Investigation of multi-periodic self-trigger plasma in an AC-driven atmospheric pressure plasma jet

Atmospheric Pressure Plasma Jets have been intensively studied due to their potential application in biological fields but some of their physics properties are still not well understood. In the present article, a helium plasma jet driven by 15–18 kHz sinusoidal voltage ignites multi-periodic self-triggered mode or random mode depending on the applied voltage, driven frequency and inter-electrode gap distance. Most of the observed multiperiodic bullets operate every 2 or 3 sinusoidal periods. Such bullets show similarities with pulsed operating mode, having a jitter of less than 100 ns. The presence of an outer grounded electrode ring is a key parameter permitting the ignition of multiperiodic bullets; it also enhances the propagation length up to 8 times. Fast imaging reveals that 2–3 self-triggered discharges occur in the gap region prior to ignition of the bullet in both positive or negative polarities; this leads to an accumulation of charges beneath the ground electrode, locally enhancing the electric field. Bullet velocities for different polarities and gap distances are compared using optical emission spectrum.


Introduction
Atmospheric non-thermal plasmas have been widely studied due to their numerous applications in the fields of environment protection, combustion, biomedical applications, plasma medicine, etc. For medical applications such as skin or cancer treatments, atmospheric pressure plasma jet (APPJ) is one of the most used and studied types of plasmas [1,2]. The plasma generated by the APPJs is close to room temperature and can * Author to whom any correspondence should be addressed.
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propagate over long distance (up to several meters) in a capillary flown by a noble gas such as Helium or Argon, which makes it safe and convenient to transport the reactive species to the biological surface to be treated. The high-voltage electrode is usually a needle-like electrode inside the capillary or a ring electrode outside of the capillary [3][4][5][6]. A ground electrode may be added such as a ring electrode on the outer surface of the capillary [3,7], and/or a target to be treated near the capillary end [8].
The propagation of the APPJs has been widely investigated. In 2005, Teschke et al reported fast imaging of the discharge in APPJ and shows that the jets are a series of ionization fronts propagating in the capillary with a high velocity. The brightness of the ionization front is due to a high electric field and makes it look like a bullet [9,10]. Although striking, the expression 'plasma bullet' may be misleading as the bright propagating head of the plasma is not electrically insulated but is connected to the high-voltage electrode via an ionized channel [11]. Depending upon the dimension of the inner diameter of the capillary, the ionization front takes the form of a doughnut shape surface discharge, propagating along the inner surface of the capillary. The velocity of these bullets is in the range of 10-10 4 km s −1 , which is much faster than the gas flow velocity [5,12]. Plasma bullets have also been referred as 'guided streamer' [13], whose propagation is enabled by photoionization near the ionization front. It is also proposed that the secondary emission plays a role on the discharge [14].
APPJs can be powered by pulsed voltage or AC voltage. APPJ powered by pulsed a power supply also shows higher propagation velocity, higher electron temperature and lower gas temperature than AC-powered APPJ [15]. APPJs driven by AC voltage generally show stochastic ignition of plasma, which may result in a non-linear interaction with targets with respect to operation conditions and time [8,[16][17][18], and raise difficulties to do time-resolved diagnostics of AC-driven plasma jets. The cause of the random behavior was attributed to the surface or gas phase memory from one period the next one [17,19,20].
However, some recent works reported that the plasma ignition in AC-driven plasma jets can be periodic under some certain conditions. Ning et al investigated the propagation of a He-APPJ with double-ring electrode configuration, and observed one periodic discharge in each positive or negative edge. They also mentioned that the discharge becomes unstable when the applied voltage is higher than 9.2 kV [7]. Walsh et al investigated the periodic and chaotic behavior of a He-APPJ with ring-to-plate electrode configuration [16]. Qi et al and Liu et al reported multi-periodic and chaotic phenomena in He-APPJ [17,18]. In the study mentioned above, charges deposited at the inner surface of the capillary are considered as the main reason of the periodic evolution of discharge current. However, there is a debate between surface deposited charges and volume charges. Schweigert et al recently reported that the touching-target discharge current of an APPJ is observed every 1-4 AC cycles. They explain that the plasma propagation length is influenced by the volumetric charge density caused by the previous discharge [21]. In the published literature, the multi-periodic phenomenon of plasma jets is mainly studied by analyzing the discharge current. The dynamics of plasma ignition and propagation in different periods are not fully understood, and the mechanism of the periodic plasma ignition remains unclear.
Although few works have reported multi-periodic discharges in plasma jets, an extensive literature has been dedicated to Dielectric Barrier Discharges (DBD), which exhibit spatial or temporal patterns. DBDs that are homogenously distributed or show self-organization such as hexagonal structures or periodicity have been investigated [22][23][24][25][26][27][28][29][30], and some of these work addressed the role of deposited charges on dielectric surfaces on the formation of discharge patterns. E.g. Wang et al simulated the DBD discharges between parallel metal plates separated by dielectric layers by taking into account the charges accumulation on dielectric surface [30]. The results show multi-periodic behavior of discharges and match well with the observation of Qi et al in their APPJ [17]. The debate between the role of surface charges and volumetric charges also exists in studies of self-organized DBDs. Becker et al investigated the transition from stable filamentary microdischarges to unstable discharge mode, and showed by simulations that memory effect is caused by the ionization of excited argon atoms [22]. Hoder et al show that the preionization controlled by pulse width has significant influence on the breakdown process [31]. Babaeva and Naidis showed that in a 2D fluid model streamer can propagate through an electron-ion plasma cloud only if the density of charged species in the cloud is low enough [32].
In the present article, multi-periodic generation of bullets is investigated using fast imaging and optical emission spectroscopy. In particular, the role of the ground electrode is described to understand the random to multi-periodic mode. The link between self-triggered discharges ignited in the gap region and multi-periodic bullets is analyzed. The role of surface charges and volumetric charges is discussed.

