Spatially resolved measurements of electron density of a magnetically confined split-ring resonator source

Split-ring resonators (SRR) are a type of microstrip resonator that have various proposed uses, such as metamaterials,¹ plasma metamaterials,^2,3 microfluidic sensing,⁴ material characterization,^5,6 material activation,⁷ and ion and plasma sources.^8–10 SRRs are of interest for use as plasma sources due to their ability to produce plasma at a wide range of pressures at a relatively low power. A SRR is created by etching a conducting ring on a dielectric substrate. The microwave power is supplied to the conducting ring, while the unetched conducting plane on the back side of the substrate acts as ground. The SRR has a gap in it as shown in Fig. 1. The circumference of the ring is designed to be half of the supplied wavelength. This results in the voltage being 180° out of phase at the gap, which leads to a large voltage difference and thus a large electric field that is capable of ionizing the working gas.

SRRs can have a second ring placed concentrically with the first ring with the gaps rotated 180° from one another. These two rings electromagnetically couple with one another. In this case, the resonant frequency of the system can be found by modeling the SRR as a LC circuit.^11–13 When used as a plasma source, this geometric configuration has the benefit of introducing a second ionization region at the second gap, which can result in a more uniform plasma.⁸ 

Most research on SRRs to date has focused on its use as a metamaterial or plasma metamaterial. This work looks to explore its behavior as a plasma source. Specifically, it seeks to observe the effects on a SRR plasma discharge placed within a magnetic cusp field. An end application is to use a SRR as a plasma source in a Hall effect thruster, which uses magnetic fields. Thus, studying how a SRR behaves in a magnetic cusp field will help to understand how a SRR might behave inside a Hall thruster and thus help in the design of such a thruster. To do this, a parametric study was performed to observe the effects of power, pressure, and magnetic field strength on the performance of the SRR plasma in the applied magnetic field. To measure the effects on the generated plasma, laser collisional-induced fluorescence (LCIF) measurements of the electron density and electron temperature were acquired.

The plasma used in this experiment was created with a SRR, with a set of permanent magnets optionally placed behind the SRR. The SRR was made using wet etching techniques with a piece of copper clad Rogers Corp. RT/duroid 6010LM laminate approximately 2.54 × 2.54 cm² in size. The front plane contains rings, which are made of copper. The back plane, also made of copper, is unmodified and acts as a ground plane. The laminate acts as a dielectric and separates the front and back planes. The outer ring is directly soldered to a coaxial cable, which provides the microwave signal to the ring. The inner ring is unpowered.

The SRR used in this work had an outer radius of 10.46 mm for the outer ring. Both rings were 1 mm thick with a separation distance of 1 mm. The discharge gaps were 500 μm wide. The powered ring's gap was positioned at 20° from the center of the SRR, and the inner ring's gap is rotated 180° from the outer gap. Using the LC circuit model given by Saha and Siddiqui,¹¹ the SRR was designed to have a resonant frequency of 820 MHz; however, it was experimentally found to have an actual resonant frequency of 844 MHz. This was measured by scanning the driving frequency and measuring the voltage standing wave ratio (VSWR) with a Bird power sensor. The discrepancy in the experimental resonant frequency and the model is likely driven by a combination of fabrication tolerances and substrate dielectric variance.

A Rigol DSG836 signal generator was used to supply microwave power to the SRR. Power was supplied at 844 MHz and at 10, 11, and 12 W. A Bird power sensor was used to measure the forward and backward power to the SRR. The backward power was subtracted from the forward power to determine the power supplied to the SRR. This was necessary as the VSWR varied depending on the operating conditions. It was observed that raising the power slightly increased the VSWR, while decreasing the pressure decreased the VSWR. The addition of the magnets and the increasing of the magnetic field strength also resulted in a decrease in the VSWR. Helium was used as the working gas. A turbomolecular pump was used to evacuate the chamber to a base pressure of approximately 6 × 10⁻⁶ Torr. The vacuum chamber had a diameter of 61 cm and a height of 46 mm. The setup was given several hours to outgas in order to improve the LCIF signal. This was needed as nitrogen has a major quenching effect on helium LCIF lines. Then, a MKS 946 Vacuum System Controller connected to a mass flow controller was used to flow helium into the chamber to raise the pressure up to approximately 1.5 Torr. At this point, the SRR was ignited, and the pressure was dropped down to the operating pressure. For this work, three operating background pressures of 250, 500, and 1 Torr were used. After the pressure was stabilized, the SRR was given 10 min to warm up.

