How can we calculate the discharge voltage in the gliding arc discharge from the current-voltage waveform?
If you have the temporal dependence of you I and V signals you can just multiply and integrate over time of int(I(t)*V(t))dt to get the total power.
The discharge voltage is the black signal. If you want it as a value, it depends what is the value do you want; RMS or peak-to-peak. Almost, RMS equals 0.707 of the peak value in the periodically sinusoidal waveform.
First of all you need to specify where you measure the voltage. I guess that you have a resistance between the gas discharge and position you are measuring the potential. Under this assumption, and observing that the current and voltage are in opposition I can say that the minimum voltage drop is due to the circuit resistance, because you have the breakdown in the gas and the maximum current, assuming that the electron mobility in the gas is very high.
On the other hand, when the current is at a minimum, the voltage drop is mainly that of the plasma. The current can be due to circuit configuration or residual elencrons. In any case, the global resistivity is due to the circuit one, that is constant, and the plama one that depends on the plasma thermodynamic state, in this case depending on time.
Things can be a little more complex if you include in the description induttance and capacitance.
First of all plot Voltage Vs charge (=Idt) plot. You can recognize two discharge regions by the sharp slope. Half of the horizontal distance between them is breakdown voltage.
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