Plasma surface ionization wave interactions with single channels

The study of plasma surface ionization waves (SIWs) in recent years has primarily focused on planar surfaces and periodic two dimensional structures. In application, substrates are likely to have non-planar morphology such as cracks, pores, and steps. Additionally, targets for the applications of medicine or catalysis may have targets with heterogeneous composition. This classification of targets are brought under the umbrella of complex interfaces. In this work, plasma SIWs were incident on a complex target consisting of a single channel cut into glass slides. The SIW velocities for the in-channel portion of the wave and radially propagating portion of the wave were tracked. It was found that surface wave velocities are not significantly affected by channel geometry, but primarily increase with pulse energy. A third propagation direction for the SIW is characterized in the azimuthal direction relative to the radial portion of the wave. Channel geometry is found to greatly effect the area treated by the plasma but not the propagation velocity of the surface wave. Surface wave morphology and the impact on application is also discussed. A simple model was introduced to understand the mechanisms behind SIW escape from a channel. It was found that the ratio of pulse energy to a geometry dependent minimum energy can predict the escape angle of a SIW from single channels.


Introduction
The interaction of atmospheric pressure plasma jets (APPJs) with materials has promising applications in the fields of plasma medicine, catalysis, and material modification [1][2][3][4].A benefit of APPJ sources is that they produce large quantities of reactive species with low gas temperature that can be directed to a target of interest [5].Often, a pulsed APPJ impacting a dielectric target results in the generation of plasma surface ionization waves (SIWs) that can propagate along the target substrate [6].Studies of AAPJ plasma-surface interaction and SIWs can be broadly broken down into two categories, plasma effect on targets and the targets effect on the plasma.The latter is key in developing a greater fundamental understanding of SIW propagation mechanics and the mechanisms that induce desired changes in materials.This work strives to contribute to the understanding of a target's effect on the plasma and produce greater insights into the fundamental behaviors of SIW interactions with interfaces.
There is abundant work studying the propagation of SIW in confined discharge channels, in open air, and impinging on various targets [7][8][9][10][11].It has been found that target dielectric properties (thickness, permittivity, etc) play a large roll in how the SIW propagates along target surfaces [12][13][14][15].For very large dielectric constants (ε > 50) it is shown that SIW propagation is greatly diminished or not present.In the case of water targets (ε ≃ 80) and metal targets (ε ≈ ∞) it is suggested that an enhancement of electric field adjacent to the substrate surface results in a re-strike, or return stroke, breakdown along the conductive gas channel [16].Viegas and Bourdon (2020) have shown numerically that the peak electric field inside a floating target is the same for floating targets with (ε ⩾ 4) but is much greater for grounded targets [13].On smooth, planar, substrates for positive polarity it has been observed for a SIW to self-organize and form a pinwheel pattern on the substrate, leading to potential non-uniformity in surface treatments [17].It has also been shown that in confined tubes, SIWs can propagate for several meters [18].
In the above mentioned works and others, the target substrate is generally planar and smooth; recent work has also explored the impact of surface topology in SIW propagation.In many practical applications including skin treatment, catalysis, and direct agricultural treatment the targets are quite non-planar and have complex morphologies [19][20][21].Complex targets are considered to be targets that have heterogeneous electrical properties and/or non-planar geometry.Both biological and catalytic targets are complex under this definition and possess varying dielectric properties across their surfaces and in their bulk.Human skin is noted to have a dielectric constant that varies with location and as a function of depth into the body [22,23].Catalytic targets present many different planes and curvatures in addition to mixtures of dielectrics and conductors in packed bed reactors [24,25].Metallic particles in packed bed catalytic reactors have been shown to enhance local electric fields and direct discharges toward them [26].This results in potential enhancements in catalytic chemical processes at the cost of limiting the propagation of streamers and SIW within the packed-bed.
More recently, numerical studies have sought to better understand how SIWs interact with complex interfaces.Konina et al modeled SIW propagation over 2D structures including wavy surfaces, single droplets, and pores cut into surfaces.It was found that positive polarity driven SIW's adhered to all surface variations except in cases where the surface is shadowing the interior of the feature, which restricts photo-ionization within the pore [14].Photo-ionization is a key mechanism in the propagation of positive polarity SIW.Another important result was that the SIW propagation into pores is limited when the opening approaches the scale of Debye length for the discharge front.Jiang et al used a fluid model to study the SIW propagation over 2D undulating surfaces of various dielectric constant and curvature of the undulating surface [27].While 2D modeling efforts provide invaluable insight into SIW mechanics that are not accessible to traditional experimental methods, they do not capture any 3D propagation effects that may greatly effect the application of APPJs in target treatment.
There is limited experimental data in the study of plasma SIW propagation over non-planar substrates.What does exist is primarily in the space of plasma catalysis, where packed beds of dielectric spheres introduce nano-structures and interfaces with compound curvature [28].Mujahid et al performed experiments using a domed array dielectric barrier discharge and utilized a numerical model to explain physical phenomena [29].It is found that SIW's are initiated and propagate from the apex of the domed surface until converging at 'contact points', in between domed features, where a filamentary re-strike to the anode occurs [29].In Slikboer et al an in-situ electric field diagnostic was developed for studying plasma-surface interactions over a biological target [30].
In this work, an APPJ was used to generate SIW in single channels cut into dielectric substrates.The pulse energy of the SIW was varied as was the cross sectional area of the single channel.SIW velocity was tracked and the morphology of the SIW as it interacts with the channel is also discussed.ICCD imaging was used to characterize the propagation and morphology of the SIW interactions.Outcomes of these observations are discussed as they pertain to the applications of APPJs and SIW in addition to providing context for modeling efforts.A simple model is introduced to better understand the mechanisms driving SIW escape from channels.This work seeks to better understand the effects of three-dimensional structures on the propagation of SIW.
The experimental setup is given in section 2.An overview of all diagnostics and data processing methods is covered in section 3. Results for all experiments are given in section 4 and include qualitative observations of the SIW propagation.The findings are discussed in section 6 with proposals for future work and their challenges.Concluding remarks are presented in section 7.

