Experimental characterisation of the thermal energy released by a Radio-Frequency Corona Igniter in Nitrogen and Air

The Radio-Frequency Corona Ignition System is characterised by a wide initial combustion volume and precursors production, via radical insemination by the streamers, in addition to high released thermal energy. These features lead to faster combustion, a higher tolerance for lean mixtures and EGR dilutions and, in general, more adaptability. The thermal energy released by the igniter to the surrounding medium can help to understand the performance, the behaviour and the application range. This paper proposes a systematic experimental analysis of the thermal energy released by the igniter at room temperature, via pressure-based calorimetry. This analysis, carried out at diﬀerent pressures (up to 10 bar) and medium type (air or nitrogen), is extended to the whole range of the corona igniter control parameters, namely streamer duration and driving voltage. The latter is proportional to the maximum electrode voltage, as shown in the model here presented, and as conﬁrmed by experiments. The results show, for all the vessel pressures, the high energetic eﬃciency of the ignition system and the high amount of the released energy. The latter is found to increase linearly with the corona streamers duration and quickly with the driving voltage up to the streamer-to-arc transition threshold. The eﬃciency tends to reach a deﬁned upper limit. For each tested point, the energy released to pure nitrogen is higher than to air, which evidences the impact of the oxygen presence under streamer exposure.


Introduction
The pressing request, in term of pollutant emissions and carbon footprint, forces the automotive industries to introduce and develop innovative technologies to allow the internal combustion engine to be competitive in the modern world market for the next years. The need for exhaust gas recirculation (EGR) [1] or ultra-lean combustion [2] requires the development of advanced and innovative ignition systems and strategies, by enhancing the thermal energy conversion efficiency, that increases quite linearly with λ [3], and allowing operating conditions characterised by poor pollutant emissions [4,5]. The water injection is also an advanced technology able to improve the combustion in the modern engines for the general performance enhancement [6,7] as well as the thermal efficiency improvement [8,9] or the knocking control strategies [10]. All these new working conditions demand high ignition energy not available for the conventional inductive Voltage amplitude applied to the igniter coil V ch Bomb chamber inner volume γ Heat specific ratio ∆p ch Pressure gradient due to a streamer event η Thermal efficiency of the igniter ν i Frequency of the igniter current spark plug [11]. The increase of efficiency to transfer the primary energy (i.e. the energy supplied to the igniter primary circuit) to the air-to-fuel mix is critical [12] and, at present, it is widely below the 3% [13]. The conventional spark ignition systems have limitations in obtaining a robust ignition in high pressure (boosted engine), lean or EGR-diluted environment [14]. Therefore, the rising of the energy transferred to the mix is mandatory for the spark plug system, in particular for high turbulence intensity [15,16]. This improvement is reached, for example, through the implementation of high-energy inductive ignition systems [3,17,18,19]. Unfortunately, this technology shows electrode ablation/erosion/fouling [11,20,21,22] where the plug electrodes widely affect the flame kernel development [23]. Furthermore, when the lean limit is extended, then the cycle-to-cycle variability increases. The reduction of the latter condition requires even higher released energy that consequently produces a sudden drop of the efficiency [19,3]. The early fluctuations of the thermodynamics and fluid-dynamics operating conditions around the spark region are the main causes of the cycle-to-cycle variation [24] while large flame kernels are less subject to conditioning [25]. Furthermore, dielectric insulation becomes an issue once higher discharge voltage is required to achieve the breakdown conditions, as in the modern engines for the high levels of boosting [5].
The plasma assisted ignition is based on the non-equilibrium low-temperature plasma and is characterised

Experimental setup of the released thermal energy measurement
the production of the streamers (normally, one streamer for each electrode-point), plasma channels free to propagate inside the chamber. The streamers activate a large volume of air-fuel mixture and release a considerable amount of energy, essential for ignition in lean conditions [18,68,65]. The igniter is controlled by a dedicated electronic system that works as a high frequency amplifier. This system allows to set the time duration of the streamers activity T on and the driving voltage V d , the input voltage of the high frequency amplifier, to control the electric potential at the firing tip electrode. Details of the ACIS are available in our previous publications [55,69].

