Introduction

Atmospheric pressure plasma jets (APPJs) and their promising applications in areas such as surface engineering, biomedical applications, and chemical processing have been investigated for several decades [1,2,3,4,5,6,7]. Optimal operation of these plasma sources necessitates a precise understanding and control of their properties to achieve the desired effects without damaging the treated samples or chemical compounds. There are many different technical realizations of APPJs, which produce a variety of plasmas [8]. In this work, the plasma source of choice is the COST (European Cooperation in Science and Technology) reference microplasma jet [6, 9, 10]. Although discharges in this system inside these kinds of jets have already been investigated [3, 11,12,13,14,15,16,17], many aspects of their operation, especially those related to the electron power absorption dynamics and plasma chemistry remained unclear. Recently, numerous studies have shifted their focus from understanding the basic physics to using the acquired knowledge with the goal of a precise plasma parameter control for applications [18,19,20,21].

Previous studies showed that the COST-jet is usually operated in the \(\Omega\)-mode at low driving voltage amplitudes and/or high concentrations of the reactive gas admixture [22]. In this mode, electrons are accelerated to high energies in the plasma bulk by strong drift electric fields at the times of high RF current within each RF period. This is ultimately caused by the low plasma conductivity due to the low electron density and/or high collision frequency. Increasing the driving voltage and/or decreasing the concentration of the reactive gas admixture was found to induce a mode transition to the Penning-mode, where ionization by electron avalanches inside the sheaths at both electrodes at the times of maximum sheath voltage within each RF period is dominant [22]. These avalanches are caused by secondary electrons emitted from the electrode surfaces and by electrons created by Penning ionization inside the sheaths for gas mixtures such as He/N\(_2\)/O\(_2\).

Gas temperature measurements in different kinds of plasma jet configurations have been reported in the literature, featuring a wide range of temperature values [23,24,25,26,27]. Gas temperatures in COST-jets have been reported by Kelly et al. [28, 29], who used thermocouples, infrared imaging, and numerical modeling to explore the heat-up time of the jet, the temperature dependence on the gas flow rate, and the heating of a substrate in front of the jet. They found that the heat-up time by the presence of the plasma is on the order of 15 min, and that the final gas temperature is gas flow rate- and voltage-dependent. Depending on the discharge conditions, the gas temperature was found to vary between 22 \(^\circ\)C and just above 100 \(^\circ\)C. Riedel et al. [10] measured the gas temperature in the effluent of several COST-jets at a distance of \(3\,\)mm from the nozzle. They found values between approximately 34 \(^\circ\)C and 60 \(^\circ\)C for varying plasma power at a constant gas flow rate. Most recently, Winzer et al. [30] investigated the gas temperature in a capillary jet which resembles the geometry of the COST-jet, but has no metal surfaces in contact with the plasma. This allows operating the discharge at higher continuous input powers compared to the standard COST-jet and, consequently, significantly higher gas temperatures were found for this system (\(\approx\)50–250 \(^\circ\)C, depending on the power). The jet was, as all of the COST-jets in the references above, operated with a helium-oxygen gas mixture. For 1 W of input power, varying the oxygen admixture concentration in the gas flow from 0 to 2 % was demonstrated to have no influence on the gas temperature in the effluent.

In this study, we aim to extend the knowledge on gas temperature effects in the COST-jet. We present measurements for this plasma source operated with gas mixtures of helium and nitrogen and excited by sine wave RF voltages at \(13.56\,\)MHz, and \(300\,\)V amplitude. The nitrogen rotational temperature and the spatio-temporally resolved electron impact excitation dynamics from the ground state into a high energy helium state are measured for different admixture concentrations with spatial resolution along the discharge channel of 30 mm length, i.e. along the direction of the gas flow in between the two parallel plate electrodes, to relate changes of the gas temperature to changes of the dynamics of energetic electrons and, thus, to the plasma operating mode. For low nitrogen admixture concentrations, the gas temperature is found to increase in gas flow direction. The results of 1d3v Particle-In-Cell/Monte Carlo Collisions (PIC/MCC) simulations, which resolve spatially the inter-electrode space and are conducted for specific values of the gas temperature, show that this gas heating along the direction of the gas flow induces a plasma operating mode transition from the \(\Omega\)- to the Penning-mode [16, 22].

