Investigation of the confinement of high energy non-neutral proton beam in a bent magnetic mirror

1.   Introduction

Atmospheric pressure plasma jets (APPJs) have been extensively studied for their applications in widely ranged areas from material processing to disinfection [1–4]. Due to the feature of producing plasmas with abundant active species and keeping a low temperature environment at the same time, APPJs show remarkable advantages in surface treatments, particularly for biomedicine. For further applications, such as large-scale material processing, bio-medical treatment and bacterial disinfection, APPJs with large treatment areas should be developed. Compared with a single APPJ with a long radius, an array of the same size consisting of packed APPJ units can achieve much better stability and flexibility [5, 6]. Nevertheless, there are still certain challenges in reaching wanted uniformity for APPJ arrays.

The first challenge is the discharge synchronism and consistency of the APPJ arrays. It is found that the units do not discharge at the same time despite decent symmetry for the whole array. Due to the complex jet–jet interaction, the behavior of these units differs from each other. Some units do not even discharge at all. Nevertheless, this problem can be solved by applying ballasts and/or injecting extra O₂ to the working gas [7–10]. After the consistency is promised, a new challenge is then raised in improving the uniformity of the plasma and active species. The spatial plasma distribution downstream is generally in mottling patterns [11], while the uniformity of the plasma directly influences the plasma dose absorbed by the target (cells and materials, etc). In many applications, the operation results vary with the plasma doses [12]. For example, the outcomes can be varied from bacteria killing to mutation breeding or wound healing according to the plasma dose [12–14]. Furthermore, a uniform plasma treatment can provide an accurate plasma dose for further studying the relations between the plasma dose and the biological effect. Thus, the uniformity improvement not only meets various needs of applications, but also promotes the development of plasma dosimetry. The studies for improving the plasma uniformity can be divided into two different categories: electric field control, and flow field control. For the electric field control, applied voltages [11], electric field direction [15] voltage waveform [16], and electrode positions [17] are adjusted to advance the uniformity of the plasma. Results show that the adjacent jets can merge together by increasing the applied voltages [14, 18]. In the flow field control, attempts of closely packing APPJs are successful in both experiments and simulations to mitigate the mottling patterns downstream [19, 20]. The homogeneity of the plasma is also upgraded by applying He inflow between adjacent jets [21].

In applications, the plasma flowing out of a jet array finally reaches the downstream substrates where fluid and electrical properties affect the discharge in turn [22]. For a flow field, the existence of a downstream substrate can change the initial gas distribution. Thus, the uniformity of the working gas as well as the plasma may get better due to the crossing flow near the surface of the substrates [21, 23]. For an electric field, the dielectric constant of the substrate directly affects the electric potential as a boundary condition to determine the charge density distribution [24, 25]. Besides, real target surfaces to be processed often have a certain roughness ranging from 10 μm of bacterial biofilms to 1 cm of complex three-dimensional (3D) structures [26]. In terms of applications, it is then a great challenge to determine the most suitable parameters facing various substrates and processed targets, since the simultaneous effect of multiple parameters on downstream plasma uniformity is very complex and has nonlinear characteristics. Thus, a convenient method for a full parameter space estimation by typical cases is needed. The artificial neutral network (ANN) method is appropriate in overcoming such a challenge. ANNs can model complex nonlinear multi-dimensional functions without specific assumptions, and the results have acceptable accuracy [27]. Building on those advantages, the ANN has been used in the study of atmospheric plasma in recent years [28–30].

Following up on previous research, in this work we quantitatively investigate the effects of substrates downstream and explore possible ways to improve the homogeneity of the plasma with flow and electric field coupling modulations. A brief description of the model applied is made in section 2. In section 3, a sloped substrate of grounded metal is placed downstream to study the effects of a non-horizontal substrate. Then, the effects of the individual control using flow or electric field, as well as the collaborative modulation using both flow and electric fields are investigated. Moreover, the ANN is also trained to predict the outcomes with various modulations. Finally, the summary and conclusion are given in section 4.

2.   Methods

2.1   The APPJ model

A multi-field coupling model developed from [18, 21] is used in this work for the APPJ arrays with a number of jet outlets. It can compute the spatial-temporal evolutions of the plasma and active species distributions with the electric field as well as the temperature distributions by solving equations of Navier–Stokes (NS), Poisson, continuity, and electron energy. Due to the great difference of computing time steps between the flow and electric fields, the NS and continuity equations of neutral species are solved to reach the steady state of the flow at first. The electric field is then computed with the steady flow field. Further, a voltage with a rising time of 5 ns is applied to the anode at t = 1 ns, and then lasts to the end of the simulation after it reaches the maximum. This peak value varies by cases corresponding to the different electric field controls. After the voltage is applied, the equations of Poisson, electron energy, as well as continuity of electrons, ions and excited species are solved.

The computed configuration of a typical three-tube APPJ array is shown in figure 1. Each tube consists of an anode with a radius of 0.2 mm and a glass tube (ε/ε₀ = 3) with outer and inner diameters of 2.6 mm and 1.8 mm, respectively. The distance between the anode top and the glass tube nozzle is 1.3 mm. The length of the glass tube shown in this figure is 2 mm. The separation between adjacent jets is fixed at 0.6 mm. Aiming to optimize the plasma distribution uniformity on the non-horizontal substrate, a grounded sloped metallic substrate with a 10° inclined angle is placed 10 mm from the bottom of the glass tube. The substrate with a 10° inclined angle was chosen as a typical three-dimensional surface example for bacterial disinfection application and was studied experimentally in the previous work [7]. The grid length for computing is the Debye length, a characteristic length of the plasma.

Figure  1.  Schematic of the three-tube APPJ array with a grounded metal downstream of 10° sloped.

