Numerical simulation of capillary helium and helium−oxygen atmospheric pressure plasma jets: propagation dynamics and interaction with dielectric

Atmospheric pressure plasma jets (APPJs) can be generated in capillary tubes flowing with pure helium and with admixtures of oxygen into the pure helium. The jet exiting the tube can be used for a variety of applications through surface interaction. In this study, a two-dimensional axi-symmetric model has been developed to provide insight into the evolution of capillary helium plasma jets with and without oxygen admixtures and their interaction with a dielectric surface placed normal to the jet axis. The model considers the gas mixing of helium and ambient air and the analytical chemistry between helium, nitrogen and oxygen species. Experiments were performed in conditions similar to those of the simulations in order to get qualitative agreement between them. The numerical and experimental results show that the evolution of the helium plasma jet is strongly affected by the introduction of oxygen admixtures. In particular, it was observed that the addition of oxygen admixtures in the helium gas promotes plasma bullet propagation on the axis of symmetry of the tube (in contrast to off-axis propagation for the pure helium plasma jet). On the other hand, the presence of the dielectric surface (a slab placed in front of the tube exit) forces the plasma bullet to spread radially. Furthermore, the plasma bullet speed decreases when the helium plasma jet is operated in the presence of oxygen admixtures. The numerical results also showed that He/O2 plasma jets induced much higher electric fields on the dielectric surface in comparison to the pure helium plasma jet.


Introduction
Atmospheric pressure plasma jets (APPJs) are very promising for application in the areas of materials science and biomedicine [1][2][3][4][5][6][7][8]. The advantage of the APPJ compared to other atmospheric pressure plasma devices is its ability to deliver in remote locations a wide range of reactive species, charge species, high electric fields and UV photons. Among APPJ devices, helium plasma jets with small amounts of nitrogen or oxygen admixtures show very encouraging results for the above applications [9,10].
In the last two decades, significant efforts have been made to further understanding of the fundamental processes behind the operation of APPJ devices. In particular, Teschke et al [11] and Lu and Laroussi [12] showed for the first time that such plasma jets are not continuous, as seen by the naked eye, but consist of plasma bullets travelling at high speeds of the order of ∼10-100 km s −1 . Furthermore, it was observed that these plasma bullets have a ring shape and propagate in the channel formed by the helium in the air [13,14]. The importance of Penning reactions (PR) behind the ring structure of plasma bullets has been indicated by many studies [15][16][17][18], as they observed the disappearance of this ring structure when admixtures were introduced into the helium gas. In [19], it was also observed that there is a minimum threshold for the helium mole fraction in the helium jet for the successful propagation of plasma bullets. Recently, many important experimental studies have been carried out providing very good insight into the characterization and understanding of these devices, the electric fields [20][21][22][23][24][25] and the various species produced [26][27][28][29][30][31]. However, in order to increase the understanding behind the operation of APPJs and to overcome some of the practical experimental limitations, numerical modelling has been increasingly used to simulate APPJ devices.
In the literature, there are remarkable simulation studies investigating the evolution of helium plasma jet devices providing insight into the fundamental processes during the discharge [32][33][34][35][36][37][38][39][40][41][42][43][44][45]. The numerical simulation studies indicate that the plasma bullet has the characteristics of an ionizing wave (streamer) [32-34, 36, 38]. The ring structure of the plasma bullet has been successfully captured in many numerical simulation studies [35,36,38,39,45]. Brenden et al [36] showed the importance of a helium−air channel for the successful propagation of the ionizing wave. Naidis [37] showed that increasing the applied voltage and the helium flow rate increases the propagation speed of the ionizing wave as well as the propagation length. On the other hand, increasing the tube radius for the same flow rate results in the decrease of the propagation length. Boeuf et al [38] showed that on increasing the voltage pulse amplitude, rise time or preionization density the plasma bullet speed increases. In the same study, decreasing the tube radius shows an increase of the electron density on the plasma bullet head. The effect of air admixtures on the evolution of a helium plasma jet has been investigated by Naidis [40]. It was observed that the ring structure of a helium plasma jet disappeared when air admixtures were introduced into the helium gas, due to the smoothing of the radial uniformity of plasma parameters inside the streamer channel. The effect of nitrogen impurities on the dynamic evolution of a helium plasma gun setup was investigated by Bourdon et al [41]. It was shown that twoand three-body Penning reactions are crucial for the discharge dynamics. It was also found that higher amplitudes of the applied voltage cause an increase of the ionization front velocity, confirming the results from Naidis et al [32] and Boeuf et al [38]. However, the ionization front velocity at different levels of nitrogen admixture in the helium gas was shown to be dependent on a complex coupling between the kinetics of the discharge, the photoionization and the 2D structure of the discharge in the tube. Norberg et al [42] investigated the production of reactive oxygen and nitrogen species (RONS) for a He/O 2 plasma jet. It was shown that high flow rates and low repetition frequency results in the production of RONS that flow outside the tube. Furthermore, a higher applied voltage results in a higher production rate of RONS. Logothetis et al [43] investigated the interaction of helium plasma jets with air. A flow alteration was observed when plasma was activated due to an induced electrohydrodynamic force acting on the fluid. Recently, Lietz et al [44] discussed processes in the He/air gas phase that heat up the gas and may cause the disturbance of the helium−air channel.
However, for practical applications, the importance of plasma jets lies in their interaction with surfaces (such as plastics, metals, biological tissue, liquids). Due to this, in the last few years emphasis has been placed on numerical simulation studies of the plasma surface interaction [46][47][48][49][50]. Norberg et al [46] investigated the interaction of a He/O 2 plasma jet with various surfaces (dielectrics with relative permittivity in the range of 2−80 and metal), and how plasma dynamics and components are affected by this interaction. It was observed that as the relative permittivity increases, the speed of the ionizing wave increases as does the density of plasma species. The metal surface presents features similar to those of the high permittivity surfaces (a conductive channel between the surface and the tube) but with negligible propagation of the ionizing wave along the metal. On the other hand, dielectrics with lower permittivity show a higher penetration of the electric field into the dielectric and a greater propagation of the ionizing wave along them. A similar observation has been made by Wang et al [48] for a helium plasma jet impinging into dielectrics with different relative permittivity. Yan and Economou [49] investigated a helium plasma jet in ambient oxygen impinging on metal and dielectric surfaces. A conductive channel was observed to develop between the plasma jet device and the metal surface without surface ionizing waves (SIW), while for the case of a dielectric surface SIW developed similarly to that reported by Norberg et al [46] and Wang et al [48].
In this work, for the first time to our knowledge, the effect of oxygen admixtures on the evolution and interaction of a capillary helium plasma jet device with a dielectric surface is investigated numerically and observed experimentally. Several components such as secondary emission flux of electrons (SEFE), Penning reactions and oxygen admixtures are all considered and integrated into the numerical model. Valuable insight is gained into the device by utilizing this detailed numerical model. For example the model gives an explanation as to why the helium plasma jet has a torus/ring like shape and it also explains why the addition of oxygen admixtures causes the plasma bullet to change to a sphere like shape. Furthermore, the model shows how a low level of oxygen impurities increases the induced electric field (IEF) on the dielectric surface, which is very important for biomedical applications of helium plasma jets. The use of capillary tubes for plasma generation [2,51], as is done in this study, is gaining attention for biomedical applications. Capillaries are small and flexible and generate low volume plasma streams that can be delivered to previously inaccessible anatomical structures. Furthermore, it has been observed that a small amount of oxygen admixed into the helium increases the effectiveness of APPJ against cancer cells [9,10]. Since the plasma bullet mainly determines the interaction of the plasma jet with the surface, it is important to understand how the bullet and its interactions are affected by the introduction of O 2 into the helium gas. This study will mainly focus on: the evolution of He plasma jet; the effect of O 2 admixtures and the dielectric on the evolution and shape of plasma bullet; and the intensity of the induced electric field (IEF) on the dielectric surface for pure helium and oxygen-admixed plasma jets. Furthermore, the effects of Penning reactions and the SEFE attributed to each ion in the mixture will also be investigated through the same numerical model. The paper is organised as follows. The experimental setup is described in section 2, the simulation model with its boundary conditions in section 3 and input parameters to the simulation model in section 4. In section 5 the experimental results are presented, and in section 6 the simulation results. Finally, the conclusions are given in section 7.