Plasma jet
The plasma is generated in a glass capillary with an inner diameter of 1 mm and an outer diameter of 4.2 mm, as shown in figure 1. The high voltage electrode is a stainless-steel tip, which is inserted into the capillary. It has a diameter of 0.33 mm and a tip curvature radius of ∼500 µm. The ground electrode is a copper ring with a width of 3 mm and is placed on the outer surface of the capillary. In the present work, the gap is defined as the region between the high voltage tip electrode and the grounded ring electrode. The gap length varies from 25 to 40 mm depending upon working conditions. Helium with a flow rate of 1000 sccm is flown in the capillary and is controlled by a mass flow controller (Brooks SLA5800 Series). The main impurities present in the Air Liquide bottle are H 2 O (<10 ppm) and O 2 (<5 ppm). The high voltage power supply (Coronalab CTP-2000K) is a sinusoidal AC voltage (V pp : 0-15 kV, with a relative standard deviation of 0.6%) in the range of 14-20 kHz. The voltage is monitored by a high voltage probe (Teledyne Lecroy PPE 20 kV) and the discharge current is monitored by a 50 Ω resistance between the ring electrode and the ground. By replacing this resistor with a 1 nF capacitor, the charges accumulated to the ring electrode is measured. A digital oscilloscope (Teledyne Lecroy Waverunner 625Zi) is used to record the signal measured by the electrical probes.  an oscilloscope. The axial space resolution is estimated to be 1 mm.

Fast imaging.
The dynamics of the ignition and propagation of plasma bullets are observed with an ICCD camera (Intensified Charge Coupled Device) (Andor iStar ICCD camera with Edmund optics 50 mm FL (1:2.8)), whose minimum exposure time is 2 ns. It is triggered by the oscilloscope, which is first triggered by either a specific high voltage, or a discharge current. There is an internal delay of about 200 ns between the triggering and the beginning of exposure. The average light intensity of a photo without plasma is considered as the background and is subtracted from each photo.

Optical emission spectroscopy (OES).
Two convex lenses f1 and f2 focalize the radial optical emission of the jet onto quartz optical fiber. The axial space resolution is estimated to be 0.5 mm. The spectra are measured by a spectrometer with 3 gratings. In this work, the grating of 600 grooves/mm is chosen. Spectra are acquired using an Andor iStar ICCD camera, similar to the one used for space imaging. It can be electronically triggered by the discharge current to achieve timeresolved spectroscopy.