Experimental setup
The APPJ used is as identified in Jiang et al and is identical in configuration to the jet used in Morsell et al [12,31].The work presented here utilizes a nanosecond DC pulse of positive polarity for power delivery.Pulse width is set to 500 ns and applied voltage is varied from 3.5-5.25 kV.Pulse repetition rate is 1 kHz for this work.Pulse rise time from 10%-90% of peak voltage is noted to be 32.7 ns on average.A 1 mm diameter tungsten electrode is nested within a 2 mm inner diameter quartz tube for primary gas flow.The working gas is helium delivered at a flow rate of 1 standard liter per minute.A copper ground ring sits outside of the quartz tube centered at the location of the electrode tip.The ground ring is 5.2 mm in height and is positioned 3.5 mm from the tip of the quartz tube.This locates the tip of the center electrode at 6.2 mm from the end of the quartz tube.
Figure 1 details the major experimental components of this work.Power is delivered by a Matsusada positive polarity high voltage DC power supply (AU-30P40).High voltage is gated using a DEI pulse generator (PVX-4110) driven by a BNC (model 575) delay generator.Imaging is performed with a PiMax 3 ICCD camera.A more detailed diagram of the imaging setup in this work is given in figure 2(a).The plasma source is horizontally oriented so that the ICCD camera view  is along the ionization wave (IW) propagation axis.The dielectric target surface is placed parallel to the ICCD camera lens.The light emitted by the source ignition and propagation is integrated as the IW transitions to the surface.This high intensity light makes viewing the SIW difficult and is omitted by placing another pane of glass between the camera and the backside of the target.This blocking plate has a black spot that blocks all light emitted as the IW travels to the surface.It is placed 3 cm behind the target and does not receive any plasma exposure.The optical block is not applied directly to the targets so that targets can be shifted while maintaining the alignment of the plasma source tip and optical block with the camera.The target substrate is a piece of quartz glass with a single rectangular channel cut into it is surface.The quartz slide that the channel is etched into is 1.0 mm thick, 50.4 mm long, and 25.4 mm wide.The channel is etched along the minor axis of the substrate.A series of six channels of varying dimension are used in this work.The dimensions of the channels are given in table 1.The etched slide is placed on top of a second slide that is the same size as the target but 1.1 mm thick for a total target thickness of 2.1 mm.This backing slide provides reinforcement to the target and is coated in a transparent indium tin oxide (ITO) conductor to create a ground path on the backside of the target assembly.The plasma IW will be incident with the bottom of the etched channel.Comparing the target geometry relative to the ground plane the top surface of the target and bottom surface of the channel have different dielectric thicknesses.Results from previous work indicate that this difference in dielectric thickness will result in different SIW velocities due to changes in substrate capacitance [12].It is expected that the SIW at the bottom of the channel will propagate slower than the SIW on the top surface.These two pieces of glass were mounted into a 3D printed frame that maintains the alignment of the target to the camera and source.Target frames were designed to be loaded as cartridges into a support structure so that targets can be changed out without disturbing the alignment of optics.The target system is connected to a three-axis stage for precision alignment of the target.Each target channel is subject to the same applied pulse excitation voltage, source spacing, and gas flow as the other samples.