Experimental setup of the released thermal energy measurement
A constant volume vessel, the bomb, in Plexiglas (low thermal conductivity, 0.187 W · m −1 K −1 ), accommodates the igniter tip for the released energy measurement at room temperature. The inner chamber has cylindrical geometry with a volume V ch = 22.5 cm 3 and allows the management of the operating conditions, i.e. temperature, pressure and gas type (air or nitrogen, 5.0 purity, Linde).
The measurement of the inner pressure variation ∆p ch , generated by the streamer discharge, is obtained by the piezoelectric low-pressure sensor Kistler Type 7261, with 2200 pC ·bar −1 of sensitivity and ≈ 10 −5 bar of resolution. The pressure sensor is installed at the opposite side of the igniter in the chamber and works as a ground electrode. It produces a charge signal collected by the charge amplifier Kistler Type 5011 and converted in a proportional voltage signal. Current and voltage supplied to the igniter coil are collected by, respectively, the current probe Teledyne LeCroy CP030 (sensitivity of 10 mA · div −1 ) and the passive probe Teledyne LeCroy PP020. A thermocouple records the temperature in the inner bomb chamber. A piezoresistive pressure transmitters Keller PA-22S (accuracy ±1% F S), once calibrated by a Scandura Pascal 100 system, measures the initial pressure inside the chamber. All these quantities are acquired by a fast oscilloscope Teledyne LeCroy Wavesurfer 3000 with a sampling frequency of 10 MHz, about ten times bigger than ACIS AC supply frequency. A pneumatic system (valves, precision pressure reducer Festo LRP, one-way flow controllers Festo GR) allows to properly control the gas pressure and the (intensive) replacement in the chamber. The medium renewal is needed before/after any test sequence as it seems the streamers products impact the igniter performance, in particular when highly electronegative and reactive species, as the oxygen, are included [70,71], arguably due to the electrode erosion/fouling [28]. Each single discharge event is triggered by the Arbitrary Wave Generator HP 33120A.

Experimental setup of the igniter electric characterisation
Performance of the overall system has been evaluated analysing input and output electrical parameters. Using nitrogen (UN1066 99, 9% of nitrogen) at 20 bar pressure, the system was stressed to simulate the operating conditions running inside an engine combustion chamber. A cylindrical constant volume vessel, made in steel AISI 316 with a tempered glass inspecting window, is used as test bench environment for system characterisation. The chamber has a constant volume of 20 mm 3 . Test is performed at constant room temperature and the system, consisting of a pressure valve Tartarini PS90A and a pressure controller, allows to maintain the 20 bar during the overall test. No gas recirculation is requested during the characterisation test. A high voltage probe Tektronix P6030A (capacitance 3.0 pF , accuracy ±3%) is mounted on the other side of the chamber, in physical contact with the electrode tip centre by means of a pin extender RS 434-790. A current probe Tektronix TCP0030A (accuracy ±1.5%) and a voltage probe Tektronix P6015A (capacitance 3.0 pF , accuracy ±3%) acquire current and voltage supplied to the igniter. The probes are connected to an RF cable bridge before the input coil connector. The oscilloscope Tektronix MS056, with a bandwidth of 350 MHz, acquires input and output current and voltage.

Electrode voltage assessment
The analysis of the igniter electrode voltage V e is led, along with the coil input voltage V s and current I s , by varying the duration T on and driving voltage V d . Actually, V e , V s and I s represent the amplitude of the corresponding alternating quantity. The power input P s is evaluated using V s and I s , functions of the duty

