Yangyang Fu, John P. Verboncoeur, and Andrew J. Christlieb ...

[Pages:81]Pressure effect on a tandem hollow cathode discharge in argon

Yangyang Fu, John P. Verboncoeur, and Andrew J. Christlieb

Citation: Physics of Plasmas 24, 103514 (2017); View online: View Table of Contents: Published by the American Institute of Physics

Articles you may be interested in Transition characteristics of low-pressure discharges in a hollow cathode Physics of Plasmas 24, 083516 (2017); 10.1063/1.4997764

Electrical model of cold atmospheric plasma gun Physics of Plasmas 24, 103510 (2017); 10.1063/1.4986023

Numerical modeling of repetitive nanosecond discharge in air Physics of Plasmas 24, 100704 (2017); 10.1063/1.4997830

Landau damping of electrostatic modes in nonthermal plasmas Physics of Plasmas 24, 104503 (2017); 10.1063/1.5006802

Slow electron energy balance for hybrid models of direct-current glow discharges Physics of Plasmas 24, 093503 (2017); 10.1063/1.4997434

Determination of the cathode layer thickness in the normal glow discharge Physics of Plasmas 24, 083506 (2017); 10.1063/1.4995266

PHYSICS OF PLASMAS 24, 103514 (2017)

Pressure effect on a tandem hollow cathode discharge in argon

Yangyang Fu,1,2,a) John P. Verboncoeur,1,2 and Andrew J. Christlieb1,2,3

1Department of Computational Mathematics, Science and Engineering, Michigan State University, East Lansing, Michigan 48824, USA 2Department of Electrical and Computer Engineering, Michigan State University, East Lansing, Michigan 48824, USA 3Department of Mathematics, Michigan State University, East Lansing, Michigan 48824, USA

(Received 6 May 2017; accepted 14 September 2017; published online 2 October 2017)

The tandem hollow cathode discharge, formulated by arranging two discharges in series, is an important method used to increase the irradiance of a hollow cathode discharge. In this paper, based on a two-dimensional fluid model we studied a five-layer tandem hollow cathode discharge, with three hollow electrodes stacked together and separated by the insulators to obtain the configuration of anode/insulator/cathode/insulator/anode from the top to the bottom. In the model, the thickness of both electrodes and insulators is set at 1 cm and the diameter of the hollow cavity is 2 cm. The pressure effect on the discharge properties is investigated with gas pressure ranges from 100 Pa to 5 kPa. The gap voltage first decreases, reaching a minimum sustaining voltage at 1 kPa, and then increases. Based on the two-dimensional electron density distributions, the discharges parameters (including the electron density, ion density, electric potential, and electric field) of one integrated hollow cathode discharge at 1 kPa and two relatively independent discharges at 100 Pa and 4 kPa are presented, respectively. The results indicate that the paralleled hollow cathode discharges can be manipulated into one integrated discharge with a higher plasma density by the monotonous control of gas pressure. Published by AIP Publishing.

I. INTRODUCTION

Hollow cathode discharges (HCDs) have been investigated by a multitude of researchers for many years due to their wide applications in various fields, such as light source, gas lasers, spectroscopy, surface treatment, and electric propulsion.1?6 There are several types of hollow cathode discharges, such as the high-voltage discharge,7,8 hollow cathode glow discharge,9,10 and arc discharge with the flow gas,11,12 which are fundamentally different in properties. As is known, the hollow cathode glow discharge has many advantages, including simple and compact structure, relatively low breakdown voltage, high concentration of electrons and ions, and high electro-optical conversion efficiency.13,14 These advantages are attributed to a specific discharge mode operating with the so-called hollow cathode effect, where the plasma column formed in the hollow cathode serves as a virtual anode and the axial electric field changes into a radial one. The cathode fall regions inside the hollow cathode are so close that high energy electrons can be accelerated back and forth around the hollow cathode axis, which leads to increased ionization on the axis.15 This discharge mode is characterized by the negative differential resistance in the voltage-current curves. Despite many attractive advantages in the HCD mode, the hollow cathode effect does not necessarily occur, which is normally influenced by the geometric sizes (hollow cathode diameter D and gap distance d between anode and cathode), gas pressure p, etc. For a typical hollow cathode discharges in argon, it was generally considered that the hollow cathode effect occurs