DownLoad: Full-Size Img PowerPoint

To solve the equations, the initial and boundary conditions are applied. All the computing domains are filled with humid air (N₂: O₂: H₂O = 79.5:20:0.5) in atmospheric pressure and room temperature at first. The working gas is room temperature/atmospheric-pressure 97% He and 3% humid-air mixed gas with an average inflow speed of 15 m s⁻¹, while the detailed inflow speed varies with cases. There is a slight air inflow with a speed of 0.5 m s⁻¹ between the adjacent jets. The glass tubes, anodes, and the substrate downstream are solid boundaries for the flow field, with both sides being open boundaries.

The density distributions of reactive species, especially reactive oxygen species such as O and OH, are vital for practical applications. Therefore, based on the model with 10 species and nine reactions developed in [18, 21], an improvement is made herein to enrich the chemical reactions, where 28 species and 61 reactions [31–35] are applied, as shown in table 1.

Table  1.  Helium–air chemical reactions used in this study.

No.	Reaction	A	B	C	Energy (eV)	References
Helium chemistry
R1	$\mathrm{e}+\mathrm{He} \rightarrow \mathrm{e}+\mathrm{He}$	BOLSIG+			0
R2	$\mathrm{e}+\mathrm{He} \rightarrow \mathrm{e}+\mathrm{He}^*$	BOLSIG+			19.8
R3	$\mathrm{e}+\mathrm{He} \rightarrow 2 \mathrm{e}+\mathrm{He}^{+}$	BOLSIG+			24.6
R4	$\mathrm{e}+\mathrm{He}^* \rightarrow 2 \mathrm{e}+\mathrm{He}^{+}$	4.661E−16	0.6	4.78	4.78	[31, 32]
R5	$\mathrm{e}+\mathrm{He}_2^* \rightarrow 2 \mathrm{e}+\mathrm{He}_2^{+}$	1.268E−18	0.71	3.4	3.4	[31, 32]
R6	$2 \mathrm{He}^* \rightarrow \mathrm{e}+\mathrm{He}+\mathrm{He}^{+}$	4.50E−16	0	0	−15.0	[31, 32]
R7	$\mathrm{e}+\mathrm{He}_2^{+} \rightarrow \mathrm{He}^*+\mathrm{He}^{-}$	5.386E−13	−0.5	0	0	[31, 32]
R8	$\mathrm{He}^*+2 \mathrm{He} \rightarrow \mathrm{He}+\mathrm{He}_2^*$	1.30E−45	0	0	0	[31, 32]
R9	$\mathrm{He}^{+}+2 \mathrm{He} \rightarrow \mathrm{He}+\mathrm{He}_2^{+}$	1.00E−43	0	0	0	[31, 32]
R10	$\mathrm{e}+\mathrm{He}^{+} \rightarrow \mathrm{He}^*$	6.76E−19	−0.5	0	0	[31, 32]
R11	$2 \mathrm{e}+\mathrm{He}^{+} \rightarrow \mathrm{e}+\mathrm{He}^*$	6.186E−39	−4.4	0	0	[32, 33]
R12	$\mathrm{e}+\mathrm{He}^{+}+\mathrm{He}^4 \rightarrow \mathrm{He}^*+\mathrm{He}$	6.66E−42	−2	0	0	[32, 33]
R13	$2 \mathrm{e}+\mathrm{He}_2^{+} \rightarrow \mathrm{He}_2^*+\mathrm{e}$	2.80E−32	0	0	0	[32, 33]
R14	$\mathrm{e}+\mathrm{He}_2^{+}+\mathrm{He} \rightarrow \mathrm{He}^*+2 \mathrm{He}$	3.50E−39	0	0	0	[32, 33]
R15	$\mathrm{e}+\mathrm{He}_2^{+}+\mathrm{He} \rightarrow \mathrm{He}_2^*+\mathrm{He}$	1.50E−39	0	0	0	[32, 33]
R16	$2 \mathrm{e}+\mathrm{He}_2^{+} \rightarrow \mathrm{He}^*+\mathrm{He}+\mathrm{e}$	2.80E−32	0	0	0	[32, 33]
Air chemistry
R17	$\mathrm{e}+\mathrm{N}_2 \rightarrow \mathrm{e}+\mathrm{N}_2$	BOLSIG+			0
R18	$\mathrm{e}+\mathrm{N}_2 \rightarrow \mathrm{e}+\mathrm{N}_2(\mathrm{VIB} \nu 1)$	BOLSIG+			0.2889
R19	$\mathrm{e}+\mathrm{N}_2 \rightarrow \mathrm{e}+\mathrm{N}_2(\mathrm{VIB} 3 \nu 1)$	BOLSIG+			0.8559
R20	$\mathrm{e}+\mathrm{N}_2 \rightarrow \mathrm{e}+\mathrm{N}_2(\mathrm{VIB} 4 \nu 1)$	BOLSIG+			1.134
R21	$\mathrm{e}+\mathrm{N}_2 \rightarrow \mathrm{e}+\mathrm{N}_2(\mathrm{VIB} 5 \nu 1)$	BOLSIG+			1.409
R22	$\mathrm{e}+\mathrm{N}_2 \rightarrow \mathrm{e}+\mathrm{N}_2(\mathrm{A})$	BOLSIG+			6.17
R23	$\mathrm{e}+\mathrm{N}_2 \rightarrow 2 \mathrm{e}+\mathrm{N}_2^{+}$	BOLSIG+			15.6
R24	$\\ \mathrm{e}+\mathrm{O}_2 \rightarrow \mathrm{e}+\mathrm{O}_2(\mathrm{VIB} 3 \nu 1)$	BOLSIG+			0.57
