this circumstance, only a small art of the ower suly outut ower is delivered to the lasma, i.e. the lasma reactor is not matched to the ower suly. The reflected ower does not contribute to lasma formation, but requires an exensive over-rated ower suly. In addition, the non-ideality of the transformer between the F ower suly and the lasma reactor also contributes an imaginary art to its imedance. Thus, the whole load for the ower suly, as seen by its outut terminals, is highly reactive. The imedance of the load seen by the ower suly should be otimized in order that the maximum ower is delivered to the lasma. However, the equivalent imedance of the lasma is strongly deendent on the ower dissiated in it. By changing the arameters of the matching network, the imedance match to the load can be otimized. For otimum erformance, an imedance matching circuit must be inserted between the ower suly and the lasma reactor in order to generate a high ower OAUGDP efficiently. This chater resents two tyes of imedance matching circuits that match OAUGDP reactors to their ower sulies. The two tyes of matching circuits are designated the secondary-side imedance matching circuit and the rimary-side imedance matching circuit, resectively, according to the matching network s location

24 1 relative to the transformer. The two imedance matching circuits are designed for OAUGDP systems, and can satisfy the unique oeration requirements of OAUGDP systems low F frequency, high voltage and high current. 3. Secondary-Side Imedance Matching ircuit 3..1 Definition of Imedance Matching Imedance matching is the connection of additional imedance to an existing circuit in order to accomlish a secific effect, such as to balance a circuit or to reduce reflection in a transmission line [9]. Imedance matching is required in order to otimize the ower delivered to the load from the source. It is accomlished by inserting matching networks into a circuit between the source and the load. At the UT Plasma Sciences aboratory, the task of imedance matching is to add a circuit comosed of assive electrical arts (inductors, caacitors and/or resistors) between the F ower suly (or its outut transformer) and the reactive load in such a way as to make the imedance of the whole load resistive, as seen by the outut terminals of the ower suly or its outut transformer. By eliminating the reactive ower, one can increase the ower factor of the whole load to nearly unity. By adjusting the imedance of the whole load to a roer resistive value, the maximum ower can be delivered from the ower suly to the load. 3.. Electrical ircuit Model of OAUGDP eactor with Plasma Initiated An OAUGDP reactor/actuator both the arallel late reactor and the lasma anel is essentially a caacitor. When the lasma is energized, a resistive comonent resonsible for the ower dissiation in the lasma is added to the basic caacitor.

25 11 Figure 3.1. Electrical Model of OAUGDP eactor with Plasma Initiated Therefore, the OAUGDP reactor with lasma initiated can be reresented by a caacitor in arallel with a resistor, as shown in Fig. 3.1, in which resistance of the lasma, and is the equivalent is the caacitance of the lasma reactor. Although this simle and crude model does not describe the hysics of the OAUGD lasma, it is sufficient to serve the task of making ossible an imedance match to the caacitive imedance of the lasma reactor. Some more comlicated lasma circuit models resented in the literature [4] [6], [3] can actually be transformed into the form of the simle circuit in Fig. 3.1 by circuit analysis techniques. Therefore, for the task of imedance matching, the simle lasma model in Fig. 3.1 not only makes the job easier, but also is no different from the more comlicated models from the oint of view of circuit analysis; although the more sohisticated models may reresent the real lasma more accurately Basic Imedance Matching Theory The classical Π-tye, T-tye and -tye matching networks [11], [13], [15] [17] should not be alied to the OAUGDP system, since their circuit leg in series with the OAUGDP reactor will share a significant art of the outut voltage of the transformer, and the generation of the OAUGDP needs a higher voltage (4 kv rms kv rms) than low-ressure glow discharge lasmas. Therefore, if a Π-tye, T-tye or -tye