Periodic plasma in single electrode configuration
To highlight the role of ground electrode, the discharge with single electrode is described in this subsection. The discharge light signal is acquired by an optical fiber located 10 mm downstream from the HV tip. An example of waveform of applied voltage and light signal is shown in figure 2.
The emission light signal shows that the positive discharge is a streamer-like discharge with most of the light emission localized at the ionization front, but the negative discharge is a glow-like discharge with a long tail. The applied instant voltage of the plasma ignition is close to 0. Statistical study shows that the light pulse in different positive half cycles has a jitter of ∼100 ns, less than 0.2% of the actual period (V pp = 6 kV and 16 kHz) and much less than the actual propagation time of the ionization front (more than 5 µs). Hence, the plasma can be considered as self-triggered. When varying the applied voltage from 3 kV to 12 kV and frequency from 10 kHz to 18 kHz, the jitter of emission light pulse remains small compared to the voltage period. However, the propagation length of the discharge is maximum 5 cm with 12 kV voltage.

Periodic multiplication observed when a ring grounded electrode is added
In many researches, a ground electrode is added on the capillary outer surface near the ground electrode, forming a DBD gap region to enhance the discharges. To enhance the electric field in the gap region, a short gap distance around 5 mm is often used. Such configuration leads to multiple random discharges in one voltage cycle. In the present work, the gap distance is increased to 25-40 mm, multi-periodic plasma ignition is ignited under some certain operation conditions. The propagation length is also significantly increased.
In this section, the role of an external ring grounded electrode is investigated. The distance between the HV electrode and the ground electrode ranges from 25 to 40 mm and is called the gap in the following. In the present work, discharges in the gap region (between high voltage and ground electrodes) are ignited in every cycle, but only a fraction of these discharges can propagate beyond the ground electrode. For the sake of clarity, in the following, the word 'bullet' refers to ionization waves propagating outside the gap region. The plasma bullets in this APPJ exhibit periodic or random behavior depending on the applied voltage amplitude, applied voltage frequency and gap distance. Figure 3 shows the discharge current and PMT signal with four different operating conditions; the PMT signal is acquired by an optical fiber at 2 mm downstream of the ground electrode; the gap distance is equal to 30 mm and the applied voltage frequency is 17 kHz for figures 3(a)-(d) and 15.2 kHz for figure 3(e). In figure 3(a), where the applied voltage is 5.88 kV, in every 3 periods (3P), a negative discharge is ignited first and is then followed by a positive discharge. The amplitudes of the discharge current, measured at the ground electrode, of positive or negative discharges are identical. In this condition, the ignition of bullets is periodic with a period of 3P, where P is the period of the applied voltage. Such denotation will be used in the rest of this report. In figure 3(b), the voltage is increased to 5.95 kV, the plasma exhibits random behavior. But there is always at most one bullet in each positive or negative cycle. In figure 3(c), the applied voltage is 6 kV, and the plasma ignition is periodic with a period of 2P (one bullet every 2 periods). When the voltage continues to increase to 8 kV, as shown in figure 3(d), the discharge is random. In some conditions, multiple random discharges may happen in one positive or negative cycle as shown in figure 3(d): the waveform of the discharge current is superposed with many spikes, which is possibly due to many micro discharges in the gap region. Although with a frequency of 17 kHz like figures 3(a)-(d), only nP modes with n ⩽ 3 can be obtained, more multiperiodic modes can be obtained by changing the gap distance and frequency, like the 5P mode which is obtained with 15.2 kHz as shown in figure 3(e). It is also worth pointing out that the amplitude of light intensity detected via the PMT is larger in the case of periodic discharges in figures 3(a) and (c) than in the case of random discharges in figures 3(b) and (d). It is also observed that the plasma bullets in periodic mode propagate longer than in the random mode. The propagation length of the jet for gap distance of 25 mm, 30 mm and 40 mm and the length of a jet with no ground electrode are plotted in figure 4 as a function of the applied voltage. The applied voltage frequency is fixed at 17 kHz, and the length 0 of the y axis corresponds to the HV tip. First, when there is no ground electrode, the propagation length increases quasi-linearly with the applied voltage. Second, the