R25	$\mathrm{e}+\mathrm{O}_2 \rightarrow \mathrm{e}+\mathrm{O}_2(\mathrm{VIB} 4 \nu 1)$	BOLSIG+			0.772
R26	$\mathrm{e}+\mathrm{O}_2 \rightarrow \mathrm{e}+\mathrm{O}_2(\mathrm{A} 1)$	BOLSIG+			0.977
R27	$\mathrm{e}+\mathrm{O}_2(\mathrm{A} 1) \rightarrow \mathrm{e}+\mathrm{O}_2$	BOLSIG+			−0.977
R28	$\mathrm{e}+\mathrm{O}_2 \rightarrow \mathrm{e}+\mathrm{O}_2(\mathrm{B} 1)$	BOLSIG+			1.627
R29	$\mathrm{e}+\mathrm{O}_2(\mathrm{~B} 1) \rightarrow \mathrm{e}+\mathrm{O}_2$	BOLSIG+			−1.627
R33	$\mathrm{e}+\mathrm{O}_2 \rightarrow \mathrm{e}+\mathrm{O}+\mathrm{O}_1(1 \mathrm{D})$	BOLSIG+			8.4
R34	$\mathrm{e}+\mathrm{O}_2 \rightarrow 2 \mathrm{e}+\mathrm{O}_2^{+}$	BOLSIG+			12.06
R35	$2 \mathrm{e}+\mathrm{N}_2^{+} \rightarrow \mathrm{e}+\mathrm{N}_2$	3.165E−30	−0.8	0	0	[32, 33]
R36	$\mathrm{e}+\mathrm{N}_2^{+}+\mathrm{N}_2 \rightarrow 2 \mathrm{N}_2$	4.184E−44	−2.5	0	0	[32, 33]
R37	$\mathrm{O}^{-}+\mathrm{O}_2^{+} \rightarrow \mathrm{O}+\mathrm{O}_2$	3.488E−14	−0.5	0	0	[31, 32]
R38	$\mathrm{e}+2 \mathrm{O}_2 \rightarrow \mathrm{O}_2^{-}+\mathrm{O}_2$	5.17E−43	−1	0	0	[31, 32]
R39	$\mathrm{O}_2^{-}+\mathrm{O}_2^{+} \rightarrow 2 \mathrm{O}_2$	2.00E−13	0	0	0	[31, 32]
R40	$\mathrm{O}_2^{-}+\mathrm{O}_2^{+}+\mathrm{M} \rightarrow 2 \mathrm{O}_2+\mathrm{M}$	2.00E−37	0	0	0	[31, 32]
He–air chemistry
R41	$\mathrm{He}^*+\mathrm{N}_2 \rightarrow \mathrm{e}+\mathrm{N}_2^{+}+\mathrm{He}$	7.00E−17	0	0	0	[31, 32]
R42	$\mathrm{He}_2^*+\mathrm{N}_2 \rightarrow \mathrm{e}+\mathrm{N}_2^{+}+2 \mathrm{He}$	7.00E−17	0	0	0	[31, 32]
R43	$\mathrm{He}_2^{+}+\mathrm{N}_2 \rightarrow \mathrm{N}_2^{+}+2 \mathrm{He}$	5.00E−16	0	0	0	[31, 32]
R44	$\mathrm{He}_2^{+}+\mathrm{O}_2^{-} \rightarrow 2 \mathrm{He}+\mathrm{O}_2$	1.00E−13	0	0	0	[31, 32]
R45	$\mathrm{He}^*+\mathrm{O}_2 \rightarrow \mathrm{He}+\mathrm{O}_2^{+}+\mathrm{e}$	2.60E−16	0	0	0	[32, 34]
R46	$\mathrm{He}_2^*+\mathrm{O}_2 \rightarrow 2 \mathrm{He}+\mathrm{O}_2^{+}+\mathrm{e}$	3.60E−16	0	0	0	[32, 34]
H2O chemistry
R47	$\mathrm{e}+\mathrm{H}_2 \mathrm{O} \rightarrow 2 \mathrm{e}+\mathrm{H}_2 \mathrm{O}^{+}$	BOLSIG+			13.5
R48	$\mathrm{e}+\mathrm{H}_2 \mathrm{O} \rightarrow \mathrm{H}+\mathrm{OH}+\mathrm{e}$	BOLSIG+			0
R49	$\mathrm{e}+\mathrm{H}_2 \mathrm{O}^{+} \rightarrow \mathrm{H}+\mathrm{OH}$	7.11E−10	−0.5	0	0	[33, 35]
R50	$\mathrm{e}+\mathrm{H}_2 \mathrm{O}^{+} \rightarrow 2 \mathrm{H}+\mathrm{O}$	3.10E−10	−0.5	0	0	[33, 35]
R51	$\mathrm{OH}+\mathrm{H}+\mathrm{M} \rightarrow \mathrm{H}_2 \mathrm{O}+\mathrm{M}$	4.30E−37	0	0	0	[33, 35]
R52	$\mathrm{O}(\mathrm{ID})+\mathrm{H}_2 \mathrm{O} \rightarrow 2 \mathrm{OH}$	2.20E−16	0	0	0	[33, 35]
R53	$2 \mathrm{OH} \rightarrow \mathrm{O}+\mathrm{H}_2 \mathrm{O}$	2.00E−18	0	0	0	[33, 35]
R54	$\mathrm{O}+\mathrm{OH} \rightarrow \mathrm{H}+\mathrm{O}_2$	3.32E−17	0	0	0	[33, 35]
R55	$\mathrm{O}+\mathrm{H}+\mathrm{M} \rightarrow \mathrm{OH}+\mathrm{M}$	1.62E−45	0	0	0	[33, 35]
R56	$\mathrm{H}+\mathrm{O}_2 \rightarrow \mathrm{OH}+\mathrm{O}$	3.55E−28	0	0	0	[33, 35]
R57	$\mathrm{OH}+\mathrm{M} \rightarrow \mathrm{O}+\mathrm{H}+\mathrm{M}$	4.15E−88	0	0	0	[33, 35]
R58	$\mathrm{H}_2 \mathrm{O}+\mathrm{O} \rightarrow 2 \mathrm{OH}$	2.34E−21	0	0	0	[33, 35]
R59	$\mathrm{He}^{+}+\mathrm{H}_2 \mathrm{O} \rightarrow \mathrm{H}_2 \mathrm{O}^{+}+\mathrm{He}$	6.05E−17	0	0	0	[33, 35]
R60	$\mathrm{He}^*+\mathrm{H}_2 \mathrm{O} \rightarrow \mathrm{e}+\mathrm{H}_2 \mathrm{O}^{+}+\mathrm{He}^{-}$	6.60E−16	0	0	0	[33, 35]
R61	$\mathrm{He}_2^*+\mathrm{H}_2 \mathrm{O} \rightarrow \mathrm{e}+2 \mathrm{He}+\mathrm{H}_2 \mathrm{O}^{+}$	6.00E−16	0	0	0	[33, 35]