Thermal energy assessment
cycle. Once the igniter is mounted on the pressure bomb, pressurised at 20 bar in nitrogen, the oscilloscope is set with a sample rate of 1.25 GS/s to reach the accuracy on acquiring the ∼ 1 MHz ACIS signal. Test is divided in two phases: phase 1. Shorter T on and continuous trigger impulse, necessary to analyse the power input in the igniter coil.
phase 2. Longer T on but a single pulse trigger to provide a more stable output voltage.
During the phase 1, T on is set at 500 µs, the trigger input signal has a frequency f tr of 25 Hz and V d changes from 20 V to 50 V with steps of 10 V . Data were acquired after 5 s on each point to have a stable result. Phase 2 has a T on of 1000 µs, single pulse as trigger input signal and V d sweep from 20 V to 50 V with 10 V step. Also in this case data is acquired after 5 s. The results are pretty well described by a linear regression ( fig. 4).
Once the data are acquired, the power supplied to the igniter coil P s is calculated considering the duty cycle acquired during the first test phase, the current I s and the voltage V s according to:

Thermal energy assessment
Once the external trigger starts an event, the AC current amplitude begins to rise from zero to the target level with a certain rate ( fig. 1, top), not dependent on the particular duration selected. The streamer discharge is active as soon as the amplitude reaches a defined threshold (CIV, the Corona Inception Voltage), depending on the bomb chamber inner pressure P ch , the gas type and the driving voltage V d (and consequently the electrode voltage V e ). Correspondingly, the pressure signal shows a current-induced electromagnetic noise with an overall rise characterised by different local maxima and minima ( fig. 1, bottom), after some tens of microseconds. This shape is consistent with the mutual interaction of sound waves propagating in the bomb chamber medium. Finally, the current falls quickly (a few tens of µs) as soon as the discharge duration reaches the assigned value. Likewise, the streamer ends once the current amplitude decreases under the CIV threshold. Then, the pressure signal is not affected by electromagnetic noise anymore and continues the oscillations around a well-defined average value.
The raw data of a streamer event are acquired and then processed to find the corresponding ∆p ch : -a 2 kHz low-pass filter is applied to smooth the signal (red solid line in fig. 1, bottom) and remove all the noise components (well visible in the frequency domain and already described in our preliminary work [65]).
-the sections before and after the streamer event are identified to calculate, respectively, p min ch and p max ch as the average of the corresponding pressure measurement data.
Note that the proper identification of the time domain section relative to p max ch is critical since the pressure signal has strong oscillations and tends to decrease quickly.
The final ∆p ch is obtained as the mean value of 20 consecutive streamer events, produced with a frequency of 10 Hz, for each parameters configuration. The number of the consecutive recorded events and the streamers generation frequency are chosen as a compromise to collect as much data as possible with no visible effect on the igniter performance.
If the bomb chamber is assumed as adiabatic [13] suitable as a first approximation for few milliseconds after the streamer event), the thermal energy E r , delivered to the chamber medium by the igniter, is given by the first law of the thermodynamics: where γ is the specific heat ratio, V ch is the chamber volume and ∆p = p max ch − p min ch , the pressure difference before and after the streamer event, respectively.
The energy E s supplied to the coil, or primary energy, is a function of the driving voltage V d and of the corona duration T on , in first approximation.
Experimentally, the supply current I s and voltage V s are simultaneously measured to determine an E s (V d , T on ) parametrization curve to simplify the experimental layout: once V d and T on are specified, E s is indeed a constant of the system. The trend of the parametrization curve, as a function of V d at fixed T on = 300 µs, is shown in fig. 2, while the dependence on T on is just linear.
Finally, the thermal efficiency η characterises the capability of the igniter to transfer the primary energy to the inner chamber medium as thermal energy and is defined as the ratio between the released (thermal) energy E r and the supplied (electric) energy E s :

