For atmospheric argon RF dielectric barrier discharges, a self-consistent one-dimensional fluid model based on the drift-diffusive approximations of the particles is established to investigate the role of the neutral gas temperature on the discharge process and the plasma characteristics. A finite difference method is used to solve numerically the model, and the numerical results are obtained for the cases that the neutral gas temperature varies from 300 to 600 K. It shows that an increase in the neutral gas temperature causes a decrease in the ionization rate peak and a decrease in the plasma density, but the electric field and the electron temperature do not change very much. Moreover, the discharge mode transition from α mode to α-γ mode occurs because the growing ion flux induces more secondary electron flux, even if the ions entering the sheaths decrease. In addition, the ground state ionization and the ground state excitation are the main collisions in the argon discharges. When metastable atoms are focused on, the three-body quenching is also an important collision progress.

In recent years, low-temperature non-equilibrium plasmas generated by atmospheric RF dielectric barrier discharge (DBD) have been one of the research hotspots in the field of gas discharge. Especially, they have application potential in biomedicine,1–5 sterilization,6,7 ozone generation,8–11 material modification,2,11–13 and environmental protection.9,14 It has been proved that the plane-to-plane electrodes covered by two dielectrics are capable of producing a more uniform plasma than other dielectric structures through experiments and simulations.15–17 Discharges using this kind of structure are widely utilized in industrial applications and laboratory settings to gain non-equilibrium plasmas.

There is a growing emphasis on studying the choice of discharge parameters,18–23 such as power voltage, permittivity and width of dielectric, and discharge gap, to meet different applied requirements. For example, non-equilibrium plasmas with high plasma density and high radical flux are preferred in fields such as cancer treatment.24 For a better investigation of the effects of these parameters on the plasma characteristics, much research has been done. Barjasteh et al.25 explored the effect of power voltage parameters including amplitude and frequency on the plasma characteristics in DBD by setting argon as the working gas. They found that an increase in the applied voltage amplitude and frequency leads to an increase in the discharge current and plasma radiation. Yao et al.26 investigated the effect of different permittivity of the dielectric on the discharge by establishing a two-dimensional (2D) fluid model. It was discovered that the discharge with a higher dielectric constant led to an enhanced space-charge electric field and a weakened surface-charge electric field, which can change the discharge mode from glow-like to streamer-like discharge.

However, gases are heated by the heavy particles friction during transmission in long pipelines and the exposure to ambient temperature. Moreover, in practice, DBD reactor operation usually makes the gas temperature rise because part of the input power is not efficiently converted into heat at the electrodes and dielectrics.27 Especially, since the atmospheric pressure discharge is relatively violent and the gas reaction rate, for example, is more vulnerable to neutral gas temperature, the plasma characteristics are in any case affected by the neutral gas temperature. Although the studies of the effect of neutral gas temperature on discharge are not as mature as the other discharge parameters, there still have been some advances made by related researchers. Among them, a related experimental study reported that in cryo-DBD, the discharge mode switches from filamentary discharge to glow discharge as the neutral gas temperature decreases from room temperature to 78 K.28 Moreover, a variation of ambient temperature from 300 to 500 K can result in a reduction of the discharge current, electron density, and electric field strength, corresponding to a mode transition from a glow-like to a Townsend discharge.27 For helium discharge, a recent study reported that changes in gas temperature allow a shift from discharge column to homogeneous discharge with an earlier breakdown time and lower breakdown voltage.29 Previous works strongly indicated that the effect of neutral gas temperature on DBD is very apparent, especially its unconventional effect on the discharge mode transition. The study of the discharge characteristics of glow discharges, as one of the most important methods for generating large-volume homogeneous plasmas, deserves to be further discussed. However, the recognition of the mode transition of glow discharges by neutral gas temperature and the plasma characteristics, especially the recognition of the ionization rate in different discharge modes are still relatively lacking. Therefore, this issue needs an urgent solution.

It is obviously unrealistic to consider all collision processes in numerical simulation studies; however, it is an urgent issue to consider what kind of collision processes can be more accurately modeled in simulations for a more realistic discharge process. Three different perspectives are offered to explore this problem: the source terms of electrons and ions, the source terms of metastable atoms, and the gain or loss of electron energy. Among them, the metastable atomic source term characterizing its creation and disappearance is of great interest. For example, Emmons et al.30 pointed out that optically pumped rare gas lasers (OPRGLs), operated in α-mode RF dielectric barrier discharge, need to require sufficient metastable Argon atoms as the lowest energy species of the laser system. In this analogous case described above, the contribution of different collisions to the metastable atoms is also very noteworthy.

The rest of this paper is organized as follows. The 1D fluid model of DBD is described in Sec. II, and its benchmark is demonstrated in Sec. III. Section IV reports the results and analysis of the main computational findings about the influence and mechanism of neutral gas temperature on the discharge process, the discharge mode transition, as well as the contribution of different collisions. Then, the conclusions of this work are given in Sec. V.