Experimental setup
The experimental setup is shown in figure 1. A high-voltage (HV) electrode made of a copper band is wrapped on a 20 cm long capillary soda lime glass tube (VWR International) with internal diameter (ID) of 0.9 mm and outer diameter (OD) of 1.35 mm. The HV electrode is 1 cm in length and is placed ∼1.5 mm away from the exit of the tube. A dielectric barrier made of fused quartz vitreosil 077 (UQG Optics LTD) of 1 mm thickness is placed in front of the capillary tube, close to the HV electrode. The gas-gap thickness is fixed at 2 mm in this study. The working gas (He or He+O 2 ) is continuously injected through the capillary tube. The flow of helium (4.6 spectral purity, Linde) and oxygen (4.5 spectral purity, Linde) is independently controlled using mass flow controllers (MKS 1179A coupled with MKS type 247 four channel readout). The total gas flow rate is 1 slm.
High-voltage monopolar pulses are delivered from a high-voltage pulse amplifier (Trek, Inc., model PD07016) driven by an arbitrary waveform generator (Tektronix, model AFG3022C). Square positive voltage pulses with amplitude of 4.0 kV, duration of 50 μs, rise time of 7.3 μs and frequency of 10 kHz are used to excite the discharge.
In order to capture the dynamic behaviour of the plasma jet, an intensified charged coupled device (ICCD) consisting of a high resolution (1344×1024 pixels) CCD camera (Hamamatsu, model C8484-05G) and an image intensifier unit (Hamamatsu, model C9546-03) with an overall spectral response of 330-880 nm is used. The ICCD camera gate (∼40 ns) is synchronized with the discharge current pulse. Additionally, an adjustable delay is used to follow the temporal evolution of the discharge current pulse. Each image is automatically stored using 1 s integration time and smoothed using a moving average filter. The temporal resolution is given by the camera gate (40 ns) and the time interval between two consecutive pictures taken along the current pulse (10 ns around current maximum and 40 ns the rest), while the spatial resolution is given by the CCD array and its objective magnification. Our experimental arrangement allows us to take pictures of the discharge gap width (2 mm) with high spatial resolution of about 8 μm.

