Kinetic simulation of the transition from a pulse-modulation microwave discharge to a continuous plasma

Guan WANG (王冠), Ye KUANG (匡野) and Yuantao ZHANG (张远涛)

School of Electrical Engineering, Shandong University, Jinan 250061, People's Republic of China

Abstract The generation of a very strong peak current in the first period (PCFP) in a pulse-modulated microwave discharge has been discussed in previous studies. In this paper we focus on the transition process from a pulsed discharge to a fully continuous one driven by the pulsed microwave power source by means of a kinetic model. The computational results show that by increasing the duty cycle or voltage modulation rate (VMR), the discharge eventually becomes fully continuous and PCFP can no longer be observed.In the transition process,the distributions of the electric field, electron energy probability function (EEPF) and plasma density are discussed according to the simulation data, showing different discharge structures. The simulations indicate that many high-energy electrons with electron energy larger than 20 eV and low-energy electrons with electron energy less than 3 eV could be generated in a pulsed microwave discharge, together with a reversal electric field formed in the anode sheath when PCFP occurs. However, only medium-energy electrons could be observed in a fully continuous discharge. Therefore, by investigating the transition process the pulse-modulated microwave discharges can be further optimized for plasma applications at atmospheric pressure.

Keywords:atmospheric plasmas,pulse modulation,radio-frequency discharge,PIC-MCC model(Some figures may appear in colour only in the online journal)

1. Introduction

In recent years, the plasma community has benefited greatly from the development of atmospheric plasma [1-4], and the stability and reactivity of atmospheric plasma have been deeply understood based on experimental observation and computational data [5, 6]. Several different ways have been proposed under diverse discharge parameters to produce stable atmospheric plasmas [7-12]. Radio-frequency (rf)discharges can provide large volume and high density atmospheric plasmas operated in the α mode; however usually as greater power is coupled into the discharge system, the plasmas can be performed in the γ mode with constrict volume [2, 13-16], and even the new discharge mode has been predicted by the models in rf discharges[17,18].On the other hand,if oxygen or air are admixed into the atmospheric helium or argon plasmas, many reactive oxygen species and reactive nitrogen species can be generated with low gas temperature, which are believed to play essential roles in the application of plasma medicine [19-21].

To avoid the mode transition from α mode to γ mode and effectively modulate the generation of high-energy electrons,pulse modulation has been introduced in atmospheric rf discharges, and duty cycle and modulation frequency are of importance as additional tools to tailor the generation of atmospheric plasmas [6, 21-24]. As we know, increasing the rf frequency to the very high frequency(VHF)range,even to the microwave range, can bring remarkable stability of atmospheric plasmas for restricting the α−γ mode transition,although the reactivity may be suppressed at a given power based on the PIC-MCC or fluid simulation results [7, 8, 25].Detailed simulations have demonstrated that energetic electrons with energy greater than 50 eV can be produced much more efficiently in a pulsed microwave helium discharge than in pulsed DC or continuous microwave plasmas, and by introducing the pulse modulation, the discontinuous discharges show very different discharge behaviors compared to the continuous plasmas.High-energy electrons generated in a pulsed microwave discharge are able to break the covalent bonds of molecules, and then control chemistry processes,which have implications for many applications such as cancer treatment,sterilization,tissue regeneration and so on[26,27].

In this paper, we focus on kinetic behavior during the transition process in a pulsed microwave discharge. In the second section a brief description of the computational model is given,and based on the numerical data the mechanisms and underpinning physics in the transition process are discussed in the third section.A summary is concluded in the last section.

2. Brief description of model

In this study,we use a one-dimensional particle-in-cell Monte Carlo collision (PIC-MCC) simulation model named XPDP1(1D3v) to investigate the transition process. Although the fluid model can produce the microscopical discharge phenomena with very high computational efficiency, the limitation of the fluid model without considering the nonlocal effects should be carefully treated in the simulation, because the velocity distribution function in the fluid description is assumed to be Maxwellian everywhere and can therefore be uniquely specified only by temperature. To reveal the kinetic information of the microwave discharge,the PIC-MCC model is preferred for exploring the transition process, especially to show the profiles of EEPF. Many characteristics of the microwave discharge can only be understood at the kinetic level, such as nonlocal plasma behavior and collisionless heating,and the kinetic description is much more detailed but more expensive. In this simulation, the electrodes with parallel-plate structure are applied with the surface area of 0.01 m2. To calculate the discharge current accurately, the external circuits are also coupled into the model.The working gas is atmospheric helium,and the gas temperature is set to be 300 K.To capture the main plasma chemistry processes in the PIC-MCC code, the elastic collisions, excitation, and ionization electron-neutral collisions are taken into account in XPDP1, and the elastic scattering and charge exchange collisions for ions are also considered. The secondary electron emission coefficient has to be considered in the code as a key surface process with a given value of 0.1 for simplification in the simulation,and the generation of secondary electrons also works as an important boundary condition, which has been discussed in the reference. In the present simulation the electrode spacing is fixed at 200 μm and microplasmas can be generated after discharges are ignited, which can be accurately described by XPDP1 code.