26 1 matching network is used, the available maximum voltage across the OAUGDP reactor will be significantly decreased and a more exensive transformer caable of generating higher voltages is necessary in order to generate an OAUGDP. Thus, all the circuit legs of an OAUGDP imedance matching network should be in arallel to the OAUGDP reactor. The schematic electrical system of an OAUGDP reactor is shown in Fig. 3.. The secondary-side imedance matching network is the circuitry within the dashed-line. It is so-called because it is connected to the secondary side of the transformer. The matching network is comosed of an inductor and a caacitor in arallel. is the resistance of the inductor winding. The matching network is in arallel with the lasma reactor and close to the transformer outut, so the stray caacitance of the long cables between the transformer and the lasma reactor can be included in the reactor caacitance and matched by the matching network. Seen by the transformer outut terminals, the imedance of the whole load the matching network lus the lasma reactor is Z = ( + jω) = + jω[ δ δ 1 // jω( + ( + + ω ( + ) // ) )] // (3.1) where δ = ω ( + ). The symbol // indicates that the two electrical comonents 1 are in arallel to each other. From Eq. (3.1), the imedance characteristic of the whole load is determined by the sign of the function [hen, ] f ω ) = δ ( + ) = ω ( + ) ( ) (3.) ( +

27 13 Imedance Matching ircuit OAUGDP eactor/actuator Power Suly Transformer Figure 3.. An OAUGDP system with secondary-side imedance matching circuit

28 By adjusting the oerating frequency ω, the sign of f (ω) can be changed. For f ( ω) <, the whole load is caacitive; for f ( ω) >, the whole load is inductive; for f ( ω) =, the whole load is urely resistive, and imedance matching is achieved. The matching frequency ω r can be derived from f ( ω) =, 1 ω r = (3.3) ( + ) 14 If the transformer is ideal, i.e., the imaginary art of its imedance is small, and it transmits almost all inut ower from the rimary side to the secondary side, then the above matching theory is sufficient. The lasma reactor is matched when the system is oerated at the matching frequency ω r. However, the high rimary/secondary turns ratio (characteristically :1) and range of oerating frequency encountered in OAUGDP alications make it difficult to avoid non-ideal transformer characteristics. If the transformer is not ideal, i.e., it has a large reactive comonent in its imedance, the transformer will reflect a large fraction of the inut ower back to the ower suly, instead of transmitting it to the secondary side. Therefore, the system is still not imedance-matched as seen by the ower suly, although the lasma reactor is matched as seen by the transformer outut when oerated at the matching frequency ω r. The ultimate imedance matching should be the match seen by the ower suly, since it is the source of the ower. In a well-matched electrical system, the ower reflected back to the ower suly should be an absolute minimum. A better imedance matching theory should consider the load seen by the ower suly outut terminals instead of the transformer outut terminals. Therefore, consideration of a non-ideal transformer is worthwhile. In the next section, a more refined imedance matching theory is investigated.

29 Primary Side Secondary Side m Figure 3.3. Equivalent ircuit of a Non-ideal Transformer 3..4 efined Imedance Matching Theory a) Equivalent ircuit of a Non-ideal Transformer The equivalent circuit of a non-ideal transformer referred to the secondary side is shown in Fig secondary side, 1' is the resistance of the rimary winding referred to the 1' is the leakage inductance of the rimary winding referred to the secondary side, is the resistance of the secondary winding, is the leakage inductance of the secondary winding, transformer, and m is the magnetizing inductance of the is the equivalent resistance of the core losses. The imedance of the magnetizing inductance m is much greater than that of the other comonents in the OAUGDP system. Therefore, the branch containing m is neglected in the following circuit analysis to simlify the task. Fig. 3.4 shows the schematic of the electrical system of the OAUGDP reactor with the non-ideal transformer relaced by its simlified equivalent circuit.

30 Power Suly Figure 3.4. Equivalent circuit of the OAUGDP system with secondary-side imedance matching circuit

31 17 b) ircuit Analysis As seen by the ower suly outut, the imedance of the whole load including the transformer, the matching network, and the lasma reactor is ( ) // ) ( )] ( [ ) ( ) ( // ) ( 1 // δ δ j j j j j j Z = = ω ω ω ω ω ω ω [ ] { } [ ] [ ] { } [ ] [ ][ ] [ ] { } [ ] 1 1 ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( j j Z = δ ω ω δ ω δ ω δ δ ω ω δ δ ω ω δ ω (3.4) where ) ( 1 + = ω δ. The imedance characteristic of the fourth term in the above exression is still determined by the sign of the function ) (ω f defined in Eq. (3.), ) ( ) ( ) ( ) ( f + + = + = ω δ ω (3.) By adjusting the oerating frequency ω and making ) ( = ω f, the imedance of the combination of the matching network and the lasma reactor can be made urely resistive. However, the imedance of the whole load seen by the ower suly still has a reactive comonent the second term in Eq. (3.4), which is caused by the leakage inductance of the transformer. If the transformer is not ideal, this reactive comonent can be fairly large and can reflect a large fraction of ower back to the