Model
For the simulation of the helium plasma jet, a two-dimensional axi-symmetric model is used. The simulation procedure is divided into two parts. In the first part, the mixing of the helium jet and the ambient air, where the air is treated as a single species, is evaluated through a gas dynamic model [52]. Due to the much slower speed of the fluid (∼50 m s −1 ) compared to that of the plasma bullet (∼10 4 m s −1 ), the gas dynamic model is solved in steady state. The calculated profiles of the air mole fraction and the mass average velocity are then fed into the second part of the simulation dealing with the time dependent plasma evolution [53]. It is noted that the gas dynamic model is solved only once (before the plasma fluid model) and the air mole fraction is fed to the plasma fluid model as initial condition for the N 2 (79% of air) and O 2 (21% of air) species. Furthermore, for the initial concentrations of N 2 and O 2 an extra 40 ppm of air is added in the helium channel (79% and 21% of 40 ppm respectively), due to the air impurities in the helium bottle (99.996% purity). This procedure is followed by many published studies [36,39,48,50], and assumes that for the time scales of interest these species can be considered to be in local equilibrium. The simulation domain, material properties and dimensions are presented in figure 2. The gas dynamic model is solved in the region ADML, while the plasma fluid model in the region HENO. At the flow rate of interest of 1 l min −1 , the Reynold's number, Re∼190 and therefore the flow is laminar. For laminar flow the necessary length for the velocity profile to be fully developed in the tube is given by » · · 0.05 Diameter Re 8.6 mm [54]. Therefore, the additional length of 10 mm in the simulation domain for the gas dynamic model is sufficient for the helium gas velocity profile to be fully developed. In order to save simulation time and to focus on the plasma interaction with the dielectric surface, the plasma fluid model is solved in a smaller domain.

Gas dynamic model
The gas dynamic model describes the flow of the helium jet in ambient air. In this model only two species are considered: helium and air. The helium−air mixing is obtained from solving the steady-state multi-component mass transport equation, without considering the chemical reaction term. This equation is appropriate when the species concentrations in the mixture are of the same order of magnitude and none of the species acts as a solvent. On the other hand, the mass average velocity of the mixture is obtained from solving the steady-state equations of the conservation of total mass and momentum. As an approximation, the heating of the gas is not considered (from the solution of the energy conservation equation), since it has been observed that it does not significantly affect the structure of the flow [55].
The multi-component mass transport equation is given below: where ρ is the mixture gas density, D i M the mixture average diffusivity of species i, w i the mass fraction of species i, M the molar mass of the mixture, u the mass average velocity of the mixture and Q the number of species in the mixture. For a binary system, as in this case, the multi-component mass transport equation reduces to one equation. Equation (1) is solved only for the helium species, and the air mass fraction is calculated using the equation Air He Due to the low gas speeds with a Mach number <0.2, the gases can be considered incompressible and the density of the mixture can be computed from the species composition and gas temperature [55]. The mass average velocity field of the mixture is calculated from the equations of the conservation of the total mass and momentum: where p is the pressure, I the unit matrix, m the dynamic viscosity of the mixture and F is the body force field. The dynamic viscosity is calculated from Wilke's formula [56]. The body force field is considered as the buoyancy force exerted in helium gas due to the mixing of the gases: where g is the gravity constant.

Boundary conditions of the gas dynamic model
The boundary conditions considered for all the equations presented in section 3.1 are summarized in table 1. In particular, the multi-component mass transport equation deals only with helium species. The flux of helium species ( ) N i from the solid surfaces is considered to be zero: where  n is the normal vector pointing towards the solid surface. The helium mass fraction is set to 1 at the entrance point of the tube nozzle, while the helium mass fraction is set to zero at boundaries located away from the tube. Regarding equations (3) and (4) describing the mass average velocity field, the following boundary condition is used for points away from the tube: This condition takes into account the normal stress but not the tangential one (it assumes the  boundary is sufficiently distant that there is no tangential flow). At the entrance point of the tube nozzle, the uniform axial velocity (u 0 ) is calculated from the helium flow rate in the tube to be = u 26.2 m s . 0 1 On the tube surface, the velocity is set to zero (no-slip condition) [57].

Plasma fluid model
The plasma fluid model describes the plasma evolution. This model has been thoroughly described in [53]. In summary, the model uses the continuity equation in the drift diffusion approximation for the description of electrons and electron energy, and the multi-component diffusion equation for the description of the heavy species in the mixture (neutral, excited and ion species). These equations are coupled with the Poisson equation for the description of the electric field. The continuity equations for the electrons and electron energy are ¶ ¶ where n e and n ε are the density of electrons and electron energy respectively, G  e and G e  represent the flux of electrons and electron energy respectively,  E is the electric field, S e is the source term for the production−destruction of electrons, e S is the source term that accounts for the energy gain or loss in elastic and inelastic collisions of electrons with the heavy species in the mixture, and u is the mass average velocity of the mixture (calculated from the gas fluid model and used as input in this model). The proportion of heavy species in the mixture is calculated from the multi-component equation: where ρ is the density of the mixture, ω i the mass fraction of species i,  j i the diffusive flux vector, S i the source term and Q is the number of heavy species in the mixture. The density of the background gas (helium) is calculated from The electric field is calculated from the solution of Poisson's equation: where  D is the electric displacement field and r v is the local charge.