a)Author to whom correspondence should be addressed: fuyangya@msu.edu

with the product of gas pressure and hollow diameter, pD, in the range of 0.026 $10 Torr?cm.16 Note that the lowest pD value was just a theoretical value based on the assumption that the mean free path for ionization is not larger than the hollow cathode diameter; however, in the experimental data from Schoenbach, hollow cathode discharge for the lowest pD is 0.53 Torr?cm, which is 20 times the theoretical value.17,18 As for the upper limit for argon, it was found to be approximately 5 Torr?cm from Schoenbach's experimental studies in microdischarges.14,16 Therefore, the pressure effect on a specific hollow cathode discharge might be different in various regimes.

In the past years, many methods were put forward to obtain high-intensity spectroscopic light and high-intensity current sources.1,19,20 One of the methods is through increasing the gas pressure of the hollow cathode discharge, and it was found that the emissions intensity is usually enhanced with the increasing pressure.21 The other commonly used method is by increasing the current through the discharge, but it is usually limited by the onset of instabilities such as glow-to-arc transitions. In order to overcome these shortages, the tandem HCDs operated in DC mode and pulse mode have already been established successfully in microdischarges at high pressure with focusing on the high intensity emissions.21,22 As is known, the conventional hollow cathode discharges usually generate the high density plasmas with two negative glows coalesce in the radial direction. Besides that, the tandem HCD expects the two discharges from the top and the bottom overlap with each other as well, which will further produce a higher plasma density than the independent ones. However, the desired tandem HCDs are

1070-664X/2017/24(10)/103514/6/$30.00

24, 103514-1

Published by AIP Publishing.

103514-2 Fu, Verboncoeur, and Christlieb

Phys. Plasmas 24, 103514 (2017)

not readily produced but could be generated under a certain range of gas pressure. Thus, it is worthwhile to examine the pressure effect on the tandem-structured hollow cathode discharge, which will help to promote the current methodologies of achieving high intensity light emissions or high dense plasmas.

The hollow cathode discharge has a long history since the earliest publication concerning the hollow cathode effect originated from Paschen's comments on its spectroscopic application in 1916.10,23 After that, the hollow cathode discharge was investigated by the experimental and theoretical methods through the 1950s to 1990s.9,10,24?27 Since the 1990s, the hybrid model was developed for the two dimensional simulation on the hollow cathode discharges; Donko and Bogaerts et al. carried out the two-dimensional hybrid simulation on the rectangular hollow cathode discharge as well as the segmented cylindrical hollow cathode discharges.28?31 In more recent years, the numerical simulations, including the fluid model,32?34 the particle-in-cell/ Monte-Carlo model,35?37 the global (volume-averaged) model,38,39 as well as the analytical model,40 were developed with growing interests for the hollow cathode discharges in various regimes. Among these models, the fluid model is a fast and less computationally expensive way to provide a reasonable insight into the qualitative trends for the hollow cathode discharges in many occasions.33,41?43

In this work, a five-layer tandem hollow cathode structure was studied by using a two-dimensional fluid model, focusing on investigating the pressure effect on the discharge parameters in the tandem HCD. In the tandem HCD, three electrodes are stacked together and separated by the insulators to obtain the configuration of anode/insulator/cathode/ insulator/anode from the top to the bottom. The external characteristic (gap voltage and average cathode current density) against the gas pressure and micro parameter characteristics (distributions of the electron density, ion density, electric potential and electric field) of the tandem HCD are presented. With pressure changing from 100 Pa to 5 kPa, the independent discharges from the top side and bottom side merge into one mixed discharge and then gradually depart from each other. The established tandem HCD could operate as two single hollow cathode discharges and one mixed HCD. The plot of the gap voltage against the gas pressure shows a Paschen-like curve, with the lowest operating voltage. The pressure effect on the tandem hollow cathode discharge was clearly observed based on the parameter evolution at different operating points.

