Negative corona discharge can deflect in transverse airflow in pin-to-plane electrodes at atmospheric pressure. In this paper, we investigate the mechanism of Trichel pulse discharge deflection in transverse airflow and give a further understanding of the dynamic process of the deflection through experiments and simulations. In experiments, we quantitatively record the deflection angle by processing the discharge images, and they show that a larger airflow speed will lead to a larger deflection angle. In simulations, the discharge deflection angle is calculated through a 2D fluid model. Besides, the periodic fluctuation of the deflection angle with Trichel pulses is revealed, and this phenomenon can be explained by the alternative dominant effect of airflow or ionization on the net production of positive ions in the vicinity of the tip. When the effect of airflow is dominant, more positive ions will generate away from the center of the tip, which will lead to an increase in the deflection angle. On the other hand, when the effect of ionization prevails, more positive ions will generate near the center because the electric field here is stronger, and the deflection angle will decrease. In addition, if these two effects balance, the deflection angle will reach its maximum or minimum value.

## I. INTRODUCTION

Corona discharge is a self-sustaining discharge that occurs in nonuniform electric fields such as pin-to-plane electrodes. It has wide industrial applications such as electrostatic precipitation^{1,2} and ozone production,^{3} where airflow is an important factor to be considered. Corona discharge in airflow is also a non-negligible topic in lightning protection, for instance, affecting the aircraft-initiated lightning strike during flight^{4,5} and causing lighting attachment on rotating wind turbine blades.^{6} Therefore, an understanding of the mechanism of corona discharge in airflow can be of great help to these fields.

Negative corona discharge is a more common discharge among the above-mentioned applications than positive corona, and the different modes of it, including the Trichel pulse mode^{7} and pulseless glow mode,^{8} have been widely explored. Negative corona discharge in airflow has been investigated through many experiments. Nygaard^{9} and Berendt *et al.*^{10} explored the relationship between Trichel pulse frequency and transverse airflow speed under different situations. Akishev *et al.*^{11} conducted experiments on the effect of airflow on the discharge mode transition and concluded that the role of transverse airflow is limited for Trichel pulse-glow mode transition while it can greatly increase the threshold current for the glow-spark mode transition. Besides, they studied the pin-to-plane self-pulsing discharge in transverse airflow.^{12} They found that by setting a dielectric plate on the airflow direction, there are two modes of the plasma filament stretched by the airflow and provided a new method of surface treatment. Usenov *et al.*^{13} studied the memory effect of micro-discharges on the barrier discharge in airflow and showed the possibility of the gas-dynamic control for parameters of barrier discharge. Wang *et al.*^{14} studied the effect of airflow on the distribution of filaments in dielectric barrier discharge. They found the four phases of the discharge filaments and analyzed the causes of the complex motions of the discharge filament. Amirov *et al.*^{15} focused on the morphology of negative corona in transverse airflow through a telemicroscope, including the Trichel pulse mode and pulseless glow mode, and their results showed that airflow can change the distribution of the discharge torch on the cathode surface. Zhou *et al.*^{16} quantitatively analyzed the morphological characteristics of Trichel pulse discharge in longitudinal airflow through experiment and found that the discharge flare angle first decreases and then increases with the increase in airflow velocity. Nevertheless, they only came up with a simple theoretical model instead of a simulation model to explain this phenomenon. Vogel and Holboll^{17} concluded that the partial discharge shows a higher dependence on airflow at positive voltage than on the negative voltage in a 20 cm long gap and presented the deflection of discharge morphology in transverse airflow through UV photography. Guerra-Garcia *et al.*^{18} carried out experiments on the corona discharge in wind for electrically isolated electrodes, and their results not only demonstrated the feasibility of using corona discharge in wind for controlled charging of a floating body but also showed the dependency of corona luminosity on airflow speed for different electrode configurations. The effect of airflow on negative corona discharge has also been investigated through many numerical models. Deng *et al.*^{19} explored Trichel pulse characteristics in transverse and longitudinal airflow, and their results showed the deflection phenomenon of corona discharge and the decrease in the pulse frequency in airflow. Despite that, they neither explained the reason for particle distribution deflection nor paid attention to the dynamic process of particle deflection. Kang *et al.*^{20,21} came up with an analytical model of flowing gas discharge by considering the deflection of the discharge path and the blowing away of electrons. Their model is based on the assumption that electrons are affected by airflow and the mean free path is significantly changed. However, it is known that compared to the velocity of electrons gained in the electric field, the influence of external airflow on them is negligible. Niknezhad *et al.*^{22} developed a 3D fluid model to simulate streamer discharges in transverse unsteady airflow. Their long-duration discharge results showed the deflection of the successive positive streamers in the direction of the airflow, and they concluded that the impact of airflow on positive streamers is driven by ions.