Test Campaign
The test campaign is built by varying each operating parameter, one at a time, starting from a defined set of values, addressed as standard conditions (tab. 1). The corona duration has an important role in ignition strategy since it could act as a reducer for the high cycle-to-cycle variability, characteristic of the ultra lean blends or high EGR levels [56]. This is possible at the cost of some extra energy in more stressing conditions. The operating interval of T on includes values from 100 µs to 500 µs, sampled in steps of 100 µs, with the remaining parameter set as in tab. 1. The dependence on the driving voltage V d needs more care because it is strictly connected with the bomb chamber inner pressure p ch . Indeed, the same test modality used for T on is applied to V d for four different chamber pressures, from 3.25 bar to 10 bar absolute, to obtain a matrix of 5×4 points. The 1 bar point, initially expected, was rejected because the low pressure moves up the arc event at very low V d and directly to the igniter external metallic shell (not towards the pressure sensor). Therefore, it loses comparability with the remaining cases.
The driving voltage operating interval strongly depends on the chamber pressure p ch . It has to be determined experimentally for each tested pressure, point by point, by looking for the opposite working conditions of breakdown voltage (streamer-to-arc transition) and corona inception voltage (minimum required for the transition to the streamer), respectively BDV and CIV, according to the nomenclature used in [72].

Model
Generally, resonant ignition systems are configured as a series-resonant RLC circuit but these simplified circuit models do not show a good prediction on the voltage output assessment. The reason is attributed to the stray electrical parameters in the igniter assembly. The circuit of fig. 3 represents this igniter assembly as lumped-parameter circuit and comprises: a coil. The inductance L 1 can be measured from prototypes at reasonable low frequency where capacitive effect has not contributes (normally, the impedance analyser instruments have a good electrical parameters prediction for simple LR circuits instead of more complicated circuit models which involve also the capacitance). The component L 1 is not purely inductive but it has some resistance, modelled separately as R 1 . This value must be assessed under operating conditions where it will be many times higher than the value measured using a DC source. R 1 includes resistance representing ohmic loss, skin and proximity effects in the winding and tanδ losses in all dielectrics. Moreover, the inductor includes the C 1 parasitic capacitance between the turns. Values of R 1 and C 1 can be estimated by FEM analysis.
a firing end. It is installed into the head of the combustion chamber and generates the corona streamers. Typically, it contributes to most of the capacitance C L of the igniter assembly. Any component and connection between the inductor and the firing end must be considered since they can contribute significantly to the system performance. Any connection component provides additional capacitance and, consequently, as for the inductor case, an additional resistance R L to take into account the ohmic resistance of air and bulk insulation. The R L and the C L , connected in parallel, represent mostly the tanδ losses in all dielectrics and the stored electrostatic energy.
Note that the lumped parameters described above may be subject to change for significantly different temperature operations.
Based on such circuit, the analytic model predicts the electrode voltage V e as a function of the driving voltage V d , given that V s is proportional to V d through the coefficient k (eq. 4). In the following, we use the complex phasor notation. Since where then Introducing the angular frequency at the resonant condition ω 0 , the electrode voltage can be expressed as

Calibration
During the calibration stage, the load capacitance C L was considered as sum of the intrinsic capacitance in the igniter assembly, of the HV probe Tektronix P6015A capacitance (3 pF ±2%) and of the estimated stray capacitance introduced by the pressure chamber. The calibration was conducted at room temperature and nominal power absorption.

Pressure chamber capacitance assessment
The pressure chamber stray capacitance contributes significantly to the system performance and behaviour. Its calibration was performed on Federal-Mogul Powertrain setup and then estimated by matching the analytic result and the measured resonance frequency (setup shown on section 2.3). The iterative process is based on the frequency resonant criterion (detailed mathematical proof in Appendix): where Electrode voltage calibration Since R 1 is the electrical parameter most affected by the operating condition, the model was calibrated basing on experimental data (par. 4.3), by tuning R 1 . After the calibration, the analytic model allows to estimate V e by adjusting the stray capacitance for each setup. The stray capacitance assessment was performed on both FM and UniPG setup. data clouds is due to the performance variation between the different igniters used for the test more than to a presumed dependence of V e on pressure p ch or on discharge duration T on , therefore V e is constant at fixed V d . The linear regression (black solid line) highlights the strict linearity of the dependence V e = f (V d ).

