A Highly Cost‐Efficient Large‐Scale Uniform Laminar Plasma Jet Array Enhanced by V–I Characteristic Modulation in a Non‐Self‐Sustained Atmospheric Discharge

Abstract Developing cost‐efficient large‐scale uniform plasma jets represents a significant challenge for high performance in material processing and plasma medicine. Here, a V–I characteristic modulation approach is proposed to reduce the discharge power and increase the plasma scale and chemical activity in non‐self‐sustained atmospheric direct‐current discharges. The electric field in discharge space is optimized to fundamentally empower simultaneously initiating all discharge cells far below Townsend breakdown potential and stably sustaining each plasma jet at low voltage. These strategies create a crucial step to fabricating a flexible and compact low‐power large‐scale uniform laminar plasma jet array (LPJA) with high activity in cheap argon. The mechanisms behind the discharge enhancement are revealed by combining V–I characteristic examination and a modulation model. Compared with conventional arrays, this LPJA possesses the widest size (90 mm) and raises its uniformity from 30% to 97%. Comparing different discharge modes shows that the LPJA scale is surprisingly increased nearly by 4 times with the discharge power reduced from 7.4 to 4.8 W. The methodology provides a highly cost‐efficient roadmap to break through the bottleneck of restricting low‐power discharge, large‐gap discharge, large‐scale discharge, parallel‐multi‐electrode discharge, and uniform discharge together. This advance will meet the urgent need for various plasma applications.


Townsend's Breakdown Criterion and Paschen's Curve
When a certain voltage V is applied on a pair of parallel electrodes in a direct-current (DC) discharge cell, an approximately homogeneous electric field can be generated in the gas gap, i.e., comes into play and produces more ionization along the path from the cathode to the anode. The steady current density follows the form [1]   2 where i  is the Townsend's second ionization coefficient for the cathode. As long as the denominator of Equation S1 is positive, the discharge is in a non-self-sustained state. When the denominator is negative, this equation becomes meaningless. The transition condition is that the denominator equals zero, based on which the Townsend's breakdown criterion is obtained: [2] [ exp( The Townsend's first ionization coefficient  for inert gases is related to the applied voltage V , electrode spacing d , and gas pressure p by an empirical formula [2] 12 exp ( ) where C and D are constants based on the gas composition. [2] Substituting Equation S3 into the breakdown criterion Equation S2, we obtain the breakdown potential It follows from Equation S4 that the breakdown potential b V is a function of the product of gas pressure and electrode spacing, which produces the traditional Paschen's curve, as plotted in Figure   S1a. Here, the constants C and D , respectively, take the values of - for argon. [2] i  is assumed to be 0.01. [2] Figure S1a shows that in the range of relatively large pd on the right-hand branch of the curve, the breakdown potential increases almost proportionally to pd and approaches the value as high as 10190 V at 760 Torr 1.5 cm  .

Non-self-sustained DC Discharge
In a non-self-sustained DC discharge aforementioned, the applied voltage is considerably less than the breakdown potential and the discharge cannot be ignited in common conditions. To ignite this discharge and sustain it stably, an external ionizer is required to provide the preionization that 3 balances the electron losses. When the external ionizer is turned off, this discharge decays rapidly.
This discharge is also named as externally sustained discharge in view of its discharge feature. [ where  is the preionization rate of external ionizer,  is the recombination coefficient, j is the current density, e is the electron charge, E is the electric field across the gas gap, e  is the electron mobility, and e v denotes the electron velocity. The electron density e n equals the ion density i n and these charged particles are lost mainly via recombination. For the non-self-sustained discharge mode, e e v n   . The electron density is obtained from Equation S5 as a function of time after turning on the external ionizer: Recently obtained experimental results show that the electron density is usually on the order of 14 -3 10 cm in atmospheric-pressure argon DC discharges sustained by an external ionizer. [4][5][6]  . The discharge can be stably sustained, provided that the preionization produced by the external ionizer persists over a long time, i.e.
pr c t t . When the applied voltage between the electrodes is given, the specific energy deposited in the discharge follows the expression Here, the electric field E is assumed to be Vd , because the cathode drop c V under the condition of non-self-sustained DC discharge is much smaller than V and the width of layer c l d . [7] To sustain a discharge at a certain current density, the electric field E should obey the following equation (8) Figure S1c is a three-dimensional graph, which depicts the electric field as a function of the preionization rate  and current density j in ranges of interest. For a given current density, the electric field decreases under conditions of strong preionization. The field, located on the red curved surface, even drops below kV / cm 0. 5 , which is much less than the breakdown field in the case of no preionization. [2] Point A represents a typical operation mode that is located on the red curved surface.
5 Figure S1. Electrical characteristics of DC discharge in argon. a) Breakdown potential in argon over a wide range of pd values (Paschen's curve). b) Temporal evolution of electron density in a non-self-sustained DC discharge. c) Three-dimension plot of electric field as a function of the preionization rate  and current density j . d) Variation of the sustaining voltage with the discharge cross-section.