presence of a grounded electrode leads to a dramatic increase of the discharge propagation length if the applied voltage exceeds a critical value V crit . The critical voltage V crit corresponds to the voltage for which the plasma is long enough to reach the ground electrode and V crit depends on the gap distance. For example, in the case of 30 mm gap region (red curve in figure 4), once the plasma length reached 30 mm with the voltage equals or higher than 5.75 kV, the discharge enters periodic modes with a period of 3P or 2P, corresponding to figures 3(a) and (c) respectively; the propagation length extends from 30 mm to around 140 mm abruptly. We will show in the following that in such multi-periodic modes 2P and 3P, all bullets are highly reproducible in terms of velocities and length.
For most of the plasma jets, applied voltage, waveform and frequency are the key factors that influence the length of the plasma. Usually, the plasma propagates further with higher applied voltage, which is consistent with our results without ground electrode shown in figure 4.
However, when a grounded electrode is present, in region II of figure 4(b) shows that a voltage increases leads to a decrease of the plasma length to about 60 cm. In this condition, plasma bullets are formed in every cycle (P mode), but their length is reduced. In region III in figure 4(b), plasma bullets are also formed every cycle, but the length is alternatively long and short and long plasma bullet can propagate to 160 mm. After region III, the discharge ignition is random, corresponding to figure 3(d). Although the applied voltage and plasma power increases, the plasma length reaches a steady state. In the transition state between two different multi-periodic modes, the plasma ignition is random, corresponding to figure 3(b). Figure 4 also shows plasma length for gap distance of 25 and 40 mm, as a function of the applied voltage. The trend is similar to case of a gap equal to 30 mm described above. The minimum voltage required for the plasma to bridge the gap and reach the grounded electrode increases with the gap length. It equals 5 V, 5.5 V and 6.8 V for gap length of 25 mm, 30 mm, and 40 mm respectively. Also, the gap length does not seem to have any influence on the maximum propagation length. The strong increase of the jet length is clearly linked to the periodic discharge and the presence of the ground electrode.
The periodic system shows dependency on several parameters, including applied voltage frequency, applied voltage amplitude and the geometry of the jet. In this report, we investigated the influence of voltage, frequency and gap distance on the periodic system. With each fixed gap distance, the discharge is periodic within a range of applied voltage and frequency, so this range can be shown with an area in a 2D voltage-frequency figure. Such mapping is repeated with gap distance equal to 25 mm, 30 mm and 40 mm, and the results are shown in figure 5, where the mapping of 25 mm, 30 mm, 40 mm gap distance conditions are shown with blue, red and green areas, respectively. Depending upon the condition, the plasma is periodic or multiperiodic in a limited range of 20-500 V. As the frequency increases, the voltage limit of the periodic system decreases slightly. The gap distance has significant influence on the plasma behavior. With a larger gap distance, it requires a higher voltage to reach the same periodicity like 2P or 3P. Under some certain conditions, the multi-periodic mode cannot be achieved by varying the applied voltage. For example, with 15 kHz frequency and 30 mm gap distance, 2P and 1P mode are not possible. A possible explanation is that the voltage range where 1P or 2P multiperiodic mode can be observed is extremely limited at 15 kHz, and is smaller than voltage fluctuations. Hence, in practice, a stable multiperiodic domain is not observed at 15 kHz. The gas composition may also influence the voltage limit of the periodic system. For example, the 5P mode with 30 mm gap distance which is shown in figure 3(e) can only be observed during about 10 min. This is probably because the plasma decreases the gas impurities by desorbing the molecules on tube inner surface. In fact, the voltage required for certain nP mode continues to decrease about 200 V during the first hour of the plasma operation.
Walsh et al plotted a map of dynamic behaviors by varying the applied voltage and the gas flow rate [16]. Similarly, as the voltage increases, the discharges change from 3P region to 2P and 1P regions. Qi et al also plotted similar mapping with driving frequency and applied voltage as parameters but the results show opposite trend to ours: as the driving frequency increases, the voltage of periodic region increases [17]. This difference may due to the fact in their jet, the ground electrode is wrapped around the needle electrode and thus there is no gap region.