ICCD imaging
Imaging of the SIW is accomplished using a Princeton Instruments PI-MAX3 ICCD camera.The lens used is a Nikon (AF-S Nikkor 18-55 mm) at a distance of 0.15 m from the jet source.The depth of field of the lens is greater than the thickness of the target and is estimated to be ∼6 cm.This means that the blocking plate, single step target, and source tip are all in focus.Triggering of the camera shutter is controlled by the same delay generator that drives the high voltage pulse.Gate width is kept at 10 ns and the delay time-step is 10 ns.Images are taken over 5000 accumulations to collect an adequate  4 has been multiplied by a factor of five to emphasize reflections.Image post-processing consists of a background subtraction for each image.The background image is collected while the plasma is running but at a time prior to plasma ignition.The method of information extraction from images is given in section 3.3.Later in this work a He 706.5 band-pass filter (Thorlabs FBH710-10) is used in conjunction with a fixed focal length magnification lens (Thorlabs MVL6X12Z) for analysis purposes.Images using this configuration are noted as such.

Electrical measurements
The jet source has an integrated current probe (Pearson 510) and voltage is measured using a high voltage probe (Tektronix P6015A), both connected to pickups on the plasma source.Current and voltage traces are collected with an 8 ps per point resolution and averaged over 1000 samples.There is a 0.66 ns delay between the voltage and the current measurement due to cable length that is taken into account when determining pulse energy.Two separate measurements of current are taken for each experiment.The first is the total current when the gas is flowing and the plasma is ignited.The second isolates the displacement current when there is no gas flow and no plasma current exists.The difference between the total current and the displacement current is the plasma current, I pl [32].An example set of VI traces is given below in figure 5.It should be noted that the source has a 500 Ω ballast resistor at the head of the source.Note that the voltage probe is placed downstream of the resistor while the current probe is upstream of the resistor.Energy per pulse is calculated according to equation ( 1) where t 1 and t 2 are the start and end times of a pulse event.
Energy per pulse, in µJ is used in place of the driving voltage unless necessary.There is an average noise floor of 2 µJ present when the absence of plasma that is noted to exist in all measurements.Plasma resistance is estimated to be between 0.7-70 Ω and is in series with the much larger 500 Ω ballast resistor.This implies a minimal change in the impedance of the jet source when plasma is ignited.

Post processing
Images were post processed using a Matlab script.The base Matlab script and tracking method is discussed in Morsell et al [12].The script makes use of two user created functions to retain only the continuous boundary of the wave front [33].
The first function locates gradients of intensity in each image of the SIW.Then a second user function filters those boundaries to the longest single boundary in the image.Modifications are made to adapt to changes in target geometry but the tracking method remains the same.The primary output of the Matlab script is the position of the SIW leading edge as a function of time.The calculated velocities are given by taking the slope of a linear fit of the positional data over a stable period of time.Prior to the SIW appearance from behind the optical block there is no trackable object and therefore no data to consider.After the SIW emerges it is observed to travel at a linear rate until the emission intensity becomes low enough that reliable tracking is difficult.The region of time where the SIW is visible and is tracked reliably is presented with linear fits in figure 6. Error for these linear fits is the standard error of the slope as calculated by the linear fit.The magnitude of the error is <5% for all but a few data points; a linear fit is therefore a good assumption for the region of study.All image sets are processed using the same post processing methods and variable set points to limit variability due to changes in the edge tracking script.Note that for the in-channel positional data there is a limit at ≈11 mm, beyond which there is not  any reliable data.This is the point at the edge of the target where the SIW interacts with the edge of the target and cannot propagate further.

SIW propagation results
As the IW impacts the target at the bottom of the channel and transitions to being a SIW it spreads out and propagates across the target.The size of the impact site is not known due to interference from the axial integration of light from the APPJ source.From previous work with the same jet the diameter of the IW 'bullet' just prior to impact with the surface can be estimated at ≈850 µm at a driving voltage of 4.0 kV [12].Figure 4 shows that the propagation of the SIW is split into two portions.The first is the portion of the SIW that remains in the target channel and propagates along it.The second is the portion that escapes the channel and propagates radially outward across the planar portion of the target.Each portion is evaluated and a velocity is determined for the SIW.