 | Show Table

DownLoad: CSV

2.2   The ANN model

The ANN is a matured method to connect the input and output parameters in machine learning. After learning the typical cases with input and output parameters, the ANN could predict the output parameters of given unknown input parameters. The input parameters can be diversified, such as inflow velocities, components of working gas, or distances between adjacent jets, as long as the parameters can be digitized. The output parameters also can be multiple. In this study, the input parameters are the modulations of the applied voltage and the working gas inflow velocity, while the output parameters are the homogeneity of electrons, $\mathrm{N}_2^{+}$, He^*, O and OH.

Figure 2 is the schematic of the ANN in this study, including two input parameters, two hidden layers, and five output parameters. The basic unit in an ANN is the neuron. Each neuron has many inputs x_i with their weights w_ij, a threshold θ_j, and an activation function f(..). The weights and thresholds can be solved during the training process by known inputs and outputs. Then, unknown outputs are predicted by these weights and thresholds as well as given inputs. The output of each neuron depends on whether the weighted sum reaching the threshold as

Figure  2.  Schematic of an ANN with two inputs, five outputs, and two hidden layers.

DownLoad: Full-Size Img PowerPoint

The outputs of the previous layer are the inputs of the next layer. The activation function is the symmetric Sigmoid function $f(x)=2 /\left(1+\mathrm{e}^{-2 x}\right)-1$.

Hornik et al proved that any continuous function could be expressed with any precision by an ANN with enough neurons [36]. However, the numbers of hidden layers and neurons are unclear. Usually, these numbers are decided by tests.

To get the most suitable weights and thresholds, the error back propagation (BP) algorithm is used [37]. One can define a loss function as

where y_j is the real output parameters and $\hat{y}_j$ is the output parameters computed by weights and thresholds. The weights and thresholds are randomly initialized. The second term is Bayesian regularization to avoid overly complex weights and thresholds [38]. The purpose of the BP algorithm is to minimize the loss function for making the computed output parameters close to real. In the BP algorithm, the gradient descent method is used as

to update the weights and thresholds, where η is the learning rate. The learning rate is 0.5 at first. After the local minimum of the loss function is found, the learning rate will increase accordingly to find the global minimum of the loss function.

To assess the generalization ability, the cases with input and output parameters are divided into training set and testing set. Generalization ability is the capability of an ANN to predict unknown output parameters. The training set is used to make the ANN acquire suitable weights and thresholds. The testing set is for assessing the generalization ability. During training, the ANNs with the same number of hidden layers and neurons are repeatedly trained with different random test sets, weights and thresholds. Two layers and five neurons are used at first. If the predicting outputs are close enough to the true outputs, the ANN is considered to be good. Otherwise, the number of hidden layers or the number of neurons will be added to. After tests, two hidden layers with four and five neurons are selected.

3.   Results and discussions

3.1   Influence of the sloped substrate

Compared to the cases with flat dielectric or metallic substrates [24], the applications of substrates with complex 3D or sloped structures would significantly distort the uniform distribution of flow and electric fields, which inevitably bring obstacles in uniformity modulation downstream. Therefore, in this study, a grounded sloped metallic substrate with a 10° inclined angle is specially chosen as a sample to explore the uniformity modulation strategy in general. The helium distribution and flow streamlines are shown in figure 3, with parallel and sloped substrates downstream. The distance between the set bottom and the substrate central point is fixed at 10 mm, as shown in figure 1. As the basic case, the average inflow speed of the working gas is 15 m s⁻¹ and the voltage peak is 5 kV. Compared with the free-burning mode, the helium distribution with a parallel substrate is more homogeneous with nevertheless slightly emerged vortexes. With a sloped substrate, the vortexes grow further, leading to the decrease of the helium homogeneity.

Figure  3.  Steady helium distributions and flow streamlines with (a) a parallel substrate and (b) a sloped substrate.

DownLoad: Full-Size Img PowerPoint

The electron density distribution at the moment when the plasma reaches the substrate is shown in figure 4. With the sloped substrate, the left unit develops much faster than the right one, resulting in significant inhomogeneity. With a shorter distance between the pin electrode and the grounded substrate, the electric field intensity around the left unit is in general higher than that around the right unit, leading to the asynchronous development of discharge propagation. This result is consistent with simulation and experiment results in [39] where the plasma flows vertically towards to the grounded substrate. The electron density distribution and its maximum value with the order of 10¹⁸ m⁻³ are also close to the results shown in [39] under comparable conditions, which further verifies the model improved in section 2.1.