A schematic of a plate-to-plate dielectric barrier discharge is shown in Fig. 1. The surfaces of the two electrodes, which are called power electrode and grounded electrode, are covered with dielectrics, whose thicknesses are a and b and relative dielectric constants are εra and εrb, respectively. The dielectric covering the powered electrode is called the powered dielectric, and the dielectric covering the grounded electrode is called the grounded dielectric. The width of the discharge gap is d. This kind of structure is widely used in different application scenarios and is proven to be the effective generation of large-volume uniform non-thermal equilibrium plasmas.17,31 When an RF source V(t)=Vasin(2πft) with enough high voltage is applied to the powered electrode, the working gas argon will be ionized and then a plasma is produced.

FIG. 1.

Schematic structure of plane-to-plane dielectric barrier discharge.

FIG. 1.

Schematic structure of plane-to-plane dielectric barrier discharge.

Close modal

At atmospheric pressure, the fluid model can commendably describe the evolution of the non-equilibrium plasma.32 The discharge properties only change along the normal direction to the large-area dielectrics. Therefore, this model is reasonably simplified to a one-dimensional form and is used to simulate different situations of argon discharge, which are briefly described as follows.

For argon discharge, the main eight collision processes are considered as shown in Table I. Ar* represents the argon atoms in the excited state, and there are many similar fine energy levels near the same energy level, which can transform into each other quickly. Therefore, they are considered to be classified as one type of metastable particle. The same thing applies to the resonance state Arr.

TABLE I.

The main collision processes of argon discharge and corresponding coefficients.33,34

No. Reactions Hj(eV) Rate coefficients
R1  Ar+eAr*+e (ground state excitation)  11.56  kex=3.712×108exp(15.06/Te)cm3/s 
R2  Ar+eAr++2e (ground state ionization)  15.7  ki=1.235×107exp(18.687/Te)cm3/s 
R3  Ar*+eAr++2e (stepwise ionization)  4.14  ksi=2.05×107exp(4.95/Te)cm3/s 
R4  Ar*+eAr+e (superelastic collisions)  −11.56  ksc=1.818×109exp(2.14/Te)cm3/s 
R5  Ar*+eArr+e (quenching to resonance)    kr=2×107cm3/s 
R6  Ar*+Ar*Ar++Ar+e (metastable pooling)    kmp=6.2×1010cm3/s 
R7  Ar*+Ar2Ar (two-body quenching)    k2q=3.0×1015cm3/s 
R8  Ar*+2ArAr2+Ar (three-body quenching)    k3q=1.1×1031cm6/s 
No. Reactions Hj(eV) Rate coefficients
R1  Ar+eAr*+e (ground state excitation)  11.56  kex=3.712×108exp(15.06/Te)cm3/s 
R2  Ar+eAr++2e (ground state ionization)  15.7  ki=1.235×107exp(18.687/Te)cm3/s 
R3  Ar*+eAr++2e (stepwise ionization)  4.14  ksi=2.05×107exp(4.95/Te)cm3/s 
R4  Ar*+eAr+e (superelastic collisions)  −11.56  ksc=1.818×109exp(2.14/Te)cm3/s 
R5  Ar*+eArr+e (quenching to resonance)    kr=2×107cm3/s 
R6  Ar*+Ar*Ar++Ar+e (metastable pooling)    kmp=6.2×1010cm3/s 
R7  Ar*+Ar2Ar (two-body quenching)    k2q=3.0×1015cm3/s 
R8  Ar*+2ArAr2+Ar (three-body quenching)    k3q=1.1×1031cm6/s 
Except for argon atoms, the other species considered in this model are electrons (e), argon ions (Ar+), and metastable argon atoms (Ar*). Due to plasma fluid theory, the densities of the particles satisfy the continuity equations as
ni,e,mt+Ji,e,mx=Si,e,m,
(1)
where the subscript i, e, and m indicate the ions, the electrons, and the metastable atoms, respectively. S refers to the source term of a particular species produced by a series of collisions, which is summarized in Refs. 35 and 36 in detail. Below, R is used to present a generating rate in a certain collision process. The source terms are specifically represented as
Si=Se=Ri+Rsi+Rmp,
(2)
Sm=RexRsiRscRrRmpR2qR3q.
(3)
The fluxes of the particles can be expressed as the following equation:
Ji,e,m=Di,e,mni,e,mx±μi,eni,eE.
(4)

Equation (4) is what is known as the key point of drift-diffusion approximation. Di,e,m and μi,e stand for the diffusion coefficients and the mobility of corresponding species, whose values are taken from Ref. 34. All these coefficients are related to the neutral gas density nn, which is equal to 7.3416×1021/Tg(cm3), where Tg represents neutral gas temperature with unit K.