Radial SIW velocity
The radial component of the SIW is defined as the portion of the wave that escapes the channel and propagates radially  away from the channel edge.Radial expansion of the SIW is tracked perpendicular to the channel and a velocity extracted.The measurements for radial velocity are made at the midpoint of the arc, perpendicular to the channel edge.This direction aligns with the axis of the ICCD sensor and is easier to process than off-axis directions.Figure 7 gives the radial velocity of the SIW for all channel geometries and a range of pulse energies.As pulse energy increases there is an increase in the radial velocity.As channel geometry is changed there is no significant change in magnitude or trend with radial velocity with either channel width or depth.SIW velocity in figure 7 appears to begin falling off after 90 µJ.This is likely not the case as other trends in velocity do not show velocity decreasing.It is most likely that the increasing trends with energy are beginning to taper off and increase with diminishing returns.This trend is also observed in the next section.The magnitudes of the radial SIW velocities are on par with those seen in previous work [12].This indicates that in cases where the SIW impacts a barrier and only a portion of the SIW is allowed to propagate along the surface the mechanisms for that continued propagation are the same as for an uninterrupted SIW on a planar surface.This is interesting as it was expected that the sharp channel edges would act to increase the local electric field magnitude and modify the propagation velocity.This behavior will be discussed further in section 6.Although not shown, the velocity of the free/volume IW as it propagates from the source to the target also increases with pulse energy.The velocities of free waves tend to be higher than on surfaces, up to 2×10 5 m s −1 in some cases [12].It is also observed in figure 4 that the radial portion of the SIW that escapes the channel and propagates across the planar surface forms a geometric arc.The shape of the arc can be defined by the region of emission outside of the channel that forms a curved SIW with endpoints noted as the locations at either end of the arc where emission ceases.The endpoints of the arc and the midpoint show a higher intensity than the rest of the SIW arc.It is not clear as to whether this patterning of the intensity is self organization or a result of the SIW interaction with the channel wall.The patterning of the radial SIW is observed to varying degrees across all experiments.Further discussions and analysis of the SIW arcs will be discussed in sections 4.3 and 6.

SIW velocity in-channel
Figure 8 shows a more detailed view of figure 4 focusing on the propagation of the SIW within the confines of the channel feature.The plasma SIW that forms in this channel is confined by the channel geometry and propagates along the channel interior until meeting the edge of the target and is no longer visible.The SIW can be seen forming two individual nodes that each occupy a bottom edge of the channel.At the highest applied voltage of 5.25 kV the emission intensity is high enough that the nodes appear as a single SIW.This is the case for channels with 1 mm widths.Wider channels show clear separation between the SIW nodes within the channel.The transition of the SIW from a uniform feature to its splitting into separate nodes is likely hidden by the optical block and is not verifiable in this work.From figure 8 it can also be seen that the nodes shrink with increasing distance.The individual nodes propagate along the channel at the same speed and same distance.In the event that the experiment is not properly aligned and the IW does not impact in the center of the channel the in-channel SIW nodes do not align side-by-side.The channel targets are positioned using a multi-axis stage until the SIW nodes align.
Figure 9 displays the velocity of the SIW in the channel as a function of pulse energy for all channel geometries.As pulse energy increases there is also an increase in SIW velocity for all channel geometries.Similar to radial velocity in figure 7 there is no trend in velocity with changing channel geometry.For energies above ∼80 µJ the velocities appear to be increasing with diminishing returns with increasing energy or decrease in a few cases.This mirrors the results of radial velocity in figure 7 at energies above 90 µJ.
Note that the velocities of SIW seen in-channel are of similar magnitude as those seen for IWs traveling in air toward the surface, much higher than velocities observed on planar surfaces.In air velocities on the order of 1 − 2 • 10 5 m s −1 are reported in previous work at 4 kV driving voltage [12].While it was predicted by [12] that the SIW in the bottom of the channel should be slower due to substrate electrical properties, the opposite is seen here.This elevated velocity is most likely due to the confinement of the SIW by the channel walls which restrict the dispersion of the wave energy.This and other possible mechanisms for this behavior will be discussed in section 6.

