Abstract The electric field in the bulk of a self-sustained radio frequency atmospheric plasma jet (RF-APPJ) in a helium:nitrogen mixture is measured for the first time, to the best of the authors' knowledge, by electric field induced second harmonic generation (E-FISH). It is shown that the electric field in the bulk of the RF-APPJ is unexpectedly high, having an amplitude of about 1.6 kV/cm, and that it exhibits a phase shift of approximately -0.2π relative to the voltage waveform. Both findings are in contrast to low pressure capacitively coupled plasmas (CCPs), where the bulk electric field is negligible and the phase shift between the current and the voltage equals approximately to -π/2. The electron density in the bulk is estimated from the measured phase shift between the electric field, i.e. the current in the bulk, and the applied voltage by using an equivalent RC-circuit model for the discharge. The measured reduced electric field combined with the estimated electron density in the middle of the jet is used to calibrate the values of excitation rates of the N2 (C3Πu) state obtained by Phase Resolved Optical Emission Spectroscopy (PROES) in arbitrary units. The results of the electric field measurements are proposed as an input for numerical models or as a benchmark for calculations. Last but not least, special attention was paid to the calibration of the E-FISH measurement in a discharge powered by AC voltage, which includes artifacts supposedly caused by the windows of the setup.
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