The paper is structured as follows: in Sect. 2 the experimental setup, the simulation method, and the data evaluation procedures are introduced; in Sect. 3 the results are presented and discussed, while in Sect. 4 conclusions are drawn.

Methods

Experimental Setup

Fig. 1
figure 1

Sketch of the experimental setup including the COST-jet, the operating, and the diagnostics hardware

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The plasma jet used in this work has been extensively described in reference [6]. Therefore, only a reduced description is given here, based on Fig. 1: the jet consists of two parallel electrodes made of stainless steel with a thickness of 1 mm. Together with two quartz glass plates and a ceramic base, which are glued to the electrodes by a two-component vacuum epoxy, they form a 1 \(\times\) 1 \(\times\) 30 mm rectangular discharge channel. Standard 6 mm stainless steel gas tubing is glued to the ceramic base, so that a constant flow of the desired gas mixture can be blown through the jet, regulated by mass flow controllers. In this work, different helium-nitrogen mixtures are used. Both gases (Alphagaz, Germany) have a 5.0 purity. Helium-nitrogen flows of 1000 (He) and 0.5, 1, or 2 sccm (N\(_2\)) are used. The upper electrode is driven by a sinusoidal voltage waveform at a frequency of 13.56 MHz and 300 V amplitude, while the lower electrode is grounded. The jet housing includes an impedance matching network. A list of all the hardware used in this work (in addition to the jet itself) can be found in Table 1.

Table 1 Hardware used in this work
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The linear stage on which the jet is mounted is computer controlled, so that the optical measurements can be automatically performed at the six evenly spaced positions along the discharge channel (z-axis) indicated in Fig. 1 (measurement positions on the z-axis: − 28.25, − 22.95, − 17.65, − 12.35, − 7.05, − 1.75 mm, where 0 mm corresponds to the position of the tip of the jet nozzle). Two other stages are used to manually adjust the jet once (by rotation and tilt), before the start of the measurements. This ensures that the distance of the jet to the optical diagnostics, and therefore the focus of these, does not change during the automated movement in the z-direction.

For Phase Resolved Optical Emission Spectroscopy (PROES) measurements, a combination of a fast, intensified CCD camera, lens, and optical filter results in a field of view of 3.58 \(\times\) 2.66 mm with a resolution of approximately 50 μm and detection of plasma emission within the wavelength range of 700 \(\pm 12.5\) nm. The temporal resolution is 1 ns, realized by synchronizing the camera gate to the waveform generator (see [31]). The centers of the images are used to indicate their positions on the z-axis. The different spatial regions of interest inside the plasma and along the direction of the gas flow are indicated by orange dashed rectangles in Fig. 1. In the data processing, the images are averaged along the z-direction (within the respective field of view region). To avoid edge effects, around 1/8 of the total width is cut from both sides of the images before averaging. At each of the positions along the z-axis, the plasma emission of a single helium line at 706.5 nm is detected. The plasma emission at this wavelength results from electron impact excitation from the helium ground state into the He I (3s)\(^3\)S\(_1\) state, followed by spontaneous emission to the He I (2p)³P state. The electron energy threshold for this excitation process is 22.7 eV. From the measured emission this electron impact excitation rate is calculated spatially resolved in the x-direction (perpendicular to the electrodes) and time resolved within the RF period based on a collisional-radiative model [31]. In this way the dynamics of energetic electrons are revealed experimentally. Note, that these measurements are not absolutely calibrated, therefore the resulting excitation rates have relative values.

