Computational studies on high frequency impedance characteristics of a microplasma device are reported. While microplasma is ignited using a primary excitation signal, frequency response of plasma impedance is determined by a secondary high frequency probe signal with significantly lower voltage amplitude such that it does not influence the plasma parameters. The computational model utilizing the drift–diffusion approximation is first validated by comparing with experimental data for microplasmas ignited at pressures ranging from 1 to 5 Torr. In spite of quantitative discrepancies, good overall agreement is obtained between the measured frequency response of impedance of the discharge. Comparisons are also presented for various plasma parameters including mean electron number density, sheath thickness, mean electron temperature, and collision frequency that were inferred from the impedance measurements. The computational model is then used to perform simulations of near-atmospheric pressure microplasmas with the probe signal frequency ranging from 3 to 20 GHz. The simulations demonstrate the presence of a resonance frequency at which the impedance vanishes. More importantly, it is shown that this resonant frequency can be tuned effectively by suitably modifying the operating parameters (gap size, pressure, and excitation voltage). The simulated impedance characteristics are used to determine the effective plasma inductance and capacitance using a non-linear fitting approach, thereby showing the dependence of these electrical parameters on the plasma operating conditions.

## I. INTRODUCTION

The interaction of electromagnetic waves with plasmas has been studied for a long time in the context of various applications including capacitively coupled plasmas,^{1,2} plasma antennas,^{3,4} and hypersonic radio frequency blackout,^{5,6} to name a few. The presence of free charged particles (electrons and ions) in plasmas enables them to demonstrate very attractive electromagnetic properties and unique interactions with electromagnetic waves. For example, plasma is the only naturally occurring material that can demonstrate a negative dielectric constant.^{7–9} This has resulted in plasmas being used as a building block in the development of metamaterials that demonstrate a negative refractive index at certain frequencies.^{10–12} Also, the limited availability of spectral resources in the high-frequency regime^{13} calls for the need of reconfigurable electronics.^{14} With the ability to tune plasma properties just by modifying the operating conditions (pressure, power delivered to ignite the plasma, operating gas, and excitation frequency, among others), plasma-based electronic devices may have a great potential for being integrated into electronic circuits. As an example, plasma capacitors have been shown to demonstrate relatively high capacitance ratio,^{15} high quality factor,^{16} good impedance characteristics,^{17,18} good tuning rate, high power,^{19} and high temperature tolerance,^{15} making them possible alternatives to traditional semiconductor-based electronic components like varactors, PIN diodes, Schottky diodes, and RF microelectromechanical systems (MEMS).

This has motivated several recent studies that have focused on obtaining a better understanding of the characteristics of plasma capacitors.^{14,15,20–25} Linardakis and Borg^{22} showed that the capacitance of a glow discharge plasma (a function of the plasma sheath width) can be tuned by varying the frequency of the input signal. A theoretical and numerical study of the impedance characteristics of a plasma based frequency tunable antenna was performed by Pascaud *et al.*^{23} It was reported that an increase in electron density leads to an increase in the resonant frequency. Semnani *et al.*^{20} performed a theoretical and experimental study to investigate the potential of utilizing a glow discharge plasma as a variable capacitor and discovered that the primary factor affecting the LC characteristics of such devices is the change in the cathode sheath width. In a following work, Semnani *et al.*^{21} performed a theoretical and experimental investigation on a new plasma-based frequency selective tunable power limiter showing that such devices could easily handle input powers up to $100W$ making them ideal for use in devices operated at high power. In another computational study, Vyas and Chaudhury^{24} studied the feasibility of frequency reconfiguring of a microstrip plasma antenna and achieved a theoretical bandwidth of $1$ GHz along with a tunability of $13.9%$. Khomenko and Macheret^{14} performed experiments to demonstrate that capacitively coupled RF discharge could be used as a variable capacitor by varying the RF plasma excitation frequency while keeping the voltage amplitude constant. They obtained a capacitance ratio of 5:1, and it was suggested that this could be increased by varying the input power to the reactor.