Since many of the coefficients in Table I are the functions of the electron temperature, the electron energy balance equation is needed as follows:
t(ne32kTe)=pn,
(5)
where pn is defined as the net electron power absorption and consists of three items
pn=pt+papl.
(6)
The first item on the right side is the thermal convective term
pt=qe,
(7)
where the total electron energy flux is
qe=32DeneTe+52kTeJe.
(8)
The second term pa is the electron power absorption (or the so-called electron heating)
pa=eJeE.
(9)
The third term pl represents the electron energy loss, which is produced by the first four collisions in argon discharges in Table I,
pl=pex+pi+psi+psc.
(10)
The electric field satisfies
(εrEx)x=eε0(nine),
(11)
Ex=Vx.
(12)

In order to make the model self-consistent for solving, the following initial conditions (t=0) are used:

In the discharge gap:
ne=ni=nm=16nεx2d2(1xd)2,Te=Tei.
(13)
In the discharge region and dielectrics:
V=0,
(14)
where nε is set to very small values, which is fixed at 1.0×1011cm3. It is proved that different small initial densities do not affect the numerical results in our simulation.

The boundary conditions are as follows:

At x=a (on the powered electrode):
V=Vasin(2πft).
(15)
At x=0 (on the powered dielectric surface), where electrons and ions take flux boundary conditions:
Ji=μiniE,Je=γJiksne,nm=0,Te=Teb.
(16)
At x=d (on the grounded dielectric surface):
Ji=μiniE,Je=γJi+ksne,nm=0,Te=Teb.
(17)
At x=d+b (on the grounded electrode):
V=0.
(18)

Here, γ and ks are the secondary electron emission coefficient and electron recombination coefficient, respectively. The equations of this model are solved numerically with implicit schemes, similar to those in Refs. 19 and 37.

The model is validated by setting the relevant parameters as follows, which are the same as those in Ref. 38. We select polyethylene terephthalate (PET) as the dielectric material, whose relative permittivity is set to εra=εrb=3.4, and its secondary electron emission coefficient is set to 0.07. The widths of the two dielectrics are fixed as a=b=1mm, and the discharge gap is d=2mm. The RF source has a frequency of 5MHz and an amplitude of Va=700V. In this case, the neutral gas temperature is Tg=400K. Previously, Magnan et al.39 also conducted a similar study and experimentally demonstrated the reliability of the simulation results, just differing in the selection of some parameters. The results of our solution match theirs very well, which can prove the accuracy of our model.

Using the above values of the parameters, our simulation results are shown in Figs. 2 and 3. If we consider the eight collisions in the discharge, the density of the metastable atoms is overall lower than the electron and the ion densities, shown in Fig. 2(a). When we remove the three-body quenching process in our model as Ref. 38, the results are illustrated in Fig. 2(b). It shows that the density of the metastable atoms in the sheath regions is larger than those of the electron and the ion densities, which is in agreement with the distributions in Refs. 38 and 39, none of which considered the three-body quenching process. The reason for the different results in the two cases is that the different collision processes are included in the model, especially the relevant processes involving metastable atoms. The corresponding collision coefficients are also different. It is found that the three-body quenching process, not considered in the references, plays a great role in the loss of metastable atoms, which will be discussed further in Sec. IV C. The corresponding spatiotemporal distributions of electric field, electron density, and metastable atom density without considering the three-body quenching process in Fig. 3 are in good agreement with the previous results, which justifies our model.

FIG. 2.

Cycle-averaged distributions of particle densities: (a) considering eight collisions and (b) removing the three-body quenching process.

FIG. 2.

Cycle-averaged distributions of particle densities: (a) considering eight collisions and (b) removing the three-body quenching process.

Close modal
FIG. 3.

Spatiotemporal distributions of (a) electric field, (b) electron density, and (c) metastable atom density without the three-body quenching process.

FIG. 3.

Spatiotemporal distributions of (a) electric field, (b) electron density, and (c) metastable atom density without the three-body quenching process.

Close modal

To fulfill the need for a better understanding of the atmospheric DBD, we change the value of neutral gas temperature (Tg), to find out how it influences the process of discharge. The effect of successively varying the neutral gas temperature from 300 to 600 K at 100 K intervals is studied in this part of the simulation. This parameter range includes or even exceeds the neutral gas temperature in the situation of common atmospheric pressure DBD in Refs. 27 and 29, which can comprehensively study different conditions of Tg. The values of other relevant parameters are shown in Table II.

TABLE II.

The values of relevant parameters.

Name Symbol Value
Width of dielectric a  a  0.10cm 
Width of dielectric b  b  0.10cm 
Gap of discharge region  d  0.25cm 
Amplitude of applied voltage  Va  1000V 
Driving frequency  f  13.56MHz 
Relative permittivity of dielectric  εra, εrb  2.5 
Initial electron temperature  Tei  1.0eV 
Electron temperature on the dielectric surfaces  Teb  0.5eV 
Secondary electron emission coefficient  γ  0.01 
Electron recombination coefficient  ks  1.19 × 107 cm/s 
Name Symbol Value
Width of dielectric a  a  0.10cm 
Width of dielectric b  b  0.10cm 
Gap of discharge region  d  0.25cm 
Amplitude of applied voltage  Va  1000V 
Driving frequency  f  13.56MHz 
Relative permittivity of dielectric  εra, εrb  2.5 
Initial electron temperature  Tei  1.0eV 
Electron temperature on the dielectric surfaces  Teb  0.5eV 
Secondary electron emission coefficient  γ  0.01 
Electron recombination coefficient  ks  1.19 × 107 cm/s 

It is essential to choose the proper spatial and time steps, in order to ensure the efficiency and accuracy of the simulation. In discharge gap, 2000 uniform grid points are chosen in spatial, and in terms of time, one RF cycle is divided into 105 steps. Results for a range of physical quantities are obtained by utilizing the finite difference method.