Azimuthal SIW velocity
It is shown in figure 4 that as the SIW propagates radially away from the channel forming a geometric arc with some radius (r) extending away from the channel edge; this portion of the SIW outside of the channel will be discussed in terms of polar coordinates.From the endpoints of this arc an angle (θ) can be measured relative to the channel edge.For context, the smaller the measured angle the larger the SIW arc becomes.The channel edge is used as the basis for measuring angle because it provides a static reference point as the SIW propagates.Throughout the course of this work it was observed that this angle changes as a function of time.The angle measured between the SIW arc and the channel edge is referred to as the 'escape angle'.
Figure 10 shows the SIW escape angle as a function of time for all channel geometries at a fixed drive voltage of 4.5 kV.As the SIW propagates outward with a radial velocity found in figure 7 the measured angle decreases.Shallower channels show a general trend of having smaller angles than deep channels.This may be due to the larger barrier that the initial SIW must overcome in order to propagate out of the channel and across the substrate.For channels of 1.5 mm in width there is no change in angle at different depths.The same variability in trend is also seen for channel width, where the widest channels (2.0 mm in width) show a much greater angle than narrower channels.For channel widths of 1.0 and 1.5 mm there is overlap in the magnitude of the 'escape angle'.For the angle to decrease with time the endpoints of the SIW must be traveling in another direction in addition to radially.The time rate of change for the escape angle can be related to the velocity of the endpoints of the SIW arc.Using the radius as determined for the radial velocity and the 'escape angle' for each point in time, the azimuthal velocity (V az ), in m s −1 , is calculated as where subscripts 1 and 2 determine the time step, ∆T is the time between images in seconds and θ is in units of degrees.The velocity is divided by two to account for the velocity at which the SIW is traveling away from the center point of the arc and not the rate at which the endpoints are travelling away from each other.This estimated azimuthal velocity of the SIW is given for all geometries and pulse energies in figure 11.
As a function of geometry the azimuthal velocities shown in figure 11 show no dependence on channel geometry.There is an exception for channel 5 which has a parallel trend to the other geometries but with a higher velocity.This is likely due to channel 5 being the largest of the channels and the SIW escape angles having a different trend than other geometries.This will be discussed further in section 5.The remainder of the channels show a tight grouping of azimuthal velocity and appear to have significant overlap across energy.The magnitude of the error in this case prevents any substantial claims regarding the close grouping of the remaining channels.Azimuthal velocity is shown to increase as a function of energy more strongly than both the radial and in-channel velocities of figures 7 and 9, increasing by up to a factor of four with increasing energy.It is noted that the magnitude of the velocity is similar overall to other velocities reported in this work.A discussion of the effect of channel width on SIW morphology will be presented in sections 5 and 6.A simple scaling law model will also be introduced to help understand the mechanisms driving the escape angle.The model can be found in section 6.1.

SIW morphology
In the interaction of the SIW with the channel walls, it is apparent that some portion of the SIW escapes and propagates across the planar portion of the target.Figure 7 shows that the velocity of the radial SIW is affected by pulse energy but not by the channel geometry.The same is observed for the inchannel and azimuthal velocities.By observing the sum of all light emitted from the area within the channel and outside of the channel across the observed time it is possible to estimate what fraction of total emitted light is escaping the channel at a given energy and for a given channel geometry.It is noted that this analysis assumes that as more light escapes the channel, a greater fraction of the total SIW energy also escapes the channel.The relationship can be expressed by equation (3).
where I escape is the fraction of total emitted light that escapes the channel, I out is the sum of light emitted by the SIW that escapes the channel, I in is the sum of light emitted by the SIW that remains in the channel.Figure 12 presents this intensity fraction for both channel geometry and pulse energy.As pulse energy increases more of the SIW escapes the channel than remains within.This trend is consistent for all channel geometries.As channel width increases it can also be seen that there is a decrease in the fraction of intensity that escapes the channel.This trend can also be seen for SIW escape angle in figure 10, where the SIW escape angle increases and covers a smaller area.Note that there is also some small amount of error in measured intensity due to reflections and scattered light present from the layers of glass present in the optical setup (figure 2(a)).
To assemble a concise summary of the escape angle as a function of geometry and pulse energy the images are stacked to integrate across time and a single escape angle is determined for each geometry and pulse energy.In figure 13 this escape angle is given for all geometries and pulse energies.Upon inspection and comparison to the light emission in figure 12 it is evident that the trends in energy and ordering with geometry are nearly identical.This suggests that the partitioning of the SIW morphology and the emission intensity are well correlated.
By applying a spectral band-pass filter to the ICCD camera it is possible to make additional observations about the SIW morphology.The 706.5 nm emission of the He (3 3 S-2 3 P) transition is isolated in this case.The 3 3 S upper state population is primarily the result of direct electron impact excitation [34].The 3 3 S state is popular in line ratio diagnostics because its population weakly depends on electron density and is primarily a function of electron energy [35,36].Regions of higher intensity at a given point in time can be approximated to have a higher mean electron energy than dimmer regions at the same point in time.Figure 14 shows a snapshot in time of the He emission of the radial SIW propagating away from the channel.The radial portion of the wave shows increased emission at the ends of the SIW arc and at the midpoint.The endpoints of the SIW arc may have a higher mean electron energy due to the interaction of the SIW with the channel edge and the mechanism that allowed that portion of the wave to escape.Given that the geometry has a significant effect on the angular propagation of the arc, it is likely the case that the mechanism dictating SIW escape is the cause.The impact of these trends to application and modeling is discussed in section 6.