Boundary conditions of the plasma fluid model
The boundary conditions for the plasma fluid model are described in detail in [53] and are summarized in table 2. The flux of electrons and electron energy on the solid surface are set as follows: where  n is the normal vector pointing towards the solid surface, v e,th the thermal velocity, m e and m e are the electron and electron energy mobility respectively, g k is the secondary electron emission coefficient, e k is the mean initial energy of secondary electrons and N A is the Avogadro constant. The constant a is defined as follows: where q is the charge of the species under consideration. The flux of the heavy species in the mixture at the solid surfaces is given by the following equation: where M i is the molar weight of species i, R i surf, the surface reaction rate, m i m , the mixture-averaged mobility and z i is the charge number of species i. For the neutral species in the mixture, the second term on the right side of equation (16) is zero. The charging of the dielectric surfaces is taken into account by using the following equation: where   D D and 1 2 are the displacement electric field in the plasma and in the dielectric surface respectively, and r s is the surface charge accumulation on the dielectric surface, which is calculated by solving the following ordinary differential equation: Represents the heavy species in the mixture, such as the neutrals, excited and ion species.
where  J e and  J i are the electron and ion current densities on the wall respectively.
The equations presented in sections 3.1 to 3.4 are solved on an Intel Xenon E5-2630 V2 2.6 kHz (12 core) server using the chemical reaction engineering module (for GDM) and the plasma module (for PFM) of the COMSOL multiphysics simulation package [58]. The models GDM and PFM have 303 940 and 169 947 elements respectively, with the smaller mesh size of 5 μm located in the region of the plasma jet evolution and the larger mesh size of 100 μm located away from the evolution of the plasma streamer. There are about 573 400 and 1231 000 degrees of freedom for the GDM and the PFM respectively. The equations for the GDM and the PFM are discretized by the Galerkin finite element method using linear element shape functions, and the resulting system is solved using the direct solver PARDISO. For the time integration (PFM) the backward Euler method is used. The performance of each simulation requires 5-7 days.

Input parameters in the plasma fluid model
g are considered in the chemistry of the model in order to calculate the electron energy lost through these reactions. However, in order to save simulation time these species are not tracked separately in the model (they are all treated as N 2 ), similarly to [48]. In the same way, the excitation of O 2 at the vibrational states = - g are taken into account for the electron energy loss but in the simulation model they are all treated as O 2 .
In appendix A (table A1), the rate coefficients of reactions 1-3, 24-38 and 52-60 are calculated from the solution of Boltzmann's equation with the two term approximation [59]. The procedure followed for these calculations is described in detail in our previous paper [53]. The above calculations also provide the transport parameters of the electrons and electron energy. The transport and rate coefficients are calculated only once, and stored in tables as a function of the mean electron energy and air mole fraction. For these calculations, the air mole fraction is varied in the range of 10 −5 to 1 (10 steps for every decade, i.e.
¼ ¼ 10 10 , 2 10 , 1 5 5 4 4 ). The interpolation between the values of air mole fraction is linear. These coefficients are then retrieved from the tables during the operation of the plasma fluid model. The transport parameters for all the heavy species and their reaction with solid surfaces are the same as defined in [53]. As the surface charge accumulation on the dielectrics is not known, the secondary electron emission coefficient (seec) is considered as an adjustable parameter. For the positive ions in the mixture, the seec is set to 0.1 since that value gives good agreement between the experimental and numerical results. Furthermore, this value lies in the acceptable range as estimated experimentally [60]. The energy of the secondary electrons is set to 5 eV for the helium ions, and 3 eV for the nitrogen and oxygen ions. No secondary electrons are considered from other species in the mixture. Photoionization is not considered in this study, but instead a uniform background density of electrons and positive/negative ions is used, similarly to other published works [39,[48][49][50]. The density of the different species in the mixture is as follows: electrons are set to 10 13 m −3 , heavy species (He m , He , ) are set to one order of magnitude lower than electrons i.e. 10 12 m −3 (electroneutrality through the concentration of He + is hence satisfied), He + is set to a value that satisfies electroneutrality in the mixture, N 2 and O 2 are determined from the gas dynamic model (79% and 21% of air respectively) and He the background gas is calculated from equation (11). For the initial concentrations of N 2 and O 2 an extra 40 ppm of air is added in the helium channel (79% and 21% of 40 ppm, respectively), due to the air impurities in the helium bottle (99.996% purity). Beyond the work shown in the manuscript we varied the initial densities of electrons and heavy species in the range of 10 8 -10 15 m −3 without noticeable changes in the results. The model uses the same voltage pulse waveform and parameters as the one applied experimentally.

Experimental results
For the experimental study, He and He+O 2 (1000 ppm) plasma jets are considered. The ICCD camera is used to capture the dynamic evolution of the plasma bullet presented in figure 3. The results presented in figure 3 correspond to the rise time of the positive applied voltage-more exactly, to the positive discharge current. The time of 0 ns corresponds to the time the maximum emission intensity of the plasma bullet coincides with the tube exit (z=0 mm). From figure 3(a), for the pure helium plasma jet, it can be seen that the plasma bullet forms two symmetric lobes during its propagation. These lobes indicate a torus (ring) like shape for the plasma bullet. Similar experimental observations were also made in [13,14]. For this case, the radius of the torus remains almost constant up to 1 mm (half way between the tube exit and the dielectric surface), while after 1 mm the radius starts increasing until the plasma bullet hits the dielectric surface. On the other hand, when 1000 ppm of oxygen admixture is introduced in the helium gas, the plasma bullet appears disk like and centred on the axis of symmetry during its propagation from the tube towards the dielectric surface. This is true up to 1 mm from the tube exit, and indicates a sphere like shape for the plasma bullet. The change of plasma bullet shape, from torus like shape (He plasma jet) to sphere like shape (He+O 2 (1000 ppm)), was also observed in [15][16][17][18]40], when admixtures were introduced in the helium gas. For distances longer than 1 mm and as the plasma bullet starts approaching the dielectric, the disk shape starts splitting and moves away from the axis of symmetry, forming a torus. The above observations can be summarized as: (a) the addition of oxygen admixtures in the helium gas promotes the plasma bullet propagation on the axis of symmetry of the tube; (b) the presence of the dielectric surface (the slab placed in front of the tube exit) forces the plasma bullet to spread radially. Furthermore, the addition of oxygen admixtures causes a reduction of the plasma bullet speed. For the interpretation of these experimental observations, the simulation results will be analysed, for both pure helium and with 500, 1000, 1500 and 2000 ppm of oxygen.

