Nanosecond repetitively pulsed plasmas with MHz bursts for CO2 dissociation

A novel pulsed power source capable of nanosecond pulses with burst frequencies up to 1 MHz is employed to create atmospheric pressure pulsed plasma in pure CO2 gas. The short bursts contain up to four nanosecond pulses. The CO2 conversion and corresponding energy efficiency are measured ex-situ with Fourier-transform infrared absorption spectroscopy. Trends in the absorption line profile of in-situ quantum cascade laser infrared absorption spectroscopy indicate an elevated vibrational temperature of CO2 with an increasing number of pulses per burst. The key result of this paper is that the dissociation energy efficiency is higher when operating the plasma in burst mode. Furthermore, a larger number of pulses in a burst is associated with a further increase of the dissociation efficiency. The highest efficiency measured is (17.7±0.3) % for single pulses spaced 2 ms apart, and (20.0±0.3) % for bursts of three pulses, with an in-burst frequency of 1 MHz and bursts spaced 4 ms apart.

Original Content from this work may be used under the terms of the Creative Commons Attribution 4.0 licence.Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.ability to efficiently generate reactive particles, which chemically and thermally activate the gas, ultimately facilitating ignition [3].Consequently, this manuscript draws upon insights and terminology from these two disciplines.For instance, in NRP air discharges, visual classification as corona, glow or spark is applied, despite their transient nature [8].We adopt the same approach.
In the context of CO 2 conversion, as explored in this experimental study, NRP discharges are far from established.A literature review reveals particular interest in dry reforming of methane (CO 2 + CH 4 ) [9][10][11][12][13][14][15][16][17][18][19][20], strong dilution in noble gases (CO 2 + He/Ar), facilitating discharge ignition and stability [21][22][23], and lastly pure CO 2 NRP discharges potentially with additional probe molecules for diagnostic purposes [24][25][26][27][28].When exposing CO 2 to a NRP discharge, strong molecular excitation, appreciably of vibrations, is observed that can promote the molecule's decomposition [21,22].However, studies, for instance by Richards et al [29] or Yong et al [30], indicate that vibration is not the dominant dissociation path because other paths are more significant [29] or it is argued that the time required to bring molecules vibrationally to the dissociation limit is longer than the nanosecond pulse time [30].Even though Moss et al [31] also question the impact of vibrations on the CO 2 conversion in their experimental conditions, they note that there are indications that for nanosecond pulses with high frequencies of around 1 MHz, accumulation of the population of vibrational levels occurs and vibrational dissociation becomes the dominant pathway.Aerts et al [32] show similar results in a simulation of a pulsed dielectric barrier discharge.To date and to the best of our knowledge, no other research was published that experimentally tested these frequencies, possibly because the required pulse repetition frequencies (PRFs) are currently very difficult to achieve.Montesano et al [10] came closest with frequencies up to 95 kHz in short bursts.They find a maximum energy efficiency of 58% at 50 kHz bursts in atmospheric pressure CO 2 , and suggest this may be due to a build-up of vibrationally excited states in CO 2 [10].
The goal of the present work is to assess and interpret the conversion performance of a pure CO 2 NRP atmospheric pressure discharge with frequencies up to 1 MHz using a novel pulsed power source.The conversion is measured exsitu with Fourier-transform infrared (FTIR) absorption spectroscopy and vibrational excitation of CO 2 is studied insitu using quantum cascade laser (QCL) infrared absorption spectroscopy.The central research question in this paper is, whether a NRP discharge in burst mode can be used to more efficiently dissociate CO 2 , compared to single pulses, potentially through preferential vibrational excitation.In the next section, the fundamentals of CO 2 conversion in atmospheric pressure NRP plasmas are explained.Afterwards, the experimental setup is discussed.The results section shows the results from ex-situ FTIR as well as insitu QCL absorption spectroscopy (QCLAS) measurements.Finally, the most important conclusions in this paper are summarised.All data can be found at this reference [33].