Discussion
The interaction of the SIW with solid barriers drives more complex behaviors like those seen in figure 12.As the SIW is generated within the channel it propagates outward and splits into two, seemingly unrelated, wave components that each have their own features and propagation characteristics.
In order to ensure that the increased velocity of the SIW in the channel is due to confinement of the SIW energy and not surface roughness, a separate experiment was conducted to compare the SIW velocity on a roughened planar surface in comparison to a smooth planar surface.Figure 15 shows the radial velocity of a SIW on a rough and smooth surface for several pulse energy set-points.It is found that the SIW velocity on both the rough and smooth target are statistically similar.This indicates that the magnitude of the SIW velocity in the channels is due to the confinement of the SIW and not surface roughness.Other work has shown that fully confined SIW within tubes propagate at higher velocities than reported on target surfaces [37,38].The roughened surface may affect the SIW in other ways, but for the scope of this work the roughness has no effect on the SIW velocity.
It is observed in figure 7 that the velocity of the SIW which escapes the channel and propagates outward is unaffected by the channel geometry.What is affected by the geometry is the angle formed between the SIW arc and the edges of the channel.This indicates that the rate at which the SIW propagates is driven primarily by the driving voltage of the discharge, while the morphology of the SIW is driven by the physical barriers presented to it.Put another way, the initial SIW that is generated at the bottom of the channel is altered and partitioned based on interactions with physical barriers but retains it propagation characteristics in the form of SIW velocity.
As highlighted in sections 4.3 and 5 the wider channels allow less of the SIW to escape than narrower channels at the same pulse energy.The result is that far less  of the surface outside of the wider channel receives plasma treatment.Figure 16 shows the extremes of this work.The first image is for the smallest channel by cross sectional area (channel 2), while the second is the largest (channel 5) for the same driving voltage (5.0 kV) and at the same time.The larger escape angle of the narrower channel directly exposes much more of the surface to plasma than the wider channel.This is supported by the time integrated light emission presented in figure 12, where more than double the fraction of total light intensity of the SIW is emitted from outside the channel for the narrower geometry.This non-uniformity has the potential to negatively impact the application of atmospheric pressure plasma treatment of surfaces.For many applications it is important that treatments be uniform and penetrate into small features such as cracks and pores.Within the channel it is encouraging that the SIW hugs the inside corner of the feature and propagates with high velocity and at an increased mean electron energy.Cracks and pores in targets present some of the most challenging to treat and can be the most critical to modify (ex.bacteria in pores and wrinkles).SIWs in this work show potential for applications in this area.
One possible mechanism for the angular propagation of the SIW arc summarized in figure 13 is the local charge gradients as described in literature [17,39].As the SIW forms on the surface there exists a strong local electric field parallel to the surface that results from charge gradients at the head of the surface wave [17].The parallel electric field has contributions from both volume charge gradients and surface charge gradients on the dielectric surface [39].As the SIW propagates outward radially this field is often designated as the radial electric field.On a planar target the SIW normally propagates outward as a circle in a radial direction.So all adjacent points along the circle have a SIW present and do not present a significant gradient in charge azimuthally.The presence of the single channel in this work segments the SIW and results in a SIW arc whose endpoints now have no charge adjacent to them.This lack of an adjacent charge results in a large charge gradient azimuthally along the SIW arc.This gradient generates an electric field and hence a propagation in the azimuthal direction.Note that it could just as well be described as propagation in Cartesian coordinates for this explanation but polar coordinates are chosen to reflect the circular nature of SIW propagation on planar surfaces.