The unique interactions of plasmas with electromagnetic waves occur at incident wave frequencies that are comparable to the plasma frequency.^{7} As a result, plasma devices for high-frequency electronic circuits in the GHz to THz regime require comparable plasma frequencies. Plasma frequencies in the GHz to THz regime require electron number densities greater than $1013$ 1/cm$3$ and is routinely achieved in atmospheric pressure microplasmas. However, there have been a limited number of studies dealing with microplasma capacitors and their impedance characteristics. While impedance characteristics of microwave microplasmas have been studied using both experiments and computations,^{16} these results correspond to the case of the excitation wave being the same as the incident wave.

In order to integrate microplasma-based capacitors into electronic circuits, we need to obtain a better understanding of these devices for situations in which the microplasma is ignited using a certain excitation frequency and a secondary probing wave interacts with the device. In other words, the impedance characteristics and their dependence on the secondary wave frequency are more crucial to the understanding of microplasma capacitors and their integration into high frequency circuits. It should be noted that the power transmitted by the secondary wave is much smaller than the ignition wave such that the plasma properties are unchanged by the secondary wave. In this context, the primary goal of the current work is to obtain an improved understanding of the frequency response of the impedance characteristics of an argon microplasma capacitor by performing continuum simulations using an in-house code. Specifically, one of the objectives of this work is to characterize the critical incident (probing wave) frequency beyond which the microplasma capacitor demonstrates negative capacitance (inductance-like behavior). The simulations reported in this work also consider a reasonably wide range of operating parameters including the gas pressure, gap size, power and excitation (primary ignition wave) frequency. It should be noted that the simulations performed in this work closely mimic the experimental setup of Khomenko and Macheret.^{26} They also formulated an analytical model which in combination with the measured impedance characteristics was used to determine various plasma properties including the spatial average of electron number density, sheath width, and electron temperature, among others. While such analytical models are extremely beneficial for exploring the design space, the assumptions involved could make them less accurate particularly in the context of microplasmas that demonstrate strong spatial gradients. Therefore, the simulations presented here may also be utilized for validating and improving the analytical models that can then be used for design and optimization purposes by exploring the entire design space.

## II. PHYSICAL MODEL DESCRIPTION

All simulations reported in this work were performed using a one-dimensional continuum model implemented in an in-house code.^{27} The model has previously been used to study microwave microplasmas^{28} and, therefore, is appropriate for the simulations considered here. While the approach utilized here is standard (for example, Baeva *et al.*^{29} and Shneider *et al.*^{30}) in the simulation of low-temperature plasmas, we briefly describe it to ensure self-sufficiency.

The particle continuity equation for each of the charged particles (electrons and ions) is given by

where subscript $i$ is the species index, $n$ refers to the number density, $\Gamma $ refers to the particle flux, and $Si$ refers to the net generation of species $i$ as a result of the chemical reactions occurring in the plasma. The particle flux $\Gamma $ is determined by employing the drift–diffusion approximation for all charged particles and is given by

where $Z$ refers to the charge number, $E$ refers to the electric field, $\mu $ refers to mobility, and $D$ refers to the diffusion coefficient with subscript $i$ referring to the species index. The electron mobility and diffusion coefficients as a function of reduced electric field magnitude ($E/N$ with $N$ being the background gas number density) were obtained using BOLSIG+.^{31} The electric field dependent mobility of ions was obtained from the literature^{32} with the diffusion coefficients calculated using Einstein’s relation^{33} given by

where $kB$ is the Boltzmann constant. $Ti$ is the ion temperature, which is assumed to be in equilibrium with the gas temperature. The electron mean energy is determined through a conservation equation given by

where $e$ is the electronic charge, $\u03f5$ is the mean electron energy density, and $\Gamma \u03f5$ is the energy flux given by

where $De$ is the electron diffusion coefficient. The electron energy source term ($S\u03f5$) appearing in the right-hand side of Eq. (4) is given by

where $\Delta Er$ is the electron energy loss/gain associated with inelastic reaction $r$ and $Se,r$ is the net generation of electrons associated with reaction $r$. The second term on the right-hand side of Eq. (4) is the Joule heating term. The reactions of argon plasma that were taken into consideration in this work are listed in Table I. Other reactions that may be important but are not considered here include the formation of the argon dimer ion and its recombination with reactions that could be particularly important at atmospheric pressure. While the reaction set considered here is limited, the authors believe that this is sufficient to demonstrate the fundamental trends that are relevant to the scope of the paper. For example, the inclusion of a more exhaustive argon chemistry set will likely change the results quantitatively but the overall conclusions of the work are likely to be unchanged. Therefore, the simplified chemistry set was chosen with the primary benefit being the reduced computational cost.