In the XPDP1 code, the sinusoidal applied voltage with pulse modulation is given by a segmented function, representing the power source. The corresponding values of applied voltage during the power-on and power-off phases,noted as Ponand Poff, are presented as

where V0is the voltage amplitude of the microwave power source, f is the driving frequency in the microwave range in the present simulation, and r is the voltage modulation rate(VMR) varying from 0 to 100%, which is applied to adjust the voltage amplitude during the power-off phase. T′ represents the whole pulse modulation period as a sum of Ponand Poff, correspondingly the modulation frequency is calculated by f′ = 1/T′, and the duty cycle is expressed as D = Pon× 100%/T′. In this study, the peak value of the applied voltage is fixed at 280 V during the power-on phase.By varying the values of D and r, the transition can be realized from a pulsed microwave discharge to a continuous discharge.In this transition process,the different distributions of the electric field,EEPF and plasma density are investigated according to the computational data from the XPDP1 code,and then the underpinning physics are deeply discussed. The code has been validated and verified by many researchers under various discharge conditions, and the pulsed microwave discharges in particular have been further discussed based on the XPDP1 code in reference [16].

3. Results and discussion

In this study we detailed the transition behaviors from a pulsed discharge to a continuous discharge with two ways,namely increasing the duty cycle and VMR. In previous experimental and numerical studies, usually the discharge currents in the initial rf cycles after the power is on are smaller than those generated in the rest cycles in a normal pulsemodulated rf discharge driven by the rf frequency of 13.56 MHz [6, 28]. Numerical studies have shown that when the driving frequency is high enough, even in the microwave range, a very big current peak can be observed in the first cycle together with the generation of high-energy electrons,which could be very useful in many plasma applications[26, 29]. Our previous investigation revealed that the PCFP can be regarded as an indicator of the discontinuous discharges, just like the pulsed discharges controlled by dielectric barriers [10, 12]. The following numerical data will show the evolution of EEPE,electric field and plasma density,which could further deepen the understanding of different discharge structures.

3.1. Increasing duty cycle

To show the PCFP clearly in a pulsed microwave discharge,figure 1 gives the temporal evolution of discharge current for various duty cycles of 10%(a),50%(b),70%and 90%driven by a 2 GHz power source with the modulation frequency of 6.25 MHz, and the current waveforms are not very smooth due to the intrinsic characteristics of PIC-MCC model. A remarkable large current peak can be observed in the first cycle during the power-on phase, and the value of PCFP varies with duty cycle, which is summarized in figure 2. As the duty cycle is increased from 10% to 90%, the number of microwave cycles rises during the power-on phase; meanwhile the interval of power-off is reduced gradually,as shown in figure 1, and consequently the discharge eventually becomes continuous. From the simulation the value of PCFP increases when the duty cycle varies from 10%to 50%,then it almost reaches the peak value of 127 A at a duty cycle of about 50%, then with the duty cycle being further increased from 80% to 100%, the current peak drops quickly, and finally disappears at the duty cycle of 100%; the discharge is namely driven by continuous power.Obviously PCFP is only observed in a pulsed discharge although less power is deposited into the discharge system due to the presence of the power-off phase; the special discharge structures of plasma density and electric fields in a pulsed discharge contribute to the generation of PCFP.