II. MODEL DESCRIPTION

The sketch of the five-layer hollow cathode geometry is shown in Fig. 1, which is widely used in the tandem HCD studies. From the top to the bottom, layers (marked as layer5 to layer1) are arranged as follows: anode, insulator, cathode, insulator, and anode. The discharge geometry is different from the conventional single HCDs and also different from the previously studied HCDs with two anodes.44?48 Despite that the HCD can be operated with arbitrary anodes, it is not appropriate to work with the planar anodes at two sides

FIG. 1. Sketch of the five-layer tandem hollow cathode structure (in r-z plane) with three hollow electrodes stacked together and separated by the insulators. The voltage source U0 is applied on two hollow anodes through a ballast resistor Rb and the hollow cathode is grounded.

when the diagnostics (such as the light emissions) are required. The thickness of both electrodes and insulators d is kept the same with d ? 1 cm, and the diameter of the hollow cathode hole D is 2 cm. This arrangement is more favorable in the actual manufacturing, which also makes the observations of the discharges more convenient. Due to the symmetry of the discharge cavity, only half of the geometry is simulated. The region of O-A-B-C is chosen as the computational domain, with the line O-A as the axis of symmetry. Boundaries D-B and G-C are the anodes and the E-F is the cathode. Boundaries D-E and F-G depict the dielectric and the A-B and O-C are the gas boundary.

The tandem HCD was described using the coupled continuity equation for each species, electron energy conservation equation, and Poisson's equation44,49,50

@nj @t

?

r

?

Cj

?

Sj;

(1)

@neee @t

?

r

?

Ce

?

Se;

(2)

er2u ? ?qe?ni ? ne?;

(3)

where nj is the electron, ion, and metastable density with j ? [e, i, m], respectively, Cj is the flux density of species j,

and Sj is the source term containing production and destruction of particle j in plasma reactions. Variable neee denotes

the mean electron energy density, and qe is the elementary charge. Variable Ce is the mean electron energy flux, and Se

is the mean electron energy source term. Variable u is the

electric potential, and e is the permittivity of working gas.

The simulation is conducted with argon. Five species are included: electrons (e), atom ions (Ar?), molecular ions (Ar2?),

excited atoms (Ar*), and the background ground state atoms

(Ar). The basic plasma reactions include (R1): elastic collision e ? Ar ! e ? Ar, (R2): excitation e ? Ar ! e ? Ar*, (R3): deexcitation e ? Ar* ! e ? Ar, (R4): ionization by single collision e ? Ar ! 2e ? Ar?, (R5): stepwise ionization e ? Ar* ! 2e ? Ar?, (R6): ionization between excited atoms Ar* ? Ar* ! e ? Ar ? Ar?, (R7): two-body collision Ar* ? Ar ! Ar ? Ar,

103514-3 Fu, Verboncoeur, and Christlieb

(R8): radiation Ar* ! Ar ? h, (R9): three-body collision 2Ar ? Ar? ! Ar ? Ar2?, and (R10): dissociative recombination e ? Ar2? ! Ar* ? Ar. The rate coefficients of electron impact reactions (R1?R5) are calculated by solving the electron

Boltzmann equation with appropriate electron energy-dependent reaction cross sections for a range of reduced electric fields.51,52 The electron Boltzmann equation solver, BOLSIG?, with the two-term approximation was used to obtain the electron energy distribution function (EEDF).53 This approximation is rather

accurate to calculate the relevant kinetic coefficients for pure argon under glow discharge conditions.54 The reaction rates for R6, R7, R8, and R9 are set at 6.4 ? 10?10 cm3?s?1, 2.3 ? 10?15 cm3?s?1, 1.8 ? 106 s?1, and 2.5 ? 10?31 cm3?s?1, respectively.55,56 The reaction rate coefficient in Arrhenius form for R10 is 5.38 ? 10?8Te?0.66 cm3?s?1. The electron mobility was taken from Ref. 57: lep ? 3.0 ? 105 cm2?Torr?V?1?s?1. For the atom ions (Ar?) the motility was taken as li1p ? 1216 cm2?Torr?V?1?s?1, and for the molecular ions (Ar2?), it was li2p ? 2052 cm2?Torr?V?1?s?1.54 The diffusivities of electrons and ions were computed from Einstein's relation, Dk ? kBTklk/qk, where kB is the Boltzmann's constant and Tk is the temperature of the corresponding species.53,58 The electron