e + Ar = e + Ar | (elastic collision) |

e + Ar = e + Ar* | (excitation) |

e + Ar = 2e + Ar^{+} | (ionization) |

e + Ar* = 2e + Ar^{+} | (ionization) |

e + Ar = e + Ar | (elastic collision) |

e + Ar = e + Ar* | (excitation) |

e + Ar = 2e + Ar^{+} | (ionization) |

e + Ar* = 2e + Ar^{+} | (ionization) |

Poisson’s equation for the electrostatic potential distribution is given by

where $\varphi $ is the electrostatic potential and $\u03f50$ is the permittivity of free space. The electrostatic potential was used to compute the electric field appearing in all conservation equations and is given by

The boundary conditions for the electron and ion fluxes are represented by the following equations:

where

$vthi=8kBTi/\pi mi$ is the thermal velocity of particle species $i$, $n^$ is the unit outward normal to the electrode, and $\gamma se$ is the secondary electron emission coefficient whose value is set constant at $0.01$ for all the simulation case.

Similarly, the boundary condition for the electron energy flux is represented as

where $Tse$ is the temperature of the electrons that are emitted from the electrode surface. The value of $Tse$ is set to 300 K for all simulations reported here.

The boundary condition for the potential was set as a Dirichlet boundary condition with one electrode grounded and the other electrode set at a prescribed voltage. In spite of the boundary conditions for potential, some of the simulations reported in this work were performed in the power-controlled mode. In the power-controlled mode, the voltage at the powered electrode is modified suitably at the end of each cycle such that the power absorbed by the plasma is equal to the desired input power.

## III. RESULTS AND DISCUSSION

The physical model described above was used to perform one-dimensional simulations of argon microplasmas at various operating conditions. Figure 1 shows a schematic of the reactor considered in this study. It should be noted that our simulations closely mimic the experimental setup of Khomenko and Macheret^{26} In these experiments, a closed cylindrical tube is filled with argon gas at a temperature ($T$) of $300K$. While the experiments only dealt with low pressures ($<10Torr$), the simulations were performed for pressures up from 1 Torr all the way to 900 Torr. The electrodes are connected to two sinusoidal voltage sources. The first source generates a high-voltage signal ($\u223c65$–$\u223c130V$) of specified power at a frequency of $200MHz$ to ignite the plasma. The second voltage source provides a low-power high-frequency (300 MHz–20 GHz) signal and is the probe wave that is used to determine the impedance characteristics of the microplasma capacitor. It should be mentioned that the probing wave amplitude was limited to 1 V and is significantly smaller than the excitation amplitude and, therefore, can be assumed to have a negligible influence on the plasma properties itself. For the purpose of the one-dimensional simulations, the cross sectional area of the electrodes was used only to convert the current density to current which, in turn, was used to determine the impedance as described later in this section. The operating conditions of the microplasma simulations considered in this work are summarized in Table II.

Gas temperature (K) | 298 |

Gas pressure (Torr) | 1–900 |

Electrode diameter (cm) | 1 |

Voltage waveform | Sinusoidal |

Plasma excitation power (W) | 0.1–1.4 |

Plasma excitation frequency (MHz) | 200 |

Probing voltage (V) | 1 |

Probing frequency (GHz) | 0.3–20 |

Gas temperature (K) | 298 |

Gas pressure (Torr) | 1–900 |

Electrode diameter (cm) | 1 |

Voltage waveform | Sinusoidal |

Plasma excitation power (W) | 0.1–1.4 |

Plasma excitation frequency (MHz) | 200 |

Probing voltage (V) | 1 |

Probing frequency (GHz) | 0.3–20 |

### A. Validation

The first set of simulations were performed with the objective of validating the simulations by comparing with the experiments performed by Khomenko and Macheret.^{26} As discussed earlier, the experiments were performed for pressures ranging from 1 to 5 Torr with the microplasma ignited using powers ranging from 0.2 to 1 W. A typical numerical simulation using the continuum model presented earlier begins with a uniform initial electron/ion number density and electron temperature and evolves the system in time using the governing equations until the simulation reaches a steady state. The temporal variation of average electron number density ($ne$) is shown in Fig. 2. Figures 2(b)–2(d) show the spatiotemporal variation of the electron number density, Ar$+$ ion number density, and electric field ($E$) for up to $250\mu s$ of simulation time. The rapid variation of plasma properties during the early times is clearly evident followed by a more gradual variation before reaching a steady state.