In terms of industrial applications such as material processing in general, high plasma densities with controlled electron or ion energies and uniformity of processing over large volumes are sought. In this section, the results of different plasma characteristics are presented in space and time.

The electric field is generally one of the physical quantities of greatest interest due to the sheath information it contains. The results of the cycle-averaged electric potentials and electric fields, as well as the localized magnifications of the electric fields in the vicinities of the powered sheath and the grounded sheath, with different neutral gas temperatures, are shown in Fig. 4. In Fig. 4(a), it is apparent that the response of the electric potential to the neutral gas temperature is significant. In the bulk plasma region, the electric potentials are almost constant, and in the dielectrics, the electric potentials are almost straight lines. In this case, the bulk plasma can be regarded as a good conductor with high electrical conductivity, and the electric potential drops exist mainly in the sheath regions. The electric potential in the bulk plasma region is called suspension electric potential. In the bulk plasma region, as Tg increases from 300 to 600 K, the suspension electric potential decreases from 674.3 to 629.5 V. In the powered dielectric, the slope of the electric potential decreases as Tg increases, and in the grounded dielectric, the slope of the electric potential increases as Tg increases. Because the electric field is a negative gradient of the electric potential, so the influence of Tg on the electric potential will reflect on the electric field. While in Fig. 4(b), the neutral gas temperature does not affect the electric field that much. In the bulk plasma region, where the electric field is almost zero (i.e., 0.040 97 V/cm), it exhibits a quasi-neutral character of the plasmas. Close to the dielectrics, two distinctly non-quasi-neutral sheath regions appear, where the absolute values of the electric field increase abruptly. It can be observed in Figs. 4(c) and 4(d) that, on the surface of the powered dielectric, the electric field increases from 14.64 to 13.25kV/cm, but in the pre-sheath, the electric field decreases; on the surface of the grounded dielectric, the electric field decreases from 14.63 to 13.25kV/cm, but in the pre-sheath, the electric field increases. While in the powered and grounded dielectric region, the electric fields are maintained at constant values, for example, 0.5644 and 0.5642kV/cm, respectively, in the case of Tg=400K.

FIG. 4.

Cycle-averaged (a) electric potentials, (b) electric fields with different neutral gas temperatures, and the partially enlarged drawings of electric fields near (c) powered sheath and (d) grounded sheath. The electric field is expressed in the form of a negative gradient of the electric potential.

FIG. 4.

Cycle-averaged (a) electric potentials, (b) electric fields with different neutral gas temperatures, and the partially enlarged drawings of electric fields near (c) powered sheath and (d) grounded sheath. The electric field is expressed in the form of a negative gradient of the electric potential.

Close modal

The results of the cycle-averaged net charge densities [ Q=e(nine)] with different neutral gas temperatures are presented in Fig. 5. The distributions of the net charges are symmetrical, accumulating mainly in the sheath regions and being almost zero (i.e., 5.681×1012Ccm3) in the bulk plasma regions, which could explain the formation of the suspension electric potential. When the neutral gas temperature is double, the maximum cycle-averaged net charge densities in the sheaths on both sides increase from 1.3490×107 to 0.9477×107Ccm3, an increase in 29.75%. Combining Eqs. (11) and (12) yields the Poisson equation 2V=eε0(nine). According to this equation, in the sheath regions, the net charge densities are not zero, so the distributions of the electric potentials are nonlinear. While in the bulk plasma region, the net charge densities are almost zero, consistent with the Laplace equation 2V=0, so the electric potentials are almost constant. The different values of the constants are determined by the different net charge densities in the sheathes. During the discharge process, the dielectrics play a non-negligible role, which allows the charges to accumulate on their surfaces. With the increase in Tg, the net charges accumulated on the dielectric surfaces decrease, thus creating a decrease in the reverse electric fields. In theory, the reverse electric fields will, in turn, affect the entire discharge process. As a result, the net charge accumulated on the dielectric surfaces is highest at 300 K, leading to the largest absolute values of the electric field in the sheath region in this case. In addition, in the sheaths, the changes of the electric fields are caused by the difference of the net charge accumulation with the varying of the neutral gas temperature.

FIG. 5.

Cycle-averaged net charge densities with different neutral gas temperatures.

FIG. 5.

Cycle-averaged net charge densities with different neutral gas temperatures.