As described above, many papers have mentioned the change in corona discharge morphology in airflow. However, the dynamic process of discharge morphology and a persuasive explanation of the deflection of the discharge are far from conclusive. For example, many have believed that the ratio of the transverse velocity of heavy ions or electrons in airflow to their longitudinal velocity in the electric field determines the deflection angle of discharge, but the angle calculated according to this ratio is far less than the value observed in the experiment. Therefore, a further and clearer understanding of discharge deflection is still required.

In this paper, the dynamic discharge morphology and a more detailed explanation of the deflection of atmospheric negative corona discharge in transverse airflow are investigated through experiments and a 2D fluid model. The structure of this paper is organized as follows: the experimental setup and simulation model are introduced in Sec. II. The corona discharge morphology and deflection in experiments, along with its verifications and analyses in simulations, are given in Sec. III. Finally, conclusions are given in Sec. IV.

## II. EXPERIMENTAL SETUP AND NUMERICAL MODEL

### A. Experimental setup

An experimental platform is designed to investigate negative corona discharge in airflow, as shown in Fig. 1, and the platform is placed at atmospheric pressure. A negative DC high voltage *U*_{s} is connected to a tungsten needle electrode. Discharge voltage is measured through a high voltage probe (Tektronix P6015A), and discharge current is measured through the voltage drop on a sampling resistor *R*_{s}. High voltage and current waveforms are recorded through an oscilloscope (Tektronix MDO34 1 GHz), while the average discharge current is measured using an ammeter (Keithley, 2000 Multimeter) at the same time. The tip radiuses of the needle electrode *r* are 120 and 200 *µ*m (the measurement error is within 5 *µ*m), the radius of the plate electrode is 4.75 cm, and the electrode space *D* is 5 mm. Speed adjustable airflow enters the electrodes through a multi-stage rectifying device to ensure that the turbulence of the inflow does not exceed 5%, and the airflow in the experiment can be regarded as laminar. The airflow speed in the gap is measured using a hot wire anemometer (Smartsensor ST866A; resolution of 0.001 m/s, range of 0–30 m/s, and accuracy of 1%FS). Short exposure discharge images are captured using an ICCD (Andor iStar DH334T) placed perpendicular (ICCD 2 in Fig. 1, captures the *y*O*z* plane) and parallel (ICCD 1 in Fig. 1, captures the *x*O*z* plane) to the airflow. The ICCD is placed far enough not to affect the airflow near the tip when it is parallel to the airflow. The exposure time is one pulse period (3–6 *µ*s), and discharge images are obtained by accumulating 20 images. The discharge deflection angle is determined by calculating the offset of the greyscale on the annulus near the tip of the needle, and the detailed process is shown in Sec. III A. In this calculation method, due to the dispersion of discharge, the number of accumulated images may have a certain influence on the calculation result of the discharge deflection angle, and 20 images can guarantee the statistical law and reflect the variation in the deflection angle.