Analysis of the simulation results
In this section, the two-dimensional axi-symmetric plasma fluid model described in section 3 is used with the input parameters of section 4 to shed light on the experimental observations presented in section 5. It is noted that all the results presented in this section correspond to the rise time of the applied voltage. From the simulation results, it is observed that the evolution of the plasma jet has the characteristics of a streamer [14,38,61]. Consequently, in order to investigate its propagation, it is important to study the ionization rate on the streamer head. This will provide good insight into the evolution of the total light observed experimentally with the ICCD camera (presented in figure 3) as it is expected to follow the propagation of the streamer. Furthermore, the interaction of the streamer with the dielectric surface and how it is affected by the introduction of oxygen admixtures is investigated in this section. In order to make comparisons with the experimental conditions, the case of pure helium and with 1000 ppm admixtures of oxygen will be analysed in detail before the effects of differences in oxygen level (500-2000 ppm) are investigated. The simulation analysis will focus on the following: • The reasons for the formation of torus shaped plasma bullet structure for the case of pure helium. • The reasons for the change of plasma bullet structure to sphere shape once oxygen is added. The helium−air mixture for the experimental setup presented in section 2 is obtained from the gas dynamic model and is shown in figure 4. This shows that inside the tube prior to the exit, it is pure helium as expected. After it exits, it starts mixing with air, but it can be clearly seen that it forms a channel of almost pure helium that extends to the dielectric surface. The width of that channel is approximately the width of the tube. The mixing with air becomes more prevalent (the mole fraction of pure helium drops) away from the axis of symmetry (r=0 mm) and as the gas propagation distance increases. This result is then fed into the plasma fluid model and the process is repeated for the case of adding 1000 ppm of oxygen to the helium gas (this is not shown here because it is indistinguishable from figure 4). For the analysis of the results, the evolution of the streamer is divided into three parts: first, propagation of the streamer from the tube towards the dielectric; second, interaction of the streamer with the dielectric surface; and third,  propagation of the streamer along the dielectric surface. In the simulation model, the streamer evolution is defined as the dynamic motion of the total ionization rate with the streamer head (plasma bullet) being the peak of that total ionization rate. The terms streamer head, plasma bullet and peak of total ionization rate will be used interchangeably throughout this study. The streamer will be analysed for the positions and times illustrated in figure 5. The time 0 ns is set to when the streamer head coincides with the tube exit (z=0 mm). Points 1-7 in figure 5 correspond to the case when the streamer is moving towards the dielectric, point 8 to the case when it reaches the dielectric and points 9-11 the propagation of the streamer in the r direction (after it hits the dielectric surface).
6.1.1. Spatio-temporal evolution of the streamer from the tube towards the dielectric. The spatio-temporal evolution of the total ionization rate is presented in figure 6, for the same points defined in figure 5. It is noted that the min and max values in figure 6 are different for each sub-figure, and therefore they are presented separately in each case. The applied voltage at time −152 ns (figure 6(a)) is 1.85 kV and is considered the breakdown voltage, as it corresponds to the instant when the streamer starts to propagate. In particular, at this time the electric field created by the positive ions in the mixture becomes high enough to cause ionization and excitation, hence propelling the streamer forward along the axis of symmetry towards the dielectric. The streamer shape changes during propagation. Initially the shape is disk like (figure 6(a)) but by the time it exits the tube (figures 6(b) and (c)) it breaks into two lobes and then remains almost constant until it reaches 1 mm away from the dielectric (see figures 6(d) and (e)). From that point onwards its radius keeps increasing forming more distinct lobes (see figures 6(f) and (g)) until it hits (reaches) the dielectric, at which point its maximum is closer to the axis of symmetry (figure 6(h)). The evolution of the streamer head (total ionization rate) presented below agrees qualitatively with the experimental results shown in figure 3(a). 6.1.2. Electron production. In order to understand the evolution of the plasma bullet, the electron production in front of the streamer head is further investigated. In figure 7 the electron production rate is presented in logarithmic scale at −152 ns, which corresponds to the same time snapshot of the total ionization rate shown in figure 6(a). Figure 7 shows the electron production being maximum at z=−0.75 mm, which coincides as expected with the streamer head in figure 6(a). Away from the streamer head at z=0.1 mm, the electron production pointed with arrows in figure 7, shows that there is also a relatively high electron production at the boundary with air (r∼0.35 mm). These electrons are mainly produced in the Penning reactions (PR) of the nitrogen and oxygen molecules with the He m species (R43, R51, R73 and R74-see figure B1 in appendix B). Those electrons will act as seeds accelerating into the tube and feeding the streamer head promoting the propagation of the streamer in the lateral direction, creating a torus shape for the plasma bullet (see figures 6(b), (c)). In order to ensure the validity of this conclusion, another simulation was performed (see figure B2 in appendix B), without considering Penning reactions in the kinetic scheme (i.e. their rate coefficients were set to zero) and the torus like shape of the plasma bullet was not observed. In this case, the propagation of the plasma bullet occurs on the axis of symmetry of the tube and has a sphere like shape. The importance of Penning reactions in the evolution of helium DBD has been shown in several studies [41,[62][63][64][65][66][67][68].
Once out of the tube and up to 1 mm away from the dielectric, the radius of the streamer remains almost constant (see figures 6(d) and (e)). This is because the electron production in front of the streamer head reaches its peak at a similar radius to the torus radius of the streamer (see figure B3(a) in appendix B). As can be seen, those electrons Close to the dielectric, the shape of the plasma bullet is affected by the electrons emitted from the dielectric surface. The SEFE attributed to each ion in the mixture when the streamer is far from the dielectric and when it approaches the dielectric surface (same time snapshots as figures 6(e) and (g) corresponding to streamer head at 1 and 1.75 mm, respectively) are presented in figures 8(a) and (b) respectively. It is noted that SEFE corresponds to the last term on the righthand side of equation (13). As can be seen from figure 8(a), the SEFE is much higher on the sides (r∼0.5 mm) than at the centre (r=0 mm). The major contributors to the SEFE are the + O 4 ions that, due to mixing with air, are higher on the sides than in the centre. It is worth mentioning that the contribution of + O 4 is dominant because most ions are eventually converted to + O 4 (see schematic diagram of figure 6 presented in [53]). However, as the streamer head approaches the dielectric surface (figure 6(g)) the electric field in the region between streamer head and the dielectric surface increases, and that causes the positive ions to accelerate towards the dielectric surface. This increases the SEFE from all the ions and particularly from the helium ions, as seen in figure 8(b). The SEFE due to the helium ions species is increased in the centre of the dielectric, eventually causing the decrease of the streamer head torus radius as seen in figure 6(h). It is noted that when seec is set to zero, the decrease of the streamer torus radius when the plasma bullet reaches the dielectric surface is not observed (see figure B4 in appendix B).