Close modal

Electron temperature is also a crux to be considered for industrial applications of plasmas. In Fig. 6, the results of the cycle-averaged electron temperatures and their localized magnifications near the sheaths are displayed. When the neutral gas temperature increases from 300 to 600 K, there is a corresponding increase in the electron temperature in the whole discharge region. When the neutral gas temperature varies from 300 to 600 K, the electron temperature values are 0.9300, 0.9436, 0.9546, and 0.9641eV at the midpoint of the discharge gap, respectively. The electron temperatures have peaks in the two sheaths and the two peak values are the same. When the neutral gas temperature varies from 300 to 600 K, the peak values are 1.848, 2.007, 2.145, and 2.262eV, respectively. The spatial distributions of the electron temperatures exhibit almost symmetrical trends. At the junctions of the sheaths and bulk region, there are a few drops of the electron temperature, which is roughly consistent with the simulation results of Magnan et al.39 in both spatial distribution trends and numerical values. This is a further confirmation of the correctness of our model. We can also clearly see the sheath structure where the electron temperature is particularly high and it is apparent that the widths of the sheaths are gradually increasing, as shown in Figs. 6(b) and 6(c). The electric fields in the sheath regions change dramatically and the electrons are heated by the electric fields in the sheaths and thus gain more energy.

FIG. 6.

(a) Cycle-averaged electron temperatures with different neutral gas temperatures and their partially enlarged drawings near (b) powered sheath and (c) grounded sheath.

FIG. 6.

(a) Cycle-averaged electron temperatures with different neutral gas temperatures and their partially enlarged drawings near (b) powered sheath and (c) grounded sheath.

Close modal

All of the variations caused by Tg reflect on the distributions of the plasma densities. Figure 7 demonstrates the results of the cycle-averaged densities of the electrons, the ions, and the metastable atoms. The distribution curves of the electron and the ion densities [Figs. 7(a) and 7(b)] are like bell-shaped structures characterized by high values in the middle and low values on both sides. The case with higher neutral gas temperature has lower electron and ion densities in the whole discharge gap, the maxima of the electron and ion densities are both 1.727×1013cm3 at Tg=300K. In Fig. 7(c), the cycle-averaged metastable atom densities have peaks in the two sheath regions. The metastable atom densities in the bulk plasma regions are much smaller than the electron and ion densities. Contrary to the case of the electrons and the ions, the metastable atom density, throughout the discharge region, increases with the rising neutral gas temperature.

FIG. 7.

Cycle-averaged densities of (a) electrons, (b) ions, and (c) metastable atoms with different neutral gas temperatures.

FIG. 7.

Cycle-averaged densities of (a) electrons, (b) ions, and (c) metastable atoms with different neutral gas temperatures.

Close modal

As we can see, the metastable atoms are distinct from the electrons and the ions, both in their distributions and in the changes induced by Tg. That is because the various collisions take place mainly in the sheaths, different species are also produced in the sheaths. Then the electrons and the ions are mainly migrated into the bulk plasma region by the electric field. Therefore, the density distributions of the electrons and the ions look bell-shaped. Because the metastable atoms are neutral and are not subjected to the migrating effect of the electric field, the motions of the metastable atoms are only from their diffusion. Thus, there is a peak of the metastable atom density both in the two sheaths.

At this point, we can make an overall summary that the neutral gas temperature has a strong effect on the electrons and the ions, as well as on the metastable atoms, but has a relatively smaller effect on the electric field and the electron temperature. Therefore, the neutral gas temperature does not affect the discharge progresses primarily by changing the electric field. For the electrons and the ions, the effects are negatively correlated, while for the metastable atoms, the effects are positively correlated. According to the formula nn=7.3416×1021/Tg(cm3), when the neutral gas temperature increases, the density of the neutral gas decreases, at atmospheric pressure. The reduced density of the neutral gas means that the ionization decreases, which results in reduced densities of the electrons and the ions produced by the discharge. The discussion of the ionization will be presented in Subsection IV B. For the metastable atoms, the higher neutral gas temperature allows the atoms to acquire higher energy to retain the metastable state, and thus the metastable atoms are less prone to degenerate to the ground state, even though the neutral gas density goes down.

It is one of the main problems of atmospheric RF discharges to keep the plasma stable in the α-mode and produce more active species. In conventional studies, the methods of realizing discharge mode transition are mainly by manipulating the coupling power of the discharge,40 for example, the control of the applied voltage or the driving frequency. Our study shows that the discharge mode transition can also occur by changing the neutral gas temperature.

Earlier studies were conducted to determine which discharge mode the current discharge case was in by judging the current distribution characteristics when the discharge parameters were changed.41,42 This approach, however, does not allow determining the successive dynamics of the discharge system during mode transitions, nor the evolutions of the individual physical quantities in each discharge case. There are other two perspectives reported for assessing which mode a discharge is in: one is to determine how or where the electrons are energized and where the plasma is generated; another is based on the region in which the plasmas are maintained and distributed.43 The work of Balcon et al.44 is also judged the two discharge mode on the basis of the above approach. The lack of an in-depth and comprehensive understanding of the inner mechanisms of this complex system is still a problem that needs to be solved as soon as possible.