Self-triggered multiple gap discharges promote multi-periodic plasma bullets
Before the formation of a plasma bullet, multiple ionization waves are observed in the gap region in this article and in the literatures. Ning et al showed the two consecutive gap discharges with a streak camera and measured the velocity of each discharge [7]. Chen et al focused on the second gap discharge in a He-APPJ with CF 4 mixtures, and concluded that the second discharge is promoted by the species generated by the first gap discharge [33]. To understand the formation mechanism of the multi-periodic plasma bullets seen in section 3.1, it is necessary to investigate the gap discharges.
The gap discharges before multi-periodic plasma bullets is similar to the self-triggered DBD discharges reported by Wang et al [30]. It is assumed that the self-organization of gap discharges are due to the periodic variation of the accumulated charges in the gap region. The multi-periodic gap discharges make possible the monitoring of the plasma bullet formation and propagation process using fast ICCD camera imaging. In this section, we studied the propagation of discharges in 3P mode. The gap distance is 30 mm and the driving frequency is fixed at 17 kHz. The ICCD camera is triggered by the discharge current peak and delayed 3 cycles to record the photo of the next bullet; the jitter is less than 200 ns. Similar results are also seen in the case of 2P mode. Figure 6 shows the propagation of negative bullets. Each photo is accumulated 100 times. The gap distance is 30 mm. The applied voltage is 6 kV. The driving frequency is 17 kHz. The high voltage tip is at the upper edge of the image and the orange area represent the ground electrode. The white dash lines represent the outer edge of capillary. The corresponding discharge current is shown above the ICCD photos on figure 6. The discharge current peak is composed of two superposed peaks, and the time 0 is defined as the maximum of the first peak. Figure 6(a) shows the discharge dynamic within about 16 µs with an exposure time of 1 µs for each photo, and figure 6(b) shows the discharge dynamic within 2.5 µs with an exposure time of 200 ns for each photo. The light intensity is shown in log scale to improve the contrast.
Before the negative bullet clearly starts, multiple ionization process occurs in the gap region. A weak gap discharge starts more than 10 µs before the formation of bullet. It continuously emits light through the whole ionized channel. When it reaches the ground electrode, it is reflected and then propagates upstream. After the reflection, the ionization wave becomes faster and brighter, until at ∼0.2 µs it stops at the ground electrode. At 0.8 µs, the negative plasma bullet is observed to ignite at the ground electrode. It can propagate over 10 cm with a velocity of 20 km s −1 .
In all reported configurations, a positive bullet starts during the positive cycle right after the negative bullet described above. The propagation of the positive discharge is shown in figures 7(a) and (b) in two different time scales. A weak gap discharge is observed to initiate at −15 µs. It propagates for maximum 2 cm and disappears at about −10 µs. Between −4 and~−1 µs, a second gap discharge is formed and propagates from the HV tip to the ground electrode. It starts with weak emission intensity and small velocity about 10 km s −1 , but it is significantly enhanced when it approaches the ground electrode at −0.5 µs. However, this gap discharge stops at the ground electrode. At −0.2 µs, most of the gap region emits light, perhaps due to a second ionization front travelling across the gap. At 1.5 µs, the positive bullet is clearly seen passing through the grounded electrode and can propagate over 10 cm at the velocity of 30 km s −1 . Interestingly, the discharge processes prior the actual plasma bullet is built up are not observed when the ring ground electrode is removed evidencing the crucial role of the ground electrode in the generation of multiperiodic bullets. Figures 6 and 7 clearly show the link between self-triggered gap discharges and multi-periodic plasma bullets formation.
In the HV cycles without plasma bullet formation, some glow-like plasma is observed in the gap. Figure 8 shows the ignition time and length of the discharges in 5P, 3P and 2P mode. The position of the bars represents the ignition time of a discharge, and the length of the bars represents the propagation length of discharges. Note that the 5P mode is only stable for about 15 min, then it disappears because the plasma changes the gas impurities by desorbing the molecules on tube inner surface.
It is clear that the long plasma bullets, i.e. discharges longer than 10 cm in sequence B, are ignited with higher voltage than the short discharges. By comparing figures 8(a)-(c), the evolution of plasma can be summarized to the repetition of discharge sequences A and B. Sequence A is a sequence of 5 discharges during two ac period, like in figure 8(b) from 100 µs to 200 µs. Sequence B is a sequence of two gap discharges during one ac period, like in figure 8(b) from 40 µs to 100 µs. In 2P mode, only sequence A happens. In nP (n > 2) mode, discharge sequence B happens n-1 times between two sequence A. Figure 8 evidences that short gap discharges similar as DBDs occur between bullets. These gap discharges (e.g. ii and iii) happen both in sequence A and B.