32 ower suly. In this situation, imedance matching is not achieved at the resonant frequency ω r defined by Eq. (3.3). 18 However, an adequate imedance match can still be achieved with the non-ideal transformer and the same matching network. By adjusting the oerating frequency ω and making f ( ω) <, the imedance of the combination of the matching network and the lasma reactor has a caacitive comonent, which can artly cancel the effect of the transformer leakage inductance. At the condition described by Eq. (3.5) below, the effect of the leakage inductance is cancelled, and imedance matching will be achieved: [ δ ( + )][ δ + ω ( + ) ] { + [ δ + ω ( + ) ]} + ω [ δ ( + )] + ( + 1 ) = (3.5) The realization of the above condition is not difficult to achieve exerimentally, although its exression is very comlex. We next derive the matching frequency ω r ' for a simle case lasma is off. When lasma is off, =. Thus Eq.(3.5) can be simlified as δ δ + ω ( + ( + ) ) + ( + 1 ) = (3.6) Moreover, since normally δ >> + ) and ( δ >> ω ( + ) for the exerimental arameters used in the OAUGDP, Eq. (3.6) can be further simlified to δ + ( + ) (3.7) 1 = It is now ossible to derive the matching frequency ω r ' from Eq. (3.7) with the hel of δ = ω ( + ), 1

33 ω r = +. (3.8) equirement on the Magnitude of the Matching Network Imedance Making the whole load imedance resistive is not sufficient to transmit maximum ower to the lasma. Since the leakage inductance of the transformer is in series with the combination of the matching network and the lasma reactor/actuator, they form a voltage divider. For a non-ideal transformer, the value of 1' + is quite large. If the imedance of the combination of the matching network and the lasma reactor/actuator is not high enough, then the leakage inductance will share a larger art of the total outut voltage, and there will be insufficient voltage across the lasma load to generate a dense lasma. In the worst case, the voltage may not be high enough to break down the gas. We now examine Eq. (3.4) again to find a way to increase the combinatorial imedance of the matching network and the lasma reactor/actuator. It can be seen that the real art of the combinatorial imedance, the third term in Eq. (3.4), needs to be increased. et us still consider the simle case the lasma is off, or the equivalent lasma resistance is so large that it can be taken as infinity. Therefore, the third term in Eq.(3.4) can be simlified to Z real δ + ω ( + ) Eq.(3.9) indicates that the load caacitance the load imedance Z real (3.9) + must be decreased in order to increase, if the oerating frequency ω is ket the same. When the lasma is on, and esecially when it s dense, its equivalent resistance is quite small

34 Transformer Power Suly Figure 3.5. An OAUGDP system with rimary-side imedance matching circuit (on the order of 1 kω ), and the caacitance of the lasma reactor,, is aroximately constant. As a result, the only way to make imedance of the matching network at the matching frequency, necessary to decrease and increase in the matching network. by Eq. (3.1), and is given by ω + [ 1 ω ( + )] ω Z real as large as ossible is to increase the Z r '. This makes it Z r ' can be calculated Z r = =. (3.1) δ Primary-Side Imedance Matching ircuit The erformance of the secondary-side imedance matching circuit is satisfactory; however, it has a coule of drawbacks. Since they are connected to the secondary side of the transformer, the inductor coil and the caacitor bank in the secondary-side imedance matching circuit must be designed to be caable of handling high voltage (at least 1 kv ).