The spatiotemporal distributions of the ionization rate and electron power absorption (electron heating) in two RF cycles are shown in Figs. 8 and 9, respectively. When the neutral gas temperature is set to 300 K, as seen in Fig. 8(a), the peaks of the ionization rate are at the outer boundaries of the sheaths, which indicates that the electrons are mainly generated at these regions. Meanwhile, from Fig. 9(a), it can be observed that the electrons mainly gain energy at the outer boundaries of the sheaths and the electrons are heated as the sheaths expand and lose energy as the sheaths collapse. In this situation, the common α-mode is formed. As the neutral gas temperature increases, the peaks of the ionization rate begin to shift to the interiors of the sheaths, where secondary electrons emitted from the dielectric surfaces are accelerated in the sheaths. These shifts then cause electron avalanches to accumulate electrons in the interiors of the sheaths. A portion of electron heating is also gradually shifted to the interiors of the sheaths, seen as in Fig. 9(d). Thus, in Fig. 8(d), when the neutral gas temperature increases to 600 K, the α-γ mode is reflected in the fact that, near one side of each sheath, the peak of the ionization rate occurs twice in one cycle. One occurs at the outer boundary of the sheath, which increases and then decreases as the sheath builds up; another occurs at the inside of the sheath, where the ionization rate reaches a maximum when the thickness of the sheath reaches a maximum. In one RF cycle, the peak of the ionization rate occurs alternately in the powered sheath and grounded sheath, periodically over time. Therefore, it can be concluded that the two discharge modes can coexist in the same discharge process and occurs alternately over time.

FIG. 8.

Spatiotemporal distributions of ionization rate at (a) Tg=300K, (b) Tg=400K, (c) Tg=500K, and (d) Tg=600K in two RF cycles. The white dotted lines represent the sheath boundaries.

FIG. 8.

Spatiotemporal distributions of ionization rate at (a) Tg=300K, (b) Tg=400K, (c) Tg=500K, and (d) Tg=600K in two RF cycles. The white dotted lines represent the sheath boundaries.

Close modal
FIG. 9.

Spatiotemporal distributions of electron power absorption at (a) Tg=300K, (b) Tg=400K, (c) Tg=500K, and (d) Tg=600K in two RF cycles. The black dotted lines represent the sheath boundaries.

FIG. 9.

Spatiotemporal distributions of electron power absorption at (a) Tg=300K, (b) Tg=400K, (c) Tg=500K, and (d) Tg=600K in two RF cycles. The black dotted lines represent the sheath boundaries.

Close modal

From Fig. 8, we can see that the maximum peak of the ionization rate decreases with the rising neutral gas temperature. The maxima of the peaks at 300, 400, 500, and 600 K of the neutral gas temperature are 11.45×1018, 10.43×1018, 9.61×1018, and 8.92×1018cm3s1, respectively. The peak is achieved in the vicinity of the sheath, where is the main region of plasma production. Meanwhile, in Subsection IV A, we obtained a negative correlation between the electron density and the neutral gas temperature. It is due to the fact that an increase in the neutral gas temperature leads to a decrease in the density of the neutral gas. Taken together, as the neutral gas temperature increases, the peak value of the ionization rate decreases and the neutral gas density ultimately leads to a decrease in the electron density produced by the discharge. Consequently, adjusting the neutral gas temperature is an effective measure to keep the discharge maintained in the α-mode and produce high-density plasmas. The work of Shi et al.42 experimentally measured the shape of the OH line by optical emission spectroscopy and compared it with the LIFBASS simulation data, and found that the gas temperature increased from 461 to 562 K before and after the mode transition. This corresponds well with our numerical simulation results and illustrates the accuracy of our simulation results.

A linchpin of discharge mode transition is that there are enough ion fluxes that bombard the dielectric surfaces to cause secondary electron emission in DBD. Therefore, discharge mode transition does not occur without considering secondary electron emission.45 In this work, the secondary electron emission generated by the ion flux bombarding the dielectric surfaces is considered. The results of the ion fluxes as the function of space and time at different neutral gas temperatures are presented in Fig. 10. When ionization is strong, the ion flux is also high. It can be seen that the ion fluxes directed to the dielectric surfaces increase with the increase in Tg. Figure 11 compares the evolutions of the ion fluxes and the secondary electron fluxes in two RF cycles on the powered and grounded dielectric surfaces with the different neutral gas temperatures from 300 to 600 K. Obviously, in Fig. 11, both the ion fluxes and the secondary electron fluxes present sinusoidal-like evolutions, and their maximum are achieved simultaneously. In Fig. 11(a), the negative values of ion fluxes represent the directions toward the powered dielectrics. As shown in Fig. 10, the absolutions of the ion fluxes on the dielectric surfaces also increase with the increasing neutral gas temperature and the directions of the ion fluxes are toward the surfaces. In this way, more ions strike the dielectric surfaces, and more secondary electrons are induced in the opposite direction. Eventually, the secondary electron fluxes on the surfaces grow, and thus a discharge mode transition occurs.

FIG. 10.

Spatiotemporal distributions of ion flux at (a) Tg=300K, (b) Tg=400K, (c) Tg=500K, and (d) Tg=600K in two RF cycles. The black dotted line represents the sheath boundary.

FIG. 10.

Spatiotemporal distributions of ion flux at (a) Tg=300K, (b) Tg=400K, (c) Tg=500K, and (d) Tg=600K in two RF cycles. The black dotted line represents the sheath boundary.

Close modal
FIG. 11.

Evolutions of ion fluxes and secondary electron fluxes in two RF cycles on surfaces of (a) powered dielectric and (b) grounded dielectric with different neutral gas temperatures.