Experimental
Even if such dependence is clear, it cannot be exported as it is to the UniPG data collection. In fact, the experimental tool used to measure the electrode voltage (i.e. the voltage probe) involves a high stray capacitance that affects the data systematically as a bias (gap between crosses and squares in fig. 4). The developed model of the igniter allows to assess the stray capacitance of the measurement system.

Stray Capacitance assessment and Electrode Voltage range
The FM model can be adapted and extended to the UniPG case to calculate V e , by evaluating the different stray capacitance given by the UniPG system igniter-pressure sensor. The measurement of the feeding current frequency of the coil ν i is required because the stray capacitance affects it (the higher the stray capacitance, the lower the ν i ). This allows to compare its value with the theoretical one and then to derive the estimated stray capacitance. The result shows a current frequency ν i = 1.029 MHz (compared with a theoretical value of 1.04 MHz) therefore the UniPG system is affected by a stray capacitance of about 2.56 pF on average and with a standard deviation of 0.2 pF , rather independent on the applied driving voltage in this range ( fig. 5). Therefore, V e is describable as a linear function of V d as in fig. 4.

Corona Duration
This test is led in pure nitrogen starting from the standard conditions (V d = 40 V and T on = 300 µs) by varying the corona duration parameter T on . Between the rise and the fall, the current has a pretty constant behaviour characterised by a different duration consistently with the assigned setup: in fig. 6 is well visible how the subsequent T on increase ( fig. 6 top, from 100 µs to 500 µs by 100 µs step) implies a wider pressure gradient ∆p ch ( fig. 6 bottom).The corresponding released thermal energy E r is a linear function of the corona duration T on ( fig. 7) in this range of pressure. Therefore, the power supply system and the coil fully support the energy demand and the streamers production rate. No. of Events C stray Capacitance, pF Since the energy supplied to the coil E s is linearly dependent on T on , the efficiency of the igniter η is pretty constant in the range 100−500 µs, η = 11.8% on average. This value is about an half of the maximum observed (beyond 20%, see section 5.3, fig. 10), due to the selected operating conditions. : the maximum V d allowed before, respectively, the corona inception and the breakdown. Note that the electronic control system accepts integer values only for V d (not designed for this fine tuning application). A brief description of the stochastic behaviour of the ACIS system near V CIV d is given in section 6.2. Fig. 8 shows the found operating range in terms of electrode voltage V e , according to the adopted definition of CIV and BDV, for the different tested pressures p ch . As the definition consequence, the BDV points fall on a Paschen curve [73] obtained by a fitting procedure for the specific gap between the electrodes.

Nitrogen
Nitrogen is used as a medium reference case for the pure thermal effect, being almost inert and with a lower radicals production than oxygen [31,50]. Furthermore, nitrogen is also used for the igniter electrical characterisation by FM, allowing a more effective comparison between results.   The corona inception voltage V CIV e increases with the applied pressure. Once p ch is set, E r grows from zero (corresponding to V 0 d as an increasing function of the electrode potential. The relation can be pretty well described by a second order polynomial (solid lines in fig. 9). Thus, E r , as a function of V e , results in a set of parabolas that move towards V e by increasing p ch . The parabolas bundle seems to be quite tight, gathering towards higher pressure. The maximum of E r can be found for BDV conditions and, therefore, depends on the Paschen curve of fig. 8. It is about 70 mJ, quite constant, except the 10 bar case (88 mJ).
As a result, higher pressure means lower energy released to the gas medium for the same potential V e applied to the electrode, in agreement with [31,74]. This behaviour is the opposite of what seen and expected for the spark case [13,65], where a pressure increase pushes the released energy and the system efficiency to higher values. Fig. 10 shows the corresponding efficiency η, defined as in eq. 3, plotted versus E s . The efficiency quickly increases with V e from 0% to beyond 20%, independently of p ch , at least four times more than the best efficiency showed by the spark [13,65]. The starting point and the particular trend instead, are functions of the pressure, according to the behaviour showed in fig. 2 and fig. 9. At 3.25 bar the efficiency highlights a strong decrease of the growth rate. This feature becomes lighter with continuity at higher pressures, where the growth rate is already lower from the beginning. It should be noted that the relative pressure gap between 3.25 bar and 5.5 bar is higher then the one between 7.75 bar and 10 bar, so that, trivially, we should expect bigger changes. Likewise E r , also the efficiency trend has a fast drop by increasing the pressure, at fixed E s .