Figure  4.  Electron density distributions with (a) a parallel substrate and (b) a sloped substrate at the moments when the plasma reaches the substrate.

DownLoad: Full-Size Img PowerPoint

The distributions of the active species are shown in figure 5. In practical applications, it is the active species that interact with substrates, e.g. the distributions of He^* and $\mathrm{N}_2^{+}$, clearly affect the discharge, and OH is one of the most important species of reactive oxygen species [3]. They are produced by electron collisions and the corresponding chemical reactions, and thus distributed where electrons appear. Furthermore, those species clearly have a better uniformity with a parallel substrate, while the left unit develops faster with a sloped substrate. The active species are mainly distributed in the discharge channel. Due to the Penning effect (R41 and R45 in table 1), the He^* density sharply falls downstream, while the $\mathrm{N}_2^{+}$ and OH densities are relatively slowly reduced in the discharge region.

Figure  5.  He^* ((a), (b)), $\mathrm{N}_2^{+}$ ((c), (d)) and OH ((e), (f)) distributions with ((a), (c), (e)) a parallel substrate and ((b), (d), (f)) a sloped substrate at the moments when the plasma reaches the substrate.

DownLoad: Full-Size Img PowerPoint

3.2   Flow field modulation

Helium distributions and flow streamlines in flow field modulation are shown in figure 6. The working gas inflows are modulated from 15 m s⁻¹ in the basic case, to 5, 15, 25 m s⁻¹ for left, middle, and right units, and marked as +10 m s⁻¹ in figure 6(a). Accordingly, the working gas inflows are modulated to 25, 15, 5 m s⁻¹ for left, middle, and right units, and marked as −10 m s⁻¹ in figure 6(b). In figure 6(a), a part of working gas in the right tube swerves to the left. In contrast, most of the working gas flows along the substrate surface in figure 6(b). For the flow, the convection speed is faster than the diffusion, so that the flow streamline decides the flow field and the helium distribution. As to the helium concentration in the left region, the concentration for the case with the modulation of 25, 15, 5 m s⁻¹ for left, middle, and right units (marked as −10 m s⁻¹) is in general larger.

Figure  6.  Steady helium distribution and flow streamline with flow field modulation of (a) +10 m s⁻¹ and (b) −10 m s⁻¹.

DownLoad: Full-Size Img PowerPoint

The electron density distributions with the flow field modulation of +10 m s⁻¹ (5, 15, 25 m s⁻¹ for left, middle, and right units) and −10 m s⁻¹ (25, 15, 5 m s⁻¹ for left, middle, and right units) are shown in figure 7. For both ±10 m s⁻¹ modulations, the major discharge areas mainly concentrate in the left region due to the enhanced electric field caused by the sloped substrate. Comparatively, the electron density distribution area with the modulation of −10 m s⁻¹ (25, 15, 5 m s⁻¹ for left, middle, and right units) is relatively larger due to the higher helium concentration coupled with a higher electric field in this region, as shown in figure 7(b). Clearly, the asynchronous development caused by the sloped substrate remains, although the homogeneity of the electron density distribution on the surface of the substrate just changes slightly.

Figure  7.  Electron density distributions with flow field modulation of (a) +10 m s⁻¹ and (b) −10 m s⁻¹ when the plasma reaches the substrate.

DownLoad: Full-Size Img PowerPoint

The He^* distributions with the +10 m s⁻¹ and −10 m s⁻¹ modulations are shown in figure 8. As described in section 3.1, the active species are mainly decided by the discharge propagation process of the APPJ array, since the process of discharge propagation plays a dominant role in the chemical reactions. As shown in figure 8, the overall profiles of He^* density distribution exhibit a similar trend to those of the electron density in figure 7, which is attributed to the reaction of the R2 list in table 1. Moreover, since the complicated helium–air chemical reactive process, the He^* region is shown smaller than that of the electron.

Figure  8.  He^* density distributions with flow field modulation of (a) +10 m s⁻¹ and (b) −10 m s⁻¹ when the plasma reaches the substrate.

DownLoad: Full-Size Img PowerPoint

3.3   Electric field modulation

Another way to adjust the APPJ is by electric field modulation. By applying different resistances [7], the applied voltages can be easily changed for each unit. The electron density distribution with the electric field modulations is shown in figure 9. The applied voltages in figures 9(a)–(d) are 4.95, 5.0, 5.05 kV (marked as 50 V bias of 5.0 kV), 4.9, 5.0, 5.1 kV (marked as 100 V bias of 5.0 kV), 4.8, 5.0, 5.2 kV (marked as 200 V bias of 5.0 kV), and 4.7, 5.0, 5.3 kV (marked as 300 V bias of 5.0 kV) for left, middle, and right units, respectively. As the modulated voltage rises, the left unit develops more slowly and the right unit develops faster. With electric field modulations of 50 V and 100 V bias, the left unit maintains the major discharge channel, while the right unit develops faster with the modulation. When the modulations are 200 V and 300 V bias, the right unit becomes the main discharge unit. With a modulation of 300 V bias (4.7, 5.0, 5.3 kV for the left, middle, and right unit), the electric field around the left pin electrode is lower than that around the right one, while the electric field near the surface of the substrate in the left region is higher than that in the right region, as illustrated by the electric potential contour lines in figure 9(d). In general, the electric field distributions above eventually modulate the development of discharge propagation, and make the major discharge areas transit from the left region to the right gradually. The balanced development of the left and right channel could be realized with suitable electric field modulation, and thus, the electron density distribution uniformity on the substrate surface downstream has been optimized.