In figure 3 the spatial distributions of the electric field are displayed for various duty cycles from 10% to 100% at the instant when the discharge current arrives at the peak value.For continuous rf discharges with duty cycle of 100%, the field in the anode sheath is negative (left side of the panel in figure 3)with the peak negative value very near the anode of 48 kV cm−1; meanwhile in the cathode sheath the electric field is positive and the top value near the electrode is as large as 173 kV cm−1together with a very low electric field region in the bulk plasma, which has been examined in detail by experiments and simulations at a common rf discharge[8, 30, 31]. However, when the discharge is discontinuous with the duty cycle from 10% to 90%, the positive field near the anode can be formed[26],and its strength decreases with the reduction of sheath width. For the cathode sheath, the electric field is also positive, but its strength increases with the duty cycle while the sheath thickness decreases.From the spatial distribution in figure 3 the field profile is flat in the cathode sheath region near the electrode after a sharp increase.When the duty cycle is 10%,the peak value of field in the anode sheath is 37.2 kV cm−1, but the top value is 67.7 kV cm−1in the cathode sheath, almost 45% larger than the former. With the duty cycle being increased to 90%, the peak positive field in the anode sheath is 23.2 kV cm−1, but 100.6 kV cm−1in the cathode sheath.

Figure 4 gives the distribution of EEPF for various duty cycles according to the simulation data.The EEPF is obtained at the moment when the discharge current reaches the peak value and at the position near the anode electrode.In general,the EEPF shows a convex shape, and the electrons can be approximately divided into three groups according to the electron energy, namely the low-energy electrons with Te≤ 3 eV,where Terepresents the electron energy,mediumenergy electrons with 3 eV ＜ Te＜ 20 eV, and high-energy electrons with Te≥ 20 eV from the EEPF profiles.When the discharge is fully continuous only very few high-energy electrons with Te＞ 20 could be produced, and low-energy electrons with 3 eV ＜ Te＜ 20 eV were relatively abundant.Considering the profiles of the electric field given in figure 3 in a continuous discharge, we can simply say that electrons are accelerated in the cathode sheath and lose energy in the anode sheath with large negative field strength.

However, in a pulsed microwave discharge at a duty cycle of 10%, the electron energy even could be larger than 60 eV although less power is coupled into the discharge system, and also many low-energy electrons with Te＜ 3 eV can be generated, which indicates that the introduction of pulse modulation can effectively tailor the energy distribution. As discussed in reference [26] the generation of highenergy electrons with Te＞ 60 eV benefits from reheating in the anode sheath after the acceleration in the cathode sheath,and on the other hand the production of abundant low-energy electrons is mainly due to the weak electric field in the cathode sheath. The generation of high-energy electrons in the initial stage of the power-on phase is consistent with the experimental observation and theoretical prediction during the pulse onset in low pressure [32-34].

From the simulation data,the profiles of electron and ion density are also plotted,and the plasma density is displayed in figure 5 for the discontinuous discharges (a)-(c) and continuous one (d), respectively. Usually a quasi-neutral plasma bulk can be observed in the central region of discharge gap in all cases and generally speaking the plasma density in the bulk plasma is homogeneous although the profiles obtained from the PIC-MCC code are not very smooth in this figure.In the cathode sheath, the ion density is larger than the electron density, especially for the continuous case. In a normal rf discharge,the density distribution is given in figure 5(d),both in the anode and cathode sheath,and the ion density is larger than the electron density. But in the pulsed microwave discharges with the duty cycle from 10%to 70%,the ion density is always larger than the electron density in the anode sheath.The different spatial distribution of plasma density indicates the different structures of the electric field in figure 3.

Thus, when the duty cycle is small in an atmospheric microwave discharge a very strong reversal electric field can be formed to reheat the electrons in the anode sheath, probably to produce high-energy electrons. However, when the discharge eventually becomes continuous, only a large amount of medium-energy electrons can be generated but with very high electron density in the bulk plasma.

3.2. Increasing voltage-modulated rate

The transition from a discontinuous to continuous discharge can be realized by increasing VMR during the power-off phase at a given duty cycle and modulation frequency.As we know, usually during the power-off phase, the power source is switched off, and the voltage amplitude is almost zero,which indicates that the VMR is zero. As the VMR is increased, the voltage amplitude gradually becomes as large as that during the power-on phase,figure 6 gives the temporal evolution of current density for various voltage-modulated rates during the power-off phase at a fixed duty cycle of 50%with the driving frequency of 2 GHz and modulation frequency of 6.25 MHz. The voltage amplitude during the power-off phase is increased from 40 V to 280 V with the VMR varying from 10% to 70%. In figure 6, the temporal evolutions of discharge currents are shown for various r values from 10%to 90%,the current peak in the first cycle is no longer very significant, and the value of PCFP decreases,which is summarized in figure 7. The value of PCFP decreases with the VMR, which also has been validated by the fluid model with more smooth simulated curves (the data from fluid model are not shown here).