Discussion: different mechanism of gap discharges and plasma bullets
The DBD ignition dynamics in the gap region shown in figures 6 and 7, and the discharge ignition time and length shown in figure 8 reveals different mechanisms of long plasma bullets and short gap discharges in multi-periodic plasma jet. To understand the mechanism of the multi-periodic modes, it is necessary to focus on the inter-electrode DBD.
Many works show the important role of surface charge in self-organized DBDs with spatial or temporal patterns. Célestin et al show how the surface charge deposited upon the dielectric plate modifies the spatial organization of microdischarges in a pin to plate AC DBD [28]. Berneker et al point out the important role of surface charges on the formation of discharges with honeycomb structure in a DBD in Neon at 100 torr and 1 mm gap [25]. Chirokov et al investigated the 2D distribution of a micro DBD, and proposed that the deposited surface charges facilitate the new avalanches and result in the formation of localized streamers [27]. Alternatively, some works also pointed out the role of volumetric residual charges on the ignition and propagation of DBDs [31,32]. However, the time between the first discharge of sequence A and the previous discharge is more than 30 µs. Some experimental measurements show that the electron density after a plasma bullet decays drastically in several microseconds [34,35]. In contrast, the life time of surface charges can be up to hours [36]. Thus, we assume that the role of volumetric charge is negligible in the working frequency range of this work and in the present work, we consider that the propagation process is mainly influenced by the surface charges. The time of breakdown is significantly influenced by the surface charges. For example, during the increase of the applied high voltage, a large amount of positive surface charges is accumulated along the inner surface, after a positive plasma bullet (discharge i in figures 8(a) and (b)). When the applied high voltage decreases, these positive surface charges enhance the electric filed near the pin electrode, as shown in figure 9(a). As a result, the negative breakdown happens when the applied voltage is close to 0 (like discharge ii in figure 8).
In the present study, the short gap discharges always correspond to absolute value of instant breakdown voltage from 0 to 500 V, while the long plasma bullets are always ignited when the absolute value of instant applied voltage is higher than 2.5 kV. We assume that the propagation length is dominated by the instant breakdown voltage, and the instant breakdown voltage is shifted because of the evolution of surface deposited charges near the pin electrode. The instant voltage can affect the propagation of ionization front because the ionization front is electrically connected to the powered electrode [11]. Similar effect has also been reported by Kim et al, who reported that in the irregular discharges of an APPJ, a discharge with higher instant voltage has increased optical intensity [37].
The discharge evolution after sequence A depends on the propagation length of following gap discharge (like gap discharge iii in figures 8(a) and (b)). When gap discharge iii is long enough to bridge the gap region (like discharge iii in figure 8(a)), it transfers some positive surface charge to the ground electrode region; these surface charges can then trigger the reflection process of negative discharge shown in figure 6. However, the multiple reflection process and formation of negative bullets is very little studied and the mechanism remains unclear. If V pp is not high enough, the gap discharge iii is shorter than the gap distance (like discharge iii in figure 8(b)), the negative bullet cannot be generated, and the sequence B happens until a sufficient amount of surface charges has been built-up.
As demonstrated in figure 9(b), during the sequence B, the negative gap discharge is longer than the positive gap discharge, thus small amount of negative surface charges is accumulated near the ring electrode, and slightly decrease the electric potential and attracts the following positive discharge. Sequence B may repeat several times until one positive gap discharge can bridge the gap region and trigger sequence A. To summarize, we consider that the multiperiodic mode occurs because the plasma jet transfers between two process: in sequence A, a positive gap discharge that can bridge the gap region triggers the following plasma bullets; if V pp is not high enough, sequence B happens is necessary to relaunch sequence A; in sequence B, negative surface charges accumulation enables the positive gap discharge which triggers sequence A.