35 In addition, the inductance required in the secondary-side imedance matching circuit is generally quite large ( ~ 1 mh ), and the inductor winding must be caable of handling large currents ( ~ 1 A ) because of the large resonant current in the imedance matching tank circuit. Therefore, the consequent inductor coil is bulky, heavy, and exensive; and the consequent high voltage, large current caacitor bank is also exensive. 1 In order to avoid the drawbacks of the secondary-side imedance matching circuit, another tye of imedance matching circuit was also develoed, called the rimary-side imedance matching circuit, shown in Fig. 3.5 within the dashed-line frame. It consists of an inductor connected in arallel with the rimary side of the transformer. is the inductance of the coil and is the resistance of its winding. Fig. 3.6 shows the equivalent circuit of Fig , l1, ' l, ', m ', r c are arameters of the equivalent circuit of the transformer. 1 is the resistance of the rimary winding, and l1 is its leakage inductance. ' is the resistance of the secondary winding ( ) referred to the rimary winding, and ratio of the transformer. = ' N, where N is the turns l ' is the leakage inductance of the secondary winding ( l ) referred to the rimary winding, and ' N l = l. m ' is the magnetizing inductance of the transformer ( ) referred to the rimary winding, and m ' = m m N. r c is the equivalent resistance of the transformer core loss. ' is the caacitance of the lasma reactor ( ) referred to the rimary winding, and ' = N. ' is the equivalent resistance of the lasma ( ) referred to the rimary winding, and ' = N. In order to simlify the circuit analysis, we assume that the transformer is ideal and can be ignored in the circuitry, and we obtain the simlified circuit shown in Fig It is easy to recognize that Fig. 3.7 is similar to Fig. 3., so the same circuit analysis rocedures were erformed and the matching frequency for the rimary-side imedance matching circuit is found to be

36 1 l1 l Power Suly m r c Figure 3.6. Equivalent circuit of an OAUGDP system with rimary-side imedance matching circuit

37 3 Power Suly Figure 3.7. Simlified equivalent circuit of OAUGDP system with rimary-side imedance matching circuit 1 ω r = (3.11) This result is similar to Eq. (3.3), but the caacitance in Eq. (3.11) is the equivalent caacitance of the lasma reactor, which is much larger ( N ) than the actual caacitance. Therefore, the matching inductance in the rimary-side matching circuit is much smaller than that in the secondary-side matching circuit for the same matching frequency. Primary-side imedance matching has several advantages over secondary-side matching. The rimary-side matching circuit is connected to the rimary side of the transformer, so the matching circuit comonents do not need to handle high voltage. The inductor coil for rimary-side matching is smaller than that for secondary-side matching, so the cost of rimary-side matching is lower. However, rimary-side imedance matching also has several disadvantages. The rimary-side matching circuit cannot be used in all situations. If the caacitance of the lasma reactor is fairly large, the required matching inductance will be too small and this

38 4 will cause unaccetably large currents through the matching inductor and the transformer rimary winding. In addition, unlike the secondary-side matching, the lasma reactor is not art of an actual tank circuit in rimary-side matching. Thus, it is more difficult to achieve a high ower inut to the lasma because energy stored in the tank circuit cannot be used to increase lasma ower. 3.5 Exerimental esults and Discussion Both kinds of imedance matching circuits were built and tested at the UT Plasma Sciences aboratory. Since the OAUGDP is oerated at a frequency much lower than radio or microwave frequency, and at high voltages on the order of matching network must have a larger inductance ( 1 kv, the inductor coil in the ~ 1 mh for the secondary-side matching circuit and several mh for the rimary-side matching circuit) than that for F or microwave lasmas. In addition, the inductor coil must also be able to handle high voltage ( ~ 1 kv, for secondary-side matching) and large currents ( ~ 1 A ). The selection of such inductor coils available commercially is very limited, so we built the required coils at the UT Plasma Sciences aboratory. The formula for designing and building ractical air-core inductors is shown in Eq. (3.1) [31], d n ( µ H) = (3.1) 18d + 4l where is the inductance in µh, d is the coil diameter in inches (from wire center to wire center), l is the coil length in inches, and n is the number of turns. Eq. (3.1) can be changed into S. I. units as shown in Eq. (3.13), d n ( µ H) = (3.13) 45.7d + 1l