FIG. 11.

Evolutions of ion fluxes and secondary electron fluxes in two RF cycles on surfaces of (a) powered dielectric and (b) grounded dielectric with different neutral gas temperatures.

Close modal

The results of the evolutions of the ion densities and the electric fields on the powered dielectric surface and the grounded dielectric surface with different neutral gas temperatures are shown in Figs. 12(a) and 12(b), respectively. In Fig. 7(b), we can also see that the ion densities decrease in the whole discharge region with the increase in neutral gas temperature. Meanwhile, in Figs. 4(c) and 4(d), the absolutions of the electric fields in the sheaths also decrease with the increase in neutral gas temperature, especially on the dielectric surfaces. According to the boundary conditions of the ions, the ion fluxes are Ji=μiniE on both the dielectric surfaces. Here, μi is the ion mobility, which can be obtained from a constant coefficient nnμi and relates to the neutral gas density under the atmospheric pressure. As the increase in the neutral gas temperature, the neutral gas density drops markedly. So the ion mobility, which characterizes the degree of that the ions are migrated by the electric field, increases. Therefore, the trend of the ion flux does not tally with the electric field as well as the ion density, but rather an increase in the ion flux directed to the dielectric surfaces due to an increase in the ion mobility, which in turn causes an increase in the secondary electron flux on the surfaces. This is the key to realizing the discharge mode transition.

FIG. 12.

Evolutions of (a) ion densities and (b) electric fields in two RF cycles on powered and grounded dielectric surfaces with different neutral gas temperatures.

FIG. 12.

Evolutions of (a) ion densities and (b) electric fields in two RF cycles on powered and grounded dielectric surfaces with different neutral gas temperatures.

Close modal

Compared with low pressure discharges, the collisions in atmospheric pressure discharges are more violent, and relevant studies have involved more and more of them. This adds much detail to the subsequent work, but not every collision process has a pivotal effect on the discharge. Considering all collisions in realistic discharges is impossible and unnecessary, and it greatly complicates the research. To simplify the collision processes and retain the most critical and relatively complete processes, the role of each collision in the discharge as well as its importance needs to be studied.

For the physical quantities involving the discharge processes in the modeling, we consider the issue from two perspectives: energy conversion and plasma generation. In this work, the electron source term S (same as the ion source term) includes three collisions, namely, Ri for the state ground ionization, Rsi for the stepwise ionization, and Rmp for the metastable pooling, respectively. Figure 13 presents the results of the cycle-averaged source term of the electrons (same as the one of the ions) and its three components at Tg=400K. From the results, we can see that the rate of electron production from the ground state ionization is almost equal to the total source term and is four to five orders of magnitude larger than the stepwise ionization and metastable pooling. Therefore, the contributions of the latter two collisions to the electron production rate can be negligible for their little contribution to the electric and ion source terms. Figure 14 presents the results of the cycle-averaged source term of the metastable atoms and its seven components at Tg=400K. In Fig. 14, the black solid line represents the source term of the metastable atoms Sm, which are combined by seven components. For the components of the metastable atom source term, in Eq. (3), only the grounded excitation Rex is a generating term and the others are losing terms. From Fig. 14, we can see that the generating term Rex is same order as the losing term R3q and the rest losing terms are at least three to four orders lower than the generating term. The results in Figs. 13 and 14 mean that, when only the electrons and the ions are interested, the ground state ionization and the ground state excitation are the main collision processes in the discharge, while these low-order losing collisions can be disregarded. However, as shown in Sec. III, these low-order losing collisions, especially the three-body quenching process, are to be taken into account additionally if attention needs to be paid to the metastable atoms.

FIG. 13.

Cycle-averaged source term of electrons (the same as the one of ions) and its three components at Tg=400K.

FIG. 13.

Cycle-averaged source term of electrons (the same as the one of ions) and its three components at Tg=400K.

Close modal
FIG. 14.

Cycle-averaged source term of metastable atoms and its seven components at Tg=400K.

FIG. 14.

Cycle-averaged source term of metastable atoms and its seven components at Tg=400K.

Close modal

In terms of considering energy conversion, for the three terms of the net energy absorption in Eq. (6), the various collisions mainly affect the electron energy loss term. While the thermal convective term and the electron heating are related to the flux and electric field, rather than the different collisions. Hence, these two are not discussed in this section. Figure 15 gives the results of the cycle-averaged electron energy loss rate with different neutral gas temperatures. The maximum electron energy loss rates occur in the sheaths. It shows that the neutral gas temperature has a definite effect on the electron energy loss, and it is observed in the sheaths that the electron energy loss decreases as Tg increases. There are only four collision processes that can cause the loss of the electron energy, namely, ground state excitation, ground state ionization, stepwise ionization, and superelastic collision, respectively. Figure 16 gives the results of the cycle-averaged electron energy loss rate of these four collisions with different neutral gas temperatures. Obviously, the first two collisions account for a larger portion. The contributions of the last two collision processes to the electron energy loss rate are so insignificant that it is almost negligible. The electron energy loss due to the ground state excitation Pex decreases with increasing Tg. Pi is caused by the ground state ionization, the double-peak structures are progressively more pronounced with increasing Tg, which can be seen from the localized magnified image near the grounded sheath. This can also clearly correspond to the generation of twice ionizations in one cycle.