Figure 8 gives the spatial profiles of the electric field at the moment when the discharge current reaches the peak value in the first cycle during power-on phase for various VMRs. From the distribution of the electric fields, the bulk plasma region is almost unchanged in the center, and the thickness of the anode sheath is approximately 0.023 mm; meanwhile the thickness of cathode sheath is about 0.03 mm from the simulation data.In the anode sheath, the electric field is positive with the VMR being increased from 10%to 50%;when the VMR is 50%,the electric field close to the anode is nearly zero although it is still positive in the central region of the anode sheath. When the VMR is increased to 70% the negative electric field near the anode is about 15.72 kV cm−1,but the positive electric field in the sheath is as large as 7.17 kV cm−1. Then, as the VMR is further increased, the electric field in the anode sheath becomes almost fully negative and eventually stronger, and is about−34.04 kV cm−1with a VMR of 90%.As discussed above,the positive electric field in the anode sheath can effectively reheat the electrons, which is responsible for the formation of PCFP with high-energy electrons. As the amplitude of sinusoidal voltage is increased during the power-off phase,the PCFP is no longer significant. For the cathode sheath, the electric field is always positive and increases with VMR, and even as large as161.71 kV cm−1when the value of VMR is 90%.

The EEPEs are given in figure 9 for various VMRs at the moment while the discharge current density reaches the peak value in the first period during the power-on phase;also three groups of electrons could be observed; the energy for lowenergy electrons is less than 5 eV from the EEPFs in figure 9,compared with those in figure 4. Generally speaking, as the VMR increases, high-energy electrons with energy of greater than 60 eV could be generated mainly due to the presence of the large positive electric field near the anode shown in figure 8, together with many low-energy electrons caused by the weaker electric field in the cathode sheath. When the discharge transits to a continuous discharge many mediumenergy electrons can be produced with the enhancement of the electric field in the cathode as the VMR increases. Consequently, the EEPE can be effectively modulated by varying the VMR in a pulsed microwave discharge.

To further understand the variation of the electric field given in figure 8, the spatial profiles of the electron and ion density are shown in figure 10 for various of VMRs from 10%to 70%. The ion density is always larger than the electron density in the cathode sheath, especially for a larger VMR value shown in figures 10(c) and (d), which indicates the positive electric field in the cathode sheath shown in figure 8.However, in the anode sheath region the plasma distribution is much more complex compared to that in the cathode sheath. When the VMR is smaller than 30%, many electrons are driven to the cathode sheath due to applied field from the bulk plasma and the ions will not have moved; then the ion density is larger than the electron density near the bulk plasma in the anode region, showing a positive electric field in figure 8, which could be used to accelerate the electrons again. But if the VMR is increased to larger than 50%, as in figures 8(c) and (d), the ions become dominative near the anode and the electric field in the anode sheath is decreased,even becoming negative.In general,the plasma density in the bulk plasma region rises with VMR as more power is coupled into the discharge system.

Consequently, according to the computational data, the electric field near the anode decreases and even changes polarity with VMR, because of the variation of the spatial distribution of the plasma density, until the PCFP finally disappears. From the simulation, many high-energy electrons could be produced in the pulsed microwave discharges with small VMRs.

4. Conclusion

In this paper we present a kinetic numerical study on the transition from a discontinuous discharge to a continuous one in a pulse-modulated atmospheric microwave discharge, and the computational data focus on the different dynamic behaviors under various discharge structures. The pulsed or discontinuous microwave discharges show the new discharge characteristics especially with very-high-energy electrons in the first cycle during the power-on phase. By increasing the duty cycle,the value of PCFP increases initially, and reaches the peak value at a duty cycle of approximately 60% in the present simulation, dropping afterwards; then the PCFP disappears when the discharge is fully continuous. On the other hand, as the VMR is increased at a fixed duty cycle and modulation frequency, the value of PCFP always decreases.The simulation indicates that the electrons could be reheated by anode sheath after the acceleration in the cathode sheath when PCFP occurs; then a large number of high-energy electrons could be produced,which could play essential roles in many potential plasma applications.However,the mediumenergy electrons are dominative in a continuous microwave plasma from the simulated EEPFs.In this paper by analyzing the transition processes from a discontinuous discharge to a continuous discharge, the intrinsic differences of various discharge structures are revealed, and the optimizing strategies of pulsed discharges are suggested according to the computational results.

Acknowledgments

This work was supported by National Science Foundation of China (Nos. 11675095 and 11975142).