CO 2 conversion in NRP discharges
The net reaction under study is where the bond strength of CO 2 is about 5.5 eV per molecule and the reaction enthalpy ∆H is 2.9 eV per molecule [34].
Ultimately, the overall efficiency of a dissociation path is determined by how much more energy is used to break apart CO 2 compared to ∆H.Ever since highest energy efficiencies for CO 2 conversion have been reported in microwave (MW) discharges and explained by preferential vibrational excitation leading to dissociation by vibrational ladder climbing [35,36], vibrational excitation, particularly of the asymmetric stretching mode ν 3 , has been at the centre of many CO 2 plasma conversion studies [37][38][39].
Herein, the study of NRP discharges for CO 2 conversion is no exception.These discharges are considered promising because their transient nature allows for very targeted energy deposition due to the thermodynamic non-equilibrium maintained on short time scales [40].The most important parameters here are the reduced electric field E/N, where E is the electric field and N the total gas number density, and thereby the electron temperature T e .The cross sections for vibrational excitation decrease rapidly for T e above a few eV [41].The same behaviour is seen in [40], indicating that for efficient dissociation via vibrational excitation, a discharge with low E/N and T e (E/N) is preferred.
Full exploitation of the vibrational dissociation path requires not only maximising the vibrational energy gain but similarly minimising the loss of vibrational energy to other degrees of freedom.To that end, a low gas temperature T gas is substantial, as the relaxation rate from vibrational to translational motion increases with T gas , creating a positive feedback loop [42].In fact, Treanor et al [43] show that only at low T gas , accumulation of higher vibrational states occurs, leading to the desired dissociation by ladder climbing.
With their very short duration that does not allow for much resistive heating, NRP discharges appear ideal to keep T gas and thereby vibrational relaxation low.However, the excitation in NRP discharges is not limited to vibrations.Electronic excitation and ionisation via direct electron impact occurs as well, and might lead to CO 2 dissociation, too.Direct electron impact dissociation is less attractive though, as it is characterised by a lower energy efficiency [44].Furthermore, quenching of electronically excited states can in turn lead to fast gas heating (FGH), well known from NRP discharges in air [5].The same has been observed in CO 2 [45].Additionally, it has been shown that a NRP discharge can turn into a fully ionised thermal spark [46].It is worth reiterating that any form of gas heating facilitates vibrational relaxation.These considerations reinforce the notion that energy should be deposited into the vibrations as selectively as possible.
The energy deposition selectivity is influenced by the PRF and the pulse width.While the importance of the latter is clear from the previous paragraph, the former benefits from additional clarification.In fact, a sufficiently high PRF might increase the vibrational-translational non-equilibrium [32].The non-equilibrium can be quantified by the characteristic time at which vibrational modes relax to translational motion of molecules τ V−T , i.e. so-called V-T transfer [47], which for atmospheric pressure and T gas ≈ 300 K in CO 2 is approximately τ V−T ≈ 2 µs [31], with τ V−T dropping quickly as T gas rises [48].With the fast bursts of the used NRP discharge, the time between consecutive pulses in the burst is supposedly shorter than τ V−T .Note again that FGH can significantly shorten τ V−T due to the increased T gas , which impedes the accumulation of energy in the vibrations.The accumulation of particles in an excited state is not limited to vibrational excitation but also includes electronically excited states as demonstrated for a MHz NRP discharge in Ar with a small amount of CH 4 [49].
Figure 1 maps the studies mentioned in the introduction by pulse width against PRF.Each marker represents one study, Figure 1.Pulse repetition frequency and width reported in literature [2-4, 6, 7, 9, 12, 13, 15, 16, 18-21, 23, 24, 29, 50-58].The marker position is the average over the reported range, indicated by the bars.The marker shape indicates the used electrode geometry and the colour the application, narrowing down the treated gas mixtures.Filled markers represent burst mode.
where the position is determined from the average of PRF and width reported, the bars show the range covered (or coverable according to the pulse source specifications when operating conditions are not clear), the shape indicates the used electrode geometry, and the colour gives the gas mixture treated.If the voltage pulses are provided in bursts, the in-burst frequency is used and markers are filled.The figure focusses on CO 2 recycling, including works on combustion and air treatment for context.
Despite a wide coverage of PRFs and pulse widths in figure 1, the distribution of studies is not uniform but exhibits gaps and accumulations.Particularly, the work prested here, namely the frequency in the MHz range, pushes forward into an underexplored regime.The accumulation of studies can be explained by the limited number of providers of NRP voltage supplies, for example FID GmbH or Megaimpulse Ltd in the upper kHz range and with pulse widths around 10 ns.We notice that (i) CO 2 conversion in NRP discharges has yet to gain widespread recognition, (ii) frequencies over 1 MHz are, to the best of our knowledge, not explored at all in this context and (iii) an extension of the covered parameter space in figure 1 might require the development of new pulse sources.All these points are addressed by the present study.
For that purpose, the conversion performance of the present NRP CO 2 discharge is quantified by the specific energy input (SEI), the CO 2 conversion X CO2 , and the conversion energy efficiency η.
where ε b is the total energy deposited into the plasma during a burst of b individual pulses, p inter−burst is the period at which the bursts are repeated, see figure 3, and Q is the gas flow rate [31].
where n i is the density of species i.It is assumed that CO and O 2 are the only products, e.g.no carbon deposition is visible after hours of operation, compliant with equation (1).Note that in a rigorous treatment, the change of the gas flow rate between reactor entrance and exit due to conversion should be taken into account [59,60].Since no internal standard or flow rate measurements at the reactor exit were available, we refer to the simplification in equation (3).It is worth mentioning that relatively small conversion values are found, associated with small changes in total flow rate and therefore a small systematic error is introduced.Accordingly, This definition of η omits all other energy losses that might be associated with the entire process of creating valuable chemicals.The energy required to purify CO 2 , separate the CO from the exhaust gas mixture and any energy losses from the pulse source is neglected.However, it allows for easier comparison of energy efficiency between different discharges, since this same definition is also shared by others using other energy sources such as MWs, at any pressure [35].The energy required to lower the pressure in the reaction chamber is another factor that is not considered, and is one of the main reasons why NRP discharges are interesting for this application.The overall energy efficiency for atmospheric CO 2 dissociation would be much higher, and more suitable to scaling to an industrial process.

Experimental setup
A schematic of the used setup is shown in figure 2. Its central element is the new pulse source.Additionally, there are the plasma reactor and the electrical and optical diagnostics.Due to strong electromagnetic interference (EMI), pulse source and plasma reactor are contained in an electromagnetic compatibility (EMC) cabinet.The interested reader is referred to the appendix for an in-depth discussion.In the following, the different components are introduced.