Fig. 2
figure 2

a Flowchart of the evaluation procedure used to compute the ratio between the \(\Omega -\) and the Penning peak in the excitation data from experiment and simulation. b exemplary experimental input data with the first two peaks marked with yellow dots. c the top 7% of values of the two peaks from panel b and the line separating their respective region, found by the watershed segmentation

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The result of a PROES measurement at a given position along the direction of the gas flow is the local spatio-temporal distribution of the electron impact excitation rate of helium from the ground state into the He I (3s)\(^3\)S\(_1\) state with spatial resolution in the direction perpendicular to the electrodes (see Fig. 2b). The same data can be extracted from PIC/MCC simulations. In this work, these spatio-temporally resolved data will be used to detect the local plasma operation mode at each position along the z-axis, where measurements are performed. This is done based on a computational method first proposed in reference [32] for distinguishing between the \(\alpha\)- and \(\gamma\)- modes in low pressure capacitively coupled plasmas. This quantitative method is based on the intensity ratio of certain spatio-temporal regions of the PROES-images, characteristic for the two plasma operating modes. The same principle can be applied to excitation data obtained from atmospheric pressure RF plasmas, because also there, distinct plasma operation modes exist (\(\Omega\)-, Penning-, constricted mode), and transitions between them can be observed when changing the plasma operating parameters [22, 33].

The data evaluation procedure of reference [32] has been rewritten and improved in the frame of this work. It is now implemented in Python utilizing functionality from numpy [34], matplotlib [35], scipy [36], and scikit-image [37]. Below, a step-by-step description of the evaluation algorithm is given. It is also shown as a flow chart and based on an exemplary PROES measurement in Fig. 2:

  1. (i)

    Define a ROI (region of interest) that includes the \(\Omega\)- and the Penning mode peak of the excitation rate.

  2. (ii)

    Find the two dominant peaks within the ROI. One will be the \(\Omega\)-, the other one the Penning peak.

  3. (iii)

    Use the positions of the two peaks as seed points for a watershed image segmentation (see [38,39,40]), performed on the inverted ROI data. Split the ROI in two parts at the border found by the watershed segmentation. The watershed segmentation treats the input data as a topographical map and finds the ridges. The ridge on the inverted ROI data corresponds to the valley between the two peaks in the original data.

  4. (iv)

    Remove the background in the two parts. Scan over different threshold values for the background reduction for error estimation.

  5. (v)

    Divide the average values of the two parts by each other to get the peak intensity ratio. This intensity ratio determines the dominant mode of plasma operation.

The gas temperature is measured by time averaged optical emission spectroscopy (OES) at different positions along the direction of the gas flow as indicated by the blue dots in Fig. 1. For this purpose an optical fiber is positioned relative to the discharge channel by initially replacing the spectrometer by a fiber coupled LED. The fiber is placed perpendicular to the discharge channel at a distance at which the diameter of the LED-illuminated dot is slightly bigger than the electrode gap (\(\ge\) 1 mm). Then the LED is removed and the fiber is connected to the echelle spectrometer. The spectral resolution of this spectrometer between 200 nm and 800 nm lies between 0.015 nm and 0.06 nm. Because of the atmospheric pressure plasma conditions, we assume the gas temperature to be in equilibrium with the rotational temperature of nitrogen molecules. This temperature is determined from the measured emission following a method described in references [41,42,43,44,45]. The N\(_2\)(C–B,0–1) emission band at 357.7 nm is used for the temperature determination. Spectra of this band are computed for a number of different temperatures, with the same resolution that the spectrometer has at the investigated wavelength. The mean intensity between 355.48 nm and 355.63 nm is calculated and normalized by the intensity of the band head at 357.7 nm for all simulated spectra. A polynomial function is fitted to this data. The relative intensities in the same spectral interval are also calculated from the measured data. Each measured spectrum is the average of 10 consecutively measured spectra. The combination of the measured relative intensities and the polynomial fit to the computed values yields the temperature. The whole procedure is repeated for two more wavelength intervals (355.18 nm to 355.33 nm and 355.34 nm to 355.48 nm), to increase the sampling and to reduce the confidence interval on the mean value.

When switching the plasma on, the whole system needs time to stabilize. This (supposedly mostly thermal) stabilization process is monitored based on a plot of the absorbed electrical power displayed live on the computer screen (for details on the power measurements see references [6, 20]). The power changes on the timescale of minutes when the system is not stable yet. At first startup, the jet is operated at the given parameters for approximately half an hour prior to the first measurements [10]. When the system has been already running for a longer time and the operating parameters are changed, the stabilization time shortens to around 10–15 min.