### B. Numerical model

A 2D fluid simulation model is developed in this paper for atmospheric pressure negative DC corona discharge in pin-to-plane electrodes, as shown in Fig. 2. A negative DC high voltage is applied to the needle electrode, and the voltage of the plane electrode is set to zero. The radius of the needle tip is set to 200 *µ*m, and the diameter of the plane electrode is set to 25 mm. The electrode space *D* is 5 mm and remains unchanged in the simulation. The model considers four species: electrons, positive ions, negative ions, and neutral gas molecules. They are represented with subscripts e, p, n, and A, respectively.

The governing equations are continuity equations for electrons, positive ions, and negative ions coupled with Poisson’s equation. The equation set is given as follows:

where *n*_{e}, *n*_{p}, *n*_{n}, *S*_{e}, *S*_{p}, *S*_{n}, **Γ**_{e}, **Γ**_{p}, and **Γ**_{n} are the densities, source terms, and outward flux of electrons, positive ions, and negative ions, respectively. *α*, *η*_{2}, *η*_{3}, *β*_{ep}, and *β*_{np} are the ionization coefficient, two-body dissociative attachment coefficient, three-body attachment coefficient, recombination coefficient for electrons and positive ions, and recombination coefficient for positive ions and negative ions (detailed swarm parameters are given in Table I), respectively. *μ*_{e} is the mobility of electrons, ** E** is the electric field, and

*V*is the electric potential. To reflect the influence of airflow effect, the outward flux terms are given as

where *μ*_{e}, *μ*_{p}, *μ*_{n}, *D*_{e}, *D*_{p}, and *D*_{n} are the mobility and diffusion coefficients of electrons, positive ions, and negative ions, respectively, which are given in Table II.^{23,24}** u** is the transverse airflow speed to the right.

Reactions . | Parameters . | Value . |
---|---|---|

Ionization: e + A → p + e + e | α (cm^{−1}) | N × 1.4 × 10^{−1} ^{6}exp(−660/(E/N)) |

Two-body attachment: e + A → n | η_{2} (cm^{−1}) | N × 6 × 10^{−19} exp(−100/(E/N)) |

Three-body attachment: e + A + A → n + A | η_{3} (cm^{−1}) | N^{2} × 1.6 × 10^{−37}(E/N)^{1.1} |

Electron–positive ion recombination: e + p → A | β_{ep} (cm^{3} s^{−1}) | 5 × 10^{−8} |

Negative–positive ion recombination: n + p → A | β_{np} (cm^{3} s^{−1}) | 2 × 10^{−6} |

Reactions . | Parameters . | Value . |
---|---|---|

Ionization: e + A → p + e + e | α (cm^{−1}) | N × 1.4 × 10^{−1} ^{6}exp(−660/(E/N)) |

Two-body attachment: e + A → n | η_{2} (cm^{−1}) | N × 6 × 10^{−19} exp(−100/(E/N)) |

Three-body attachment: e + A + A → n + A | η_{3} (cm^{−1}) | N^{2} × 1.6 × 10^{−37}(E/N)^{1.1} |

Electron–positive ion recombination: e + p → A | β_{ep} (cm^{3} s^{−1}) | 5 × 10^{−8} |

Negative–positive ion recombination: n + p → A | β_{np} (cm^{3} s^{−1}) | 2 × 10^{−6} |

^{a}

*N* is the density of neutral molecules in cm^{−3}, *E*/*N *is the reduced electric field in Td.

Parameters . | Value . |
---|---|

μ_{e} (cm^{2} V^{−1} s^{−1}) | −3.41 × 10^{22} × (E/N)^{−0.25}/N |

μ_{p} (cm^{2} V^{−1} s^{−1}) | 2.43 |

μ_{n} (cm^{2} V^{−1} s^{−1}) | −2.7 |

D_{e} (cm^{2} s^{−1}) | 1800 |

D_{p} (cm^{2} s^{−1}) | 0.028 |

D_{n} (cm^{2} s^{−1}) | 0.043 |

Parameters . | Value . |
---|---|

μ_{e} (cm^{2} V^{−1} s^{−1}) | −3.41 × 10^{22} × (E/N)^{−0.25}/N |

μ_{p} (cm^{2} V^{−1} s^{−1}) | 2.43 |

μ_{n} (cm^{2} V^{−1} s^{−1}) | −2.7 |

D_{e} (cm^{2} s^{−1}) | 1800 |

D_{p} (cm^{2} s^{−1}) | 0.028 |

D_{n} (cm^{2} s^{−1}) | 0.043 |

^{a}

*N* is the density of neutral molecules in cm^{−3}, and *E*/*N* is the reduced electric field in Td.