Figure  9.  Electron density distributions and electric potential (contour lines with the unit of V) with electric field modulations of (a) 50 V, (b) 100 V, (c) 200 V, and (d) 300 V bias of 5.0 kV when the plasma reaches the substrate.

DownLoad: Full-Size Img PowerPoint

With the electric field modulation, there is always a low electron density region between the left and the middle channels due to the flow field variation. The gas flows from the gap between the left and middle jets, so that the helium there is diffused. Thus, the helium concentration in that region is lower than those in other areas, leading to a lower ionization rate. With the minor modulation up to 300 V bias, the plasma evolution changes significantly. It is in sharp contrast with the results shown in figure 7, where with a considerable modulation of the flow field, the main discharge channel does not change obviously.

The He^* distributions with electric field modulations are shown in figure 10. The He^* mainly distributes in the left channel with the modulations of 50 V and 100 V bias, or in the right channel with the modulations of 200 V and 300 V bias. Besides the main discharge channel, the He^* appears at the head of the plasma bullet and in the tube with the high helium concentration.

Figure  10.  He^* distributions with electric field modulations of (a) 50 V, (b) 100 V, (c) 200 V, and (d) 300 V bias of 5.0 kV when the plasma reaches the substrate.

DownLoad: Full-Size Img PowerPoint

3.4   Coupled modulation of flow and electric fields

As shown in figures 7–10 of sections 3.2 and 3.3 detailed above, the modulation effect on the APPJ array uniformity downstream by adjusting the flow or electric field individually is limited; as such, a coupled modulation of flow and electric fields will be explored in this section. Figure 11 shows electron density distributions with a flow field modulation of −10 m s⁻¹ and electric field modulation of 100 V, 200 V, 300 V, and 400 V bias when the plasma reaches the substrate. With electric field modulation enhancing, the main discharge channel transfers from the left to the right channel. Compared with the electric field only modulation, the plasma region with the coupled modulation enlarges with a better homogeneity. The helium flows from the left to the right side with a flow field modulation of −10 m s⁻¹, resulting in a homogeneous helium distribution on the substrate surface. At the same electric field modulation of 300 V bias, the discharge condition with or without the flow field modulation is completely different from each other. With the flow field modulation of −10 m s⁻¹, the right channel develops slightly faster than the left one, while it is much faster without the flow field modulation (figure 9(d)). It indicates that the best electric field modulation result varies with the flow field.

Figure  11.  Electron density distributions with flow field modulation of −10 m s⁻¹ and electric field modulations of (a) 100 V, (b) 200 V, (c) 300 V, and (d) 400 V bias of 5.0 kV when the plasma reaches the substrate.

DownLoad: Full-Size Img PowerPoint

He^* distributions with flow and electric field modulations of −10 m s⁻¹ and 100 V, 200 V, 300 V, and 400 V bias, when the plasma reaches the substrate, are shown in figure 12. As described above, the development of the active species is decided by the electrons. The major He^* distribution transfers from the left to the right channel with enhanced electric field modulations. Differing from electrons, there is a region with a lower He^* density in the left channel for electric field modulations of 300 V and 400 V bias due to the flow field distribution. Thus, the He^* distribution is more sensitive to the flow field distribution than that of the electrons.

Figure  12.  He^* distributions with a flow field modulation of −10 m s⁻¹ and electric field modulations of (a) 100 V, (b) 200 V, (c) 300 V, and (d) 400 V bias of 5.0 kV when the plasma reaches the substrate.

DownLoad: Full-Size Img PowerPoint

Taking all cases into consideration, the flow field modulation should be a subtractive function of the distance between the substrate and the pin electrode. One may improve the uniformity by increasing the flow velocity in units near the sloped substrate and reducing that away from the sloped substrate, as revealed in figure 6(b). Increasing the flow velocity near the substrate, the working gas flows along the substrate and enhances uniformity near the substrate. For other units, the working gas flows out to form discharge channels. The helium diffusion velocity ($\boldsymbol{u}_{\mathrm{D}}=-D \nabla n / n$) in the steady state flow is 0.8 m s⁻¹ at the interface between the surrounding air and helium channel, and 0.02 m s⁻¹ on the surface of the substrate, much less than the inflow speed. Clearly, the flow field is mainly described by its streamlines. Then, the working gas flows along those streamlines. If the inflow velocity is high enough (such as on the order of the working gas inflow of 15 m s⁻¹), it can then form a uniform distribution along the streamline. On the other side, if the flow velocity is comparable to diffusion velocity, the gas sprayed out of the nozzle will quickly diffuse into the surrounding air, leading to a sharp fall in working gas density; as such, the jet discharge channel cannot therefore be established effectively. In this case, the working gas inflow velocity should be faster than 0.8 m s⁻¹ to form the discharge channel.

On the other hand, the electric field modulation should be an increasing function of the distance between the substrate and the pin electrode. One may improve the uniformity by reducing the voltage in units near the sloped substrate and raising that away from the sloped substrate. The electric field near the sloped substrate is asymmetrical which leads to local space charges, and a significant local space-charge field then appears near to the surface of the substrate. This local space-charge field accelerates the development of the discharge channel. In the case with a modulation of 300 V bias and −10 m s⁻¹, the left channel develops more slowly than the right one at first, but reaches the sloped substrate at the same time with the help of the local space-charge field near to the substrate. However, the local space-charge field varies with the curvature radius of the surface of the substrate and the distance between the substrate and the pin electrode. For the case with or without the flow field modulation, the best outcome under the electric field modulation happens at 200 V or 300 V bias, respectively. Thus, though the detailed electric field modulation varies, the basic rule is to make sure that the plasma in all channels reaches the substrate almost at the same time.