FIG. 15.

Cycle-averaged electron energy loss rates with different neutral gas temperatures.

FIG. 15.

Cycle-averaged electron energy loss rates with different neutral gas temperatures.

Close modal
FIG. 16.

Cycle-averaged electron energy loss rates from four different collision progresses: (a) ground state excitation, (b) ground state ionization, (c) stepwise ionization, and (d) superelastic collision, with different neutral gas temperatures.

FIG. 16.

Cycle-averaged electron energy loss rates from four different collision progresses: (a) ground state excitation, (b) ground state ionization, (c) stepwise ionization, and (d) superelastic collision, with different neutral gas temperatures.

Close modal

The proportions of these four collisions are shown in Table III. The mean electron energy loss was affected by Tg, and the ratio of the four collisions produced a significant change. For the ground state excitation, its ratio decreases with increasing neutral gas temperature, while the contribution of the ground state ionization to the electron energy loss increases. This indicates that the ground state excitation and the ground state ionization differ in their corresponding changes to the neutral gas temperatures, with the former being negatively correlated and the latter being negatively correlated.

TABLE III.

Contributions of four collisions to energy loss.

Neutral gas temperature (Tg) (K) Mean electron energy loss (W/cm3) pex (%) pi (%) psi (%) psc (%)
300  4.1939  86.43  13.56  0.006 31  0.00287 
400  3.7393  84.67  15.32  0.009 41  0.00412 
500  3.4782  82.92  17.07  0.012 79  0.00539 
600  3.3261  81.16  18.83  0.016 36  0.00665 
Neutral gas temperature (Tg) (K) Mean electron energy loss (W/cm3) pex (%) pi (%) psi (%) psc (%)
300  4.1939  86.43  13.56  0.006 31  0.00287 
400  3.7393  84.67  15.32  0.009 41  0.00412 
500  3.4782  82.92  17.07  0.012 79  0.00539 
600  3.3261  81.16  18.83  0.016 36  0.00665 

Among the eight main collisions in the argon discharge, the role of the two collision processes, the ground state ionization, and the ground state excitation are far ahead of the others in a situation with no need to consider the metastable atoms. However, considering only these two processes makes the density of the metastable atoms higher. Thus, if research on metastable atoms is involved, it is necessary to include at least the three-body quenching process as well.

A self-consistent one-dimensional fluid model has been used to analyze the processes of the argon discharge. We obtained numerical results for the plane-to-plane DBD by applying a finite difference method, as well as the drift-diffusion approximation. Further, the physical mechanisms underlying the effect of the neutral gas temperature on the discharge are studied and clarified, paving the way for a deeper understanding of the process of the gas discharge. The following conclusions can be obtained.

Under the same discharge parameters except for the neutral gas temperature (Tg), we find that the influence on the discharge can be traced back to the influence on the neutral gas density. The results show that an increase in Tg, leads to decreases in the densities of the electrons and the ions produced by ionizations due to a decrease in the density of the neutral gas, although the ionization rate increases accordingly. Conversely, the atoms are more likely to be maintained in metastable states at the higher neutral gas temperatures, which causes more metastable atoms.

As the neutral gas temperature grows, the discharge mode transition occurs, from α-mode to α-γ mode. Depending on how and where the plasma is produced during the discharge and the electrons acquire and lose energy, the locations of the plasma production have shifted from the outer boundaries of the sheaths to the interiors. The electrons are energized at the outer boundaries of the sheaths in the α-mode with the sheath oscillating, and transferring to the interiors of the sheaths in the α-γ mode. The reason for the discharge mode transition is that as the neutral gas temperatures increase from 300 to 600 K, the ion fluxes to the dielectric surfaces become higher and then cause more secondary electron emission.

Analyzing the role of different collisions in the argon discharges, it is found that the ground state ionization and the ground state excitation contribute overwhelmingly to the discharge. Additional consideration of at least the three-body quenching process is required when the metastable atoms are focused on. It offers new insights to simplify the model.

This work is supported by the Scientific Research Fund Project of Liaoning Education Department of China, Award/Contract No. L2019049. The author would like to thank Miss. Na Gao and Dr. Nan-Nan Li for their valuable comments on this work.

The authors have no conflicts to disclose.

Ze-Hui Zhang: Data curation; Methodology; Software; Validation; Visualization; Writing – original draft. Ke-Xin Zhong: Data curation; Methodology; Software; Validation; Visualization; Writing – original draft. Yue Liu: Conceptualization; Funding acquisition; Methodology; Software; Supervision; Validation; Writing – review & editing. Wei Wang: Methodology; Software; Validation; Visualization; Writing – review & editing. Yi-Nan Wang: Methodology; Resources; Software; Supervision. De-Zheng Yang: Conceptualization; Investigation; Supervision.

The data that support the findings of this study are available from the corresponding author upon reasonable request.

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