V-I Characteristic Modulation Model
We assume that the DC discharge cell consists of a cathode, an anode, and dielectric walls. The discharge cell is ignited and sustained by a DC power supply. Figure S2a shows the equivalent circuit for the DC discharge. The cathode is grounded and the anode is connected to the high voltage (HV) terminal of the power supply via a ballast resistor b R that is used to limit the discharge current and 6 prevent the discharge from transition to an arc mode.
where a V is the output voltage of the power supply, V is the sustaining voltage applied between the two electrodes, and A is the discharge cross-section area and approximately the same value as the cross sectional area of the electrodes. Here, e n means the average value of electron density in the gas gap. It is generally accepted that with increasing the output voltage the discharge will be transformed from a Townsend discharge to a normal glow one via a subnormal region. [8] In the subnormal glow mode, the size of cathode spot is on the order of several micrometers and a thin discharge channel bridges the two electrodes. [2] Since the loss of charged particles in the lateral direction is harmful for multiplication due to free diffusion of electrons to the side walls, the average electron density is relatively low. To increase the average electron density for high plasma chemical activity in practical applications, the discharge is usually allowed to work in a normal or abnormal mode by further raising the output voltage. But this manipulation brings about another harmful factor, i.e., generation of considerable Joule heat both in the discharge cell and in the ballast resistor because of the increase in the discharge current. The most desirable way is realization of a normal or abnormal glow discharge at a smaller discharge current.
7 Figure S2. Schematic diagram of equivalent circuit models. a) Model for a single DC discharge cell.

b) Model for two DC discharge cells arranged in parallel.
To explore this method, we substitute the equation It follows from Equation S6 that in the non-self-sustained DC discharge, the electron density, as well as its average value e n , is largely determined by the preionization rate  and changed little in the subnormal transition region. [7] Thus, when the output voltage  It should be noted that the reduction of sustaining voltage with an approximate constant electron density means that loss of charged particles in the lateral direction slows down and the discharge is likely to transform from the subnormal mode to a normal one. The cross-section increase can be fulfilled by enlarging the cross-section of the discharge cell itself. Additionally, arranging several discharge cells in parallel is another effective way to increase the discharge cross-section. Two DC discharge cells arranged in parallel is the most simple case. Figure S2b shows its equivalent circuit.
The total discharge current and sustaining voltage are expressed as follows where A and A , respectively, represent the discharge cross-sections of the two discharge cells and -3 2 Figure S1d, it follows that when the discharge cross-section increases from through the parallel connection, the sustaining voltage in the two discharge cells will be abruptly reduced from S V  3 680 V to N V  2 478 V. The operating point shifts from P 0 to P 1 . Here, we assume that the discharge at a higher sustaining voltage S V 3 is a subnormal one, which occurs at a smaller discharge current S I 3 . It is generally recognized that the discharge is likely to extinguish due to the abrupt reduction of sustaining voltage in a self-sustained discharge. But in the non-selfsustained DC discharge, discharge sustainment is ensured by seed charges from the external ionizer.
It should be noted that the reduction of sustaining voltage in the discharge with an approximate constant electron density means that loss of charged particles in the lateral direction slows down and the discharge is likely to transform from the subnormal mode to a normal one. Referring to the , we find that the total discharge current I increases in the parallel circuit.
But, the discharge current flowing through each discharge cell does not increase but decreases to 9 some extent, which is ascribed to the decreasing electric field between the electrodes as a result of  for each discharge cell is operated in the normal or quasi-normal glow mode, the luminous current spot on the cathode surface is still limited on the order of several micrometers. [2] With increasing the output voltage a V , the electron density and current density remain constant in the discharge channel, but the luminous current spot on the cathode surface expands outwards and the discharge channel occupies more portions of the gas gap. [2] After the discharge covers the entire cathode surface, the discharge transforms to the abnormal mode and any further increase of the output voltage increases the current density in compared with the normal value. [2] Either the expansion of discharge channel in the normal mode or the increase of current density in the abnormal regime inevitably increases the discharge current in the gas gap.
It is concluded that the V-I characteristic modulation model proposed above includes two key steps, i.e., 1) arranging non-self-sustained DC discharge cells in parallel with the output voltage unvaried, and 2) raising the output voltage until the discharge current increases to the initial value.
This model succeeds in realizing a normal or abnormal glow discharge with a higher average electron density at a smaller discharge current, which creates a new road map for the enhanced gas discharge basic theory.  Figure S3c. It is likely that a diffuse plasma is achieved in the DBD. But the waveforms of applied voltage () ut and discharge current () it (the total current subtracting the displacement current), as shown in Figure S3d, indicate that the DBD operates in a filamentary mode, because the width of current pulses is about 360 ns and much less than that (several to tens of μs) observed in the glow-like discharge. [9,10] From Figure S3d, it is also found that only one current pulse occurs each half cycle with its amplitude ranging from 10 to 30 mA, when the peak voltage peak u is set at 2.5 kV. The electric power DBD p dissipated in the DBD is determined by Manley's theory: [11] 4 ( )