To prove that the additional terms of airflow speed ** u** in the above-mentioned equations are reasonable, the momentum transfer equation

^{25}is used to estimate the acceleration process of positive ions, as given in Eq. (3a), where

*m*

_{p}is the mass of the positive ions,

*u*

_{p}is the rate of positive ions,

*u*

_{a}=

**is the airflow speed, and**

*u**v*

_{ap}is the ion-molecular nonresonant momentum transfer collision frequency,

^{26}which is given by Eq. (3b), where

*n*

_{a}is the molecule density (in cm

^{−3}) and

*C*

_{ap}is the collision frequency coefficient. If we consider the collision of O

_{2}

^{+}ions and N

_{2}molecules (

*C*

_{ap}is in the same order of magnitude for other ion-molecular collisions) and the transverse speed

*u*

_{p}(0) = 0 m/s, we can get

*u*

_{p}=

*u*

_{a}−

*u*

_{a}· exp(−

*v*

_{ap}·

*t*) by solving differential equation (3a). Taking the estimated collision coefficient

^{26}

*C*

_{ap}= 4.13 × 10

^{−10},

*u*

_{a}= 10 m/s, and

*n*

_{a}= 2.45 × 10

^{19}cm

^{−3}and considering that

*u*

_{p}and

*u*

_{a}have the same speed when their difference is less than 0.01 m/s, we can get

*t*≈ 0.5 ns. The momentum transfer time for electrons is shorter.

^{27,28}Compared to the microsecond discharge, it can be considered that the electrons and ions are accelerated to

*u*

_{a}instantaneously by molecular collisions. Therefore, the speed of all particles caused by airflow is

**, which is the same as the 3D simulation by Niknezhad**

*u**et al*,

^{22}

The current calculation method in this simulation is proposed by Morrow and Sato in Eq. (4a);^{29} note that *e* is the elementary charge, *V*_{a} is the applied voltage, and *E*_{L} is the Laplacian field. The boundary conditions are also shown in Fig. 2. The secondary emission coefficient *γ* induced by positive ions is set to 0.01, and the initial distribution of electrons and positive ions near the needle tip is given by a Gaussian distribution in Eq. (4b), in which (*x*_{0}, *y*_{0}) is the coordinate of the tip, *s*_{0} = 25 *µ*m, and *n*_{max} = 10^{13} m^{−3},

## III. RESULTS AND DISCUSSION

### A. Experimental results on the discharge deflection in airflow

It is found in experiments that the deflection of negative corona discharge in airflow is too small to be identified, so MATLAB is used in this paper to calculate the deflection by processing discharge images. The schematic diagram of the extraction process of the discharge deflection angle from the discharge images is shown in Fig. 3. The left and right boundaries are determined by 30% of the maximum greyscale value (the choices of different thresholds have little effect on the experimental trend). The discharge deflection angle *θ* is the angular bisector of the two boundaries instead of the position with the maximum greyscale value. The reason for this definition is that there may be multiple maximum greyscale values in some ICCD images due to some stochastic behaviors. The discharge deflection angle captured by ICCD 1 at different airflow speeds is shown in Fig. 4. Each point in the figure is the result of processing 20 discharge images. The discharge images in the figure are typical discharge images at the airflow speed. According to the curve, with the increase in airflow speed, the discharge angle in the *x*O*z* plane is at ±3°. These small deflections can be considered as the random behavior of the corona shape and do not depend on the airflow velocities. In addition, it can be considered that there is no deflection in this direction, and the fact that the corona discharge in airflow only changes in the *y*O*z* plane is another reason for using a 2D model for simulation. With the increase in airflow speed, the luminous point of the discharge gradually overlaps the tip of the needle because the discharge deflection angle in the *y*O*z* plane increases gradually with the increase in airflow speed.

