Numerical and experimental investigation of the stability of radio-frequency (RF) discharges at

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1 Home Search Collections Journals About Contact us My IOPscience Numerical and experimental investigation of the stability of radio-frequency (RF) discharges at atmospheric pressure This article has been downloaded from IOPscience. Please scroll down to see the full text article Plasma Sources Sci. Technol ( View the table of contents for this issue, or go to the journal homepage for more Download details: IP Address: The article was downloaded on 03/09/2010 at 21:02 Please note that terms and conditions apply.

2 IOP PUBLISHING Plasma Sources Sci. Technol. 18 (2009) (10pp) PLASMA SOURCES SCIENCE AND TECHNOLOGY doi: / /18/2/ Numerical and experimental investigation of the stability of radio-frequency (RF) discharges at atmospheric pressure A Chirokov 1, S N Khot 2, S P Gangoli 2, A Fridman 1, P Henderson 2, A F Gutsol 4 and A Dolgopolsky 3 1 Department of Mechanical Engineering and Mechanics, Drexel Plasma Institute, Drexel University, Philadelphia PA 19104, USA 2 Material Research Center, Air Products and Chemicals, Inc., Allentown, PA 18195, USA 3 Department of Mathematics, Drexel University, Philadelphia, PA, USA 4 Chevron Energy Technology Company, Richmond, CA 94801, USA Received 5 November 2007, in final form 3 July 2008 Published 31 March 2009 Online at stacks.iop.org/psst/18/ Abstract The stability and uniformity of a radio-frequency (RF) discharge is limited by a critical power density. Beyond this critical power density, instability occurs in the form of physical changes in the plasma (such as contraction due to arcing). The RF discharge used in this study is the non-equilibrium Atmospheric Pressure Plasma Jet (APPJ ) developed by Apjet, Inc. This discharge is known to operate uniformly in helium gas. However, for some proposed applications such as surface modification, there is a need to operate with reactive gases such as O 2. Our experimental studies show that addition of molecular gas to a discharge operating in helium increases its power density (W cm 2 ), until it reaches the critical unstable arcing limit. Moreover, an increase in the frequency of operation (from 13 to 27 MHz) allows the plasma to sustain higher molecular gas concentrations and power densities before instability occurs. Further, it is observed that this critical power density is dependent on the type of molecular gas added. These results provide a motivation for the development of a mathematical model that can provide insight into the causes of instability and potential methods of suppression. The two commonly studied modes of instability are (1) thermal instability (TI) and (2) α γ arc mode transition. For the APPJ discharge conditions, the development time scales of TI are much longer ( 1 ms) as compared with discharge oscillation period ( 100 ns). Hence, if the instability was indeed thermal, discharge frequency increase would have no consequence, contrary to experimental findings. A 1D fluid model based on the local field approximation is developed to study instability in APPJ discharge. The analysis of modeling results confirmed our hypothesis that the instability development actually takes place via breakdown of sheath i.e. α γ arc mode transition and not by TI. (Some figures in this article are in colour only in the electronic version) 1. Introduction The use of plasmas in materials processing is well established. These applications can be placed into basic categories of etching, cleaning, thin film deposition and surface modification [1]. The use of vacuum plasmas to accomplish these surface treatments is well established in industries such as semiconductor, architectural glass and medical. However, the costs associated with vacuum plasma systems have limited their use to high value industries such as these. Besides the capital costs associated with vacuum processes, the batch nature of vacuum systems is not well suited for the conventional continuous manufacturing methods of other industries (e.g. textiles and plastic films). Recently, there has been a rapid growth into developing atmospheric pressure plasma technologies and identifying /09/ $ IOP Publishing Ltd Printed in the UK

