Effect of the Electric Field Profile on the Accuracy of E-FISH Measurements in Ionization Waves

Electric field induced second harmonic (E-FISH) generation has emerged as a versatile tool for measuring absolute electric field strengths in time-varying, non-equilibrium plasmas and gas discharges. Yet recent work has demonstrated that the E-FISH signal, when produced with tightly focused laser beams, exhibits a strong dependence on both the length and shape of the applied electric field profile (along the axis of laser beam propagation). In this paper, we examine the effect of this dependence more meaningfully, by predicting what an E-FISH experiment would measure in a plasma, using 2D axisymmetric numerical fluid simulations as the true value. A pin-plane nanosecond discharge at atmospheric pressure is adopted as the test configuration, and the electric field evolution during the propagation of the ionization wave (IW) is specifically analyzed. We find that the various phases of this evolution (before and up to the front arrival, immediately behind the front and after the connection to the grounded plane) are quite accurately described by three unique electric field profile shapes, each of which produces a different response in the E-FISH signal. As a result, the accuracy of an E-FISH measurement is generally predicted to be comparable in the first and third phases of the IW evolution, and significantly poorer in the second (intermediate) phase. Fortunately, even though the absolute error in the field strength at certain time instants could be large, the overall shape of the field evolution curve is relatively well captured by E-FISH. Guided by the simulation results, we propose a procedure for estimating the error in the initial phase of the IW development, based on the presumption that the starting field profile mirrors that of its corresponding Laplacian conditions before evolving further. We expect that this approach may be readily generalized and applicable to other IW problems or phenomena, thus extending the utility of the E-FISH diagnostic.