The creation of electric wind due to the electrohydrodynamic force

Understanding the interactions between ionized matter and neutral particles is a prerequisite for discovering their impact on natural phenomena. One such phenomenon is the electric wind, which supposedly occurs due to the charged particle–neutral coupling in systems of weakly ionized gases, but this mechanism remains unclear. Here, we report direct evidence that electric wind is caused by an electrohydrodynamic force generated by the charged particle drag as a result of the momentum transfer from electrons/ions to neutrals. The model experiment is based on a pulsed plasma jet as a source of weakly ionized gases generated in the helium gas at atmospheric pressure using Schlieren photography. Studying the helium gas flow trajectories at different discharge parameters allows one to distinguish between the effects of streamer propagation or space charge drift causing the electric wind as well as to determine the role of electrons and (positive) ions in wind generation.

occurs when the helium plasma jet interacts with the neighboring air environment. The experimentally measured N 2 + spectrum and the well-fitted synthetic spectrum with the LIFBASE software [1] presented in Supplementary Fig. 1b indicate a rotational temperature of 340 K. In Supplementary Fig. 1a, the plotted spectra are shifted to facilitate easy comparison.
Supplementary Figure 1 | Gas temperature estimation of helium plasma jets under different conditions. (a) Rotational distribution of N 2 + �B 2 Σ u + − X 2 Σ g + � emission with different pulse widths (10,30, and 50 μs at 3 kV) and heights (3 and 5 kV at 50 μs) and (b) representative experimental and synthetic spectra obtained with rot = 340 K. The synthetic spectrum of nitrogen molecular emission was simulated using the LIFBASE [1].
Supplementary Note 2: On the background of active species and reaction scheme in the He jet.
Here, we attempt to highlight basic mechanisms and reactions inside the atmospheric pressure helium discharge and at the flow boundary during reactions with the ambient air. There are numerous reactions (Supplementary Table 1) that occur inside the He plasma jet and during interaction with the ambient air. The photo-ionization mechanism based on Dawson's theory frequently plays an important role. In addition, a considerable amount of helium metastables and excited nitrogen molecules exist during the excitation cycle.
The electrons are produced by step-wise ionization, super-elastic ionization and metastable pooling of helium metastables as well as through Penning ionization. The channels of electron production become more effective and complex in the continuous mode than in the bullet, or pulsed streamer, mode and can significantly affect the spatial distribution of space charges, which can even overwhelm the contribution of photo-ionization. [2] When ionized helium gas interacts with the ambient gas, the highly energetic metastables [He * (2 1 S) and He * (2 3 S)] are able to cause the ionization of nitrogen molecules. The helium discharge inside the glass tube generates a large flux of long-lived helium metastables (with lifetimes as long as 7870 s [3]); however, due to Penning reactions, the effective lifetimes become much shorter. This leads to a rapid reduction in helium metastables in the interaction zone with ambient air. Here, it is worth noticing that the Penning effect between two nitrogen molecules is crucial in maintaining stable glow discharges, where even N 4 + ions are produced from interactions of excited N2 molecules. Otherwise, the typical ions produced in atmospheric helium plasmas and in contact with nitrogen are He + , He 2 + , N + , N 2 + , N 3 + and N 4 + , which can be described as positive ions in our descriptions.
Note: (Te) is given as a function of electron energy. The obvious difference is the emission from the jet, which is the result of the hollow shape jet generated with positive polarity and the more uniform shape in the negative polarity discharge. The pictures also present some general features of our experiment and results with a schematic representation of the plasma species distribution in such discharges as observed by other authors [12].

Supplementary Methods
On the model for fitting wind speeds. Because the plasma jets are significantly perturbed by conventional instruments for measuring the flow speed, such as a pitot tube, the experiment for measuring the flow speed of neutral helium in the plasma jet is quite limited. Here, to estimate the electric wind speed, the flow trajectories are analyzed in terms of the gas speed based on the following analytical model [13]: where c is the centerline speed of the flow, is the distance along the jet, is the angle of inclination of the jet axis with the horizontal, is the entrainment coefficient, R is the width of the flow, X is the horizontal distance from the flow exit, and Y is the vertical upward distance from the center of the flow. Some variables, denoted by primes, are made dimensionless by dividing by the tube diameter D. c is the dimensionless centerline temperature, defined as c = ( c − ∞ )/( i − ∞ ), where c is the local temperature measured at a center of the flow, i is the measured inlet temperature of the jet, and ∞ is the ambient air temperature.
is the ratio of the density and velocity field. In the present work, a value of of 1.0 was chosen, and the variations in with the discharge along the jet axis are ignored. The parameter α, which is rather insensitive to the flow trajectory [13], was taken as 0.05. A detailed description of the notations and assumptions can be found in [13]. The governing equations were solved numerically via the fourth-order Runge-Kutta method in MATLAB. The governing parameter of this model is the Richardson number Ri, which is a dimensionless parameter that expresses the ratio of potential energy to kinetic energy. The Richardson number is based on the magnitude of the gravitational acceleration , the inner diameter of the tube , the average gas velocity , and the mass densities of air air and helium jet : The Richardson numbers are calculated using air = 1.2041 kg·m -3 and jet = 0.164 kg·m -3 . As expressed in the equation, the Richardson number is decreased when the gas flow rate is enlarged. All Richardson numbers are less than unity, which indicates that the buoyancy force is insignificant. The starting conditions for governing Eqs. 1-6 are identical to those described in [13]. First, the helium flow trajectory without the plasma jet was compared with a modeled trajectory. As seen in Supplementary Fig. 7a, the trajectory of the pure helium jet (open circles) is well fitted with a synthetic trajectory (red solid line) of 0.925 slpm. The discrepancy may come from the inaccuracy of the mass flow controller or the above approximated model. All measured trajectories obtained by Schlieren photography were fitted, and corresponding flow speeds were estimated. Supplementary Fig. 7b shows the helium flow trajectories (same data as in Fig. 4a  An example of fitted data (black scatters) for helium plasma jet trajectories with the electric wind, which is the same data as in Fig. 4a in the main text.