Air
The partial replacement of nitrogen with oxygen changes quantitatively the bunch of curves showed in fig. 9 with no sensitive behaviour twisting ( fig. 11): the fast energy fall with the pressure increase and E r growth with V e are still well highlighted. Finally, the maximum E r , just before the breakdown, is quite constant (with the exception of 5.5 bar), included between 70 mJ and 80 mJ: as for the nitrogen case, this trend reflects the impact of the BDV behaviour described by the Paschen curve. On the other hand, compared to the nitrogen case, the bunch is not so tight. Furthermore, the curves move to higher V e almost linearly with the increase of p ch starting from the zero-point (that reflects the CIV trend of fig. 8). These differences seem to widen at high pressure.
The bunch broadening and the higher requested potential for the CIV are probably due to the quenching effect of the oxygen component of the air, as observed in [75]: since the oxygen easily captures a fraction of the emitted electrons, it limits and prevents the corona effect occurrence. The wide multiplicity of the produced oxygen states, molecular or atomic ionised, excited and metastable states [76], generates a variety of different available channels to degrade the energy absorbed by the chamber medium. Not all the energy referred to these channels is, finally, measurable as thermal energy. Furthermore, the oxygen presence highlights a feature that the nitrogen case just hinted: the theoretical possibility of having an intersection between consecutive curves (in particular, the 3.25 bar and the 5.5 bar curves). This would mean a radically new, opposite, behaviour: after the crossing of the curves, E r would increases with the pressure instead of decreasing (see deeper analysis in sec. 6). The high voltage zone, here not reachable because of the arc onset, could be explored in future work in different operating conditions to experimentally confirm this supposed inversion.
The igniter efficiency η confirms what seen in the nitrogen case, stressing some features as the tendency to sharply increase to reach a plateau, clear at 3.25 bar while more indefinite at higher pressure ( fig. 12). The efficiency reaches its maximum value around 20% at the lower pressure (3.25 bar) for the higher electrode potential available. Anyway, at the applied operating conditions with air, the efficiency is generally lower than the nitrogen case since it needs higher value of the E s to release a comparable amount of thermal energy.
Generally, the air data suffers of a larger uncertainty (compare fig. 10 and 12): this could be related to the aggressive byproducts of the oxygen chemistry that affect somehow the performances, increasing the measurement dispersion.

Discussion
The collected data establish some evidences here summarised: -the electrode voltage is linearly proportional to the driving voltage (V e ∝ V d ); -the released energy, at fixed chamber pressure and driving voltage, is linearly proportional to the streamers time of activity, the corona duration (E r ∝ T on ); -E r , at fixed p ch and V d , is experimentally proportional to the square of the driving voltage (E r ∝ V 2 d ) and thus to the square of the electrode voltage (E r ∝ V 2 e ); -the same E r drops quickly by increasing p ch , at fixed V d ;