Pulse source
Traditional pulse sources are made using spark gaps, but suffer from low lifetimes, repeatability and PRFs.Developments in solid-state switches and diodes have led to faster and more reliable high-voltage switches, although the combination of high voltages (>10 kV) with large pulse widths (>60 ns) and very high PRF (1 MHz in bursts) remains challenging [61].The pulse source used in this paper was designed and produced specifically for this application, based on a design by Pang et al [62].An important improvement in this design compared to previous work comes from using only a single external gate driver and high-voltage power supply for all series-connected MOSFETs.This not only improves the turn-on or rise time from hundreds of nanoseconds to less than 10 ns, it also makes it possible to create a much more compact design [62].A picture of the pulse source with some additional information can  2 that is triggered by an optical signal, is a number of MOSFETs in series.The maximum voltage the pulse source can reliably maintain is around 11 kV and the MOSFETs can handle a peak current up to 100 A. In practice, the current is usually limited to less than 50 A to protect the MOSFETs, avoid excess heating and electrode degradation as well as to limit the power deposited into the plasma.The pulse source is designed to produce bursts of pulses with a burst frequency up to 2 MHz.The number of pulses in a burst and their amplitude are limited by the energy stored by the capacitors on the circuit board, as the charging time of the capacitors is on the order of 100 µs.Hence, the minimum inter-burst period is around 1 ms. Figure 3 illustrates the signals used to turn on the pulse source and the QCL, discussed later in this section, as well as defining the inter-burst period p inter−burst , in-burst frequency f in−burst , pulse width w and QCL scan time t QCL as used in this paper.An example of a pulse train with four pulses of 60 ns pulse width and an in-burst frequency of 1 MHz is shown in figure 4. The voltage is set to 11 kV and the current limited to 30 A by the R 3 = 330 Ω resistor between the pulse source output and the anode, see figure 2. The gas breaks down around 10 kV, at which point the voltage at the anode drops significantly as a lower resistance path through the gas is created.At this point, the voltage drop occurs almost entirely over the current-limiting resistor R 3 .Given the high current at low voltage, the short inter-pulse period suggesting a not negligible initial charge density, and the erosion of the electrodes shown in figure A.2, makes us assume that the discharge is in the spark regime [63].Adjacent regimes like glow or thermal  spark are deemed less likely [8,46,64].For example, NRP glow discharges occur only in narrow parameter ranges [8].
In situ characterisation would be required to clarify the state of the discharge.Note here also the absence of current or voltage reflections in figure 4.This is because the compact pulse source is placed close to the discharge gap, connected with a short cable of 10 cm-15 cm length.Since the rise time of the pulses (<10 ns) is much longer than the pulse propagation time over this short length of wire (<1 ns), the voltage at the discharge cell is almost identical to the voltage at the pulse source.

Plasma reactor
The plasma reactor vessel is made from Pyrex glass and has six ports: two for the gas inlet and outlet, two for the QCLAS measurements and a further two as a direct viewing port as well as for future optical emission spectroscopy or LIF measurements, see figure 5(b).The pin-to-pin electrode configuration ensures that the plasma is always created in the same location, so that the QCL beam reliably intersects the relatively small plasma volume.Gas in-and outlet are located at the sockets of the stainless-steel electrodes.The gas flow rate is controlled by a mass flow controller.Unless mentioned otherwise, the discharge is operated at atmospheric pressure.Note that the vessel was designed to maximise optical access rather than conversion performance.
The residence time of the gas in the plasma volume is an important factor in determining the conversion of CO 2 .When the inter-burst period is longer than the residence time of the gas, then a lot of gas never gets in contact with the plasma.In this case, we cannot use the SEI to compare measurements since the untreated gas artificially lowers the SEI.Due to the vessel geometry, a considerable part of the feed gas passes far from the discharge volume, i.e. it spatially never gets in contact with the plasma.Hence, the conversion and the SEI with respect to the total gas flow through the reactor is very low.X CO2 and SEI are first corrected for the fraction of gas that flows through the plasma.The zeroth-order approach is to assume the flow is uniform throughout the entire vessel, which for the current setup means the gas residence time t r is where r vessel is the radius of the cylindrical part of the plasma reactor, d gap is the distance between the electrode tips and Q the flow rate as previously defined.This gives t r = 23.6 ms for d gap = 1.6 mm, r vessel = 12.5 mm and Q = 2L min −1 .However, given the position of the gas inlets and outlets in this setup, a uniform flow is unlikely.For this reason, a 3D fluid simulation is made in COMSOL that uses a simplified model to determine the approximate t r .The geometry is approximated as axi-symmetric and the flow is restricted to the laminar regime.While the laminar flow study with the aforementioned simplifications is not a perfect representation of the real flow conditions, it gives a more realistic indication of the CO 2 conversion than the inflated values achieved using uniform flow calculations.The cross-sectional plot of flow velocities resulting from a simulation for a feed gas inflow of 2L min −1 is shown in figure 5(a).Under laminar flow conditions, approximately 1.4% of the gas flows through the plasma volume as found by calculating the volumetric flow rate through a circle with radius 0.8 mm perpendicular to the flow direction located exactly in the middle between the two electrodes.The gas residence time is then where r electrodes = 0.8 mm is the radius of the electrodes.This gives t r = 6.9 ms for d gap = 1.6 mm and Q = 2L min −1 as before.In the experiments that follow, d gap = 1.6 mm and Q < 2L min −1 unless specified otherwise so that t r ⩾ 6.9 ms.Hence, the largest inter-burst period used in this paper for measurements of X CO2 is 7 ms.An additional layer of complexity would be added when the influence of the discharge on the gas flow pattern is considered.With the sudden gas heating that comes with discharge ignition, shock waves are formed that facilitate gas mixing.From plasma-assisted combustion studies it is known that this mixing increases particle conversion [65] and similar effects are likely in CO 2 conversion [66].However, more advanced flow dynamics simulations are beyond the scope of this manuscript.

Voltage measurement
The voltage at the anode is measured, about 5 cm from the discharge, by a custom high-voltage sensor commonly referred to as a D-Dot sensor [67], since commercial probes either do not fit in the EMC cabinet, do not have the right bandwidth or are too costly.The D-dot sensor is essentially a cylindrical strip of copper that is capacitively coupled to the high voltage electrode.The circuit is shown in figure 6.The shielding around the sensor ensures that the parasitic capacitance is well-defined and that the sensor is shielded somewhat from EMI.The transfer function of the D-dot sensor is then where C D is the capacitance between the high voltage electrode and the D-dot sensor, C par is the parasitic capacitance to ground, Z cable is the impedance of the cable connecting the sensor to the oscilloscope (Waverunner 610Zi, LeCroy Technologies) and ω the angular frequency.The approximation is valid for jωZ cable (C D + C par ) ≪ 1, which is the regime the D-dot sensor is operated in.The D-dot sensor is designed to have a high-frequency cut-off that is higher than the 1 GHz bandwidth of the oscilloscope used.An RC integrator is used to integrate the signal to obtain a sensor voltage registered by the oscilloscope that is proportional to the voltage at the high voltage electrode.This measured signal is then processed, first by undoing the hardware integration step, followed by software integration.This procedure is necessary because the hardware integrator is not a perfect integrator for lower frequencies.It is still crucial to do hardware integration though, since it eliminates an integration offset due to random noise.The final processed signal is proportional to the high voltage signal, the proportionality factor can be found by calibrating the sensor.This is done with a commercial voltage probe before closing the EMC cabinet.