To quantitatively describe the homogeneity, a variation coefficient σ is defined as the standard deviation divided by the mean value, i.e. a lower σ means a better homogeneity. The plasma region included for the average is shown in figure 13 by a rectangle, perpendicular to the substrate and limited by the inner wall of the tubes. The homogeneity of active species at 0 and 2 mm from the surface as well as in the plasma region is shown in table 2.

Figure  13.  Schematic of the plasma region and different positions.

DownLoad: Full-Size Img PowerPoint

Table  2.  Homogeneities of species with various flow and electric field modulations at different positions.

	Flow field modulation (m s−1)	Electric field modulation (V)	$\sigma_{\mathrm{e}}$	$\sigma_{\mathrm{He}^*}$	$\sigma_{\mathrm{N}_2^{+}}$	$\sigma_{\mathrm{O}}$	$\sigma_{\mathrm{OH}}$	$\sigma=\sum\limits_i \sigma_i$
Surface	0	0	5.29	5.81	5.33	5.84	6.19	28.45
	−10	0	4.74	5.12	4.35	5.50	5.71	25.41
	10	0	5.26	5.60	4.81	5.87	6.18	27.71
	0	50	5.25	5.88	5.32	5.87	6.22	28.55
	0	100	5.22	6.00	5.37	5.94	6.29	28.81
	0	200	2.10	2.56	2.07	2.43	2.44	11.59
	0	300	2.19	2.61	2.21	2.47	2.56	12.05
	0	500	2.41	2.83	2.44	2.67	2.79	13.14
	−10	50	4.59	4.95	4.23	5.38	5.58	24.72
	−10	100	4.30	4.65	3.98	5.09	5.31	23.33
	−10	200	3.70	4.03	3.44	4.56	4.79	20.52
	−10	300	1.64	1.79	1.43	1.85	4.01	10.71
	−10	400	2.09	2.51	1.97	2.32	3.02	11.92
2 cm from surface	0	0	3.11	2.85	3.00	3.14	3.50	15.59
	−10	0	1.79	1.84	1.78	1.82	1.85	9.08
	10	0	2.70	2.80	2.68	2.67	2.78	13.63
	0	50	2.42	1.94	2.32	2.60	2.90	12.19
	0	100	1.36	1.02	1.35	1.78	1.65	7.16
	0	200	0.84	0.9	0.83	0.85	0.91	4.33
	0	300	0.96	1.04	0.96	0.98	1.03	4.96
	0	500	1.09	1.15	1.09	1.11	1.16	5.59
	−10	50	1.74	1.78	1.72	1.76	1.79	8.79
	−10	100	1.63	1.66	1.61	1.66	1.70	8.26
	−10	200	0.97	0.97	0.97	1.15	1.21	5.28
	−10	300	0.41	0.57	0.40	0.39	0.39	2.16
	−10	400	0.70	0.89	0.71	0.70	0.54	3.53
Plasma region	0	0	1.34	1.88	1.30	1.33	1.27	7.12
	−10	0	1.15	1.64	1.12	1.05	1.03	6.00
	10	0	1.37	1.86	1.35	1.28	1.28	7.14
	0	50	1.28	1.90	1.23	1.18	1.14	6.73
	0	100	1.10	1.73	1.06	1.01	0.94	5.85
	0	200	0.35	0.48	0.35	0.32	0.41	1.92
	0	300	0.54	0.67	0.54	0.51	0.59	2.84
	0	500	0.66	0.83	0.65	0.64	0.73	3.51
	−10	50	1.06	1.45	1.03	0.98	0.95	5.47
	−10	100	0.96	1.41	0.94	0.87	0.83	5.02
	−10	200	0.66	0.99	0.64	0.62	0.55	3.46
	−10	300	0.22	0.28	0.22	0.28	0.35	1.36
	−10	400	0.47	0.54	0.48	0.56	0.65	2.70
*Cases with best homogeneity are underlined.

 | Show Table

DownLoad: CSV

As shown in table 2, the variation coefficients for all species get slightly lower with the flow field modulation in all positions (0 and 2 mm from the surface of the substrate and plasma region), i.e. the homogeneity of species is improved a little with a considerable flow field modulation. Comparatively, with the electric field modulation, the variation coefficients drop significantly. The total variation coefficient on the substrate surface decreases from 28.45 to 11.59 with an electric field modulation of 200 V bias. Taking the advantages of flow and electric field coupling modulations, the total variation coefficient on the substrate surface is further reduced to 10.71. Accordingly, with the flow and electric field coupling modulations, the total variation coefficients of the areas 2 cm away from the substrate surface and in the plasma region fall down from 15.59 to 2.16, and from 7.12 to 1.36, respectively. These results have demonstrated that the plasma inhomogeneity caused by the sloped substrate downstream can be effectively reduced by the flow and electric field coupling modulations. In applications with sloped substrates, to get a decent uniformity of the plasma and active species, the flow field modulation should be applied first to form uniform distributions of the flow and the electron density on the surface and to supply discharge channels. Then, according to the flow field and the substrate, the suitable electric field modulation is used to make sure the plasma in all channels reaches the substrate almost at the same time.

3.5   Uniformity improvement by ANN prediction

The previous investigations [11, 18] have indicated that the adjacent plasma jets can merge together by crossing the helium contour line or adjusting applied voltages properly, and thus shown that the plasma uniformity could be improved effectively. However, it is still an open issue to acquire the actual implement method in different plasma generators, since parameters such as the flow velocity and the applied voltage vary with plasma devices and treatment effects. Therefore, if the appropriate input parameters could be predicted in advance, it will definitely be very attractive for practical applications. The ANN is then developed and employed to meet the challenge.