temperature was calculated from the electron mean energy. The

ion temperature was taken as a constant with the value equal to

background gas temperature which is 300 K. In the fluid model,

this assumption is usually included, which is reasonable in most areas of the discharge.26,46,59 If the cathode sputtering is

included, for more accurate modeling the ion temperature in the

cathode fall layer needs to be calculated with considering the gas heating as well as the effect of the high electric field.60,61 In

our cases, the gas heating and cathode sputtering were neglected

since the current densities were relatively low (less than 1.5 mA/ cm2).28 As is aforementioned, with the fluid model the treatment

of the sheath in the cathode fall region might be less accurate

due to the high electric fields. Nevertheless, since the axial distri-

butions of the global discharge properties (including the electron

number density distribution) were our main focus, the present

model can still successfully predict the transition processes of

the discharges' overlapping phenomenon. For the external circuit model, a dc voltage U0 is applied

through a series ballast resistor Rb on the two parallel anodes while the cathode in the middle is grounded. Since the gas pressure effect is our main focus, the applied voltage U0 ? 1000 V and ballast resistance Rb ? 100 kX are used for all the simulated cases. The zero gradient conditions were used

at the far sides (A-B and O-C) for electrons, ions, and meta-

stable species. At the electrode surfaces (B-D, E-F, and

G-C) and the dielectric layer surfaces (D-E and F-G), the

ions and the metastable species were quenched to neutral state due the surface reactions Ar? ! Ar, Ar2? ! 2Ar and Ar* ! Ar. Assuming there is no reflection, the electron flux at the electrodes is given by Ce ? ne?vth/2--c?Ci, where c is the secondary electron emission coefficient and vth is the electron thermal velocity. The secondary electron emission coefficient c is assumed at 0.1 for cathode and 0 for anode.62 As for the electric potential u, u ? 0 at the cathode and is obtained by u ? U0--I?Rb at the anode, where I is the total discharge current.

Phys. Plasmas 24, 103514 (2017)

III. RESULTS AND DISCUSSION

In the model, only gas pressure was changed correspondently in all cases since the main focus was the pressure effect. Simulations were carried out with pressure range from 100 Pa to 5 kPa. In all cases, the results show discharge properties at the steady state. Figure 2 shows the gap voltage (electrical potential difference between the anode and the cathode) and the average cathode current density against the gas pressure. It can be seen that the relationship between gap voltage and gas pressure is "U" shaped and looks like a Paschen's curve. For the operating point a (gas pressure at 100 Pa), the gap voltage is 192 V. As the pressure increases, the gap voltage drops and has a minimum of 120 V at 1 kPa. The gap voltage increases with further increase in the gas pressure and is about 146 V at 4 kPa. The gap voltage is in the range of 100 V to 200 V, which is typical for hollow cathode glow discharge in argon. Since the total cathode surface area (%6.28 cm2) is fixed, the average cathode current density Jav is estimated at 1.28 mA/cm2 to 1.4 mA/cm2. This discharge region is found close to Donko's results, of which the calculations were carried out with two cathodes and two anodes facing each other in a rectangular configuration and the corresponding current density operating at moderate ($1 mA/cm2) for the hollow cathode glow discharges.28

For a given discharge gap, once gas pressure, gas composition and the applied external circuit are fixed, the gap voltage and the discharge current will be automatically generated. As is mentioned before, in our cases only the gas pressure is changed while other parameters, including the applied voltage U0 and the ballast resistance Rb, are kept unchanged. In this situation, the discharges with different pressures will stay at different operating points, of which the gap voltage and the discharge current at the steady state will be adjusted correspondingly. On the other hand, due to the parameters U0 and Rb are fixed, the gap voltage Ugap and the discharge current I vary dependently according to Ugap ? U0--I?Rb at different pressures. This results in a negative slope straight line if the voltage-current curve is plotted. Therefore, the detailed transition processes of the gas discharge in the hollow cathode cannot be identified by the voltage-current curve but the distributions of micro parameters. In order to observe the complete pressure effect on transition properties in the given hollow cathode gas gap, the micro parameter characteristics (including the electron

FIG. 2. The gap voltage and the average cathode current density against the gas pressure.