Current, power and energy
For NRP discharges the most suitable method to determine the power P is to multiply the measured voltage V Ddot by the current I [68].The current is measured at the ground electrode, also about 5 cm from the discharge, with a current monitor (Pearson 6585) and must be corrected to remove the capacitive current I C , which does not contribute to energy deposited in the plasma.Of course, it is also important that the voltage and current signals are not delayed with respect to each other.The capacitive current can also be used to match these signals, so that they can be time-shifted if necessary.A measurement of the current and voltage at lower voltages, when there is no breakdown and the vessel acts as a capacitor, can be used to calculate the capacitance of the setup as well as the required time shift to synchronise the signals.The energy deposited is then where b is the number of pulses in the burst and f −1 in−burst as defined in figure 3.  Another important aspect of NRP discharges is the inherently large spread in the energy deposited during each pulse due to the stochastic nature of plasma ignition.Figure 7 shows a histogram of the deposited energy for single-pulse operation.The mean energy deposited and the corresponding error in the mean are then used to calculate the SEI.For figure 7, this yields 2.67±0.03mJ.For bursts of pulses, the power deposited in each subsequent pulse is lower due to the limited energy stored in the capacitors of the pulse source, see figure 8.More details on the determination of the time lag, capacitive current and the variation in the deposited energy can be found in appendix C.

FTIR
FTIR spectroscopy (Bruker Vertex 80v) is used in this paper to determine the neutral gas densities of CO 2 and CO in the exhaust gas of the plasma vessel operated at atmospheric pressure.A fitting and simulation script developed by Klarenaar et al [69] is used to determine the percentage of CO 2 and CO in the exhaust.The conversion, in turn, is used to calculate the energy efficiency of dissociation.For each spectrum, ten scans are performed and averaged together.The error in the measured conversion is estimated by measuring three spectra a few minutes apart and then calculating the standard deviation.In all cases, the relative error was below 2% and in most cases below 0.5%.

QCLAS
The QCL setup (neoplas control) introduced by [37] is used for in-situ absorption spectroscopy because the time resolution achievable with the FTIR spectrometer is 1 µs [69], whereas the time resolution we can achieve with QCLAS is between 100ns and 200ns.In addition, the instrumental broadening of the QCL is negligible, whereas the instrumental broadening of the FTIR spectrometer used in this paper has a sigma of around 0.06 cm −1 , comparable to pressure broadening.However, with pressure broadening alone it is already difficult to measure individual lines.
The QCL used in this paper has a tunable wavelength range between 2245 cm −1 and 2260 cm −1 and a chirp of on average 5 × 10 −3 cm −1 ns −1 over a 200 ns period, which then corresponds to a tuning of 1 cm −1 .As the left-hand side of figure 9 shows, the simulated transmission spectra of a nonplasma vessel filled with CO 2 and an identical vessel with a 1.6 mm diameter plasma are very similar in the wavelength range of 2254-2255 cm −1 .This specific wavelength range is chosen because the absorption lines of the ν 3 = 1 → 2 transition of CO 2 do not overlap with the ν 3 = 0 → 1 transition.The right-hand side of figure 9 shows an alternative wavelength range where the line strengths of CO 2 are higher, with the caveat that more lines will be saturated.Finally, the dotted lines show that reducing the size of the reactor in the spectrum simulation so there is less background CO 2 makes detection easier.For this paper, QCLAS measurements are performed at 175 mbar, reducing pressure broadening and making it easier to distinguish individual peaks compared to atmospheric pressure.Note that reducing the pressure changes the discharge properties, like reducing the required voltage for ignition.Any conclusions from QCLAS measurements with respect to the FTIR results can therefore only be qualitative.

Results
The key result of this paper is that the dissociation energy efficiency is higher when operating the plasma in burst mode.Furthermore, a larger number of pulses in a burst is associated with a further increase of the dissociation efficiency.The highest efficiency measured is 17.7±0.3%for single pulses, and 20.0±0.3% for bursts of three pulses.In the rest of this section, the results of both FTIR and QCLAS measurements are presented and discussed.