Once the simulation reaches a steady state, the impedance characteristics at the probing wave frequency were obtained by post-processing the time history of current and voltage between the electrodes. Specifically, we computed the fast Fourier transforms (FFTs) of current and voltage to obtain the Fourier components at the probing signal frequency. The impedance of the microplasma capacitor at the probing signal frequency ($\omega $) was then obtained as

where $V(j\omega )$ and $I(j\omega )$ refer to the Fourier components at the probing signal frequency. In general, the impedance is a complex quantity and comprises of a real component and an imaginary component. The real component [$Re(Z)$] refers to the resistance, while the imaginary component [$Im(Z)$] refers to the reactance and includes capacitive and inductive contributions from the microplasma device. While $Re(Z)$ is always positive due to the non-negative nature of the device resistance, $Im(Z)$ can take positive or negative values depending on whether the capacitive or inductive contributions dominate. A positive $Im(Z)$ signifies inductive behavior and a negative $Im(Z)$ signifies capacitive behavior.

Figure 3 compares the frequency response of the real component of impedance obtained from our simulations with the measurements of Khomenko and Macheret.^{26} It should be noted that three different operating pressures are considered with the plasma ignited at different powers at different pressures. The choice of input powers for each pressure was governed by the data presented in the experimental work to enable direct comparison. The simulations at all pressures predict a gradual decrease in the microplasma resistance as the probing frequency is increased. At a given probing frequency, the resistance decreases with increasing pressure/power, which is a direct consequence of the increase in electron number density. The increase in charged particle density increases conductivity and decreases resistance. While the simulations predict the same order of magnitude for the resistance as measured by Khomenko and Macheret,^{26} the local maximum observed in the experiments is not captured by the simulations. Khomenko and Macheret^{26} attributed this peak to correspond to the condition of

at which the plasma permittivity is zero, but the simulations does not capture this behavior. The measurements do predict a gradual decrease in resistance beyond the peak which agrees qualitatively with the simulations.

Figure 4 compares the frequency response of the imaginary component of impedance obtained from the simulations performed in this work with the measurements of Khomenko and Macheret^{26} for the same conditions as before. Both simulations and measurements predict an overall increase in the reactance values. While the reactance magnitudes are comparable, the simulations predict a slightly greater magnitude of reactance than the measurements. Also, the measurement for the $1Torr$ case captures a local maxima at same frequencies at which the resistance measurements showed a maxima that is not captured by the simulation. The simulations predicted a monotonic increase with the reactance magnitude increasing with the increasing electron number density. Both simulations and experiments predicted negative reactance values, confirming the capacitive behavior of the microplasma device at all conditions considered. Figure 5 compares the temporal variation of electron number density obtained without the probing signal with those obtained using probing frequencies of 1, 2, and 3 GHz. Results are shown for two different power values to compare and contrast the trend. We calculate that the change in electron number density inside the reactor with and without the addition of probing signal is less than 1%.

The primary focus of the experimental work of Khomenko and Macheret^{26} was to use the impedance measurements to determine various microplasma properties as a function of input power and gas pressure. In order to validate our simulations, we compare the electron temperature, sheath thickness, electron number density, and collision frequency from the simulations in this work with the measurements. Experimental data are available for each of these plasma parameters as a function of input power. Since the plasma parameter profiles predicted by the simulations demonstrate spatial variation, we computed the average values in the quasi-neutral region of the plasma to compare the simulated results with the single value reported in the experiments. Since the experiments use a model to interpret their impedance measurements thereby determining the plasma properties, the average value is an appropriate quantity for comparing simulations and experiments.