103514-4 Fu, Verboncoeur, and Christlieb

Phys. Plasmas 24, 103514 (2017)

density distributions, the ion density distributions, the electric potential distributions, as well as the electric field distributions) of different operating points, (a) at 100 Pa, (b) at 1 kPa, and (c) at 4 kPa, are presented in the following.

Figure 3 shows the contour plots of the electron density distributions in the five-layer hollow cavity for the working points (a)?(c), in Fig. 2, with gas pressure at 100 Pa, 1 kPa, and 4 kPa, respectively. It can be clearly seen that the two discharges from the top and bottom of the hollow cathode behave differently at different gas pressures. In Fig. 3(a), with the gas pressure at 100 Pa, the electron density is generally in the order of 1016 m?3 and the two peak density positions stay away from each other, which indicate that the discharges are two relatively independent hollow cathode discharges. For the gas pressure at 1 kPa, as shown in Fig. 3(b), only one peak of electron density appears at the center position of the gas gap. The electron density profile has a maximum density in the order of 1017 m?3, which is more than two times larger than that in Fig. 3(a). It implies that the two discharges overlap with each other at 1 kPa since the discharge inside the cavity turns out to be an integrated shape. After further increase in the gas pressure up to 4 kPa, as shown in Fig. 3(c), the two peaks of electron density appear again, similar to that in Fig. 3(a). The electron density decreases while the distribution has an extended decay in the axial direction. It tells that the discharges at 4 kPa develop to two separate discharges with lower electron density (in order of 1016 m?3) compared to discharge at 1 kPa. Therefore, the pressure effect on the evolution of electron density can be clearly observed by the monotonous control of the gas pressure.

To show a clear evolution of all charged species, the axial distributions of both electron and ion densities are presented in Fig. 4. As we mentioned in Sec. II, the molecular ions and atomic ions are both considered in the simulations. Since the plasma is quasineutral in most of the region along the axial direction, the density profiles of electrons and dominant ions are presented correspondingly for each pressure case. It can be seen that at 100 Pa, the atom ions (Ar?) and the electron distribution are almost the same in the linear plot, which indicates that atom ions are the dominant ions in this case. The obtained molecular ion density is in the order of 1014 m?3 which is less important. At the pressure of 1 kPa, the atom ion

FIG. 3. Two dimensional distributions of electron density for the discharges at different pressures.

FIG. 4. The axial distribution of charged particle densities (electrons, atom ions, and molecular ions) at different gas pressures.

density is found to be lower than the electron density as is shown in Fig. 4. In the central position, the maximum electron density and the atom ion density are 1.75 ? 1017 m?3 and 1.17 ? 1017 m?3, respectively. The maximum of the obtained molecular ion density is 5.88 ? 1016 m?3, which is nearly one order of magnitude lower than that of atom ions in the center. In spite of this, the molecular ions constitute a significant part of ions at 1 kPa. For the gas pressure at 4 kPa, the roles of the atom ions and molecular ions are reversed. The dominant ions turn out to be the molecular ions, whose density is very close to the electron density. As is shown in Fig. 4, the profiles of the electrons and molecular ions are almost the same at 4 kPa. The peak value of the electrons and molecular ions are 4.24 ? 1016 m?3 and 4.04 ? 1016 m?3, respectively. The maximum density of the atom ions is found to be 2.04 ? 1015 m?3 at the corresponding electron density peak position. At 4 kPa, the molecular ions become the dominant ions in the plasma, which is similar to the previous results of argon plasma in high-pressure regimes.62 In the high-pressure regime, the three body collisions for the molecular ion conversion become more important, which leads to the destruction channel of the atom ions and the production channel of the molecular ions.