Dissociation efficiency and conversion of CO 2
The conversion X CO2 and energy efficiency η are determined by FTIR spectroscopy for a variety of experimental conditions.For the following experiments, the in-burst frequency f in−burst , flow rate Q, inter-burst period p inter−burst , pulse width w and voltage V are varied, see figure 3. The aggregate of all experimental conditions is shown in figure 10.Note that 1 pulse per burst corresponds to the aforementioned single pulses.Besides the general trend of decreasing η with increasing SEI, the results show a higher η (i) in burst mode and (ii) at a higher number of pulses per burst.
Figure 11 shows that for a given η, a burst of pulses translates to a higher X CO2 .Likewise, for a given X CO2 , a burst of pulses gives a higher η.Taken together, this is in agreement with the hypothesis that preferential vibrational excitation is facilitated through fast bursts: under a wide variety of experimental conditions and when controlling for the SEI, the dissociation proceeds more efficiently for bursts of pulses.
Figure 12 shows the measured X CO2 as a function of SEI, along with a linear fit for single pulses extended to the full axis range.All X CO2 measurements of three and four pulses in a burst are above this line and its 95% confidence interval.The measurements discussed here were taken over the course of a few weeks.Any variation of results for experiments with identical parameters fall within the measurement errors, indicating that the results are reproducible.
In figure 13, the Pioneer database on CO 2 plasma conversion [71] is consulted to compare the results presented here with X CO2 reported in CO 2 NRP literature.For better visibility, the grouping according to the number of pulses in the burst is omitted and our data is shown as one red line.Just like our new results, all measurements from literature have been conducted at (close to) atmospheric pressure.Their PRF and pulse width can be taken from figure 1.The present results agree well with the overall trend and show X CO2 in good agreement with those in literature, which is remarkable considering the fact that the used NRP reactor is optimised for diagnostic access rather than performance.
These same measurements also show that the increase in η and X CO2 between a burst of three and four pulses is smaller than the increases from one to two pulses and from two to  three pulses in a burst, respectively.This is likely due to the fact that the energy deposited in the plasma drops for each successive pulse in the burst, see figure 8.In parallel, we see in figure 4 that V, and thereby E/N, is much larger for the first pulse compared to the subsequent ones, which influences the processes induced by electron collisions.A MATLAB simulation of the (reduced) Laplacian electric field as a function of the position on the axis between the electrodes is shown in figure 14(solid) with the E/N at which ν 3 vibrational and electronic excitation cross sections peak (dashed) [41].For the first pulse, the so-calculated E/N corresponds to the maximum of the electronic excitation cross section while for the following pulses rather the vibrational excitation cross section is largest.Note that the calculated Laplacian electric field neglects the effect of space charges and must therefore be considered a rough first approximation, illustrating the general trends of the electric field distribution within the discharge.More intricate diagnostics like EFISH [72] would be required for a quantitative assessment.The self-induced electric field at the streamer heads might actually be more important for   12,15,18,23,25,70] as extracted from the Pioneer database [71], see figure 1 for pulse repetition frequency and width.the ongoing chemistry than the applied field.For a sufficiently high initial charge density as expected for the high f in−burst used here, the discharge ignition occurs via avalanche ionisation rather than steamers, though [4].
In the following, the influence of individual process parameters is discussed by keeping all other parameters constant.Unless varied or mentioned otherwise, V = 11 kV, Q = 1.48l min −1 , f in−burst = 1 MHz, w = 60 ns and p inter−burst = 4 ms.An increase of V from 10 kV-11 kV does not lead to a significant change in the η, but leads to a 12% increase in X CO2 when comparing a burst with two and three pulses respectively.The SEI is also higher, of course, but more importantly over 90% of the extra energy deposited in the plasma goes into the first pulse, the rest into the subsequent pulses.This important observation shows that when more energy is added to the pulses, the η does not improve when this energy is not deposited during the pulses characterised by a lower E/N.
The important question is then whether increasing the energy deposited during the subsequent pulses does increase Figure 14.A MATLAB simulation of the (reduced) Laplacian electric field at atmospheric pressure as a function of the position on the axis between the electrodes, as well as the location of the peak of the cross section where most of the electron energy gets transferred to, respectively, ν 3 vibrational and electronic excitation of CO 2 [40].
the overall η.Increasing the energy deposited selectively in only the subsequent pulses is difficult to achieve with the present pulse source, but by increasing w from 60 ns to 80 ns, we can deposit up to 45% of the extra energy into the second and third pulse for the burst mode with three pulses.For a burst of three pulses, η = 18.5 ± 0.3% for w = 60 ns and η = 20.0 ± 0.3% for w = 80 ns.This further goes along with the hypothesis that vibrational states get excited leading to a higher η due to the burst mode operation of the plasma.In addition, it suggests a pathway to improve the efficiency by selectively increasing the energy deposited in the pulses.The setup is limited in how much energy can be deposited to the plasma by the energy stored in the discharge capacitor C 1 in figure 2. Increasing w to 80 ns for a burst with four pulses does not lead to increased energy deposited in the subsequent pulses, because the source does not have enough stored energy.
Next, a variation of f in−burst from 1 MHz to 0.5 MHz is discussed.There are two competing effects expected.On the one hand, a f in−burst higher than the relaxation frequency allows for maintaining a high population of highly excited vibrational states.On the other hand, a lower f in−burst means that for an equal number of pulses in a burst, the burst is longer in duration.For f in−burst from 1 MHz to 0.5 MHz the two effects seem to cancel each other out, although X CO2 is about 0.1% higher for 0.5 MHz bursts with three or four pulses.The mean efficiency measured is not significantly increased.The SEI is identical when varying f in−burst (within the error margin of our measurement).
Finally, the impact of Q or p inter−burst is investigated.These two parameters are a direct way of changing the SEI, see equation (2).As shown in figures 10 and 12, an increasing SEI leads to a higher X CO2 but lower η.

Vibrational excitation of CO 2
An example of an obtained QCL IR absorption spectrum 2 µs after a single pulse is shown in figure 15.While the peaks can be identified, their number is too little to allow for a robust fit.The absorption peak areas of a ν 3 = 0 → 1 (red) and ν 3 = 1 → 2 (black) transition against time (on a logarithmic axis) for a burst with a single pulse (darker lines) and three pulses (lighter lines).The transitions use the notation (ν 1 ν l2 2 ν 3 , r) to show that they belong to different excited states of the ν 12 mode.The second and third plasma on boxes are only applicable to the burst with three pulses.Where the areas of peaks in a single pulse burst decrease at 20 µs, they keep increasing until 60 µs after the first pulse for a burst with three pulses.The pressure is 175 mbar, the applied voltage 9 kV, the pulse width 80 ns, the in-burst frequency 1 MHz and the inter-burst period 13.4 ms.
The result in figure 16 shows that the areas of the absorption lines increase rapidly during the first 10 µs for both one and three pulses in a burst, note the logarithmic time axis.Whereas the transitions decrease in strength for a single pulse after 20 µs, they continue increasing slowly for a burst of three pulses until 60 µs.It appears that in the afterglow of the plasma, the population of these vibrational states of CO 2 increases.Similar observations on long time scales are reported in [24].A full determination of the vibrational and rotational temperatures would give a better insight [21], e.g.showing an elevation of the vibrational temperature with respect to T gas , and requires fitting more transitions.However, the result is in agreement with the hypothesis that vibrational excitation is responsible for the increased energy efficiency and conversion in our experiments.