Figure 6 compares simulated and measured variation of mean electron number density as a function of input power. The range of pressures considered for the comparison was from 1 to 5 Torr. The results indicate good overall agreement between the simulations and experiments. Specifically, the discrepancies decrease with increasing pressure with 5 Torr simulations, showing the best agreement with the experiments. At the lower pressures, the simulations over-predict the electron number densities and could be attributed to various sources ranging from potential lack of accuracy of the continuum model at low pressures to inaccuracy of the model used to convert impedance measurements to plasma parameter measurements in the experiments. Figure 7 compares the simulated and measured variation of sheath thickness for the same conditions considered for the electron number density variation. The simulated sheath thickness was computed using the ratio of electron to ion number density profiles and was taken to coincide with the location where the electron number density was equal to 95% of the ion number density. For a given pressure, both simulations and experiments predict a rapid decrease in sheath thickness for the lower power values before stabilizing to a nearly constant value. The stabilization to a constant value is particularly evident in the simulations with the experiments demonstrating small changes in sheath thickness even at higher input powers. The simulations are also consistent with the experiments in predicting a decrease in sheath thickness with increasing pressure.

Finally, Figs. 8 and 9 compare the mean electron temperature and mean collision frequency obtained from the simulations and experiments as a function of input power for background gas pressures ranging from 1 to 5 Torr. While the experiments infer these quantities independent of each other, the simulations compute reduced collision frequency at a given electron temperature using a zero-dimensional Boltzmann solver (BOLSIG+). The mean electron temperatures that are reported from the simulations were computed only for the quasi-neutral region since the sheath region typically has more variation. The electron temperature predicted by the simulations show negligible dependence on pressure as well as input power at pressures between 2 and 5 Torr, while the 1 Torr case shows a gradual increase with input power. This trend qualitatively agrees with the experimental data where the 1 Torr case shows a rapid variation with increasing power. In spite of the qualitative agreement, quantitative discrepancies do exist with the experiments, predicting a lower electron temperature (except for 1 Torr at higher input powers) than the simulations. Reasons for this discrepancy are not clear. Since the collision frequency is strongly related to the electron temperature, the comparisons of collision frequency mirror that of the electron temperature.

In spite of the quantitative differences, we conclude that the good overall agreement between the simulations and experiments serves as a validation of the framework for application to other similar problems and extend the simulations to atmospheric pressures and higher probe frequencies.

### B. Impedance characteristics of atmospheric pressure microplasmas

This section focuses on the computational study of impedance characteristics of atmospheric pressure microplasmas for various operating conditions and probe signal frequency. The primary objective of varying the operating conditions is to determine the ability to tune the impedance characteristics by modifying parameters such as the electrode gap, gas pressure, and electrode voltage. While the excitation frequency is a potentially attractive way to modify the plasma characteristics,^{14} it was not considered in this study. All simulations reported here used an excitation frequency of 100 MHz. Figure 10 summarizes the dependence of the mean electron density on the parameters considered in this study. The electron density is an important parameter that governs the impedance characteristics of the microplasma device. The results show that the electron number density increases linearly from about $7\xd71012$ to $4\xd71013$ 1/cm$3$ when the excitation voltage is varied from 75 to 160 V. It should be noted that the electrode gap and pressure for this parametric study were fixed at $300\mu m$ and $760Torr$, respectively.

For the parametric study on the electrode gap (with excitation voltage fixed at 100 V and gas pressure at 760 Torr), the electron number density decreases rapidly from $8.3\xd71013$ to $2.3\xd71013$ 1/cm$3$ as the gap size is varied from 100 to 700 $\mu m$. However, it was observed that the mean electron density was almost the same for electrode gaps of 500 and 700 $\mu m$.

Finally, changing the background pressure from 600 to 900 Torr increases the electron number density from $1.25\xd71013$ to $4\xd71013$ 1/cm$3$. It should be reiterated that tuning the electron number density directly leads to a change in the plasma frequency and hence a change in the impedance characteristics as will be described below.