Interaction of the streamer with the dielectric surface.
As the streamer propagates towards the dielectric, it causes the accumulation of a surface charge. That surface charge induces an axial electric field that opposes and eventually negates the axial electric field of the streamer. That will stop the axial propagation of the streamer. Consequently, the radial electric field dominates, and the streamer starts propagating laterally (parallel to the dielectric). To illustrate that, the surface charge accumulation and the electric field in z and r directions along the dielectric surface are presented in figure 9, at times corresponding to the cases before (121, 164 and 190 ns), during (204 ns) and after (303, 403 and 586 ns) the streamer head reaches the dielectric surface. The positions of streamer head for these times are indicated in figure 5. As can be seen from figure 9, as the plasma streamer approaches the dielectric surface, the electric fields (in z and r directions) on the dielectric surface start increasing. As the streamer head reaches the dielectric surface (204 ns), the electric fields in z and r directions increase considerably,  leading to surface charge accumulation. The axial electric field, E z , due to the interaction of the streamer with the dielectric surface is ∼37 kV cm −1 . It is important to note that the axial electric field and the surface charge accumulation during the interaction of the streamer with the dielectric surface present their peaks off-axis, indicating a torus like interaction of the plasma streamer with the dielectric surface. After that time, the surface charge accumulation continues to build up causing the reduction in the axial electric field. After some time, the radial electric field dominates, and the streamer proceeds to propagate radially (parallel to the dielectric surface). The results shown in figure 9 associated with the streamer propagation in the radial direction (times 303, 403 and 586 ns) are analysed below when this case is investigated.
6.1.4. Spatio-temporal evolution of the streamer along the dielectric surface. The spatio-temporal evolution of the total ionization rate during the propagation of the streamer along the dielectric surface is presented in figure 10, for three different times (positions of the streamer head from the axis of symmetry of the tube: 0.6, 0.8 and 1.1 mm-see figure 5). It is shown that when the streamer reaches the dielectric surface, it continues parallel to it at a height of ∼60-70 μm charging the surface below it (see figure 9(a)). This increases the surface charge, eventually shielding the axial electric field behind the streamer head (see figure 9(b)). However, the axial and radial electric fields decrease gradually (figures 9(b) and (c)), causing a reduction of the ionization rate on the streamer head (see figure 10). This continual reduction of ionization rate will eventually stop the propagation of the  streamer. From the simulation results, it has been found that the electron concentration during the plasma bullet's propagation along the dielectric surface is about · 5 10 18 m −3 , while the mean electron energy reduces from 20 eV to 10 eV. These results provide a Debye length in the range of 10 to 15 μm. The sheath thickness found here (60-70 μm), as expected, corresponds to a few times the Debye length, which is in agreement with previous studies [69].