As it was reported in the previous studies,21,22 in the tandem hollow cathode discharges, the excimer molecules do not significantly reabsorb their own radiations, so the irradiance generated by n discharge plasma should be approximately n times that of a single discharge. This characteristic pushes forward the tandem hollow cathode discharge used to increase the irradiance of excimer emission in a hollow cathode discharge. In this work, based on the aforementioned results, it was confirmed that at a certain range of gas pressure, two relatively independent distributions of charged particles in a specific hollow cathode transit into an integrated distribution. Lower or higher than this pressure regime, the discharges will turn out to be two relatively independent discharges again. Besides the peak position shiftiness, the pressure effect on the integrated tandem discharge results in an enhancement of the plasma density is also observed. As is shown in Fig. 4, the peak electron density at 1 kPa is much higher than that at 100 Pa, with a density ratio %4.13, which manifest the great enhancement of the plasma density.

Figure 5 shows the axial distribution of the electric potential at different gas pressures. The electric potential

103514-5 Fu, Verboncoeur, and Christlieb

Phys. Plasmas 24, 103514 (2017)

FIG. 5. The axial distribution of electric potential for gas pressure at 100 Pa, 1 kPa, and 4 kPa.

curve shifts down as the pressure increases from 100 Pa to 1 kPa, but shifts up when the gas pressure is further increased. The electrical potential in the central position (z ? 2.5 cm) at 100 Pa, 1 kPa, and 4 kPa is 204, 120, and 132 V, respectively. The fluctuation of the electric potential in the axial direction is minor. It can be seen that the electric potential curve is almost flat in the middle for the pressure at 100 Pa and 1 kPa, while a dimple appeared in the middle of the potential distribution for gas pressure at 4 kPa.

Figure 6 shows the axial electric field distribution at different pressures. It is observed that the electric field at the boundary decreases as the pressure increases. For pressures at 100 Pa and 1 kPa, the electric filed is approximately zero in most of the region except in the boundary regime. For the pressure at 4 kPa, the electric field reversals (the field changes from negative to positive) are clearly observed. This phenomenon is in consistent with the existence of the potential dimple at 4 kPa at z ? 2.5 cm in Fig. 5. The presence of electric field reversals can be explained with the conservation of the discharge current, which is determined by the ionization rate by the high energy electrons and ion transport in the sheath region. The electric field reversal was previously confirmed in both low-pressure and atmospheric glow discharges.63?66 The variations of the electric field due to the different pressure effect are found to be consistent with the electric potential distributions.

FIG. 6. The axial distribution of electric field for gas pressure at 100 Pa, 1 kPa, and 4 kPa.

IV. CONCLUSIONS

The effect of gas pressure on the tandem hollow cathode

discharge was studied by the two-dimensional fluid simula-

tions. With the changes of pressure, the discharges in the tan-

dem hollow cathode can either operate as the two relatively

independent hollow cathode discharges or as one mixed dis-

charge. In the five-layer tandem hollow cathode gap, by

increasing the gas pressure, the sustaining gap voltage

decreases at first and then increases, resulting in a Paschenlike curve of Ugap? f(p). At a certain range of gas pressure, the two independent hollow cathode glows coalesce and the

plasma densities rise greatly. The results indicate that the gas

pressure effect will lead to the transitions between two dis-

charge modes: two single HCDs and one mixed HCD. The

parallel hollow cathode discharges can be manipulated into

one overlapped tandem hollow cathode discharge by the

monotonous control of the gas pressure.

ACKNOWLEDGMENTS

The work was supported by the Air Force Office of

Scientific Research and a Department of Energy Plasma

Science Center Grant No. DE-SC0001939.