39 where d is the coil diameter in cm, and l is the coil length in cm. 5 Although it is said in the reference that the above formulae are restricted to calculating the inductance of single-layer long air-core coils, we found by exeriment that they are also adequate for multi-layer air-core coils, as long as the asect ratio of the coils (the ratio of length to diameter) is no less than 3:1, and d in the formula should be the average coil diameter (of the middle layer). Our inductor coils were built by winding insulated wire around a standard 4-inch-diameter ( 1. cm ) PV ie. The coil for the secondary-side matching circuit is diameter is 4 cm long, wound with AWG-14 wire. Its average 15 cm. The coil has 1 layers, and each layer has a ta, so a range of inductances is available to achieve different matching frequencies. inductance of this coil is for the rimary-side matching circuit is three tas, and its maximum inductance is The maximum 8 mh, and its maximum winding resistance is 6 Ω. The coil 35 cm long, wound with AWG-1 wire. It has mh. The caacitor bank for the secondary-side matching circuit was built by connecting tens of 1 µ F electrolytic caacitors in series to rovide the desired variable caacitance while withstanding high voltage. The caacitance of OAUGDP reactors was measured by a caacitance meter. The caacitance of the MOD V OAUGDP remote exosure reactor (with 11 lasma anels in arallel) at the UT Plasma Sciences aboratory is about caacitance of the MOD IV OAUGDP arallel late reactor is about 3 nf, and the 1 F. The caacitance of a arallel late reactor can also be calculated by the formula, = εa d. The axi-symmetric MOD IV arallel late reactor at the UT Plasma Sciences aboratory has a radius of quartz, and the ga between the two quartz lates is 9 cm, the dielectric lates on each electrode are 1.5mm-thick mm. The relative ermitivity of quartz is 4. Therefore, the caacitance of the MOD IV reactor is calculated to be 8 F.

40 The measured caacitance is larger than this theoretical value because of the arasitic caacitance of connecting cables. 6 The rocedure to redict the value of and used in the matching network to match the OAUGDP reactors at the desired frequency is illustrated by the following examle. Fig. 3.8 shows the voltage and current waveforms of a set of OAUGDP lasma actuator anels energized without imedance matching. The waveform with many filaments is the current through the lasma anels. The large sinusoidal comonent in the current waveform is the large reactive current, which is not in hase with the voltage waveform. We tried to match the MOD V OAUGDP remote exosure reactor at 1.5 khz, which consists of the same set of lasma anels used in Figure 3.8. In this case, the maximum inductance of the coil was used. One reason for this was discussed in Section 3.3 of this chater. The second reason was that, because the desired frequency was relatively low, a larger inductance would be advantageous in decreasing the resonant current in the matching circuit tank, which in turn minimizes the Ohmic losses in the coil. Substituting the following numbers into Eq. (3.3), 9 f = 15 Hz, = 3 1 F, =.8 H, = 6 Ω, r we obtain 7 = F. Since each caacitor in the caacitor bank is 1 µ F, we need 8 caacitors connected in series to achieve this. Since the caacitance of 8 caacitors in series is actually.15 µ F, the actual matching frequency that would be achieved in exeriment can be calculated by substituting into Eq. (3.3) the following numbers, 7 9 = F, = 3 1 F, =.8 H, = 6 Ω,

41 7 I (A) V (1kV) Time (µsec) Figure 3.8. Exerimentally-obtained voltage (sinusoidal waveform) and current waveforms without imedance matching

42 from which we get f r = 1.57 khz 8, exactly the resonant matching frequency observed. Fig. 3.9 shows the voltage and current waveforms of the lasma discharge for this exerimental set-u. Fig. 3.9 shows the voltage and current waveforms that result when oerating the same set of lasma anels used in Figure 3.8, but with secondary-side imedance matching. It can be seen that the voltage and current waveforms of the transformer secondary outut are in hase, indicating that the imedance matching circuit in addition to the OAUGDP reactor/actuator are urely resistive seen by the transformer and imedance matching has been achieved. Fig. 3.1 shows similar voltage and current waveforms that result when oerating the MOD V OAUGDP remote exosure reactor with secondary-side imedance matching, but these waveforms were obtained digitally from a digital oscilloscoe. The sinusoidal waveform is the voltage across the lasma anels. With imedance matching, the lasma discharge current has been dramatically increased and the reactive current has been minimized. Since the voltage and current waveforms of the transformer secondary outut are in hase when imedance matching is achieved, the equivalent resistance of the lasma,, can be estimated by Ohm s aw. In this case, 5.7kV.3A = 19kΩ. By using Eq. (3.1), we can also calculate the imedance of the matching network at this matching frequency and get Z r ' = 19kΩ. Fig shows the waveforms of the ower suly outut voltage and current rior to the rimary-side matching circuit and the transformer, and the waveform of the discharge current of the rimary-side imedance matched MOD IV OAUGDP arallel late reactor. The ower suly outut voltage and current waveforms are in hase with