Ground electrode enhances the propagation length
In figures 6 and 7, ICCD imaging shows that the ionization wave slows down at the gap electrode for about 500 ns prior launching the bullet. The formation of plasma bullets in the vicinity of the ground electrode has been reported by Jiang et al [38,39]. When a gap discharge reaches the ground electrode, it slows down or even stops due to the potential drop and charge accumulated by the previous gap discharge with opposite polarity. When the residual deposited charges are compensated, the charges are accumulated beneath the ground electrode, and create a potential that increases abruptly. This fast-rising potential is similar to a pulsed power supply, can ignite a plasma bullet about 1 µs after the gap discharge reaches the ground electrode. Jiang et al called the plasma jet generated by the accumulated charges an 'overflow' jet. The jet had the characteristics of a pulsed discharge although driven by a sinusoidal high voltage and was suitable for biomedical applications such as sterilization [40]. The generation threshold voltage and propagation length of an overflow jet is influenced by the width of the ground electrode. In the present work, the width of the ground electrode is only 3 mm, thus accumulated charges beneath the ground electrode is localized in a small region, which allows the formation of local high electric field and bright plasma bullets with lower applied voltage compared to the article of Jiang et al [39].
To evaluate the potential created by the accumulated charges beneath the ground electrode after the gap discharge reached the ground electrode and before plasma bullet is ignited, we calculated the electric field by solving Poisson equations with COMSOL. Note that this numeric simulation is based only on electrostatic model without volumetric space The boundary A represents the capillary inner surface beneath the ground electrode and has surface charge density of σ(z). When z < 50 mm, we assume σ(z) = σ gap due to the gap discharge propagation. When z > 53 mm, the surface charge deposition σ(z) is due to the plasma bullet in the previous negative plasma bullet, and is assumed to be σ(z) = −σ gap . Boundary B represents the ring-shape ground electrode. Boundary C and D represents the extremity of simulation area which is set to be grounded.
The value of accumulated surface charge density beneath the ground electrode (50 mm < z < 53 mm) is estimated from experimental measurement. The 50 Ω resistance shown in figure 1 is replaced by a 1 nF capacitor C m . When the discharge is initiated at the ground electrode, the voltage increase U g across the C m capacitor is measured. The surface charge density σ beneath the ground electrode is estimated as equation (1): where d jet is the inner diameter of the glass capillary equal to 1 mm, and l g is the length of the ground electrode equal to 3 mm. This is a rough estimation assuming that most of the charges measured using the capacitor C m are located in the immediate vicinity of the ground electrode. Typically, the value of σ is 50 nC cm −2 with a ± 10% variation from one bullet to another.
In the gap and downstream the ground electrode region, the value of deposited charges σ gap is estimated from published numerical simulations as an estimation. For example, Jansky et al shows by simulation that the surface charge density deposited by a plasma bullet ranges from 0 to 10 nC cm −2 , depending on the dielectric material [41]. In our simulation, we assume σ gap = 5 nC cm −2 . So the surface charge deposition on boundary A along z axis is shown in figure 10(b).
The potential can be calculated by solving Poisson equations. Considering the ring-shape of the plasma bullets, we deduce the z-component of electric field close to the inner surface (r = 0.4 mm) and the results is shown in figure 10(b), where the downstream is the positive direction. It is shown that the accumulated charges create an electric field as high as 10 7 V m −1 , which is similar to the electric field at the high voltage tip if the potential of tip is 2.2 kV. Varying the value of σ gap in the range of 0-10 nC cm −2 has negligible influence on the electric field.

Comparison between 2P and 3P mode
Since plasma behaviors are non-linear with the operation conditions, it is important to compare the characterization of plasma in different multi-periodic modes. In this section, the propagation and optical emission of discharge in 2P and 3P mode are compared.