Released Energy Parametrization
-it is expected that the trend is reversed at high V e and low p ch .
Generally speaking, V e establishes on the bomb chamber medium an electric field that, by means of intermediate stochastic processes as ionisation or photo-ionisation, produces free electrons and accelerates them, activating the avalanche production mechanism [35,67]. Once electrons and positive ions are created, the latter move towards the negative electrode with a drift velocity v ion drif t . For low ratio between the electric field E and the pressure p ch (i.e. the reduced electric field E/p ch , or more accurately E/N , where N is the gas particle concentration, proportional to the medium density), v ion drif t is proportional to the reduced electric field: For high values of the ratio E/p ch , the ions drift velocity is proportional to the square root of the reduced electric field [66]: The drift velocity is the main ionic velocity component, once averaged. Ions' kinetic energy, proportional to the square of the gained drift velocity, is then transferred to the medium during the thermalization process. Therefore, the experimental data imply a linear dependence between the electrode voltage and the ions drift velocity. Intuitively, it can be assumed that the dependence described by eq. 13 could affect the lower pressure test (3.25 bar) at higher electrode voltage (10 − 15 kV ), recognisable in a linear trend (in particular for the air case). Of course, this hypothesis should be conveniently verified.
Electron drift velocity v el drif t follows as well a relation similar to eq. 13 at ionising energies [66]: Since the curves of fig. 9 and 11 do not show linear behaviour, we should conclude that the electrons contribution to the thermal energy is lower than the ions' one as long as the eq. 12 is true. Furthermore, not the whole electron kinetic energy is degraded into thermal energy since it is also employed in radicals production and photons emission.

Released Energy Parametrization
This kind of considerations let us expect the behaviour showed in fig. 9-11 and, therefore, it allows to use a second order polynomial as a model, according to the expression E r = aV 2 e + bV e + c (15) and to find the best fitting curves (namely, a, b and c) to represent the collected data. Fig. 13 (top) compares the trends of the a coefficients for nitrogen (a N2 ) and air (a Air ). The a coefficient is an estimator of how quickly E r grows with V e . Both trends increase until the coefficients reach a plateau at high pressure values. The nitrogen case (dashed line) is much more stable and the growth is small. The air coefficient a Air starts from a lower value, compared to a N2 , and quickly increases. Probably, this is due to the availability of higher V e (V BDV e | air is higher than V BDV e | N2 see fig. 8), corresponding to higher E s (and power). a Air tends towards very low values at low p ch . Consequently, the relation E r = E r (V e ) approaches a transition to a linear behaviour.
The coefficients b and c are less meaningful, even if both monotonic: they contribute with a to determine V e | Er=0 , the electrode tension value such that E r is null, i.e. the abscissa intercept. The latter corresponds to the experimental value found for V CIV e and therefore shows analogous monotonic increasing trend.  fig. 14, where only the two highest E s levels are pointed out (for both gases). The released energy behaviour showed in the map is not trivial. The iso-energy curves E s establish a tight bundle for low and high pressure while it is wide in the middle range of p ch . This happens for both pure nitrogen and air. A tight bundle means that a lot of E s is needed to reach relatively high value of E r . This is particularly true for air at highest pressure and it is related to the igniter difficulty to quickly reach high efficiency in such operating conditions ( fig. 12). Nitrogen is much more stable, with no dramatic fall at high pressure.
The area around 5.5 bar in fig. 14 is of a certain interest, since the density reduction of the isoenergy curves denotes an easier condition to reach high efficiency. In addition, for the air case this area is featured with a maximum for the highest iso-energy curves. The remaining ones, instead, are monotonic decreasing. The decreasing trend with p ch is the typical behaviour observed in fig. 11. A maximum means that the released energy, locally, does not depend on the chamber pressure. As a consequence, there is an E r = E r (p ch ) trend transition from decreasing (at higher pressure) to increasing (at lower pressure): a real behaviour inversion. The local maximum of fig. 14 is related to the intersection, experimentally still not reached, in fig. 11 between the 3.25 bar and 5.5 bar curves at the higher value of V e .
Such inversion is only inferred since the breakdown occurs and prevents to achieve the corresponding operating conditions. On the other hand, the breakdown is due only to the geometrical features of inner chamber (gap between the electrodes). The monotonic trends of the polynomial coefficients ( fig. 13) imply that the curves intersection eventually occurs.
Under this assumption, at higher V e , i.e. at higher free electron energy, a pressure increase, that means Released Energy, mJ P ch , bar  Figure 14: Map of the inferred trend of the released energy Er to the bomb chamber medium as a function of the inner pressure p ch and for various level of energy supplied to the coil Es, for both tested gas types, nitrogen (dotted lines) and air (solid lines).
a particle density increment and a mean free path decrease, would produce: -a growth of the scattering occurrences; -an improvement of the energy transfer efficiency in the medium.
Anyway, the change of behaviour at low pressure is not completely unexpected since many variables affect the system. For example, the low pressure supports the atomic oxygen excited state production [31]. As already reported in the introduction, this is an efficient channel to heat the gas: E r differences between air and nitrogen are smaller at the lowest pressure, where the maximum of fig. 14 takes place. Furthermore, we already saw that the ions' kinetic energy is heavily affected from the E/p ch ratio and therefore the trend change may suggest a slow transition from the eq. 12 regime description towards the eq. 13 one, by lowering p ch . Finally, high pressure produces a change in the streamer propagation [31] due to a change in the ionisation-recombination balance [77] and in mechanisms as photoionisation by the excited-state quenching of molecular nitrogen [78].