Typical discharge images obtained by ICCD 2 at different airflow speeds under −7.5 kV with a 120 *µ*m tip radius are shown in Figs. 5(a)–5(f). The discharge is the Trichel pulse mode. The discharge has a shape of a cone and can be divided into two parts: the concentrated discharge point at the top of the discharge cone and the dispersed discharge area at the bottom of the cone. Compared with the discharge in still air shown in Fig. 5(a), both the concentrated discharge point and the dispersed discharge area deflect. Besides, with the increase in airflow speed, the deflection angle of the discharge increases. In addition, the increase is very limited above 10 m/s, for the discharge has reached the edge of the tip.

Typical discharge images at different airflow speeds obtained by applying −7.5 kV voltage to the needle with a tip radius of 200 *µ*m are shown in Figs. 5(g)–5(l). The discharge is also the Trichel pulse mode. The discharge with a larger tip radius can also be regarded as a concentration point at the top of the discharge cone and a dispersed discharge area at the bottom of the cone. Similarly, with the increase in airflow speed, the deflection angle increases, but the increase is too limited to identify with the naked eye. Hence, we use MATLAB to process images and get the statistical trend of the deflection angle.

The discharge deflection angles with different tip radii at different airflow speeds under the same voltage are shown in Fig. 6. It shows that the discharge deflection angle is larger at a smaller tip radius with the same airflow speed and that the deflection angle also increases with the increase in airflow speed. The variation range of the deflection is larger at a smaller tip radius. The deflection ranges from 0° to 13.5° at *r* = 200 *µ*m and ranges from 0° to 40.1° at *r* = 120 *µ*m. Combining Figs. 5 and 6, it can be seen that the *r* = 120 *µ*m tip is more easily affected by airflow and has a larger deflection. This may be because the surface area of the *r* = 120 *µ*m tip is so small that the discharge can easily reach the edge of the tip in airflow. In addition, the discharge remains there due to the special geometric structure at the edge, resulting in a large angle [see Figs. 5(d)–5(f)], which is also an important reason for its slower increase in deflection after 10 m/s, as shown in Fig. 6. In this paper, we mainly discuss the effect of airflow on discharge deflection. Therefore, to exclude the deflection caused by the discharge reaching the edge and other factors, an *r* = 200 *µ*m tip is used in the simulation to compare with the experimental results.

### B. Numerical results and analysis on Trichel pulses in still air and transverse airflow

#### 1. The simulated Trichel pulse current

The simulation results of the Trichel pulse train in still air and 10 m/s airflow under *U*_{s} = −14.5 kV applied voltage of the *r* = 200 *µ*m tip are shown in Fig. 7. The average currents are 17.06 and 17.66 *µ*A. *t*_{1}, *t*_{2}, *t*_{3}, and *t*_{4} are four typical stages of the second Trichel pulse, as shown in Fig. 7. *t*_{1} is the pulse initiation stage, *t*_{2} is the electric field suppression stage, *t*_{3} is the negative ion drift stage, and *t*_{4} is the preparation for the next pulse stage. It can be noticed that the magnitude of the first pulse is about 6–15 times larger than the subsequent Trichel pulse, which means that^{30} the ionization avalanche is extremely fast and intense in a charge-free space compared to subsequent pulses. Besides, the pulse frequency is about 321 kHz in still air and 316 kHz in 10 m/s airflow. The slight increase in discharge current and decrease in Trichel pulse frequency have been reported and discussed in other reports.^{9,19,31,32}