Escape angle model
In order to better understand the mechanisms that dictate the escape of the SIW from the channel, a simple model has been developed to predict the escape angle as a function of channel geometry and pulse energy.It is assumed that the energy per pulse (ε) is linearly proportional to the peak electric field E in the system.Previous work has shown that plasma IW velocity increases with both voltage and electric field [40][41][42].SIW velocity is shown in this work to increase linearly with pulse energy (also with voltage).In order for SIW to propagate along a dielectric surface, a radial electric field is needed.As mentioned above, the gradient of charge from within the SIW to the region ahead of it generates this radial field.For a radial propagating SIW on a planar surface the radial field would extend outward at an angle normal to the curvature of the SIW. Figure 17(a) illustrates this using a simple diagram.
From figure 13 it can be inferred that for a sufficiently large channel or for a low enough pulse energy that the SIW would fail to escape the channel and be confined by the channel.This means that some minimum electric field (E m ) must exist to escape a channel of a particular geometry.As the SIW interacts with the channel wall, it is assumed that only the electric field perpendicular (E ⊥ ) to the channel wall will contribute to the SIW propagation over the barrier.Figure 17(b) illustrates how E ⊥ would generally trend based on the impinging angle of the SIW radial electric field.Note that for an E ⊥ > E m that only a portion of the wave will escape the channel.The ratio of E m to E ⊥ can be related to the escape angle (θ), in degrees, measured in experiment by equation ( 4): where ε m is the minimum energy that the SIW must possess to escape the channel and is a function of channel geometry.The form of equation ( 4) is derived from the trigonometric relationship between a chord segmenting a circle and the angle that is formed between the origin of the circle and the chord endpoints.The transition from E to ε is allowed under the assumption that pulse energy is linearly proportional to the radial electric field in the SIW.
Equation ( 4) establishes that the SIW escape angle is a function of both channel geometry and the pulse energy contained within each SIW.The geometric dependence of ε m is defined as: where γ w is a weighting term to weight the relative importance of the channel width (W) and depth (D).γ m is the scaling term used to relate the geometry function to an energy.A number of geometric relationships were considered including channel cross sectional area, width, depth, and perimeter.The best relationship to the experimental data was found to be a linear summation of channel dimensions.Where the channel width had more effect on the escape angle than channel height.It has be shown that positive polarity SIW adhere more closely to surfaces than negative waves due to in part to their reliance on photoionization to propagate [14].In this way it makes sense that the best relationship between channel geometry and escape angle should be linear and relatable to path length.Equations ( 4) and ( 6) are solved for the range of pulse energy observed in this work (30-100 µJ) and for the channel geometries listed in table 1.The scaling factors γ g = 23 and γ w − 0.5 were used.Figure 18 shows the escape angles as predicted by equations ( 4) and ( 6).The two major trends captured by the model are the decreasing escape angle as pulse energy increases and the increase in escape angle with channel geometry.For the γ w chosen, the ordering of the channels by increasing escape angle is the same as in figure 13.The overall scaling of escape angle with energy is not exact, as the model predicts a sharper decrease with energy than in experiments.A concavity exists in the escape angle trends which is much more subdued in experiment.The discrepancy between model and experiment is likely due to the simplicity of the model and the oversimplification of dependencies on both geometry and pulse energy.The assumption relating E to ε may also be at fault.
The ratio ε m /ε in equation ( 4) establishes that for cases where ε ⊥ < ε m there is no real solution and θ is restricted to 90 • .For the definition of escape angle given, this equates to all of the energy remaining trapped within the channel and no angle being visible.This limiting condition can be evaluated at the extremes where the pulse energy decreases toward zero or the channel geometry increases towards infinity.In the case of energy decreasing the pulse energy will reach a limit where the generation of a SIW is not possible or a plasma is not ignited.In the case for increasing geometry it can be said that a channel of infinite width and depth would also require a SIW infinite energy to overcome and therefore would not result in any of the wave escaping the channel.
As the ratio trends toward zero the solution to equation tends toward a solution of 0 • .This is equivalent to all of the energy escaping the channel and the circular propagation of the SIW being unbroken by the wall interaction.Such a condition can be evaluated at the extremes where the pulse energy increases to infinity or the channel geometry decreases towards zero (a planar surface).In the case of decreasing geometry there is likely some feature size which is not a planar surface but does not inhibit the propagation of the SIW.It is unclear whether or not this minimum feature size would be affected by pulse energy or some SIW other propagation parameter.It is noted that a topic for future work should be the characterization of how feature sizes on multiple scale lengths affect SIW propagation.
The simple model described here shows that SIW interactions with single channels are a function of both channel geometry and SIW pulse energy.The simplified mechanism dictating the escape of SIW from a channel structure is related to ε m /ε ⊥ and E m /E ⊥ by assumption.The mechanisms dictating the escape of the SIW from the channel are likely more complicated than this, where field enhancement due to the shape of the top edge of the channel wall is not taken into account.The effect of the surface wave re-orienting the radial portion of the field to climb the channel wall is also not considered as part of this model.Plasma parameters such as electron density, electron temperature are also not accounted for.The simplicity of the model does help to guide the design of complex substrates and predict the impact on SIW propagation in various applications.If a target surface has features which would predict a large escape angle, then an increase in pulse energy would limit the fraction of energy trapped by those features.