Evolution of the He+O 2 (1000 ppm) plasma jet
Similarly to the analysis for pure helium plasma jet, the present analysis is divided into three parts: evolution of the streamer from the tube towards the dielectric surface, interaction of the streamer with the dielectric surface and evolution of the streamer along the dielectric surface. The spatio-temporal evolution of the total ionization rate during the streamer propagation will be analysed for the positions and times illustrated in figure 11. 6.2.1. Spatio-temporal evolution of the streamer from the tube toward the dielectric. The propagation of the streamer from the tube towards the dielectric surface for the He+O 2 (1000 ppm) plasma jet is analysed here. The total ionization rate is presented in figure 12 for the same points as in figure 11. As can be observed from figure 12(a), the total ionization rate initially increases in the region close to the electrodes on the axis of symmetry of the tube and has a disk like shape. At this time (−181 ns, corresponding to the instant when the streamer starts to propagate) the applied voltage is 1.23 kV (breakdown voltage). The decrease of the breakdown voltage once oxygen admixtures are introduced in a helium barrier discharge is explained in our previous study [53]. In particular, in such discharges (helium with admixtures of air components), the ions in the mixture are mainly increased due to the increase of He + and He m species (see figure 6 in [53]). The increase of O 2 concentration in the mixture benefits the reactions associated with this species (such as Penning ionization reaction, charge transfer reaction etc.). As a result, a lower concentration of He m and He + is required for ion production. The concentration of the former species is highly dependent on the electron temperature and consequently on the breakdown voltage. Thus, in helium with admixtures of air components, the increase of air concentration results in a decrease of the breakdown voltage.
Once the streamer begins to move towards the dielectric surface, its propagation remains on the axis of symmetry up until 1 mm from the tube exit (figures 12(b)-(e)). After 1 mm from the tube exit, the streamer forms two symmetric lobes centred on the axis of symmetry ( figure 12(f)). However, as the streamer approaches the dielectric surface, its maximum approaches the axis of symmetry of the tube (see figures 12(g) and (h)). The streamer exhibits qualitatively similar behaviour to the experimental results presented in section 5 (see figure 3(b)). Figure 11. Positions and corresponding times of the streamer head (total ionization rate) propagation for the He+O 2 (1000 ppm) plasma jet. The time 0 ns corresponds to the streamer head coinciding with the tube exit (z=0 mm).

Electron production.
In order to further understand the evolution of the plasma bullet, the electron production in front of the streamer head is investigated. In figure 13 the electron production rate is presented in logarithmic scale at −181 ns, which corresponds to the same time snapshot of the total ionization rate shown in figure 12(a). Figure 13 shows the electron production being maximum at z=−0.75 mm which, as expected, coincides with the streamer head in figure 12(a). However, unlike the case for pure helium there is no off-axis (on the side) peak production of electrons outside the tube. Therefore, the streamer does not break to form a torus shape and remains disk like propagating on the axis of symmetry (see figures 12(a)-(c)).
Those electrons are mainly produced from the Penning ionization of the oxygen molecules by the He m species (R73 and R74-see figure B5 in the appendix B), and due to the high amount of oxygen admixtures in the helium channel are not affected much by the mixing with atmospheric air. As a result, the electron production around the centre (for r<0.35 mm) is almost constant and does not exhibit strong peaks on the edges (r∼0.35 mm). This is in contrast to the pure helium plasma where the mixing with air plays an important role in the production of electrons.
Once out of the tube, the streamer continues to propagate on the axis of symmetry (see figures 12(d), (e)), as electrons in front of the streamer are mainly produced in the helium channel. Those electrons are mainly produced in Penning reactions of He m with O 2 (see figure B6(a) in appendix B). After 1 mm of the streamer from the tube exit, the maximum of electron production in front of the streamer head occurs off-axis. Those electrons feed the streamer head from the sides, promoting its propagation in the lateral direction creating a torus shape for the plasma bullet (see figure 12(f)). The off-axis production of electrons is mainly due to the Penning reaction of He m and He 2 m with nitrogen molecules (see figure B6(b) in appendix B). It is noted that when the Penning reactions are eliminated from the kinetic scheme (i.e. their rate coefficients are set to zero) the torus like shape of the plasma bullet is no longer observed (see figure B7 in appendix B).
In order to investigate the effect of the dielectric on the plasma bullet shape, the SEFE attributed to each ion in the mixture when the streamer is far from the dielectric and when it approaches the dielectric surface (same time snapshot as figures 12(e) and (g), corresponding to streamer head at 1 and 1.8 mm, respectively) are presented in figures 14(a) and (b) respectively. As can be seen from figure 14(a), the SEFE is much higher on the sides (r∼0.5 mm) than in the centre (r=0 mm). However, as the streamer head continues approaching the dielectric surface, the SEFE peak is at the axis of symmetry (r=0 mm) as shown in figure 14(b). This promotes the propagation of the streamer on the axis of symmetry of the tube, making the shape more disk like again (shown in figures 12(g) and (h)). The major contributor to the SEFE close to the centre are the He + species. It is noted that when the seec is set to zero the streamer is not observed to approach the axis of symmetry (see figure B8 in appendix B).

Interaction of the streamer with the dielectric surface.
The interaction of the streamer head with the dielectric surface ( figure 12(h)), causes the accumulation of surface charge. That surface charge induces an axial electric field that opposes and eventually negates the axial electric field of the streamer. This stops the axial propagation of the streamer. Consequently the radial electric field dominates and the streamer starts propagating laterally (parallel to the dielectric). To illustrate this, the surface charge density on the dielectric surface and the electric fields in z and r directions before, during and after the streamer reaches the dielectric surface are presented in figure 15. The positions of streamer head for these times are indicated in figure 11.
As can be seen from figure 15, before the streamer reaches the dielectric surface (times=163, 227 and 261 ns), the surface charge density and the electric field on the  dielectric surface are low. Once the streamer reaches the dielectric (267 ns), they both increase. During the interaction of the streamer with the dielectric surface, the axial electric field reaches the value of ∼51 kV cm −1 , which is higher in comparison to the pure He plasma jet (∼37 kV cm −1 ). The difference in the peak values of E is most likely caused by the higher concentration of electrons in the He/O 2 plasma jet (∼1.25 · 10 19 m −3 ) in comparison to the He plasma jet (∼5 · 10 18 m −3 ). Furthermore, the electric field in the He/O 2 plasma jet does not have a torus like shape as in the pure helium plasma jet case but presents its peak on the axis of symmetry. After the streamer reaches the dielectric surface, the charge density increases until it cancels the axial electric field of the streamer. The remaining radial electric field causes the streamer to continue to propagate parallel to the dielectric. The results, shown in figure 15, associated with the streamer propagation in the radial direction (times 432, 506 and 601 ns) are analysed below. 6.2.4. Propagation of the streamer along the dielectric surface. The spatio-temporal evolution of the total ionization rate during the propagation of the streamer along the dielectric surface is presented in figure 16, for three different positions of the streamer head from the axis of symmetry of the tube (0.6, 0.7 and 0.8 mm). After the streamer reaches the dielectric surface, its propagation continues along the dielectric surface at a height about 60-70 μm above it. During the propagation of the streamer head, positive ions are accelerated towards the dielectric surface (charging the dielectric surface, see figure 15(a)) causing the eventual shielding of the electric field behind streamer head (see figure 15(b)). Furthermore, as can be observed from figures 15(b) and (c), the axial and radial electric fields decrease gradually, causing the reduction of the  ionization rate on the streamer head (see figure 16). This continual reduction of ionization rate will eventually stop the propagation of the streamer.