Conclusion
In this paper, we show that the energy efficiency and conversion of CO 2 in a NRP discharge in pure CO 2 at atmospheric pressure is increased when bursts of multiple pulses are used, compared to single pulses.These bursts are characterised by two to four pulses with an in-burst frequency of 0.5-1 MHz, with bursts spaced a few milliseconds apart.This is made possible by the setup developed in this study based on a novel pulsed power source.For each parameter combination tested, the bursts of pulses outperform single pulses created under the same conditions.The first pulse in a burst is characterised by a higher reduced electric field.This indicates that during the first pulse the electron energy is preferentially transferred to electronic excitation [40].The subsequent pulses are characterised by a lower reduced electric field that favours vibrational excitation of CO 2 .
Inspired by the variation of the excitation pathways of CO 2 for the different pulses in the burst, we investigate the effect of selectively increasing the energy deposited in the plasma during the first pulse compared to increasing the deposited energy during the subsequent pulses in the burst.We find that an increase in energy deposited during the first pulse is associated with a 12% relative increase in the conversion of CO 2 , with no significant change in the energy efficiency.Conversely, increasing the energy deposited preferentially into the subsequent pulses leads to an 8% relative increase in energy efficiency, as well as a 7% relative increase in the conversion of CO 2 .This observation is in line with vibrational excitation playing a distinct role in CO 2 dissociation.
A more direct method of determining the role of vibrational excitation is to measure the vibrational temperature of the plasma in-situ.In this paper, we developed a working proof-of-concept for in-situ QCLAS for plasmas in atmospheric pressure based on the work by Damen al [37].We successfully obtained transmittance spectra that show clearly identifiable vibrational transitions.However, limitations in the bandwidth of the detector and the size of the plasma volume mean that the present state of the work in this paper does not yet allow for a quantitative determination of the vibrational and rotational temperatures in the plasma.A qualitative analysis of the absorption lines of ν 3 transitions indicates that these states are more densely populated for bursts of three pulses than for single pulses, at least at lower pressures.An alternative setup, closer to the corona discharge of Moss et al [31], can potentially overcome the remaining challenges.The work in this paper hereby opens up an exciting avenue for atmospheric pressure CO 2 conversion using high in-burst frequency NRP plasmas.Here the work of Shen et al [76] is worth mentioning.They argue that the commonly observed voltage reflections in NRP circuits can be used to reignite the plasma.Variation of the PRF in the tens of MHz range is realised through changing the cable length between the discharge location and the pulse source.It is important to acknowledge that this approach lacks precise control over the amount of energy deposited in each pulse, as we have demonstrated to be significant.Nevertheless, this method provides an opportunity for research groups with existing NRP setups but lacking a pulse source capable of operating in the MHz range.They can utilise this approach to employ their spatio-temporally resolved in situ diagnostics in this relatively unexplored regime.This, in turn, could shed further light on the role of vibrational excitation.There are a few important considerations when designing a setup using nanosecond rise time pulses.Far from just a nuisance, the EMC of the setup and diagnostics becomes a crucial design parameter, as noted by e.g.Moss et al [31].The large transients in both current and voltage create interference signals.The interference can couple to nearby equipment, disturbing measurements or even damaging sensitive equipment such as the QCL that is part of the infrared absorption spectroscopy diagnostics in this study.The rules for limiting EMI therefore generally dictate limiting the switching speed, the signal strength and proximity of an EMI source to a potential victim [79].Lowering the switching speed or signal strength is not an option, since the rise time needs to be as fast as possible and the voltage high enough to initiate gas breakdown as discussed in section 2. For practical reasons, the plasma source will be near to the diagnostics for in-situ measurements.
There are two options to limit the EMI, then.Either the diagnostics are contained in an EMC enclosure, or the plasma and pulse source are contained.The most flexible option is enclosing the plasma and pulse source, as that opens up more options for diagnostics.For this reason, the choice was made to develop a setup with a plasma reactor, pulse source and power diagnostics (current and voltage) inside an EMC enclosure.
The following section provides additional information on the design of such an enclosure and the quantification of its shielding capability.