1R. M. Sankaran, K. P. Giapis, M. Moselhy, and K. H. Schoenbach, Appl. Phys. Lett. 83, 4728 (2003). 2K. H. Becker, K. H. Schoenbach, and J. G. Eden, J. Phys. D: Appl. Phys. 39, R55 (2006). 3J. K. Evju, P. B. Howell, L. E. Locascio, M. J. Tarlov, and J. J. Hickman, Appl. Phys. Lett. 84, 1668 (2004). 4B. Vancil, J. Lorr, V. Schmidt, W. Ohlinger, and J. Polk, IEEE Trans. Electron Devices 63, 4113 (2016). 5A. P. Papadakis, S. Rossides, and A. C. Metaxas, Open Appl. Phys. J. 4, 45 (2011). 6C. Lazzaroni and P. Chabert, J. Phys. D: Appl. Phys. 44, 445202 (2011). 7A. Gunterschulze, Z. Tech. Phys. 11, 49 (1930). 8W. Krug, Arch. Elektrotech. 30, 157 (1936). 9P. F. Little and A. von Engel, Proc. R. Soc. A 224, 209 (1954). 10D. J. Sturges and H. J. Oskam, J. Appl. Phys. 35, 2887 (1964). 11C. M. Ferreira and J. L. Delcroix, J. Appl. Phys. 49, 2380 (1978). 12L. M. Lidsky, S. D. Rothleder, D. J. Rose, S. Yoshikawa, C. Michelson, and R. J. Mackin, Jr., J. Appl. Phys. 33, 2490 (1962). 13Y. Fu, J. P. Verboncoeur, A. J. Christlieb, and X. Wang, Phys. Plasmas 24, 083516 (2017). 14K. H. Schoenbach, A. E. Habachi, W. Shi, and M. Ciocca, Plasma Sources Sci. Technol. 6, 468 (1997). 15K. H. Schoenbach and K. Becker, Eur. Phys. J. D 70, 29 (2016). 16K. H. Schoenbach, A. E. Habachi, M. M. Moselhy, W. Shi, and R. H. Stark, Phys. Plasmas 7, 2186 (2000). 17H. Helm, Z. Naturforsch. A 27, 1812 (1972). 18K. H. Schoenbach, R. Verhappen, T. Tessnow, F. E. Peterkin, and W. W. Byszewski, Appl. Phys. Lett. 68, 13 (1996). 19E. E. Kunhardt, IEEE Trans. Plasmas Sci. 28, 189 (2000). 20A. El-Habachi, W. Shi, M. Moselhy, R. H. Stark, and K. H. Schoenbach, J. Appl. Phys. 88, 3220 (2000). 21B.-J. Lee, H. Rahaman, S. H. Nam, M. Iberler, C. Teske, J. Jacoby, and K. Frank, Appl. Phys. Express 5, 056001 (2012). 22B.-J. Lee, H. Rahaman, I. Petzenhauser, K. Frank, and K. Giapis, Appl. Phys. Lett. 90, 241502 (2007). 23F. Paschen, Ann Phys. 355, 901 (1916). 24P. J. Slevin and W. W. Harrison, Appl. Spectrosc. Rev. 10, 201 (1975). 25R. Mavrodineanu, J. Res. Natl. Bur. Stand. 89, 143 (1984). 26J. P. Boeuf and L. C. Pitchford, IEEE Trans. Plasma Sci. 19, 286 (1991). 27V. I. Kolobov and L. D. Tsendin, Plasma Sources Sci. Technol. 4, 551 (1995). 28Z. Donko, Phys. Rev. E 57, 7126 (1998). 29Z. Donko, J. Phys., D: Appl. Phys. 32, 1657 (1999). 30N. Baguer, A. Bogaerts, and R. Gijbels, Spectrochim. Acta, Part B 57, 311 (2002).

103514-6 Fu, Verboncoeur, and Christlieb

31N. Baguer, A. Bogaerts, Z. Donko, R. Gijbels, and N. Sadeghi, J. Appl.

Phys. 97, 123305 (2005). 32J. P. Boeuf, L. C. Pitchford, and K. H. Schoenbach, Appl. Phys. Lett. 86,

071501 (2005). 33X. X. Jiang, F. He, Q. Chen, T. Ge, and J. T. Ouyang, Phys. Plasmas 21,

033508 (2014). 34H. J. Kim and H. J. Lee, Plasma Sources Sci. Technol. 25, 035006 (2016). 35L. Zhang, G. Zhao, J. Wang, and Q. Han, Phys. Plasmas 23, 023508

(2016). 36D. Levko, Y. E. Krasik, V. Vekselman, and I. Haber, Phys. Plasmas 20,

083512 (2013). 37J. Zhang, X. Liu, and Q. Zhang, Phys. Plasmas 24, 053515 (2017). 38C. Lazzaroni and P. Chabert, J. Phys. D: Appl. Phys. 44, 445202 (2011). 39C. Lazzaroni and P. Chabert, J. Appl. Phys. 111, 053305 (2012). 40G. J. M. Hagelaar, D. B. Mihailova, and J. van Dijk, J. Phys. D: Appl.