43 9 Voltage V rms across the load (1 kv/div) Total current I rms across the load (75 ma/div) Discharge current I - through the lasma anels ( A/div) Figure 3.9. Time variation over 3 cycles of half the alied voltage (sinusoidal waveform) and the discharge current in the imedance matched MOD V emote Exosure eactor with 11 anels energized (The waveforms were exerimentally-obtained)

44 3 Figure 3.1. Time variation over 3 cycles of half the alied voltage (sinusoidal waveform) and the discharge current in the imedance matched MOD V emote Exosure eactor with 11 anels energized (The waveforms were exerimentallyobtained)

45 31 Amlitude (Arbitrary Unit) Time (.1 ms) Power suly outut current Power suly outut voltage Plasma discharge current Figure Exerimentally-obtained waveforms of the measured ower suly outut voltage and current before the rimary-side matching circuit and the transformer, and the measured discharge current of the rimary-side imedance matched MOD IV OAUGDP arallel late reactor

46 each other. This clearly shows that the system is matched at the rimary side of the transformer. 3 In order to investigate the effect of the imedance of the matching network, on lasma ower, different combinations of inductance and caacitance in the secondaryside matching circuit were alied to a arallel late OAUGDP reactor at an affiliated comany. Z r ', The oerating frequency was adjusted to maximize the lasma ower. Exerimental results are shown in Table 3.1. The results clearly show that the maximum lasma ower increases with increasing inductance and decreasing caacitance. However, the inductance in the matching network should not be too large, and the caacitance not too small. The reason for this is that the inductor and the caacitor in the matching network form a tank circuit, which can store energy. The stored energy can enhance the formation stage of the lasma discharge. If the inductance in the secondaryside matching network is increased and the caacitance is decreased, the energy stored in the tank circuit will be decreased. This might have an adverse effect on lasma formation and lasma ower. A change in the shae of lasma discharge current waveform was observed in exeriments when the matching caacitance was changed.

47 33 Table 3.1. Maximum lasma ower with different combinations of inductance and caacitance in the secondary-side matching circuit Inut Signal (mvrms) Inductance (mh) aacitance (nf) Plasma Power (Watts)

48 34 hater 4 PSice Simulation of OAUGDP eactor/actuator Systems 4.1 Introduction The characteristics of many electrical systems can be simulated with rorietary comutational tools such as PSice. Devices emloying lasmas are embedded in electrical systems. In many situations, it is advantageous to simulate the comlete system, including the lasma, with such commercial software. Previous work regarding the comutational circuitry simulation of lasmas has been ublished [18] [3]. In these aers, simulation of low-ressure lasmas in gaseous discharge lams, as well as ulsed, F, and/or inductively couled electrical discharges were investigated. Other aers rovide lasma circuit models caable of incororation into circuit simulations, although simulation of comlete reactors was not reorted in those aers [4] [6]. The One Atmoshere Uniform Glow Discharge Plasma (OAUGDP ) [1, ] reactor/actuator system consists of a ower suly, a transformer, an imedance matching network, and the lasma reactor. This electrical system is a candidate for simulation with such comutational tools. The lasma arameters of the OAUGDP vary as a function of distance between the instantaneous anode and cathode. Unlike D glow discharges oerated at low ressure, the lasma arameters of the OAUGDP vary with time, and follow the F cycle. haracteristic values of the lasma arameters of a arallel-late OAUGDP reactor are listed in Table 4.1. In Ben Gadri s aer [7], the hysical rocesses in such a lasma were simulated by one-dimensional numerical methods. However, his simulation was not a comlete

49 35 Table 4.1. haracteristic values of the lasma arameters of a arallel-late OAUGDP reactor Plasma Parameters of the MOD IV Parallel-Plate OAUGDP eactor Gas Neutral ressure atmosheric air or other gases, relative humidity below 14% 76 ± 5 Torr (1 atmoshere) Electron number density /m (time averaged) Electron collision frequency Electron kinetic temerature not well known Volumetric ower dissiation watts/cm Ga distance F voltage Frequency of oeration 5 mm 8 16 kv MS 3 khz 1 khz collisions/sec