#### 2. The simulated distributions of particle number densities and electric field

The densities of electrons, positive ions, *n*_{e}, *n*_{p} (in m^{−3}), and the reduced electric field *E*/*N* (in Td) of the four stages of the Trichel pulse in still air are shown in Fig. 8. With the development of the discharge, *E*/*N* in the vicinity of the tip reaches the maximum value at *t*_{2} (about 2000 Td) and then gradually decreases as the discharge quenches at *t*_{4} (about 400 Td). The maximum *n*_{e} and *n*_{p} at *t*_{1} are about 10^{16} and 10^{18} m^{−3}, respectively, and both of them increase to 10^{20} m^{−3} with the discharge area rapidly shrinking at *t*_{2}. Finally, the maximum *n*_{e} and *n*_{p} decreases to 10^{13} and 10^{18} m^{−3}, respectively, with the discharge area gradually expanding at *t*_{4}. The above-mentioned process is consistent with the 2D axisymmetric simulation results by Dordizadeh *et al.*,^{33} and the density is of the same order of magnitude. The discharge current and the distribution of charged particles can prove the validity of this 2D fluid model.

*n*_{e}, *n*_{p}, *n*_{n}, and *E*/*N* in airflow are similar to those in still air, except that there is a certain deflection in distribution. The deflection angle varies with airflow speed and stages of the discharge. *n*_{e}, *n*_{p}, and *E*/*N* in 10 m/s airflow during their second pulse are shown in Figs. 9(a)–9(c). The deflection angle at *t*_{1}, *t*_{3}, and *t*_{4} of electrons in Fig. 9(a) is greater than that at *t*_{2}, and the same rule applies to positive ions in Fig. 9(b) and reduced field distribution in Fig. 9(c). The comparison between simulation results and experimental results is shown in Figs. 9(d) and 9(e). First, it shows that the discharge morphology in both experiments and simulations has the shape of a cone and it can be divided into two parts: a more concentrated discharge point at the top of the cone and a dispersed discharge area at the bottom of the cone. The concentrated discharge point and the wide discharge area have the same deflection degree in airflow. Moreover, they share a similar level of deflection degree (2.1° in simulation and 4.9° in experiment), and the definition of deflection in simulation is given in Sec. III B 3. Although the definitions between simulation and experiment are different, these deflection values can show that the deflection angles are quantitatively on a similar level. Considering the experimental error and that the simulation model is a 2D model instead of an axisymmetric model, the experimental and simulation results are in good agreement.

The reasons for the deflection of electrons and heavy particles (positive and negative ions) are different. For heavy particles, the airflow speed ** u** (10 m/s) is of the same order of magnitude as the transverse speed where heavy particles are obtained in the electric field (10–10

^{2}m/s), so their distribution in the transverse direction will be easily affected by airflow. However, the transverse speed of electrons obtain in the electric field is about 10

^{5}m/s, which is much greater than the airflow speed, so their transverse distribution cannot be directly influenced by the airflow. Therefore, some explanations of discharge deflection from the perspective of electrons blowing away are not applicable. There are two main reasons for the deflection of electrons. First, since the distribution of positive and negative ions deflects in airflow, the ion induced secondary electron emission at the tip of the needle also deflects. As shown in Fig. 10(a), it is clear that the maximum value of secondary emission flux does not coincide in still air and 10 m/s airflow. Second, after the distribution of space charge deflects in airflow, the enhancement of the electric field due to space charge deflects, leading to a deflection of the ionization, as is shown in Fig. 10(b).

#### 3. The periodic deflection phenomenon and its mechanism

In this work, the discharge deflection angle *θ* is defined through the coordinate *x*_{p} of the peak of ion induced secondary electron emission flux on the surface of the cathode as shown in Eq. (5), where *r* is the tip radius,

The calculated deflection angle and corresponding current are shown in Fig. 11. It can be seen that *θ* varies periodically with the discharge process. The sharp inflection points at the minimum deflection angles correspond to the peaks of discharge current. *θ* starts at 0° from the first pulse and gradually increases. Then *θ* varies from 2° to 4° after the discharge enters the stable pulse mode (after about 15 *µ*s).