Phys. 43, 465204 (2010). 41I. G. Mikkelides, Phys. Plasmas 16, 013501 (2009). 42J. Jia, C. Yuan, A. A. Kudryavtsev, S. I. Eliseev, G. V. Kirsanov, V. S.

Bekasov, R. Gao, and Z. Zhou, IEEE Trans. Plasma Sci. 44, 2973 (2016). 43G. Sary, L. Garrigues, and J. P. Boeuf, Plasma Sources Sci. Technol. 26,

055007 (2017). 44S. He, Z. Zhang, J. T. Ouyang, and Q. Li, J. Phys. D: Appl. Phys. 49,

365201 (2016). 45P. S. Kothnur and L. L. Raja, Contrib. Plasma Phys. 47, 9 (2007). 46T. Deconinck and L. L. Raja, Plasma Processes Polym. 6, 335 (2009). 47S. He, J. Ha, S. Liu, and J. Ouyang, Phys. Plasma 20, 123504 (2013). 48N. Baguer, A. Bogaeters, and R. Gijbels, J. Appl. Phys. 93, 47 (2003). 49Y. Fu, H. Luo, X. Zou, and X. Wang, Plasma Sources Sci. Technol. 23,

065035 (2014).

Phys. Plasmas 24, 103514 (2017)

50Y. Fu, H. Luo, X. Zou, and X. Wang, IEEE Trans. Plasma Sci. 42, 1544

(2014). 51H. A. Hyman, Phys. Rev. A 20, 855 (1979). 52C. Yamabe, S. J. Buckman, and A. V. Phelps, Phys. Rev. A 27, 1345

(1983). 53G. J. M. Hagelaar and L. C. Pitchford, Plasma Sources Sci. Technol. 14,

722 (2005). 54N. A. Dyatko, Y. Z. Ionikh, I. V. Kochetov, D. L. Marinov, A. V.

Meshchanov, A. P. Napartovich, F. B. Petrov, and S. A. Starostin, J. Phys.

D: Appl. Phys. 41, 055204 (2008). 55A. Fiala, L. C. Pitchford, and J. P. Boeuf, Phys. Rev. E 49, 5607 (1994). 56A. Bogaerts and R. Gijbels, Phys. Rev. A 52, 3743 (1995). 57F. Liu, Y. He, and L. Dong, Phys. Plasmas 21, 123503 (2014). 58Y. P. Raizer, Gas Discharge Physics (Springer, Berlin, 1991). 59H. C. Kim, M. S. Hur, S. S. Yang, S. W. Shin, and J. K. Lee, J. Appl.

Phys. 91, 9513 (2002). 60J. A. S. Barata and C. A. N. Conde, Instrum. Methods Phys. Res. A 619,

21 (2010). 61J. V. Jovanovic, S. B. Vrhovac, and Z. Lj, Petrovic, Eur. Phys. J. D 21,

335 (2002). 62T. Farouk, B. Farouk1, D. Staack, A. Gutsol, and A. Fridman, Plasma

Sources Sci. Technol. 15, 676 (2006). 63J. A. Bittencourt, Fundamentals of Plasma Physics (Pergamon, Oxford,

1986). 64R. A. Gottscho, A. Mitchell, G. R. Scheller, Y. Y. Chan, and D. B. Graves,

Phys. Rev. A 40, 6407 (1989). 65J. P. Boeuf and L. C. Pitchford, J. Phys. D: Appl. Phys. 28, 2083 (1995). 66Q. Wang, D. J. Economou, and V. M. Donnelly, J. Appl. Phys. 100,

023301 (2006).

 ................
................

In order to avoid copyright disputes, this page is only a partial summary.

Google Online Preview   Download