Plasma Simulation Method

The simulation results shown in this work were obtained from 1d3v PIC/MCC simulations with spatial resolution in the direction perpendicular to the electrodes (x-direction), described in detail in [22, 46]. The charged species considered are electrons, He\(^+\), He\(_2^+\), N\(_2^+\) and N\(_4^+\) ions. The cross sections of the electron impact processes in helium (including elastic scattering, two excitations and ionization) are taken from reference [47], while those of nitrogen (consisting of elastic scattering, excitations to one rotational, eight vibrational and twelve electronic states, one dissociation and ionization) are based on reference [48]. It is assumed that half of the excitations of helium leads to the formation of metastable helium atoms (He I 2\(^1\)S, He I 2\(^3\)S), included as one species in the simulation, He*) (cf. [46]), which participate in Penning-ionization [22]. All electron collisions are assumed to be isotropic in the center of mass (COM)-frame. The heavy particle processes include: (i) elastic scattering for He\(^+\) (consisting of an elastic and a backward scattering channel) [49], (ii) isotropic elastic scattering for He\(_2^+\), N\(_2^+\) and N\(_4^+\) (each based on a Langevin cross section) [22], (iii) conversion of He\(^+\) into He\(_2^+\) [50], Penning ionization [50] and conversion of N\(_2^+\) into N\(_4^+\) [51]. The latter three reactions are based on reaction rates from [46]. The surface model includes electron reflection (with a value of 0.7) and secondary electron emission (with values of 0.2, 0.12, 0.07, 0.07 for He\(^+\), He\(_2^+\), N\(_2^+\) and N\(_4^+\), respectively) [16]. In order to keep the collision probability in the simulation below 10% within each timestep, the electron timestep is set to \(\Delta t_\textrm{e}=2.315\cdot 10^{-14}\) s, while the timesteps for the heavy charged particles are chosen to be \(\Delta t_{\mathrm{He^+}}=10\Delta t_{\textrm{e}}\), and \(\Delta t_{\mathrm{He_2^+}}=\Delta t_{\mathrm{N_2^+}}=\Delta t_\mathrm{N_4^+}=100\Delta t_{\textrm{e}}\). Simulations were performed for a range of experimentally relevant gas temperatures (300–400 K). In this way, despite the 1d character of the simulations, the experimental data measured at different positions along the direction of the gas flow, which are not resolved spatially in the simulation, can effectively be reproduced by performing multiple 1d3v simulations for different gas temperatures. Each simulation then resembles results at one specific position in z-direction.

Results

Gas Temperature

Fig. 3
figure 3

Experimental results: gas temperatures at 6 distinct positions along the channel of the COST-jet determined by analysis of the 0–1 band of the 2nd positive system of nitrogen for three different gas mixtures (1000 sccm of helium with 0.5 sccm, 1 sccm, and 2 sccm of nitrogen, respectively). The amplitude of the 13.56 MHz sinusoidal driving voltage waveform is 300 V. The “square” and “plus” shaped data points are horizontally offset to avoid overlapping error bars

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Figure 3 shows the neutral gas temperature determined by time averaged OES, spatially resolved along the channel of the jet for three different nitrogen admixture concentrations (0.5 sccm, 1 sccm, 2 sccm, respectively) added to 1000 sccm of helium gas flow. Two main trends can be observed:

  1. (i)

    The gas temperature increases as the gas traverses the discharge channel

  2. (ii)

    The smaller the N\(_2\) admixture, the greater the temperature increase.

The temperature increase along the jet channel is in agreement with results obtained by Kelly et. al. [28, 29]. In general, the background gas can be heated by collisions of neutral particles with ions, electrons, and the boundary surfaces. In the COST-jet, it has been shown that mainly electrons, but also ions heat the gas [28]. To identify the respective contribution of each of these heating mechanisms for our operating conditions, we extracted the power density transferred to neutrals by elastic collisions between charged particles and the background gas, as well as the ion fluxes and energy distributions at the electrodes, from the PIC/MCC simulations. The latter information determines the power transfer and, thus, the heating of the electrodes, which could, in turn, heat the neutral gas.