Figures 11(a) and 11(b) show the dependence of the microplasma device impedance characteristics on the probe signal frequency at four different excitation voltages. Results are shown for both real and imaginary parts of the microplasma impedance as in the case of the low pressure cases. The results in Fig. 11(a) indicate that the real part of impedance which is same as the resistance of the microplasma device is nearly independent of the probe signal frequency. Small changes in the resistance are likely due to the numerical algorithm utilized to compute the Fourier transforms of the current and voltage time histories. This would be expected since the probe signal does not play any role in altering the microplasma characteristics and since resistance of a given circuit element is independent of frequency, it remains unchanged at different probe signal frequencies. Also, as the excitation voltage is increased, the device resistance decreases and is consistent with the increase in the electron number density.

The imaginary part of the impedance (reactance), as expected, shows a strong dependence on probing frequency since both inductive and capacitive reactances depend on frequency. The simulations used for comparing with the experiments restricted the probe signal frequencies such that only negative reactances were observed. However, with the large range of probe frequencies considered for the atmospheric pressure simulations, the results demonstrate a change in the sign of the microplasma reactance with the value of resonant frequency (in this context, defined as the frequency at which the reactance becomes zero) depending on the excitation voltage. The resonant frequency increases from about 14 GHz at an excitation voltage of 70 V to about 41 GHz at an excitation voltage of 160 V. It should be mentioned that the exact resonant frequency is not determined since the simulations were performed at an interval of 1 GHz for the probe signal frequency.

It can be seen that the nature of the $Im(Z)$ vs probing-frequency graph closely resembles an LC circuit in which an inductor of inductance L is connected in series with a capacitor of capacitance C. The inductance of such a circuit is given by

Therefore, the equivalent inductance (L) and capacitance (C) of the microplasma were obtained by fitting an equation of the form of Eq. (14) through the simulated $Im(Z)$ profiles. The values of L and C obtained from a non-linear least squares fitting algorithm (available in standard numerical software such as OriginLab, MATLAB, Python, Microsoft Excel, etc.) are plotted as a function of excitation voltage in Fig. 11(c). The fitted curves themselves are included in Fig. 11(b) to demonstrate the goodness of fit. With an increase in voltage from 70 to 160 V, the microplasma capacitance demonstrates only a small range of values between 10 and 14 pF. It can, therefore, be concluded that the capacitance does not depend on the voltage amplitude for the range of values considered and any change in device characteristics is largely an outcome of the changing inductance. The inductance, on the other hand, demonstrates a much stronger dependence with a decrease from about 13 to 1 pH for the same change in voltage. Therefore, the resonant frequency corresponding to zero reactance increases with increasing voltage amplitude. It should be noted that the resonant frequency is obtained as $1/(2\pi LC)$, and the values reported earlier are consistent with this.

Figures 12(a) and 12(b) show the impedance characteristics of the microplasma device at four different gap sizes. As the gap increases, the resistance increases as a result of the decrease in the electron number density as shown in Fig. 10. The frequency dependence of reactance shows capacitive behavior at lower frequencies and inductive behavior at higher frequencies with the resonant frequency changing from about 8 GHz at 0.7 mm to more than 30 GHz at 0.1 mm. The values of capacitance and inductance extracted from the non-linear fitting of the $Im(Z)$ profile are plotted as a function of the gap width in is increased from $0.1$ to $0.5mm$, the inductance of the microplasma increases from Fig. 12(c). As the gap width 1.97 to 8.61 pH, while its capacitance demonstrates a small decrease from 14.1 to 13.9 pF. No significant change in the value of capacitance is observed upon increasing the gap width from $0.5$ to $0.7mm$. However, the value of inductance increases from $16.1$ to $30.6pH$ upon increasing the gap width from $0.5$ to $0.7mm$

The frequency dependence of the impedance characteristics of the microplasma device for three different pressures is shown in Figs. 13(a) and 13(b). The increasing electron number density accompanies the decrease in the resistance of the microplasma as the pressure is increased from $600$ to $900Torr$ [see Fig. 13(a)]. The resonant frequency increases from $\u223c12.83$ to $\u223c19.46GHz$ as the pressure of the gas is increased from $600$ to $900Torr$. The inductance and capacitance of the microplasma extracted from the non-linear least squares fitting of the $Im(Z)$ profiles are plotted in Fig. 13(c) for three different values of gas pressure. The value of capacitance increases monotonically from $9.2$ to $18.3pF$ as the pressure is increased from $600$ to $900Torr$ thereby demonstrating a stronger influence than obtained by modifying the voltage and gap size. The decrease in inductance values ($16.7$ to $3.6pH$) are comparable to the decrease obtained by increasing the voltage from $70$ to $160V$.