11
Here, dis u is the average discharge voltage across the gas gap, while where the electron mobility e  and ion mobility i  are assumed to be and that the contribution of these charged particles to the downstream DC discharge is negligible. Figure S3e shows the optical emission spectra (OES) from the DBD. Argon emission lines from the 4p→4s transitions are dominantly presented in the visible and infrared region between 690 and 950 nm due to the argon feeding gas. In addition, strong OH emission line at 309 nm is also observed because of the gas impurity vapor. The OES indicates that sufficient excited argon atoms exist in the discharge. It has been reported that the lifetime of argon metastables can reach up to several seconds. [2] Since tens of milliseconds is required for the gas to flow from the DBD region to the DC discharge space, many argon metastables will arrive at the downstream DC discharge space and ionizations due to collisions between argon metastables are able to efficiently create new charged 13 particles there by the Penning effect [ These charged particles, served as seed charges, accelerate the formation of electron avalanche and enhance the ionization efficiency of the DC discharge. Additionally, the secondary electron emission from a cold cathode is caused by positive ions, excited atoms, electrons, and photons.
Among them, the excited atoms coming from the DBD are very efficient in the DC discharge. [2] Due to the enhancement of ionization efficiency, the DC discharge can be initiated in a large gas gap (15 mm) far below the Townsend breakdown potential. Thus, we conclude that the Penning ionization of argon metastables from the DBD plays a crucial role in improvement of the downstream DC discharge.

Enhancement of the Plasma Chemical Activity
Since the LPJA is composed of three independent discharge units, as illustrated in Figure 2c in the main text, each of the plasma jets in the discharge unit shows a similar or same optical emission characteristic to that in the array. Thus, Case 2 shown in Figure 6b in the main text was selected as alternative to make a comparative OES examination in contrast to Case 5 shown in Figure 6i in the main text by using a moderate-resolution spectrometer. It should be noted that the two-arrayed plasma jet shown in Figure 6i is composed of two independent discharge cells and its V-I characteristic (Not shown here) is similar to that of Case 3 shown in Figure 6g in the main text. The coordinate origin is set at the transverse center of the two-arrayed plasma jet and just above the outlet of the discharge chamber in the two cases. Figure S4a shows the OES detected in Case 2 and Case 5 at a specific point with the relative position x = 7.5 mm and y = 1 mm in accordance with the axes labeled in Figure 2a in the main text. For both the cases, various argon emission lines are dominantly presented due to the argon feeding gas in the visible and infrared region between 690 and 950 nm.
Additionally, the OES from the As we know, the energy carried by the excited argon atoms (11.5-13.5 eV) is slightly higher than the energy level of 3 2 μ N (C Π ) (~ 11.1 eV). [14,15] Energy is easily transferred from the excited argon atoms to the ground state nitrogen molecules in the ambient air to generate abundant excited state molecules . [16] Thus, the OES originated from the excited OH and 2 N are clearly presented in the plasma jets, even if the electron-impact excitation is not fully ensured. It should be noted that the OH radical has a strong oxidative effect on the cell outer structure and is identified as a major contributor in the plasma inactivation. Comparing the spectra in the two cases shows that the spectral intensity of the plasma generated in the normal/abnormal glow discharge is approximately increased by two times compared to that in the subnormal glow discharge. This means that the concentration of reactive species in the plasma, as well as the plasma chemical activity, can also be enhanced by modulating the V-I characteristics of DC discharge.
The spatial distributions of OES from OH, 2 N , and Ar in the plasma produced in the two cases 15 were also examined at y = 1 along the x axis with the results shown in Figure S4b Since the central part of each plasma jet in Case 5 just extends out of the discharge chamber outlet, the spatial distributions of OES from reactive species have not been examined. Figure S4e, f show the spectral intensity varies along the y direction with x = ± 7.5 mm only for Case 2. It is found that a similar or same spatial emission profile is presented for the same reactive species at x = ± 7.5 mm. The spectral intensity of Ar first declines slowly near the outlet ( y < 1 mm ), then drops quickly with increasing the distance from the outlet (1 mm y < 3 mm  ), and finally tends to be zero when the length increases further than 3 mm. But for OH and 2 N , the emission intensities first rise, approach their maximum at y = 1 mm, then fall, and fade away at the length of 4 mm or greater. The spectral intensity of Ar prevails against others all along the length, with the OH spectral intensity remaining weakest throughout the region. Characterizing the spatial distributions of OES suggests that most of the reactive species assemble in the vicinity of the nozzle ( y 2 mm  ). The fast degradation of Ar spectral intensity along the length is mainly due to the high quenching rates by vapor, nitrogen molecules, and oxygen molecules from the ambient air (Reaction 1, Reaction 2, and Reaction 3: 10 -10 ). [15] The distinct spatial emission profiles of OH, 2 N , and Ar are attributed to the different generation and quenching mechanisms of their corresponding excited states, i.e., 2+ OH(A Σ ) , 3 2 μ N (C Π ) , and Ar(4p) / Ar(4s) in the plasma jets.
The light emitted from the plasma is originated from the energy transition of species from the excited state to the lower or ground one. For Case 1, after ejecting out of the outlet, the argon plasma jets interact with the ambient air. The interaction processes are closely associated with the dynamic behavior of flowing feeding gas, mixing characteristics of feeding gas and ambient air, and the different generation and quenching mechanisms of excited species in the plasma. [15,17] Due to the flat duck-mouth structure of the discharge chamber and the central single loop gas supply mode, the argon flow rate is not strictly uniformly distributed along the transverse direction, but with greater values in the center than at the edges, which is indirectly reflected by the spatial distribution of light intensity along the transverse direction at y = 0 mm shown in Figure 4b in the main text. Thus, more excited argon atoms are gathered in the central region of the LPJA, where the interaction between the argon plasma with the ambient air is more intense through Reactions 1, 2, and 3. Since the spectral intensity of Ar remains dominant all along the length, as shown in Figure S4e, f, more intense reactions occurring in the center give a chance to degrade the light intensity in a greater degree there. This is the possible reason for the transverse profile evolution of light intensity with the length depicted in Figure 4b.