Figure 4 shows the combined power density dissipated to neutrals via electron and ion elastic collisions with the background gas for the three helium-nitrogen mixtures for different gas temperatures. As discussed before, the increase of the nitrogen admixture concentration lowers the total power density dissipated to the gas by collisions with charged particles, which can be clearly seen in the figure. The dissipated power is approximately constant over the investigated temperature range, considering that the maximum of the experimentally observed temperature is slightly below 350 K. Due to the difference between the time scales of the flow, i.e. the time it takes a neutral particle to move from the gas inlet to the tip of the nozzle (which is on the order of milliseconds), and that of the charged particle dynamics, i.e. the time it takes an electron to move from one electrode to the other (which is on the order of nanoseconds), this power input can be considered to be a spatial and temporal constant heat source and should lead to a linear increase of the gas temperature over the length of the jet - exactly what can be observed (see Fig. 3, excluding the \(-\) 1.75 mm point).

The reason for the gas temperature dependency on the N\(_2\) admixture concentration is the following: electrons in the plasma excite and ionize the nitrogen molecules. This effectively lowers the electron energy and, thus, a higher concentration of N\(_2\) leads to a lower electron density at constant driving voltage amplitude [12]. Consequently, at high N\(_2\) admixture concentration there are less charged particles that can heat the background gas via collisions and the gas temperature remains lower, as observed in Fig. 3. We note, that the energy stored in the N\(_2\) vibrational modes could contribute to gas heating via vibrational-translational (VT-)relaxation, however, combining the rate constant of VT-relaxation of N\(_2\) in helium (\(5\cdot 10^{-18}\) cm\(^3\)s\(^{-1}\), [52, 53]) with the atmospheric pressure helium density (\(2.1\cdot 10^{19}\) cm\(^{-3}\)) yields a mean lifetime of \(\approx 10\) ms for the vibrational states. The gas flow of 1000 sccm results in an approximate residence time of the gas in the jet of 1.8 ms. Thus, the vibrationally excited nitrogen molecules will be blown out of the jet before they can heat the gas, and, therefore, gas heating is even more reduced. A more detailed analysis of the physical effects causing and caused by the gas heating follows in Sect. 3.2.

We note, that Winzer et. al. [30] reported, that the gas temperature in their capillary jet operated with a helium–oxygen mixture has a negligible dependency on the oxygen admixture concentration, even though at first glance the oxygen, as a molecular gas, should take a similar role as the nitrogen in our work (reducing plasma density). The difference stems from the fact that Winzer et al., kept the input power to the jet constant, while in our work the voltage was kept constant. Consequently, in our work the total power input and therefore the gas heating decreases with higher molecular gas admixture concentrations due to the decreased electron and ion densities [18]. On a second note, Kelly et al. reported a modeled temperature of \(\approx \,\)40 \(^{\circ }\)C for COST-jet operation with 300 V and a mixture of \(0.6\,\%\) of oxygen in helium at 1000 sccm gas flow. The oxygen addition seems to inhibit the gas heating significantly less compared to nitrogen, because the cross sections for vibrational excitation are almost two orders of magnitude smaller in oxygen than in nitrogen. Therefore, more energy is transferred to the background gas via elastic collisions in the oxygen case.

Fig. 4
figure 4

Simulation results: power density dissipated to neutral particles by elastic collisions between charged particles and the background gas depending on the background gas temperature for different helium-nitrogen mixtures. The amplitude of the 13.56 MHz sinusoidal driving voltage waveform is 300 V

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Fig. 5
figure 5

Gas temperature increase along the COST-jet based on the collisional power dissipation of electrons and ions to the neutral gas obtained from the simulation and the gas residence time in the active plasma region of the jet for different background gas temperatures and for different helium–nitrogen mixtures

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Figure 4 shows the power density of elastic collisions between charged particles and the background gas depending on the background gas temperature and the gas mixture. This power is greater for electrons than for ions for all cases. The fact that the energy transfer between an electron and a much heavier helium atom is small is counteracted by the atmospheric pressure conditions, at which the number of these collisions per unit time is large. For both electron and ion elastic collision power, an increased nitrogen content leads to overall smaller power values. Most striking, with increased background gas temperature the electron elastic collision power decreases, while the corresponding ion power increases. The simulation also shows, that the power dissipated in surface collisions is many orders of magnitude smaller than the power of the collisional gas heating and can, therefore, be neglected. The increase of the background gas temperature leads to a gas density decrease, since the flow velocity is usually on the order of 10 m/s, and thus the Mach-number is too small for compressible effects to be of importance.