Effects of different level of oxygen admixtures on the plasma evolution and interaction with the dielectric surface
The general behaviour of the streamer and its interaction with the dielectric surface does not change significantly as oxygen admixtures vary from 500-2000 ppm, and therefore the detailed analysis presented in sections 6.1 and 6.2 will not be repeated here. Two important parameters such as the streamer speed and IEF (during the interaction of the streamer with the dielectric surface) are presented here. The propagation speed of the streamer, derived from figure 17, shows a significant difference between pure helium and He+O 2 , albeit little variation with different admixture levels. The average speed is 7.7 km s −1 and 6.1 km s −1 for pure helium and He+O 2 plasma jets, respectively. This reduction of the speed of the plasma bullet when 1000 ppm of oxygen admixture is introduced in the helium gas is also observed experimentally (see section 5).
The IEF built on the dielectric surface (during the streamer surface interaction) at different levels of oxygen admixture in the helium gas is presented in figure 18. The results presented correspond to the times of 204, 265, 267, 264 and 258 ns for the cases of 0, 500, 1000, 1500 and 2000 ppm of oxygen admixture in the helium gas. As can be observed, for the case of He+O 2 plasma jet there is a time delay for the interaction of the plasma jet with the surface. Furthermore, the He+O 2 plasma jet generates higher IEF in comparison to the pure He plasma jet. Furthermore, the peak of the IEF on the dielectric surface is on the axis of symmetry for He+O 2 plasma jets and off the axis of symmetry for pure He plasma jet. The maximum IEF (∼55 kV cm −1 ) occurs for the case of 1500 ppm of oxygen admixture in the helium gas. Even though this will be the subject of future studies, it is worth mentioning that the higher electric fields for He+O 2 plasma jets could have significant implications for biomedical applications. They could make cells more susceptible to electroporation and could account for the observation that the presence of oxygen impurities in the Helium plasma jet can increase cancer cell apoptosis [9,10].

Conclusions
In this study, a two-dimensional model is used to shed light on the evolution of a capillary helium plasma jet with and without oxygen admixtures, and its interaction with a dielectric surface. The level of oxygen admixtures considered in this study is in the range of 500 to 2000 ppm. The simulation results show that oxygen admixtures strongly affect the streamer shape, the propagation speed, and the electric field induced on the dielectric surface. The shape of the plasma bullet during its propagation is controlled by the generation of seed electrons in front of the streamer head. For He+O 2 plasma jets, the shape of the bullet remains sphere like for propagation up to 1 mm away from the dielectric. This is because the seed electrons are mainly produced uniformly along the axis of symmetry in the helium channel. They are produced through Penning ionization of helium metastable species with the admixture of O 2 molecules. After 1 mm from the tube exit, the streamer forms two symmetric lobes centred on the axis of symmetry due to the offaxis production of electrons in front of the streamer head. Those electrons are mainly produced through Penning reactions of He m and He 2 m with N 2 molecules. In the case of the pure helium jet the bullet will be torus shaped because seed electrons in the helium channel are mainly generated on the edges of the channel through Penning ionization of nitrogen and oxygen molecules by He m and He 2 m species (due to the higher N 2 and O 2 in this region from atmospheric air mixing). It should be noted that in both cases, once the streamer head gets very close to the dielectric (∼0.1-0.2 mm) it is pulled towards the centre (the axis of symmetry) due to the high generation of SEFE on the axis of symmetry. Furthermore, it is observed that the plasma bullet speed decreases when the helium plasma jet is operated in the presence of oxygen admixtures. Finally, one of  the most significant results is the observation of much higher induced electric field on the dielectric surface with the introduction of the optimal amount of oxygen admixture. This is very important, since in some applications where the APPJ is to be used to destroy (or cause the apoptosis of) diseased cells, higher electric fields mean higher electroporation of the cells and consequently higher amounts of reactive species or even therapeutic drugs successfully introduced into the cells.

Acknowledgments
This work has received funding by the European Union Horizon 2020 Marie Skłodowska-Curie Actions Individual Fellowship (MSCA-IF-2015) under grant agreement number 703497.
Appendix A.      Simulation results of the spatio-temporal evolution of the total ionization rate for He+O 2 (1000 ppm) plasma jet without considering the Penning reactions in the kinetic scheme. Figure B8. Simulation results of the spatio-temporal evolution of the total ionization rate for He+O 2 (1000 ppm) plasma jet where the seec is set to zero.