3 applications for them. These plasma technologies do not require vacuum equipment and are amenable to continuous treatment processes. The gas consumption by these technologies is much higher than typical vacuum processes. Consequently, the most prevalent systems were initially airbased plasma technologies such as corona or dielectric barrier discharge [2]. Using air is acceptable for slight increases in surface energy, which is usually temporary in nature. However, the use of pure gases, such as helium, argon, nitrogen or mixtures thereof, can strongly improve the uniformity, durability and extent of the surface treatment. And with the development of gas recycle systems, technologies using more expensive gases such as helium can be made economically viable for many industrial applications [3]. A recent non-equilibrium plasma technology development is the Atmospheric Pressure Plasma Jet (APPJ ) technology [4 7]. This technology, originally invented at Los Alamos National Labs (Sandia, NM) and commercialized by APJet, Inc. (Santa Fe, NM), utilizes bare metal electrodes and can operate with a range of ionizing gases, including helium, argon and neon [8, 9]. It has been found to be extremely efficient at producing reactive chemical species at concentrations orders of magnitude higher than other atmospheric pressure plasma sources. A number of applications using this plasma technology have been demonstrated, including etching [10 12], deposition [13 16] and biological decontamination [17]. The power density achieved by a uniform RF discharge is limited by several instability pathways. Instability here is defined as spontaneous, rapid transition from uniform nonthermal discharge to an arc. These instabilities compromise plasma uniformity via physical changes in the discharge, which is undesirable in material processing applications where uniformity of treatment is of critical importance. The two most commonly encountered pathways are thermal and α γ mode transition instabilities described below Thermal instability (TI) TI is the most common instability pathway in high pressure discharges. Considerable research has been previously conducted [18 24] to study TI in plasmas and is well understood. We apply the TI analysis developed for general RF/glow plasmas to the APPJ discharge. Here, we consider a chain of successive processes that leads to TI as enlisted below and summarized in equation (1): δn e δ(j e E) δt δn δ(e/n) T e n e. (1) Here, j e is the current density (A cm 2 ), E is the electric field (V cm 1 ), n e is the electron number density (cm 3 ), n is the gas number density (cm 3 ), T e is the electron temperature (K) and T is the gas temperature. (a) Positive fluctuation (a small random increase) in the electron density δn e increases the electric current density δj e, since electron drift makes up most of the discharge electric current. (b) An increase in current density δj e results in an increase in power dissipation δ(j e E) ; this is true only if the electric field (E) remains unchanged. (c) An increase in power dissipation δ(j e E) leads to an increase in gas temperature δt. (d) An increase in gas temperature δt decreases gas density δn and in turn increases the reduced electric field δ(e/n). (e) An increase in δ(e/n) causes a corresponding increase in electron temperature δt e and hence an increase in the ionization processes that further increases δn e. This instability mechanism may start due to a positive fluctuation in any of the parameters mentioned in the list above. However, this mechanism is based on the assumption that the electric field remains unchanged during the fluctuation process. A thermal balance for helium plasma is given by equation (2). The source terms that cause the change in temperature of the gas are joule heating (j e E) and cooling via pathways of conduction and convection. c p ρ dt = j a E c p ρ(t T 0 ) ν c. (2) dt Here, c p is the specific heat capacity (J kg 1 K 1 ), T 0 is the ambient temperature (K) and ν c is the cooling frequency (s 1 ). The TI condition indicates that the discharge is unstable if the rate of gas heating (ν h ) is higher than the rate of cooling (ν c ) divided by a factor, ν. Known as the logarithmic sensitivity (given by equation (3), it is commonly used to describe discharge instabilities [25, 26]. ν = d(ln(ν i(e/n) ν a (E/n)). (3) d(ln(e/n)) Here, ν i is the ionization frequency (s 1 ) and ν a is the attachment frequency (s 1 ). In order to derive a condition for discharge instability, we introduce the growth rate of thermal fluctuations,, where, δt is proportional to e t ). Using mathematical manipulations on equations (2) and (3), it can be shown that is a function of heating and cooling frequencies as given in equation (4). Here, <0implies that the discharge is thermally stable and >0implies that it is not stable. = ν h (ν +1) ν c. (4) Using the above relations and typical values of logarithmic sensitivity ν 5 10 [25], it can be shown that a 10 20% increase in gas temperature can result in TI or, stability is maintained if T<( ) T α to γ transition instability Thermal stability condition ( < 0) is necessary but not sufficient for discharge stability. Another commonly found discharge instability is via α to γ transition. The two modes differ in the pathway of sustenance of the discharge. In α-mode discharge, the plasma is sustained by volumetric ionization, while in γ -mode discharges it is sustained by secondary electron emission (or emission from the electrode surface). 2