50 36 OAUGDP reactor system, and simulation of such a system has not been reorted by other researchers. In an OAUGDP system, the inductor and caacitors in the imedance matching network [8], the ower suly, and the transformer are ordinary electrical comonents and have well-develoed PSice models. However, there is no available electrical model in PSice for the lasma discharge in an OAUGDP reactor, so a rincial simulation task is the develoment of such a model. In this aer, secific circuit models of One Atmoshere Uniform Glow Discharge Plasma (OAUGDP ) arallel-late and co-lanar lasma actuator systems have been formulated. In addition, simulations with the electrical characteristics of these OAUGDP reactor/actuator systems have been obtained with the rorietary circuit simulation software, PSice, and comared with exerimental data. A arallel-late OAUGDP reactor consists of two arallel metal electrode lates with a ga between them. At least one electrode is covered with a dielectric late, as shown in Fig The dielectric late can be modeled as a caacitor, as can the ga containing the lasma. Based on the henomenology of glow discharges, the lasma discharge itself can be modeled as a voltage-controlled current source that is switched on as long as the voltage across the ga exceeds the lasma initiation voltage. The current source and its outut current follow a ower law of the alied voltage [1], an observed henomenological characteristic of the voltage-current behavior of normal glow discharges. Fig. 4. shows the universal voltage-current characteristic of a D electrical discharge tube [1, Fig. 1.1]. The normal glow discharge regime is between F and G on the diagram. oth reorted that the current-voltage relationshi of the glow discharge in the Electric Field Bumy Torus exeriment, a high ower glow discharge, was and 3 I V I V,, deending on oerating regime [1]. Ben Gadri s aer shows that an atmosheric ressure F glow discharge in helium exhibits the same luminous and dark structures as low-ressure D glow discharges [7]. In the next section, we will resent a PSice model for OAUGDP lasma reactors, which simulates the current waveforms exerimentally observed in OAUGDP reactors [3].

51 37 Electrode d1 1 1 Ω d1 Sheath s1 s1 1 1 Ω G 1 G Plasma g Sheath s s 1 1 Ω Dielectric d d 1 1 Ω Figure 4.1. A PSice Model for arallel-late OAUGDP reactors

52 38 Figure 4.. Universal voltage-current characteristic of the D electrical discharge tube [1, Fig. 1.1]. The normal glow discharge regime is between F and G on the diagram

53 39 4. A PSice Model for Parallel-Plate OAUGDP eactors A arallel-late OAUGDP reactor consists of two arallel metal electrode lates with a small ga between them. At least one electrode is covered with a dielectric late or coating, as shown in Fig The PSice model for the dielectric late or coating can be reresented by a caacitor, as can the ga containing the lasma. The sheath between the lasma and the dielectric late can also be modeled as a caacitor, which may have a larger caacitance than the dielectric late if the thickness of the sheath is smaller than that of the dielectric. The lasma discharge within the ga is the only comlex comonent to be modeled. Thus, it is necessary to consider the hysical rocesses in an OAUGD lasma in order to construct a useful PSice model for it. A arallel-late OAUGDP reactor characteristically oerates at an F voltage of about 1 kv rms and 7 khz alied across the two arallel electrode lates. During the first half of an F cycle, when the voltage across the ga exceeds the lasma initiation voltage, the air in the ga is ionized and a lasma is formed. A discharge (dislacement) current flows through the lasma in resonse to the high voltage across the ga. The time-averaged value of this current is a ower law function of the voltage across the ga, an observed henomenological characteristic of the voltage-current behavior of normal glow discharges. As the discharge continues, electrons reach the dielectric late on the instantaneous anode and accumulate on it. This electron density decreases the rate of voltage increase, and later the voltage across the ga itself [7]. This build-u of negative charge on the dielectric late revents dramatic discharge current increases or decreases. As soon as the voltage across the ga is decreased below the lasma initiation voltage, the discharge current ceases and the lasma extinguishes. In the second half of the F cycle, the lasma discharge restarts, and the current flows in the oosite direction due to the change of F voltage olarity [7].