Taking the specific heat capacity of helium, the gas residence time in the jet, and the elastic collision power densities from the simulation, we can approximate the total gas temperature increase for different background gas temperatures. The results are displayed in Fig. 5. The increase is inversely proportional to the nitrogen admixture and approximately constant over the investigated temperature range. Comparing the estimated values with the temperatures measured via OES (Fig. 3) shows reasonably good agreement given the simplicity of the estimation.

An additional effect visible in Fig. 3 is the drop of the gas temperature at the \(-\)1.75 mm position close to the tip of the nozzle of the jet compared to the next position located further inside the active plasma region (\(-\)7.05 mm). We suspect that this is caused by the back diffusion of ambient air into the jet. This addition of mainly nitrogen and oxygen should, as already described above, inhibit the gas temperature increase. The effect of ambient gas intrusion into the jet is also visible in the numerical model results reported in reference [29] (Figure 6, panel c2).

Effects of Gas Heating on the Charged Particle Dynamics

Fig. 6
figure 6

Experimentally determined electron impact excitation rate from the helium ground state into the He I (3s)\(^3\)S\(_1\) state, spatially resolved between the electrodes of the COST-jet and temporally resolved during the first half of the RF period at different positions along the direction of the gas flow inside the plasma region of the jet (see Fig. 1). The amplitude of the 13.56 MHz sinusoidal driving voltage waveform is 300 V, the helium and nitrogen flows are 1000 sccm and 0.5 sccm, respectively. Above each plot the respective central position on the z-axis and gas temperature determined by OES (cf. Fig. 3) are shown

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Figure 6 shows measured spatio-temporal plots of the electron impact excitation rate from the ground state into the He I (3s)\(^3\)S\(_1\) state for 0.5 sccm nitrogen added to a flow of 1000 sccm of helium at different positions along the channel of the jet. Only half of the RF period is shown in each plot on the horizontal axis in order to focus on the effects of the gas heating along the direction of the gas flow on the electron power absorption mode. In each plot, intensity peaks corresponding to the \(\Omega\)- and Penning-mode can be identified. Comparing the plots from left to right, the ratio between the Penning- and \(\Omega\)-peak is found to change along the gas flow direction in the jet; the Penning peak becomes stronger.

Fig. 7
figure 7

Computed electron impact excitation rate from the helium ground state into the He I (3s)\(^3\)S\(_1\) state, spatially resolved in a 1 mm electrode gap and temporally resolved during the first half of the RF period for different values of the background gas temperature. The voltage amplitude of the 13.56 MHz sinusoidal driving voltage waveform is 300 V, the helium to nitrogen ratio is 1000 to 0.5

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Figure 7 shows computed spatio-temporal plots of the electron impact excitation rate from the ground state into the He I (3s)\(^3\)S\(_1\) state for background gas temperatures from 300 to 400 K. Just like in the experimental data, the intensity peaks corresponding to the \(\Omega\)- and Penning-mode can be identified. The simulation reproduces the experimental trend: the higher the gas temperature, the more pronounced the Penning-peak becomes compared to the \(\Omega\)-peak. Comparing the experimental plots (Fig. 6) to the computed ones (Fig. 7), the expected background gas temperature value should be approximately between 300 K and 350 K, depending on the position in the jet. This agrees well with the gas temperature results obtained from OES (Fig. 3).