4 Figure 1. APJeT unit (e-rio 100 4) used to generate the APPJ discharge. A detailed description of both these modes can be found in the literature [25]. The transition instability arises when the electric field in the sheath increases beyond a critical value and breakdown of sheath occurs. This critical field can be obtained from the Townsend condition [26]. This type of instability is much faster than thermal instability as it is defined by the drift of positive ions ( μs). Figure 2. Voltage current correlation for pure helium, 1% and 2% N 2 addition at 75 SLPM gas flow rate. 2. Experimental setup and procedures 2.1. The APPJ system The APPJ system used in this work was the 4 e-rio manufactured by APJeT, Inc. The e-rio contains a 10.2 cm 11.3 cm RF powered aluminum electrode placed in between two aluminum ground electrodes as shown in figure 1. The gap between the RF powered electrode and the two ground electrodes was set at (1.524 mm) for MHz supplied power and (1.143 mm) for MHz. The MHz power was supplied by an AE RFX-II 3000W power supply, AZX matching unit and TCM II Tuner control, all manufactured by Advanced Energy Industries (Fort Collins, CO). The MHz power was supplied by a Cesar W power supply and VM1500 matching unit both manufactured by Dressler HF-Technik GmbH (Stolberg, Germany). The RF electrode and both ground electrodes are cooled by circulating cooling water at 20 C supplied by a Thermo Neslab Merlin M75. The AErfZ60 probe (tuned impedance probe) was placed between the matchbox and APPJ plasma (i.e. at the output of the matchbox). Helium (airgas ultrapure carrier grade), O 2 (airgas regular grade) and N 2 (airgas regular grade) were all delivered to the e-rio using Brooks mass flow controllers (Emerson Electronics) APPJ discharge ignition phenomena Typically, very little power is required to ignite the plasma, and ignitions generally occur at first in one of the gap spaces between the RF electrode and the two ground electrodes. The ignition initially occurs at the outlet (figure 1) of the e-rio, probably due to a perturbation of the electric field caused by Figure 3. Absolute values of phase angles as a function of discharge current for pure helium and 1% N 2 addition at 75 SLPM. the electrode s corner edge. As the power is increased, the plasma spreads upstream towards the gas inlet filling the rest of the gap that first ignited. Once the discharge completely fills this first electrode-ground gap, a second ignition occurs in the second gap, again near the outlet. With increasing power the discharge continues to expand filling the entire gap space Stability testing Experiments to determine the regions of stability for the e-rio are conducted in the following manner. The desired gas compositions and flows are sent to the e-rio system and allowed to reach stable flows. Power is then supplied to the system and ramped slowly in 10 W increments at a rate of approximately 120 W min 1. This rate was found to be slow enough to allow the matching unit ample time to adjust accordingly to the new set-point. The power was increased in the aforementioned manner until arcing occurred between the powered electrode and one 3

5 Figure 4. Dependence of power density as a function of voltage for [1] pure helium, 1% and 2% N 2 addition at MHz and 75 SLPM; [2] 3%O 2 addition at MHz and 40 SLPM. Figure 6. Effect of frequency (27.12 and MHz) on the power density voltage correlation in a pure helium APPJ plasma operating at 40 SLPM. Figure 5. Effect of N 2 and O 2 (addition to helium) on the arcing limits of the discharge; it can be observed that N 2 addition (13.56 MHz, 75 SLPM) has little effect, whereas O 2 (13.56 MHz, 100 SLPM) addition increases the power density level that can be achieved without encountering instability. of the ground electrodes. This power level, referred to as the arcing limit of the discharge. Arcing was generally indicated by the appearance of a hot singular filamentary discharge between the two electrodes. These stability tests were conducted under varying gas concentrations using both O 2 and N 2 as reactive gases added to the helium. 3. Discharge physics description of one-dimensional APPJ model The numerical model of APPJ discharge was developed to better understand mechanisms of instability and not to quantitatively match the experimental results. This model allows simulation of instability in the APPJ discharge in a wide range of parameters and shows excellent qualitative agreement with experimental trends. The gap between electrodes (d mm) in an APPJ discharge is much smaller than the size of the electrodes. Hence, it may be adequately described using a one-dimensional model. At atmospheric pressure the mean free path (MFP) of species is in the sub-micrometer range. This allows us to consider that the plasma behaves fluid like i.e. Knudsen number MFP/d 1. Thus, a fluid model can be employed to simulate interactions in the APPJ discharge. This is advantageous from the point of view of computational time in comparison with kinetic models (using Monte Carlo techniques). Since the APPJ discharge is a nonequilibrium plasma discharge, the electron energy distribution functions (EEDF) can deviate significantly from Maxwellian [25, 27]. We apply the local field approximation (LFA) to incorporate non-equilibrium effects into the EEDF. In the LFA, plasma properties are assumed to be functions of reduced electric field E/n or E/p. We employ BOLSIG+ [28, 29], a Boltzmann equation solver that calculates the dependence of plasma parameters such as electron mobility (μ e ), average electron energy (ε), diffusion coefficients (D e ), drift velocities (ve d) and rate coefficients (K r) of various kinetic processes. This is done offline and a look up table is used, from which source values can be obtained via interpolation while solving the fluid model. A general fluid model consists of mass, momentum and energy conservation equations. We consider three species, namely, electrons, positive ions and negative ions (for electronegative gases). In order to minimize the number of equations and optimize the computational time, the drift diffusion approximation can be used. The approximation is used by neglecting the time and inertia derivatives in the momentum equation and deriving a modified continuity equation that is dependent on diffusion and drift velocity components in addition to reaction rate source terms (shown in equation (5)). The reaction rates and transport properties were obtained from the literature [30 32]. Further, the electron energy equation need not be solved as it is calculated from BOLSIG+. Hence, the following sets of equations are adequate 4

6 Figure 7. Last five cycles of a converged solution in a helium discharge in α-mode. (a) electron density in cm 3 ;(b) positive ion density in cm 3 and (c) electric field in V cm 1. Table 1. Simulated helium discharge parameters. Plasma property Value Applied voltage amplitude (V) 600 Current density (rms, ma cm 2 ) 18.1 Average power density (W cm 2 ) 5.2 Sheath thickness (mm) 0.71 Sheath voltage amplitude (V) 507 Plasma voltage (V) 160 the electrodes incorporates two components thermal flux of electrons (at both electrodes) and secondary electron emission at the cathode as shown in equation (9) below. Figure 8. Time-averaged species concentration in the converged solution for pure helium. to describe the APPJ discharge physics: n e t n p t n n t + (ν d e n e D e n e ) = (α η)n e v d e krec ie n en p, (5) + (ν d p n p = αn e v d e krec ie n en p k rec ii n p n n, (6) + (ν d n n n = ηn e v d e krec ii n p n n, (7) 2 = e ε 0 (n p n e n n ). (8) Here, n p is the positive ion number density (cm 3 ), n n is the negative ion number density (cm 3 ), α is the ionization coefficient (cm), η is the attachment coefficient (cm 1 ), is the electric potential (V), e is the electric charge (C), ε o is the electric permittivity (C 2 N 1 cm 2 ), νp d are the drift velocities (cm s 1 ) and kie rec are the recombination rates between ions and electrons (cm 3 s 1 ). In order to complete the description of the model, we provide boundary conditions at the two electrodes (which are points in our 1D simulations). The flux of electrons at j e = n ev t 4 γj p. (9) Here, v t is the thermal velocity of electrons given by (8kT e /πm e ) 1/2 and γ is the coefficient of secondary electron emission, j e and j p are electron and ion fluxes to electrodes, respectively. Initial simulations were conducted with a coefficient of secondary electron emission (γ ) of 0.01 (one electron emitted for every hundred ion bombardments onto the cathode surface). The flux of positive and negative ions to the electrodes is mostly due to drift given by equation (10). It is assumed that the electrons have zero reflectivity coefficients (or sticking coefficient of 1). The boundary condition for Poisson s equation is set such that one electrode is set to zero potential and the other is assumed to have a sinusoidal waveform potential with RF frequency. j p = n p v d p. (10) Here, n p is the ion density and vp d is the ion drift velocity. From the viewpoint of heat transfer, the typical time for thermal change can be estimated as τ = 2 /λ s, where is the characteristic length ( 0.1 cm) and χ is the thermal diffusivity coefficient ( 1.9cm 2 s 1 ). The RF cycle time is much smaller than typical heat transfer time. Hence, we solve the time-independent (steady state) gas heat transfer equation once during each RF cycle to obtain temperature distribution. The source terms into the heat transfer equation are obtained 5