Such periodic fluctuation of the deflection angle is difficult to be captured in experiments because the luminescence in experiments can only be detected in a short pulse period, which corresponds to the period between *t*_{1} and *t*_{3} shown in Fig. 7. In this case (Fig. 11), *θ* is near its minimum value of about 1.95° during this period. Therefore, the deflection angle captured in experiments corresponds to the minimum *θ* in simulation in Fig. 11(a).

As mentioned above, the deflection of positive ions is essential to the secondary emission and ionization process. To explain the periodic fluctuation of the deflection angle quantitatively, we calculate the net production rate of positive ions (*R*_{l,r}) in space as obtained by Eq. (6a), which is the integration of Eq. (1b) in the vicinity of the tip, as colored in Fig. 12(a). The subscripts *l* and *r* represent the integration areas on the left and right sides of the tip in Fig. 12(a), respectively. The two areas are divided by the connection line between the center of the needle tip and the maximum secondary electron emission flux point on the tip surface. The integrated sector length is 450 *µ*m, and the sector angle is 40°, as marked in Fig. 12(a). In addition, we need to note that the integral area varies with time. According to Green’s theorem, the integral of the first term on the right of Eq. (6a) equals the integral of the inward flux of positive ions **Γ**_{p} on the left or right closed curve ∂*S*_{l,r}, as shown in Eq. (6b) and Fig. 12(b), in which −**n** is the inward normal vector of the closed surfaces and **Γ**_{p} = *n*_{p}*v*_{p}. Figure 12(b) shows the composition of positive ions in the right integration area; orange balls represent ions produced by the airflow effect, purple balls represent ions produced by the ionization reaction, and blue balls represent ions produced by other effects such as diffusion, drift, and secondary emission. Hence, the net production rate *R*_{l,r} can be regarded as the sum of positive ions produced in the area and the positive ions moving into the area,

When *R*_{l} − *R*_{r} < 0, it means that the net production rate of positive ions in the right side area is higher, so more positive ions are concentrated in the right side area in unit time, resulting in the discharge deflects to the right; similarly, when *R*_{l} − *R*_{r} > 0, the discharge deflects to the left. Hence, by comparing the value of *R*_{l} and *R*_{r}, the variation trend of discharge deflection angle can be obtained, i.e., the deflection angle *θ* increases when *R*_{l} − *R*_{r} < 0 and decreases when *R*_{l} − *R*_{r} > 0.

To further explain the reason for the change in *R*_{l} − *R*_{r}, we rewrite *R*_{l} and *R*_{r} according to different mechanisms. The first integral term on the right side of Eq. (6a) includes diffusion, drift caused by electric field, and airflow. The second integral term on the right side includes ionization and recombination involving positive ions. According to calculation, the integral difference caused by airflow (Δ*S*_{u}) and ionization (Δ*S*_{i}) are the two most essential terms in *R*_{l} − *R*_{r}, as shown in Eqs. (7a) and (7b). The relation between *R*_{l} − *R*_{r}, Δ*S*_{u}, and Δ*S*_{i} is shown in Eq. (7c),

Δ*S*_{i} is always greater than 0 because the left side area is closer to the tip of the needle where the electric field is stronger, so the ionization here is more intense, and Δ*S*_{i} remains positive. On the other hand, Δ*S*_{u} is always less than 0 for the positive ions to keep moving from the left to the right side area due to the airflow effect.

The effect of airflow Δ*S*_{u} and ionization Δ*S*_{i} plays a dominant role in different discharge stages, which leads to the change in *R*_{l} − *R*_{r}, and then causes the change in the discharge angle.