Nonequilibrium Characteristics of the LPJA
Nonequilibrium characteristics of the plasma were verified for Case 1 shown in Figure 4a  The coordinate origin is set at the transverse center of the LPJA and just above the outlet of the discharge chamber. Based on the emission spectrum recorded by a high-resolution spectrometer at the point with x = 7.5 mm and y = 1 mm, the rotational temperature and vibrational temperature of the LPJA were obtained by analyzing the OES of OH and 2 N second positive system, respectively. [18][19][20][21] Figure S5a shows the best-fitting synthetic spectrum to the experimental spectrum for the 2 + 2 OH(A Σ X Π,Δν = 0)  band transition from 306 to 312 nm. The rotational temperature r ot T is determined to be about 640 K. As for the vibrational temperature, this spectrum fitting method was applied to the spectral profile of the nitrogen second positive system T is estimated to be about 2630 K and much higher than the rotational one. Comparison of the rotational and vibrational temperatures indicates that the LPJA is under nonequilibrium condition, which contributes much to the enhancement of plasma chemistry.
As mentioned above, the energy transfer from excited argon atoms plays an important role in production of the excited 2+ OH(A Σ ) . It is unsuitable to determine the gas temperature through the estimation of the rotational temperature of OH due to its overpopulation at high rotational states. [15] Thus, a fiber thermocouple was used to measure the gas temperature of the LPJA at y = 1 mm along the x direction. Figure S5c shows the transverse spatial distribution of the gas temperature. It is found that the gas temperature is periodically distributed in space due to the periodic electrode structure. Different gas temperatures are observed near the electrodes, with the value approaching 120 ℃ at the cathode but only about 88 ℃ at the anode. The lowest gas temperature is approximately 70 °C in the central part of each plasma jet. Additionally, the gas temperature was also examined along the length at x = 7.5 mm, with the result shown in Figure S5d. It is found that the gas temperature first declines slowly and remains about 70 °C near the nozzle ( mm  2 z ), where relatively more reactive species are accumulated. Then, the gas temperature is decreased with a greater rate with increasing the distance from the outlet. Finally, it falls to 63 °C at the length of 4 mm, where the excited OH, 2 N , and Ar nearly disappear. Spatial examination of the LPJA gas temperature shows that this temperature is far less than the rotational temperature, but close to the room temperature, which is beneficial to treating samples that are susceptible to high temperatures.