Appendix B. EMC enclosure design
Working with high-frequency pulses at high voltages generally creates EMI problems.At higher frequencies, the EMI is predominantly radiated whereas at lower frequencies EMI is mainly conducted along wires.An EMC cabinet, i.e. an EMI shielding cabinet, is necessary to shield any sensitive nearby equipment.Figure B.1 shows the design of the EMC enclosure used in this paper.During operation of the pulsed power source in the enclosure, the total emitted noise is lower than the existing background noise in the lab, and has no measurable influence on the measurements in this paper.Where conductive cables exit the EMC enclosure, a coaxial connection is required (as is the case for the high voltage power supply) or filtering is necessary to filter out conducted emissions.For the rest of the EMC enclosure design, the focus is on the higher frequencies that are radiated from the setup.This is due to the fact that small loops in the circuit radiate as an antenna, and antennas only efficiently radiate when they are about a quarter of a wavelength of the emitted radiation in size [80].
A solid plate made of a conductive metal would be an excellent shield, with just the absorption loss being [79] For a steel plate with thickness t = 1 mm and a skin depth of δ = 76 µm, equation ( 9) gives a shielding effectiveness of around 114 dB, which increases for higher frequencies as the skin depth drops.The reflection losses would increase the shielding effectiveness even further.This level of shielding is equivalent to a factor 5 × 10 5 reduction in noise amplitude, at which point the noise could not even be effectively measured anymore.The actual shielding, however, is mainly determined by any holes or seams in the enclosure, and to keep the equipment visible and ventilated a mesh is commonly used.The shielding effectiveness of a is given by where λ is the wavelength of the radiation to be shielded, L is the maximum linear dimension of the hole and n is the number of holes lined up in a straight line within half of λ [79].When a larger hole is needed, e.g. for a laser beam for diagnostics, a waveguide can be used to shield from radiated EMI.The shielding effectiveness of a waveguide is given by for frequencies lower than the cut-off frequency where l is the length of the waveguide and d is the diameter of the waveguide [79].Finally, for proper shielding it is important that all shielding, including waveguides and bulkhead connectors, make good electrical contact at each connection point.Note that equations ( 10) and ( 11) both contribute to the shielding effectiveness.Shielding for higher frequencies is clearly more difficult than for lower frequencies.A good indication of the highest frequency component in the signal f max is given by the rise time τ r [81] For the setup used in this paper, see figure B.1, the maximum hole dimension is L = 7.5 mm.For a rise time of τ r = 10 ns, the frequency f max ≈ 35 MHz and so the maximum wavelength we need to shield for is λ = 8.56 m.Given the maximum dimension of the setup is 50 cm and the spacing between holes of 1 cm, n ≈ 50.Equation (10) then gives SE dB = 38 dB.The 38 dB shielding corresponds to a factor 80 reduction in noise amplitude and a factor 6300 reduction in noise power, which is sufficient to shield any sensitive equipment nearby.Two waveguides are also installed for the diagnostic laser beam with depth l = 5 cm and d = 3 cm.Since 35 MHz is far below the cut-off frequency in equation ( 12), equation (11) gives a shielding effectiveness for the waveguide of SE dB = 53 dB.
The shielding effectiveness of the EMC cabinet was experimentally confirmed by running the plasma in continuous mode at a 1 kHz PRF and an applied voltage of 6.8 kV.A noise probe (figure B.2) was used to measure the noise generated by the plasma and pulse source.By comparing the power spectra with and without a closed EMC cabinet, the shielding effectiveness of the EMC cabinet can be measured.The resulting graph in figure B.3 shows that for frequencies up to 10 MHz the shielding effectiveness is indeed close to 38 dB, but for higher frequencies it decreases.

Appendix C. Current, power and energy-extra information
An important concern in the setup is to limit the stray capacitance and inductance of the setup as a whole.This is because the circuit can form an RLC circuit, which can cause unwanted oscillations in the current.In addition, a larger vessel capacitance or inductance also leads to slower rise times.Figure C.1 shows an LTSpice simulation of the current during the rising edge of a pulse when there are two inductors (of 300 nH and 100 nH respectively) in series with a 290 fF capacitor.These values are slightly larger than those expected in the current setup, to show the effect more clearly.These oscillations indeed exist in the current setup, but are sufficiently small that they do not affect the power and energy measurements, see figures C.4 and C.5.The inductance of the setup is minimised by ensuring the ground loops are as small as possible.
In an RG58 cable, signals travel at approximately 66% of the speed of light, i.e. at nearly 20 cm ns −1 .Through careful design and choice of cable lengths, the distance the signal needs to travel from point of creation to oscilloscope is kept the same to within approximately 20 cm.The required time shift can be easily found by correlating the (purely capacitive) current and the measured voltage when the reactor acts as a capacitor.At sufficiently low voltages, there is no gas breakdown and the electrodes behave essentially as a capacitor.A measurement of the current and voltage at low voltages can thus be used to calculate the capacitance of the setup, as well as the required time shift to synchronise the signals.The capacitive current is I C = C dV dt , however, numerical differentiation of the measured voltage signal can amplify existing noise and make the determination of the capacitance less accurate.Instead, the capacitance C is determined by comparing the measured voltage to the integral of the measured current, which should be purely capacitive, so that For this calculation, it is again important that both signals are synchronised.The required time lag for synchronisation is given by the location of the maximum of the cross correlation of the numerator and denominator in equation ( 14 Different other methods have been proposed for energy measurements in NRP discharges [82].Instead of placing the current and voltage probes close to electrodes, they can be used a few metres of cable away from the discharge which facilitates separating forward signal and reflections [46].Since pulse source and plasma reactor are place in the same EMC cabinet this method is not feasible here.Alternatively, the current and the time derivative of the voltage can be decomposed into their Fourier components and afterwards reconstructed from the dominant frequencies.The cross-correlation of the reconstructed signals allows to determine the time lag [1].As the determined capacitance and the cross-correlation in figure C.2 seem good, we did not further look into this alternative.The variation in deposited energy is due to the stochastic process of gas breakdown, which does not always occur at exactly 3 kV mm −1 in atmospheric pressure CO 2 .This is especially true since Paschen's law is valid for ideal conditions, such as the presence of homogeneous electric fields.In the present setup, this is definitely not the case.A graph of typical voltage and current pulses is shown in figure 4. Figure C.4 the difference between the and largest energy pulse in a single measurement series, figure C.5 shows the corresponding power deposited plots.

Figure 3 .
Figure 3.An overview of the settings for the triggers of the pulse source and QCL, as well as the inter-burst period (here p inter−burst = 1 ms), in-burst frequency (here f in−burst = 1 MHz), pulse width w and QCL scan time t QCL .

Figure 4 .
Figure 4. Voltage at the powered anode and discharge current over time for a burst of four pulses at 1 MHz in-burst frequency and 60 ns pulse width, a voltage of 11 kV and the current limited to 30 A. Note the decrease of anode voltage due to the pre-ionised gas created in the first pulse.