In this work, we try to map the flow and electric field modulations and the species homogeneities on the surface of the substrate through the ANN method. The ANN model is run on the Neural Net Fitting application. Herein, the ANN model has two inputs, including the electric field modulation and gas flow field modulation, and both are used. For the former one, electric field modulation with the bias voltage of 0, 50, 100, 200, 300, 400, 500 V are selected. Comparatively, for the latter one, data are less, and three typical conditions are given as representative, including (1) 15, 15, 15 m s⁻¹ for left, middle, and right units (marked as 0 m s⁻¹), (2) 5, 15, 25 m s⁻¹ for left, middle, and right units (marked as +10 m s⁻¹), (3) 25, 15, 5 m s⁻¹ for left, middle, and right units (marked as −10 m s⁻¹). The maximum of the bias voltage is fixed as 500 V, and the range of the gas flow was also fixed (−10 m s⁻¹ to +10 m s⁻¹), and then, the ANN method is applied within the parameters' range indicated above.

The data input to the ANN are the first 13 rows shown in table 2, which are obtained by simulation in this work. The modulations of −10 m s⁻¹ and 50 V bias, as well as −10 m s⁻¹ and 100 V bias are randomly chosen as a test to verify the accuracy of the predictions in the final training. Other data are used as the training set. The relative error ($\left(\sigma_{\text {true }}-\sigma_{\text {predicted }}\right) / \sigma_{\text {true }}$) of the ANN in the test set is shown in table 3. After learning, the average absolute value of relative error of the test set is 2.82% and the average absolute value of relative error of the training set is 1.78%, which is comparable to the accurate level of [30] with the prediction error of around 3%. Through the ANN, the computing time for getting results by a group of given parameters falls substantially from days for simulations to milliseconds for the ANN. Taking advantage of the quick calculation, it is possible to scan a large range of parameters easily and to provide a detailed direction for further optimizing.

Table  3.  Relative error of the ANN in the test set.

Flow field (m s−1)	Electric field (V)	e	He*	$\mathrm{N}_2^{+}$	O	OH
−10	50	−0.19%	−1.16%	−0.93%	−1.38%	3.88%
−10	100	−4.75%	−5.11%	−3.77%	−6.00%	0.98%

 | Show Table

DownLoad: CSV

In such a frame, the ANN predicts that the total homogeneity on the surface is best with an electric field modulation of −10 m s⁻¹ and a 269.70 V bias. The homogeneities are predicted as 1.49, 1.68, 1.28, 1.81, and 3.54, for electrons, He^*, $\mathrm{N}_2^{+}$, O, and OH, respectively, as well as 9.79 for the total homogeneity. Then, the case with flow and electric field modulations of −10 m s⁻¹ and 269.70 V bias is simulated and shown in figure 14. The simulated homogeneities are 1.43, 1.58, 1.25, 1.88, 3.92, and 10.06 for species and total homogeneity. These results meet the prediction and realize a further improvement on the total homogeneity. The possibility and feasibility of using an ANN to improve the plasma homogeneity are preliminarily proved.

Figure  14.  Electron density distributions with flow and electric field modulations of −10 m s⁻¹ and a 269.70 V bias when the plasma reaches the substrate.

DownLoad: Full-Size Img PowerPoint

Moreover, the flexibility of the APPJ array could be fully utilized in practical applications through an ANN. How to maximize the processing effect with minimum cost is always a challenge. There are various flow and electric field parameters to adjust the APPJ array plasma parameters, such as electron or oxygen atom average densities and uniformities. However, the target plasma parameters vary with processing effects, such as bacteria killing or mutation breeding [12]. It is a challenge to acquire the optimal flow and electric field parameters for target plasma parameters. There are also several combinations of flow and electric field parameters to reach the same processing effect. Therefore, it is a question for how to confirm flow and electric field parameters according to processing effects. The traditional method is to study the relationship between them step by step, which however costs a lot. But the ANN is capable of predicting or finding patterns in the behavior of a complex system by observing many input–output samples without any prior assumptions about the nature of the relationships, and provides good approximations. Therefore, it could provide a possible approach to mapping the input key parameters and the processing effects required from several experimental data [30]. In this way, the optimal combination of input parameters for a given processing effect could be predicted by scanning parameters, which is promising in terms of improving the experimental efficiency and cost saving. It should be noted that, firstly, we would like to have an attempt and preliminarily prove the possibility and feasibility of an ANN method in the uniformity modulation of an APPJ array, and thus, an ANN method including just two inputs within a specific parameters range is studied in this work. Actually, besides the two factors mentioned above, the slope angle, the material of the processing object, the distance between each unit and other key parameters also influence the downstream uniformity of the APPJ array, and further specific research with larger datasets will be made in the near future based on the method investigated above.

4.   Conclusion

The plasma uniformity on the surface of the substrate is a key issue for practical applications. In this paper, we have discussed and analyzed the influence of a sloped grounded substrate downstream and modulations to the uniformity on it. The main influence of the grounded sloped substrate is the electric field intensity near the pin electrode and the substrate, resulting in an asynchronous discharge development. In the view of multi-field coupling, flow and electric field modulations are applied. For the flow field modulation, the flow velocity in the unit near the substrate should increase to move along the substrate and form a homogeneous distribution on the surface. The simultaneous breakdown can be realized by the electric field modulation. In the multi-field coupling model, flow and electric field modulations are helpful for solving the spatial distribution in the case with a sloped substrate. Taking advantage of the flow and electric field modulations, a large area of uniform discharge forms. An ANN method with acceptable accuracy is also established to predict results beyond cases done. By the ANN, the plasma homogeneity gets further improvement in a much faster and more convenient way. This work may be considered as an indication of the possibilities and feasibility to preliminarily prove the validity of improving the plasma homogeneity through the ANN method, and research with more parameters and larger datasets will be conducted in the future with this method.