The maximum electric field *E*_{max} around the tip and the discharge current are shown in Fig. 13(a). The time-dependent curves of Δ*S*_{i} and Δ*S*_{u} are shown in Fig. 13(b), where the absolute value |Δ*S*_{u}| is taken. The difference in the net production rate between the two areas *R*_{l} − *R*_{r} and the deflection angle *θ* are shown in Figs. 13(c) and 13(d). As shown in Fig. 13, when the discharge current reaches its peak at 27.58 *µ*s, *E*_{max}, Δ*S*_{i}, |Δ*S*_{u}|, and *R*_{l} − *R*_{r} also reach their maximum at the same time because the space charge field reaches the maximum at the Trichel pulse peak while *θ* reaches its minimum at 1.96°. After the peak, *E*_{max} decreases rapidly due to the electric field suppression by negative ions, and Δ*S*_{i} also decreases rapidly. However, |Δ*S*_{u}| decreases gradually because it is not directly affected by the electric field, so |Δ*S*_{u}| > Δ*S*_{i} during this period, which means the airflow effect prevails, then causing *R*_{l} − *R*_{r} < 0 and a gradual increase in *θ*. Then, with the increase in *E*_{max} due to the removal of negative ions and the electric field recovery, Δ*S*_{i} starts to increase again. Until 29.62 *µ*s, Δ*S*_{i} = |Δ*S*_{u}|, *R*_{l} − *R*_{r} ≈ 0, and *θ* reaches its maximum at 4.24° [correspond to the blue dot in Figs. 13(c) and 13(d)]. After 29.62 *µ*s, the electric field in the gap continues to increase, Δ*S*_{i} > |Δ*S*_{u}|, and the ionization process prevails, causing *R*_{l} − *R*_{r} > 0; *θ* starts to decrease until another current peak shows up.

We briefly illustrate the above-mentioned processes in Fig. 14. The number of small balls in the figure represents the relative value of the net production rate of positive ions in the left or right side area instead of the actual number of positive ions. The purple balls represent the relative net production rate contributed by the ionization effect, and orange balls represent that contributed by the airflow effect. The red line is the discharge current containing two pulses. When the discharge gradually quenches and the airflow effect dominates (stage I), the discharge deflection gradually increases. As the electric field gradually recovers and the next discharge starts, the ionization effect becomes dominant (Stage III), and the discharge deflection gradually decreases. When the two effects balance, the discharge deflection reaches its maximum (stage II) or minimum value (stage IV, corresponds to ICCD images). In summary, the reason for the periodic fluctuation of the discharge deflection angle is that the airflow effect and the ionization process take turns to dominate the variation in the net production rate of positive ions in the vicinity of the tip.

## IV. CONCLUSION

In this work, by performing simulations and processing the time-resolved images in experiments, we have investigated the dynamic process and given a further understanding of the deflection of atmospheric negative corona discharge on the Trichel pulse mode in transverse airflow.

It is found in both experiment and simulation that corona discharge will have a certain deflection in the transverse airflow direction and that the experiment and simulation share a similar deflection angle. The reason and importance of positive ions in discharge deflection are re-analyzed from the perspective of secondary emission and ionization. It is revealed through simulation that the deflection angle varies periodically with the Trichel pulse, and it is explained by the alternating dominant effect of airflow and ionization on the net production rate of positive ions around the tip. After each pulse, the airflow effect is greater than the ionization process due to the rapid decrease in the electric field, so the net production rate of positive ions away from the tip is higher, resulting in the increase in the deflection angle. With the recovery of the electric field during the pulse interval, the ionization process gradually becomes greater than the airflow effect, leading to a higher net production rate of positive ions near the center of the tip, and then the deflection angle starts to decrease. When the two effects balance, the deflection angle reaches its minimum or maximum.

## ACKNOWLEDGMENTS

This work was supported by the National Natural Science Foundation of China (Grant No. 51777164).

## AUTHOR DECLARATIONS

### Conflict of Interest

The authors have no conflicts to disclose.

## DATA AVAILABILITY

The data that support the findings of this study are openly available in Zenodo at https://doi.org/10.5281/zenodo.5515431.^{34}