Conclusion
In this work, plasma IWs of various energy are incident with the bottom of a rectangular channel cut into a glass substrate.A number of different channel geometries are used.The subsequent SIW is studied for its propagation both within the channel and across the planar surface outside of the channel.Time resolved ICCD imaging shows that the velocity of the SIW within the channel and propagating radially outside the channel is unaffected by channel geometry.Both components of the SIW velocities increase with increased pulse energy.The SIW within the channel shows a splitting where each bottom corner of the SIW having a portion of the SIW.It was determined that the portion of the wave which escapes the channel takes the shape of an arc.An escape angle was determined from arc relative to the channel edge and is found to be strongly dependent on channel geometry.As channel width increases, the angle increases corresponding to less of the SIW escaping the channel.The ends of this SIW arc has an increased optical emission associated with increased mean electron energy.Endpoints of the SIW arc also show an additional degree of freedom with propagation azimuthally relative to the radial propagation at the midpoint of the arc.This angular component has a velocity that depends only on pulse energy and not on channel geometry.A simple scaling model was developed to determine that the minimum energy needed for a SIW to escape a channel is driven by channel geometry, among other useful insights.
The results of this work are of consequence in the understanding of plasma application of complex interfaces.Many applications of atmospheric pressure plasmas have interfaces with in-homogeneous electrical properties and non-planar surfaces.Additional work is needed to probe the fundamental mechanisms driving the escape of the SIW from the channel.Studying progressively smaller feature sizes will reveal to what extent the effects observed in this work are of consequence at smaller length scales.In this work, the effect that the sharpness of the channel top corner might have on the SIW propagation is not studied.The effect that radius of curvature has on SIW propagation has been previously modeled to show that SIW penetration into features can be affected [27].Future experimental work to characterize the effect of channel edge radius of curvature on SIW propagation is needed.The results of this work highlight the need for future development of 3D models studying SIW propagation.The simplified 2D approach of most models is computationally convenient and yields many valuable insights into SIW physics, but lacks the ability to resolve 3D effects like those seen in this work.

Figure 1 .
Figure 1.Block diagram of the pulsed DC power delivery and ICCD imaging system for SIW propagation.(a) DC power supply (b) Delay generator (c) DC pulser (d) Oscilloscope (e) Gas delivery (f) Plasma source (g) Monitoring computer (h) ICCD camera (i) Target stage.

Figure 2 .
Figure 2. (a) Block diagram of the pulsed APPJ plasma source and ICCD imaging system for axial imaging.(i) ICCD camera (ii) Blocking plate (iii) Target (iv) 3-axis stage (v) Plasma source.(b) Diagram of single channel target construction.Note that items in the figures are not to scale.

Figure 3 .
Figure 3. ICCD image of the target plane with channel installed.Note the blocking plate in the center of the image.

Figure 4 .
Figure 4. ICCD images of a SIW propagating along and outside of a target channel.Channel width is 1.0 mm, depth is 0.25 mm, and pulse energy is 48 µJ.Note the arrows indicating reflections present in the images.Multiplication factors for intensities are shown if they deviate from 1×.Radius and SIW angle are also given.

Figure 5 .
Figure 5. Example voltage and current traces for a pulse event.

Figure 6 .
Figure 6.Process steps for extracting data from ICCD images.(a) in-channel position data and linear fit.(b) radial SIW data and linear fit.Images are for channel 2 (width = 1 mm, height = 0.25 mm) at a pulse energy of 48 µJ.

Figure 7 .
Figure 7. Radial velocity of SIW that escapes the channel.Channel dimensions are given as width × depth.

Figure 8 .
Figure 8. ICCD of the a SIW traveling along a channel and splitting into two individual nodes.Channel width is 1.0 mm, depth is 0.25 mm, and pulse energy is 48 µJ.

Figure 9 .
Figure 9. Velocity of the SIW in-channel as a function of channel geometry and applied pulse energy.

Figure 10 .
Figure 10.'Escape angle' measured as a function of time for all channel geometries at a fixed driving voltage of 4.5 kV.

Figure 11 .
Figure 11.Angular velocity of the SIW for all geometries and energies.

Figure 12 .
Figure 12. of light intensity escaping the channel and propagating across the planar portion of the target.

Figure 13 .
Figure 13.Time averaged escape angles given for all channel geometries and pulse energies.

Figure 14 .
Figure 14.Optical emission of the 706.5 nm helium line for a 1 mm wide channel with a depth of 0.25 mm and at 4.0 kV driving voltage.The radial portion of the SIW is captured with propagation direction marked.

Figure 15 .
Figure 15.Velocity of the SIW on a rough surface or a smooth surface.Roughness is comparable to the channel bottom.

Figure 16 .
Figure 16.SIW spreading over a planar surface for two different geometries.Surface coverage of the SIW is highly dependent on channel geometry.Channel geometries are: left(width = 2.0 mm, height = 0.5 mm) and, right(width = 1.0 mm, height = 0.25 mm).

Figure 17 .
Figure 17.Diagram illustrating radial electric field lines in a SIW.(b) How a minimum energy effects the fraction of the SIW allowed to cross a barrier.ϕ denotes the angle at which the SIW radial field is incident with the channel edge.

Table 1 .
Single channel dielectric target dimensions.Values are as-ordered from the manufacturer and are within 30 µm of the listed values.