7 Figure 9. Last five cycles of converged electric field for 1% O 2 addition to helium; it can clearly be seen that the sheath size is reduced (compare with figure 6(c)). from average value joule heating (je) calculated at the end of each cycle. The boundary condition for temperature at the electrodes was 300 K, i.e. set to the temperature of water cooled electrodes. At the end of each RF cycle the distribution of average dissipated power in plasma is computed and used as a source term in the steady state heat transfer equation (equation (11)) to solve for temperature distribution. This temperature distribution is then used to compute bulk plasma parameters for the next RF cycle. (λ T)= q = ω t+ 2π ω j(t )E(t ) dt. (11) 2π t Here, q is the heat source (W cm 2 ), j is the current density (A cm 2 ), E is the electric field (V cm 1 ), ω is the angular frequency of the applied voltage and λ is the thermal conductivity of helium. The above system of equations is discretized in space using the finite volume method [33]. Fluxes are calculated using the Scharfetter Gummel approximation [33, 34], wherein the fluxes are calculated based on the Peclet number (Pe). The time integration was accomplished by an implicit VODE solver [35]. The time steps (at least 100 steps per RF cycle) were chosen dynamically by the VODE solver based on absolute and relative tolerances 10 8 and 10 6, respectively. A more detailed description of the numerical scheme used can be found elsewhere [36]. 4. Results and discussion 4.1. Experimental results The root-mean-square (rms) voltage current correlation for a pure helium APPJ discharge is shown in figure 2, wherein the arcing limit (point of instability) is identified. This result is consistent with literature data [8, 37]. The figure also shows the V I correlation for 1 2% N 2 addition to the helium discharge. For the same current, the operating voltage is much higher with N 2 addition. This effect can be attributed to higher resistivity in the discharge because of the distribution of energy to additional excitation modes, i.e. vibrational and rotational. Figure 3 shows the variation in the absolute value of the phase angle (or impedance angle, ϕ) with current. It is noted that after discharge initiation, the phase angle decreases with an increase in current. It is identified that the phase angle drops rapidly at the arcing limit, i.e. moving towards strongly resistive mode of operation. The real power dissipated in the plasma discharge is calculated using the relation, VRMS I RMS cos ϕ. Accordingly, a relationship between voltage and power density Figure 10. Time-averaged species concentration in the converged solution for 1% O 2 addition to helium; it is possible to observed spikes closer to the electrodes in comparison with the result in figure 7. Table 2. Simulated helium + 1% O 2 discharge parameters. Plasma property Value Applied voltage amplitude (V) 600 Current density (rms, ma cm 2 ) 28.2 Average power density (W cm 2 ) 9.8 Sheath thickness (mm) 0.59 Sheath voltage amplitude (V) 460 Plasma voltage (V) 261 can be established as shown in figure 4. Here, the power density is estimated by taking the ratio of real discharge power and the total surface area of electrodes 200 cm 2. It must be noted here that actual discharge coverage on the electrodes was not monitored, and hence, the power densities reported here may be underestimated. The APPJ discharge stability limits for % O 2 additions to helium at MHz and 100 SLPM are shown in figure 5. The dependence of the arcing limits on the % concentration of added O 2 indicates that it helps to stabilize discharge at higher power densities. This effect is much different in comparison with N 2 addition (13.56 MHz and 75 SLPM), wherein there is very little effect of gas addition on maximum achievable non-arcing discharge power density (see figure 5). It is not immediately obvious why O 2 would help to increase critical discharge power. The thermal instability theory does not describe this effect. The effect of frequency on the stability limits for pure helium plasma powered by MHz compared with MHz supply, both operated at a flow rate of 40 SLPM 6

8 Figure 11. Contour plots of electron density, positive ion density and electric field for last five cycles of converged solution in helium + 1% N 2. Table 3. Simulated helium + 1% N 2 discharge parameters. Plasma property Value Applied voltage amplitude (V) 600 Current density (rms, ma cm 2 ) 12.2 Average power density (W cm 2 ) 3.7 Sheath thickness (mm) 0.80 Sheath voltage amplitude (V) 496 Plasma voltage (V) 172 can be seen in figure 6. Some observations are as follows: (1) discharge operated at higher frequency achieves higher power densities at lower values of voltage, (2) the non-arcing maximum power density achieved by the discharge is higher at higher operational frequency Visualization of the discharge in model The last five cycles before convergence are presented as the simulation result in the following sections. The vertical axis represents the gap between the electrodes whereas the horizontal axis is the time evolution (length of time axis is 5 RF cycles). It should not be mistaken for a 2-spacedimensional simulation Modeling of discharge in Helium Shown in figure 7, is a simulation result of discharge in helium. It reveals the typical structure of α-mode discharge. Figures 7(a) (c) represent the converged electron density, positive ion density and electric field results, respectively. The electrons move from one electrode to another as they respond quickly to the changes in