Stochastic Behaviour Description
The nitrogen 7.75 bar data explain the typical stochastic behaviour of the Corona effect just over the CIV condition. To each V e corresponds a series of raw measurements of E r versus time, each one characterised by a small dispersion ( fig. 15). On the contrary, the 12 kV series (black cross) shows a particularly fluctuating trend, with many zeros too. This data collection can be gathered as in the histogram of fig. 16 (white-filled bars) where it is easy to distinguish five different energy values around which the data are concentrated. Therefore, we can rearrange consequently the histogram with just five groups as in fig. 16 (black-filled bars) and find the corresponding five energy levels (included the 0 mJ level). The energy of each group is simply defined as the energy average of the corona events belonging to the same group. Fig. 17 reports the five energy levels relative to the 12 kV series compared to the whole sequence of 7.75 bar data collection, included the corresponding fitting curve. The series is distributed from 0 mJ up to the fitting curve, that corresponds to the higher energy level (∼ 9.9 mJ). This unpredictable behaviour was clarified by a previous test led on the optical engine and reported in [56]: indeed, approaching the V CIV    conditions from higher voltage, V e is not high enough to generate all the four standard streamers for every shot, so we can obtain from four to no streamers at all for each shot. As observed, the behaviour is strongly stochastic and suggests that, under a certain threshold of V e and above V CIV e , the production of a particular number of streamers has its own probability, depending on how close V e is to V CIV e .

Conclusions
In this work, we tested a radio-frequency igniter based on the corona effect (ACIS) to have a systematic characterisation of the thermal energy released by the igniter in a constant volume vessel both in pure nitrogen and pure air. The inner pressure of the vessel, the type of medium (nitrogen or air) and the operating parameters of the igniter (driving voltage and the corona discharge duration) are all settable and matter of analysis.
We can summarise the main results as follow: -A lumped-parameter circuit model of the igniter was developed and calibrated with experimental data to determine the stray capacitance of the calorimeter and to foresee the electrode voltage of the igniter, depending on the control parameters.
-The thermal energy released to the medium from the igniter is linearly proportional to the duration of the corona discharge.
-The thermal energy released to the medium grows proportionally to the square of the electrode voltage (or, operatively, of the driving voltage).
-In general, higher pressures of the medium need higher electrode voltage values to release the same amount of thermal energy.
-Air, as vessel medium, brings a lower value of thermal energy released compared to nitrogen in similar operating conditions. It is worth noticing that air is much more aggressive towards the electrode and needs special care to guarantee a reliable measurement process.
-Both in nitrogen and air, the igniter is able to reach more than 20% of efficiency.

21
A C C E P T E D M A N U S C R I P T

REFERENCES
-A map of the thermal energy released, as a function of the medium pressure and of the electrode voltage, was produced for both nitrogen and air. The behaviour is not trivial and, in particular operating conditions, shows a maximum that produces an inversion of the dependence between thermal energy and pressure.
-The behaviour of the igniter becomes stochastic when the electrode voltage values approaches the corona inception voltage. This is due to the lost capability to constantly generate the default four corona streamers for each corona shot.

27
A C C E P T E D M A N U S C R I P T