Fig. 8
figure 8

Ratio of Penning- to \(\Omega\)-peaks for three different gas mixtures of helium and nitrogen along the discharge channel of the COST-jet based on experimental results. The “square” and “plus” shaped data points are horizontally offset to avoid overlapping error bars

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To quantify the change of the peak ratios, the algorithm described in Sect. 2 is used. The results obtained from the measured data for different operating conditions are displayed in Fig. 8. The trend of this intensity ratio along the direction of the gas flow is correlated with the corresponding trend of the gas temperature (see Fig. 3): (i) the peak ratio increases along the direction of the gas flow, (ii) the more nitrogen is added to the mixture, the smaller the increase of this ratio is along the channel, (iii) in the 0.5 sccm and 1 sccm nitrogen admixture cases, the ratio at the point closest to the jet exit drops compared to the point further inside the plasma volume.

Fig. 9
figure 9

Ratio of Penning- to \(\Omega\)-peaks for three different gas mixtures of helium and nitrogen for different background gas temperatures based on simulation results. The “square” and “plus” shaped data points are horizontally offset to avoid overlapping error bars

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Figure 9 shows the peak ratio obtained from the simulation results for different gas temperatures, which can be assigned to different positions along the direction of the gas flow. Comparing this plot to Figs. 3 and 8, it can be seen that the general trends agree well in simulation and experiment. Less nitrogen as well as higher gas temperatures lead to higher peak ratios. The absolute values of the ratios are in the same range for measured and computed data, but do not match perfectly. For the data in this study, they are not directly comparable, due to the moderate differences between the measured and computed excitation plots (Figs. 6 and 7).

Fig. 10
figure 10

Simulation results: Space and time averaged charged particle and helium metastables densities depending on the background gas temperature and the amount of nitrogen addition for all simulated cases

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Figure 10 shows the spatially and temporally averaged densities of charged species and helium metastable atoms for all simulated cases to enable a more detailed analysis of the causes and effects of the nitrogen admixture and gas temperature changes: The major ionic species are N\(_4^+\) and N\(_2^+\), while He\(^+\) and He\(_2^+\) are practically irrelevant. The ion densities are 5 orders of magnitude lower than the gas density. The discharge is non-neutral, meaning that the total space and time averaged ion density is much higher than the electron density for all cases (see, e.g. [17]). Helium metastables are the particle species most affected by both the gas temperature and nitrogen admixture change. The metastables are created by electron impact excitation, which is more effective at higher gas temperatures due to the longer electron mean free path. At the same time, in the Penning ionization process, N\(_2^+\) and additional electrons are created close to the electrodes in the presence of more metastables at higher gas temperature. This causes the shift to the Penning-mode, as both the electrons generated directly in Penning ionization, and the additional secondary electrons caused by the enhanced flux of N\(_2^+\) ions to the electrodes are accelerated by the high electric field in the sheaths. Additionally, the increase in the ion density results in an increased space charge in the plasma, which increases the magnitude of the electric field. The increase of the nitrogen content (which, in turn, lowers the electron energy) has a directly visible effect on all the species shown in the figure: their densities decrease. Again, the helium metastable density is affected most strongly (more details in the next paragraph), but the decrease is also visible for N\(_2^+\) and N\(_4^+\). Also, since the rate of creating N\(_4^+\) depends on the densities of helium and nitrogen molecules, an increased temperature attenuates the N\(_4^+\) generation, but not as much as it enhances the N\(_2^+\) generation.

Fig. 11
figure 11

Simulation results: Ionization rates of helium and nitrogen for all three different gas mixtures and the whole investigated background gas temperature range, split by ionization process

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Figure 11 shows simulation results for the spatially and temporally averaged ionization rates (electron impact ionization of He, N\(_2\) and Penning-ionization) as a function of the background gas temperature for various nitrogen admixtures. The ionization dynamics is dominated by Penning-ionization. Therefore, considering Fig. 10, the main consequence of increasing the nitrogen concentration is the decrease of the helium metastable density. The threshold energy of the excitation of He (\(\approx 20\) eV) is considerably higher than the various excitation processes for nitrogen (rotational, vibrational as well as electronic). Since at atmospheric pressure the number of elastic collisions is orders of magnitude higher than that of the inelastic channels, it follows that the dominant contribution to gas heating comes from elastic collisions. The power lost by the sum of all charged species being absorbed at the electrodes is at maximum \(\approx\)1 µW and therefore negligibly small compared to the \(\approx\) 300 mW of elastic collision power.