electric field. The ions, however, do not respond to temporal variations of electric field (more sensitive to time-averaged variations) and are restricted mostly to the centre of the discharge. The time-averaged solutions are presented in figure 8 and are qualitatively consistent with experimental observations, i.e. the bulk of the plasma is located at the centre Figure 12. Power density in the discharge as a function of applied voltage consistent with experimental observations (section 2). between the electrodes in the α-mode [38]. More details from a sample simulation result are presented in table 1. When the relative change in current density between two subsequent cycles becomes less than reaches 0.1% of that in the previous cycle, the simulation is assumed to reach periodicity (convergence). Here, periodicity was reached after 200 cycles Modeling of discharge in He + %O 2 addition The obvious effects of the addition of % volume O 2 into the helium APPJ discharge are electron attachment (production of O 2 ) and increase in power density (at the same applied voltage compared with helium) due to the increase in resistivity of the discharge. Figures 9 and 10, present converged electric field and time-averaged species densities for 1% O 2 addition to helium, respectively. Simulation results show that compared to the pure helium discharge, there are additional spikes of electron density, which appear on either side of the central peak, in He + %O 2 discharge. Further, the sheath thickness decreases from 0.71 mm (pure He) to 0.59 mm (with 1% O 2 addition). Consequently, the voltage in the bulk of the plasma increases 7

9 Figure 13. Instability solution (c) compared with stable solutions for (a) Pure He and (b)he+1%o 2 cases; the unit of electron density presented here is logarithm of cm 3. from 160 to 261 V, since higher E/n is necessary to sustain a molecular discharge. Due to increased attachment, the density of electrons is much lower than positive ions. More details from a sample simulation result are presented in table Modeling of discharge in He + %N 2 addition The percentage volume addition of N 2 causes significant deviation in the EEDF since electrons lose energy due to inelastic collisions. Hence, the He + 1% N 2 discharge requires higher applied voltage to operate at comparable power densities to that in pure He (compare with figure 4). Structurally the discharge in helium+% N 2 addition (figure 11) is closer to that in helium (figure 7), than in O 2 (the uniqueness in O 2 occurs due to increased attachment, figure 9). More details from a sample simulation result are presented in table Effect of power density (W cm 2 ) As discussed earlier, the stability and thus uniformity of an APPJ discharge is limited by power density. Figure 12 shows the simulated dependence of power density on applied voltage for operation in pure helium, He + (1 2)% O 2 and He + 1% N 2. The average gas temperature predicted by the last stable simulation is shown at the end of each curve. These results are consistent with our qualitative observations in experiments (section 4.1), i.e. not much effect of N 2 addition on discharge stability, whereas a significant increase in power density is observed with O 2 addition (compare with figure 5) The instability solution As the power density is increased to the critical value (figure 12 last point on curves), we encounter an instability solution. A sample instability result in pure helium case is shown in figure 13. Here, we compare the unstable solution with stable solutions in pure helium and helium + 1% O 2 additions. The logarithmic solutions are compared to closely monitor the gradient of electron density in the sheath. It can be clearly seen Figure 14. Discharge instability predicted by changing the secondary electron emission coefficient. that the instability occurs when the electron density increases exponentially due to avalanches within the sheath formed by secondary electron emission. Avalanche formation inside the sheath eventually leads to the sheath breakdown and transition from alpha to gamma discharge mode. The simulation was repeated with fixed gas temperature in the simulation domain in order to investigate effects due to local temperature increase, but the same result was obtained. Therefore according to the model, discharge stability is not affected by thermal effects and instability develops regardless of whether or not temperature is allowed to vary Effect of secondary electron emission (SEE) processes In order to verify the fact that the instability or arcing limits discussed in section 4.1 and figure 12 are indeed due to sheath breakdown and transition from α- to γ - mode followed by TI, we investigate the effect of changing the SEE coefficient (γ ), i.e. using γ = 0, 0.001, Figure 14 shows that instability occurs at lower voltages and lower power densities when SEE is set to higher values. It is important to point out here that the increase in electron density in the sheath is not 8