54 4 Based on the hysical rocesses in an OAUGDP, the discharge can be simulated by a voltage-controlled current source in PSice. As long as the voltage across the ga exceeds the lasma initiation voltage, this current source is switched on and its outut current increases with the voltage across the ga according to the ower law discussed by oth [1, Eq ], k J = J V (4. 1) where k has been observed to range over the values 1 < k < 1. A resistor should be added in series with the current source in the PSice model to account for ower dissiation in the lasma. The schematic of a PSice model for arallel-late OAUGDP reactors is shown in Fig.4.1. In this model, both electrodes are covered with dielectric lates, so there are two dielectric caacitors, d1 and d, in the schematic. g is the gas caacitance of the ga. The caacitance of the lasma sheaths is reresented by s1 and s, which may be much larger than d1, d and g if the lasma sheath is thinner than the dielectric. is an equivalent lasma resistance to account for ower dissiation in the lasma. There are two voltage-controlled current sources G 1 and G. Each of them generates the discharge current in one half of the F cycle, so a full F cycle can be reresented. The outut current of G 1 and G is defined in Eq. (4.) by a ower law function of the difference between the ga voltage, V g and the lasma initiation voltage, V i in order to simulate the voltage-current behavior of a normal glow discharge lasma. If one of the two electrodes is not covered with a dielectric late, the model must be modified by shorting the corresonding dielectric caacitor. =, I ( V V ) g for V i g < V i (4.) α, for V V g i

55 In Eq. (4.), α is an integer that ranges from 1 to 1 in different glow discharge lasma devices. esistor d1, d, s1 and 41 s are required by the PSice software to kee the caacitor terminals from floating. Since their values are very large, these resistors have no effect on simulation results. The schematic of a comlete arallel-late OAUGDP reactor system for PSice simulation is shown in Fig The circuitry will be described in Section A PSice Model for o-planar OAUGDP Actuators A co-lanar OAUGDP actuator anel for aerodynamic flow control consists of a flat anel with multile co-lanar lasma electrode stris alternating in F olarity, and with each olarity connected in arallel on either the to or the bottom of the anel. Fig. 4.4 shows a schematic of such a anel, and Fig. 4.5 shows an image of such a lasma actuator anel as was used in subsonic lasma aerodynamic exeriments [4] [6]. This actuator anel consists of a thin dielectric late either with electrode stris on one or both sides, or with electrode stris on one side and a metallic electrode sheet on the other. When an F voltage of about 4 kv rms and 1 7 khz is alied to a flat anel lasma actuator, a lanar lasma layer is generated either on both sides of the dielectric or only on the side having the electrode stris, deending on the electrode configuration. Fig. 4.6 illustrates a cross section of a flat anel with lasma energized on both sides. Since the lasmas generated on each side of the dielectric late resemble the lasma in a arallel-late reactor, we can construct a PSice model for co-lanar actuators based on the model for arallel-late reactors. Fig. 4.6 also illustrates an aroximate circuit model for the co-lanar lasma actuator. A PSice model for colanar OAUGDP actuators is shown in Fig. 4.7, which is a merging of two coies of the circuit model for arallel-late reactors.

56 4 Equivalent ircuit of a Non-ideal Transformer referred to the Secondary Side Imedance Matching Network Parallel-late OAUGDP reactor d1 1 1 Ω d1 1 1 s1 s1 1 1 Ω Power Suly G 1 G g Ideal Transformer m s 1 1 Ω s Figure 4.3. Schematic of a arallel-late OAUGDP reactor system for PSice simulation

57 43 HIGH VOTAGE POWE SUPPY UPPE EETODE PASMA DIEETI OWE EETODE Figure 4.4. Schematic of a flat layer of OAUGDP lasma on a lasma actuator anel

58 44 To Figure Bottom Photograhs of an OAUGDP actuator anel omuter Simulation and omarison with Exerimental esults Fig. 4.3 shows the schematic of a comlete arallel-late OAUGDP reactor system for PSice simulation. In the schematic, the real (non-ideal) transformer is modeled as an ideal transformer with an equivalent circuit of a non-ideal transformer referred to its secondary side. An imedance matching network between the transformer and the OAUGDP reactor matches the caacitive OAUGDP reactor to the ower suly. The imedance matching network reduces reflected ower and increases ower suly efficiency [8]. The arameters used in this simulation are of a arallel-late OAUGDP reactor system oerated at an affiliated comany. Since only one electrode of the reactor is covered with a dielectric coating, there is only one dielectric caacitor in the PSice model for this OAUGDP reactor; the other is shorted out. A list of comonent arameters used in the PSice simulations of the arallel-late reactor is shown in Table 4..