Propagation velocity.
The propagation velocity of positive and negative bullets outside the gap region is measured with one optical fiber connected to PMT. This optical fiber is placed at different positions along the glass capillary, and at each position, the time difference between the PMT signal and discharge current peak is measured. Then the average velocity between two positions can be deduced. The velocity measured in different conditions are shown in figure 11. The position x = 0 represents the inner edge (close to the high voltage electrode) of the ground electrode. It is remarkable that the trend of the bullets velocities does not seem to depend on the gap or 2P vs 3P. Generally, the plasma after the ground electrode starts with a velocity of 10-20 km s −1 . It accelerates to its maximum velocity after about 15 mm of propagation, which is higher than the initial speed by a factor of 2, approximately. Then the velocity decreases linearly with the distance. Figure 11(a) shows that the velocity of positive discharges in different periodic modes have a maximum difference of about 20%. The maximum velocity is observed in the discharges in a jet with 30 mm gap distance in 3P mode, showing that the velocity is not directly linked to the driven voltage. Figure 11(b) shows that the velocity of negative discharge is significantly slower that the positive discharges, which has been reported in other experiments [42]. It can be explained by the higher electric field in positive discharges than in negative discharges, which has been reported in numerical and experimental researches [43].

OH and He line emission intensity.
In the following, time-resolved OES is performed to study the emission of discharge in different periodic systems and different polarities. The gap distance is fixed at 30 mm. Optical emission spectrum with long exposure time shows that the main emission is the He I transition 3s 3 S 1 →2p 3 P • at 706.5 nm and the 309 nm from OH band (A 2 Σ+ → X 2 Σ transition). Figure 11 shows that the first 10 mm of the propagation seems to be the initiation stage of the plasma jet, so the optical emission is acquired at 20 mm downstream of the ground electrode, where bullets velocity is maximum. The exposure time of the camera is set to 10 µs to ensure that each shot collects only the emission of one single discharge. Each spectrum is the accumulation of signal of 5000 discharges. We measure the peak value of the emission at the 706.5 nm and 315 nm, and normalize to the value of 706.5 nm in the positive discharge of 3P mode to 1. The results are shown in figure 12, where Helium emission is shown with bar in pink and OH in purple. It is important to point out that the line intensities of positive and negative bullets are not comparable, because the velocity of negative bullets are lower than the positive bullets, the negative bullets need more time to pass the field of view of the optical fiber, thus more photons from the negative bullets are collected than from the positive bullets. It is shown that compared to the positive bullets, the emission of negative bullets has significantly smaller fraction of He lines. This change of He emission fraction is even more significant in 2P mode than 3P mode.
The different ratio of He and OH emission has been reported in previous researches with He-APPJ driven by pulsed power supply [6], and compared to the positive cycle, the negative discharge tends to have higher fraction of OH emission than He emission. The relative intensity of He vs OH lines is an indication of the electric field strength: it is expected that a higher electric field increases He/OH line ratio due to higher electron impact excitation threshold of helium lines. The comparison between positive and negative bullets on figure 12 shows that He/OH ratio is higher in the case of positive polarity, which is consistent with higher electric field for positive bullets than for negative bullets reported in the literature [44,45].

Conclusion
In this paper, an experimental study on a helium Atmospheric Pressure Plasma Jet driven by 15-18 kHz AC power supply is performed by fast imaging and Optical Emission Spectroscopy.
The discharge exhibits multi-periodic behavior and random behavior depending on the driving voltage, driving frequency and gap distance. The multi-periodic mode is self-triggered generating ionization waves -bullets-with a jitter less than 100 ns, similar to pulsed mode condition. In multi-periodic mode, negative and positive plasma bullets are initiated every 2, 3 or more period depending upon working conditions. Negative bullets always immediately precede positive ones. Such multi-periodic bullets are observed only when a ground electrode is located 20 mm away or more from the HV pin electrode.
It is remarkable than during cycles when no bullets are ignited, positive and negative gap discharges can be detected using fast ICCD imaging. The gap discharges are similar to self-triggered DBD discharges. It is assumed that such gap discharge build-up a surface charge accumulation in the gap region, particularly in the vicinity of the ground electrode. This charge accumulation at inner surface of the capillary surrounded by the ground electrode lead to an electric field enhancement near the ground electrode and the generation of a fast travelling bullet.
Bullets of different periodic modes shows small differences in terms of velocity, propagation length and optical emissions. Compared to the negative bullets, the positive ones have higher propagation velocity, and larger fraction Helium lines intensities, possibly indicating a larger electric field.

Data availability statement
The data that support the findings of this study are available upon reasonable request from the authors.