Figure 5 .
Figure 5.A simulation of the flow of CO 2 in a simplified plasma vessel for a volumetric flow rate of 2L min −1 , assuming only laminar flow.The maximum flow rate is 6.2 ms −1 near the inlet, but the colour scale saturates at 1 ms −1 to better show the flow near the two electrodes in the middle.The low flow rates near the outside of the vessel justify the simplified geometry compared to the actual plasma vessel (a).The actual vessel used in this paper has a maximum inner diameter of 27 mm with 1.5 mm thick walls, the top part shows a cross section of the gas flow and electrode assembly (b).

Figure 6 .
Figure 6.Design of the D-dot sensor used in this paper, with the electrical circuit drawn in.

Figure 7 .
Figure 7. Histogram of the number of pulses as a function of the measured deposited energies in the pulse from the measurement series corresponding to figure C.4 with mean energy 2.67±0.03mJ.

Figure 8 .
Figure 8. Power deposited in the plasma vessel corresponding to voltage and discharge current in figure 4.

Figure 9 .
Figure9.Simulation of transmission spectra as a function of the wavenumber for a 100 mm total absorption length vessel (corresponding to the current setup) and a 45 mm total absorption length vessel.The plot shows the difference between a vessel filled with pure CO 2 and an identical vessel that also has a 1.6 mm diameter plasma.Plasma (i) has Trot = 300 K, T 12 = 400 K and T 3 = 900 K. Plasma (ii) has Trot = 450 K, T 12 = 450 K and T 3 = 900 K, where Trot, T 12 , and T 3 are the rotational, symmetric stretching and bending, and asymmetric stretching temperature, respectively.

Figure 10 .
Figure 10.Measured efficiencies η as a function of the specific energy input (SEI) at atmospheric pressure, categorised by the number of pulses in a burst.Error bars correspond to the standard deviation calculated from repeated measurements.For better visibility, the error bars in the efficiency have been replaced by a shaded background.

Figure 11 .
Figure 11.Measured conversions X CO2 against efficiency η at atmospheric pressure, categorised by the number of pulses in a burst.Error bars correspond to the standard deviation calculated from repeated measurements.

Figure 12 .
Figure 12.Measured conversions X CO2 as a function of the specific energy input (SEI) at atmospheric pressure, categorised by the number of pulses in a burst.Error bars correspond to the standard deviation calculated from repeated measurements.

Figure 15 .
Figure 15.Measured and simulated transmission spectra as a function of the wavenumber.The simulated spectrum has Trot = T 12 = 750 K and T 3 = 900 K at 175 mbar.The contributions of the two lowest excited states of the ν 3 vibration to the simulation are included.All measurements are averaged over 50 spectra to reduce the noise on the signals.

Figure 16 .
Figure16.The absorption peak areas of a ν 3 = 0 → 1 (red) and ν 3 = 1 → 2 (black) transition against time (on a logarithmic axis) for a burst with a single pulse (darker lines) and three pulses (lighter lines).The transitions use the notation (ν 1 ν l2 2 ν 3 , r) to show that they belong to different excited states of the ν 12 mode.The second and third plasma on boxes are only applicable to the burst with three pulses.Where the areas of peaks in a single pulse burst decrease at 20 µs, they keep increasing until 60 µs after the first pulse for a burst with three pulses.The pressure is 175 mbar, the applied voltage 9 kV, the pulse width 80 ns, the in-burst frequency 1 MHz and the inter-burst period 13.4 ms.

Figure A. 1 .
Figure A.1.Picture of the pulse source used in this paper.The black components arranged in a semicircle are the MOSFETs, the optical trigger and low-voltage supply are on the bottom right of the board where the driver circuit is located, the high-voltage supply is at the top left of the board.Two ground connections are near the top left and bottom left.The capacitors that store the charge for pulsing are mounted on the bottom of the PCB and hence not visible in this image.The protective dielectric coating on the board can be seen from the glossy reflection of the light in the bottom right.

Figure A. 2 .
Figure A.2. Photograph of the stainless-steel electrode before use (a) and after approximately 50 h of use (b).

Figure B. 1 .
Figure B.1.The EMC cabinet that encloses the setup used in this paper.For visibility, the top plate is removed to show the pulse source (A) on the left and the gas line connecting to the plasma vessel on the right (D).Also shown are the current-limiting resistor (B) connecting the electrodes to the pulse source, the D-dot sensor (C) and copper strips (E) where the steel mesh connects to the frame of the cabinet to ensure the shielding makes full electrical contact.

Figure B. 2 .
Figure B.2.The noise probe made from copper wire and RG58 BNC cable.

Figure B. 3 .
Figure B.3.Measured shielding effectiveness of the EMC cabinet in figure B.1.The first vertical line from the left indicates the highest frequency component in the rise time from equation (13), the second line indicates the 3 dB limit of the oscilloscope.

Figure C. 1 .
Figure C.1.LTSpice simulation of oscillations in current due to parasitic capacitance and inductance in the pulsing circuit.Note the small steps in the rising edge of the voltage signal.Both phenomena are also present to some extent in the measured voltage and current, see e.g.figure C.4.

Figure C. 2 .
Figure C.2. Cross-correlation of the measured voltage and integrated measured current as a function of the time lag.
) above at the rising edge of the voltage signal, shown in figure C.2.The two signals agree well with each other.The capacitance is calculated by fitting a normal distribution to all values for the capacitance found from 60 traces.The resulting capacitance is C = 90 ± 22 fF .Figure C.3 shows the agreement between the integrated current and measured voltage.The bold part is the part of the signal that is cross-correlated in figure C.2 to determine the time lag.

Figure C. 3 .
Figure C.3.Measured voltage and reconstructed voltage from integrating the current and dividing by the capacitance.

Figure C. 4 .
Figure C.4.Voltage and current traces belonging to the minimum (a) and maximum deposited energy pulse (b) in a single measurement series.

Figure C. 5 .
Figure C.5.Power deposited belonging to the minimum (a) and maximum deposited energy pulse (b), corresponding to figure C.4.