# Current Filaments in Asymmetric Surface Dielectric Barrier Discharge
## 4 Plasma Diagnostics
### Rogowski Coil  
The electrical parameters involved in the discharge events are clearly the most relevant to be measured. This includes the sampling of the instantaneous value of the voltage, as close as possible to the exposed electrode. Since a direct measure of the electric field or potential in the discharge region is generally not feasible, because of the perturbations it induces, the second leg of this diagnostics system is a measurement of the instantaneous value of the current flowing between the electrodes. In our experiments, this was done by means of Rogowski coil sensors [44, 45]. A Rogowski coil usually consists of a conductor winding wrapped around a toroidal support of a non-ferromagnetic material, such as an air core. This ensures excellent linearity to the response of the coil due to the absence of saturation and fast timing sensitivity. To use a Rogowski coil as a probe, the cable transporting the current has to pass through the toroid. Then, the current flowing in the cable generates a voltage variation at the output of the coil proportional to the rate of the current variation, \(\mathrm{d}I/\mathrm{d}t\). This voltage signal should be passed through an integrating circuit, that could simply be a resistance, for measuring \(I(t)\). Using a small resistance for the integrating system, the probe operates in the so called self-integrating mode in a large frequency range. Within this range, the voltage signal produced by the coil is directly proportional to the instantaneous current value. Outside this range, however, the probe response displays a frequency-dependent attenuation and phase-shift. Thus, in order to recover the actual value of the current, an accurate calibration and a FFT decomposition of the signal is required [45]. There are some difficulties related to air core Rogowski coils, such as the variation of the coil parameters with temperature and the sensitivity to the exact location and orientation of the circuit section passing through the torus. However, the main drawbacks in our application are due to the fact that Rogowski coils with air core have small sensitivity to  
Figure 3: (**a**) Amplitude of the amplified voltage \(V_{\text{HV}}\), resulting from the applied reference DC voltage, \(V_{\text{DC}}\) (of which few values are indicated), as a function of the corresponding optimal frequency. The latter is chosen to maximize the output voltage \(V_{\text{HV}}\), for each reference value \(V_{\text{DC}}\). (**b**) Typical applied signal \(V_{\text{HV}}(t)\) vs. time, employed in our experiments. weak currents. This cannot be overlooked, since our aim is to identify the signal produced by single microdischarges. To overcome this problem, a ferromagnetic coil can be employed for the Rogowski coil core. Here, we use NiZn ferrite N30 with \(\mu_{i}\sim 4300\), with 50 \(\Omega\) integration resistance and 3.5 windings, and a 50 cm-long RG-59 BNC coaxial cable with a 50 \(\Omega\) resistance, which were calibrated with our Rogowski coil. Data were digitized by an Agilent Infinium MSO8104A oscilloscope with 1 GHz bandwidth and maximum acquisition rate of 4 GSamples/sec, which was found to be suitable for the applications we envisaged. The electric current signal sampled by the Rogowski coil has two main components: the first one consists of the microdischarges producing the plasma state, and the second one is due to the displacement current within the insulated electrode as a result of the HV applied voltage. Thus, for a time-dependent applied voltage, a displacement current is always added to the actual discharge current flow, that is mainly determined by the capacitance behavior of the electrode system. In the case of an oscillating voltage supply, the displacement current has a sinusoidal trend with the same frequency as the applied bias. Above a voltage threshold, the electric field ignites the plasma.