While the results presented above demonstrate the ability to tune the impedance characteristics of atmospheric pressure microplasma devices, it is important to discuss the consequences of these results in the context of potential applications. An important parameter that needs to be considered for any component that is utilized in electronic circuits is the quality factor, $Q$. For capacitors and inductors, it is defined as the absolute value of the ratio of the reactance to the equivalent series resistance. It should be noted that real capacitors and inductors (unlike ideal components) always have a non-zero resistive component that makes their quality factor finite. The microplasma devices simulated here were shown to be no different with a resistive component that depended on the operating parameters. Therefore, the specific application of the microplasma devices considered here will be governed by the design constraints placed by the targeted application. For example, the microplasma devices considered here could be integrated into any electronic circuit (including filters, resonators, etc.) instead of capacitors or inductors. In fact, as demonstrated by the simulations, the same device could be used as a capacitor or an inductor by tuning the operating conditions. Therefore, we anticipate microplasma devices similar to the ones considered here to be used (in combination with other passive electrical components) as building blocks for various electronic circuits such as high-frequency filters, resonators as well as impedance matching for electrically small antennas. While the simulations performed here focused on frequencies at which the transition from a capacitive behavior to an inductive behavior could be captured, the microplasma devices will respond as an RLC series circuit even at other frequencies. Also, while the reactance values were fitted to an equivalent LC circuit for the range of frequencies considered, we do expect the resistance, inductance and capacitance values to show some dependence on the probing signal frequency. Quantifying these behaviors is beyond the scope of this work and should be performed in future. The microplasma devices will also provide the added benefit of being significantly more robust than semiconductor-based devices when operated at high temperature environments.

## IV. CONCLUSIONS

We presented a computational study of the impedance characteristics of argon microplasmas with an emphasis on the influence on operating parameters such as applied voltage amplitude, pressure, and the gap size. While the microplasma is ignited using a primary sinusoidal excitation of suitable voltage amplitude, the frequency response of impedance was obtained using a probe signal with a voltage amplitude that was small enough to not modify the plasma parameters. The one-dimensional simulations performed using an in-house code were first validated by comparing with recently published experiments for pressures ranging from 1 to 4 Torr and plasma ignition powers ranging from 0.1 to 1.4 W. Good overall agreement was obtained for impedance characteristics for probe signal frequencies ranging from 400 MHz to 3 GHz even though certain features observed in the experiments were not captured by the simulations. The plasma parameters extracted from the impedance measurements also showed good overall agreement with the simulations. The simulations were then extended to near-atmospheric pressures with the probe signal frequency varied between 3 and 20 GHz. The impedance characteristics of the microplasma were used to extract the resonant frequency (frequency corresponding to zero reactance), effective inductance, and capacitance as a function of operating parameters. The simulations demonstrated that the resonant frequency could be tuned by suitably choosing the operating parameters. For the range of operating conditions considered in this work, resonant frequency demonstrated an almost linear relationship with all the three operating parameters taken under consideration. It was observed that pressure had the biggest influence on capacitance and the weakest influence on the resonant frequency. The results presented here show that microplasma devices could be used as building blocks for traditional electronic circuits such as filters and resonators with benefits including ability to tune circuit parameters and robustness under high temperature environments. While the current work primarily focused on determining the impedance characteristics of the microplasma devices, future work will focus on demonstrating the design and construction of practical electronic components using microplasma devices as building blocks.

## ACKNOWLEDGMENTS

This work was partially supported by the Office of Fusion Energy Sciences within the Department of Energy Office of Science under Award No. DE-SC0019044. The simulations were performed using the MERCED cluster funded by the National Science Foundation (Grant No. ACI-1429783).

## DATA AVAILABILITY

The data that support the findings of this study are available from the corresponding author upon reasonable request.

## REFERENCES

*2017 Progress in Electromagnetics Research Symposium-Fall (PIERS-FALL)*(IEEE, 2017), pp. 252–257.

*The 8th European Conference on Antennas and Propagation (EuCAP 2014)*(IEEE, 2014).