## Case Study  
To perform the characterization of streamer variability, tests were carried out in motored conditions, while the evaluation of combustion onset was performed at three different \(\lambda\) values, i.e., 1.0, 1.2, and 1.4, still far from the lean stable limit [15]. At the same time, further leaner values would imply difficulties in maintaining a stable combustion with ignition timing (IT) and electrical parameters far from a narrow optimal range, which is strongly dependent on lambda [11]. Throttle position and ignition timing, as well as the corona electrical parameters, were fixed for all the test points, in order to guarantee the highest repeatability in terms of in-cylinder pressure and turbulence levels at the moment of discharge to isolate the streaming phenomenon, highly stochastic by itself [46]. A proper choice of such parameters was not simple, since they had to ensure an effective combustion in conditions far from the maximum brake torque (MBT) case [32].  
In Table 4, the main parameters to set the operating conditions can be found, together with the main indicating results. Note that, with a different choice of parameters, tuned case by case, the stoichiometric point would have shown an indicated mean effective pressure (IMEP) up to 4.5 bar [15]; in such a wide span of lambda, the need for a common IT required an excessive advance for the \(\lambda=1.0\) case. This evidence is supported by the evaluation of \(\theta_{50}\), i.e., the crank angle of mass fraction burned (MFB) 50; a properly phased combustion (e.g., IT \(\approx\) 6 CAD bTDC at \(\lambda=1.0\)[15]) in that operating point would show a \(\theta_{50}\) in the range of 8-10 CAD aTDC. This justifies the low IMEP value, especially in the stoichiometric point.  
The choice of V\({}_{d}\) value is also critical. A higher V\({}_{d}\) denotes that more thermal energy is released in the combustion chamber [21]. At the same time, a more advanced ignition timing results in lower in-cylinder pressure at the beginning of the discharge; this requires a reduction in the driving voltage to prevent the streamer-to-arc transition [21; 32; 36]. For all test cases, the chosen V\({}_{d}\) value was 28 V. This value was the maximum required not to incur spark events at the moment of ignition, when the in-cylinder pressure was about 7.4 bar (absolute), as can be noted from the pressure traces of the four test cases in Figure 4. Finally, the 300 \(\upmu\)s T\({}_{d}\) value was a good compromise to ensure an effective ignition without requiring too much energy from the supply circuit, as explored in previous works [11; 15; 32]. Moreover, a prolonged discharge is slightly more likely to generate a streamer-to-arc transition [32; 36]. Note that a duration of 300 \(\upmu\)s corresponds to 1.8 CAD at 1000 rpm of engine speed. This means that the corona discharge lasted about 24 frames at 79,000 fps.  
To summarize, the choice of a common set of V\({}_{d}\) and T\({}_{d}\) parameters was crucial to ensure stable combustion for all the three different firing conditions at the same IT. A reduction of V\({}_{d}\) and T\({}_{d}\) would imply poor combustion conditions or even misfires, while an increase would result in arc transition.