10 Figure 15. Comparison between cases with varied SEE coefficients, here (a) γ = 0.01 and (b) γ = 0. The unit of electron density presented here is logarithm of cm 3. due to numerical diffusion, which is demonstrated by setting γ = 0 and comparing with the result obtained at γ = 0.01, in figure 15. Thus simulation shows that when electron emission is suppressed, the sheath remains intact and the discharge can be operated at much higher power densities Effect of frequency The effect of RF frequency on instability is also captured successfully by the model. Figure 16 shows the effect of O 2 addition on instability encountered at two different RF frequencies (13.56 and MHz). This result is again qualitatively consistent with experimental results (section 4.1, figure 6), i.e. it is possible to operate at higher power densities at lower voltages for higher frequency of operation, before instability sets in. This bolsters our supposition that instability is caused by sheath breakdown and not TI, since the latter is not sensitive to frequency of operation. There are quantitative discrepancies between the model and the experimental results. This may be because the simulation assumes perfect electrode surface, uniform gap distance, no-multidimensional effects etc., which are not the case in reality, wherein the electrode surface is not perfect and the gap is not uniform. This results in a stronger local electric field predicted by simulation in comparison with experiments. Additionally, all experimental power densities were estimated by dividing power by total electrode surface area (actual discharge coverage was not monitored accurately). Hence, the power density values may have been underestimated in the experiments. The intent of the model was to better understand qualitatively the mechanisms of instability and not to quantitatively match the experimental results. 5. Conclusions A modeling study was conducted to understand the mechanism of instability initiation that was observed experimentally in the APPJ discharge. The model qualitatively captures the effects seen in experimental studies. Experimentally, it was determined that the uniformity of the discharge (in α-mode) in pure helium was compromised when the power density exceeded a critical value, accompanied by arcing. From the point of view of applications, percentage volume addition Figure 16. Discharge instability predicted by changing the discharge operational RF frequency for different % O 2 additions. (1 3%) of molecular gases such as oxygen and nitrogen was studied. However, it was observed that arcing occurred at varied percentage additions and critical power densities. This provided the motivation for development of a model to study the possible cause of arcing. A 1D fluid model developed using the local field approximation was able to explain the discharge behavior observed in experiments. The discharges in pure He and He+% N 2 addition behave nearly the same, whereas discharge in He +%O 2 operates at much high power densities before arcing occurs. From the simulation results, it was construed that the instability developed due to α γ regime transition leading to arcing. It was clearly demonstrated that the transition occurs via sheath breakdown. A back-of-the-envelope calculation and modeling helps us rule out the possibility of TI leading to arcing. In the APPJ discharge system, the typical development time for TI is 1/ν h ν, which is 1 ms. Hence, the response time of TI is much slower than the time scales of change in plasma parameters such as frequency of operation. Also, recalculation of critical power density (from the above theory for our experimental conditions), which is high enough to initiate instability via the thermal mode in a helium discharge yields 3Wcm 2. However, it is clear from our experimental and simulation results that the discharge is stable up to 4 7Wcm 2, in the case of pure helium (figures 4 and 6). This extended stability is provided by the presence of the sheath 9

11 that prevents arcing. Further, experimental and modeling results show that the discharge is able to operate at higher power densities without arcing at higher frequencies (figures 6 and 16). At high frequencies of operation, TI should not be sensitive to changes in frequency. On the other hand, frequency affects the extents of motion of ions between electrodes, i.e. the ion bombardment of electrodes. This in turn may affect the SEE coefficient and hence α γ regime transition (this effect is discussed in section 4.8 and demonstrated in figure 14). References [1] Lieberman M and Lichtenberg A 1994 Principles of Plasma Discharges and Materials Processing (New York: Wiley) [2] Becker K, Kogelschatz U, Schoenbach K and Barker R 2005 Non-Equilibrium Air Plasmas at Atmospheric Pressure (Bristol: London Institute of Physics Publishing) [3] Bowe D 2004 Helium recovery and recycle makes good business sense Indust. 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