Both, the experimental and computational results, reveal an effect of the gas temperature on this ratio and, thus, on the mode of plasma operation. According to the ideal gas law, an increase of the gas temperature leads to a decrease of the neutral gas density at constant pressure. Thus, the electron mean free path increases. Consequently, electrons generated by Penning ionization inside the sheaths at the times of high sheath voltage within the RF period can gain more energy, as they are accelerated by the high sheath electric field over a longer distance without collisions. Under the atmospheric pressure conditions studied here, this change of the reduced electric field induced by neutral gas heating leads to an increase of the Penning- relative to the \(\Omega\)-peak. This explains how the observed neutral gas heating by collisions of charged particles with the neutral background gas can induce a transition of the electron power absorption mode. A shift in the direction of the Penning-mode can, as we show, even be observed along the discharge channel of the jet at stable operation.

In the simulation, the gas temperature can be changed over a larger range compared to the temperature increase observed experimentally. In this way, the effects of increasing the length of the active plasma volume of the jet and/or of intentional pre-heating of the gas on the electron dynamics can be studied. The latter is used for some applications of plasma catalysis to control the thermal component of catalytic reactions (see, e.g., [54,55,56]). As indicated in Fig. 7, a gas temperature variation over a larger range can induce a full mode transition from the \(\Omega\)- to the Penning- and potentially also other modes such as the constricted mode [6, 57]. Such a mode transition can strongly affect the electron energy distribution function [22] and, thus, the energy-dependent electron impact-driven dissociation of the neutral background gas as well as chemical/catalytic reactions induced by such reactive neutrals.

Conclusion

In this work, we presented spectroscopic measurements of the neutral gas temperature and of the spatio-temporally resolved dynamics of energetic electrons along the discharge channel of the COST plasma jet accompanied by 1d3v PIC/MCC simulations. The jet was operated in helium-nitrogen mixtures (1000 sccm helium and 0.5, 1, or 2 sccm nitrogen), with a sinusoidal driving voltage waveform with an amplitude of 300 V and 13.56 MHz frequency.

Our experimental results on the gas temperature support earlier findings based on models and simulations [28, 29], that the temperature of the neutral gas can increase on its way through the jet at low admixture concentrations of molecular gases (N\(_2\) in our case). Based on PROES measurements and spatially one-dimensional PIC/MCC simulations (resolving the inter-electrode space and performed at different gas temperatures), this gas heating effect was found to induce a mode transition of the electron dynamics along the direction of the gas flow from the \(\Omega\)-mode at lower neutral gas temperature to the Penning-mode at higher gas temperatures. This was explained by neutral gas depletion as a consequence of the gas heating, which enlarges the electron mean free path and allows electrons generated inside the sheaths by Penning-ionization to gain more energy over one mean free path. This leads to enhanced helium metastable generation, which is the discharges’ main ionization mechanism, ultimately causing more excitation at the time of maximum sheath voltage during each RF period as compared to the excitation during the sheath expansion phase.

A quantitative comparison of experimental and computational results was realized by calculating the ratios of the characteristic Penning- and \(\Omega\)-peaks of the spatio-temporally resolved electron impact excitation rate from the He I ground to the He I (3s)\(^3\)S\(_1\) state obtained from experiments and simulations. The simulation results revealed collisions of electrons and ions with the neutral gas to be the main source of the neutral gas heating. The addition of nitrogen to the gas mixture generally inhibits the gas heating as its excitation processes act as a loss channel for electron energy, therefore lower the plasma density, and in turn reduce the gas heating.

The insight that neutral gas heating can induce mode transitions in atmospheric pressure capacitively coupled RF plasma jets and the obtained understanding thereof can be highly relevant for a variety of applications of such and other plasma sources. This includes plasma-induced gas conversion and plasma catalysis, where a change of the electron energy distribution function induced by such mode transitions can strongly affect the generation of process-relevant radicals by electron impact-driven dissociation of the background gas. For plasma catalysis, pre-heated gas is often used and/or strong gas heating naturally occurs in the plasma. Based on our results, such effects can be understood and potentially be controlled to realize a knowledge-based optimization of plasma processing applications.