A pair of permanent ring magnets were placed behind the SRR to generate the cusp fields. The rings were placed concentrically with one another with matching poles facing 180° from each other as shown in Fig. 2 in order to create a cusp field around the SRR. For this experiment, four magnetic field cases were considered. These will be referred to as no field, low, medium, and high. Simulations in FEMM estimated the magnetic field strengths at the gap to be 0, 0.21, 0.24, and 0.29 T.

Helium was used as the working gas to generate the plasma due to an established ability to determine electron density and temperature with LCIF and a collisional radiative model (CRM) developed at Sandia National Laboratories (SNL).^14,15 A schematic of the setup is given in Fig. 3. For this experiment, an Ekspla NT230 laser was used. The laser had a repetition rate of 50 Hz and a pulse width of 3 ns, which supplied laser light with ∼1 mJ of energy to the system at 388.86 nm. The two plano-convex lenses were used to expand the laser beam before it went through the cylindrical lens. The cylindrical lens then resulted in a laser sheet that was approximately 400 μm thick and 5 cm tall in the region of the plasma. An Andor iStar DH334T ICCD camera was used. Each pixel has an effective resolution of 100 × 100 μm². One of three bandpass filters was attached to the ICCD camera. The bandpass filters were centered on 390, 450, and 589 nm (±10 nm FWHM). Acquisition time and the number of accumulations varied for the three filtered wavelengths: 390 nm (0.04–0.2 s, 100 accumulations), 589 nm (0.05–0.7 s, 50–100 accumulations), and 447 nm (3–40 s, 5–25 accumulations). The SRR was attached to a translation stage which allowed LCIF measurements to be acquired at multiple locations. Due to the length of image acquisition, hours allowed on site, and operating conditions in some cases, the number of locations that data could be acquired for each case was limited to five. Based on what was visually observed, these five locations were evenly distributed from edge to edge of the magnet holder as indicated in Fig. 3(c). However, it was discovered in post processing that the electron densities in locations 1, 4, and 5 were often too low to obtain useful information. There was not enough time to go back and redo the measurements. Thus, only data from steps 2 and 3 are presented.

As future work will seek to use a SRR as a plasma source in a Hall thruster, an understanding of how the addition of a magnetic field to a SRR plasma affects the plasma is needed. Toward this goal, this work seeks to study the effects of power, pressure, and magnetic field strength on the performance of a SRR plasma. Toward this end, spatially resolved measurements of $ne$ and $Te$ were acquired using LCIF paired with a CRM. In LCIF, a laser is tuned to the wavelength corresponding to a specific excited state transition from a lower energy to a higher energy. The electrons at this higher energy state are then further excited to adjacent energy states through collisions with free electrons and other plasma species. As the excited electrons relax and fall back down to lower states, the difference in energy between the states is released as a photon which is known as fluorescence. Knowledge of the interactions between the excited electron species and the species in the plasma can be used in a CRM¹⁵ to acquire information about $ne$ and $Te$ from the spectral emission data.

For this work, the He LCIF scheme and CRM used by Barnat and Frederickson¹⁵ are used. This scheme is illustrated schematically in Fig. 4. Laser light with a wavelength of 388.86 nm is used to excite the metastable 2³S state to the 3³P state. Electron collisions then redistribute the electron population to the adjacent 3³S, 3³D, and 4³D states. Radiative relaxation then causes fluorescence at 707 (3³S to 2³P), 389 (3³P to 2³S), 588 (3³D to 2³P), and 447 nm (4³D to 2³P). These lines are then captured by the ICCD camera, which is equipped with one of the three bandpass filters. The 707 nm state is independent of 389 nm state and thus is not used.¹⁴ For each measurement, the ICCD camera captures four images for each filter. The first three of these images correspond to the background signal with no plasma emission or laser probe, the pure plasma emission, and the pure laser probe. These can then be subtracted from the plasma emission with a laser probe signal in order to remove all the background signal and acquire the pure LCIF signal.

A MATLAB script uses the LCIF signal with the CRM in order to find $ne$ and $Te$⁠. This is done by creating intensity ratio images between the 588:389 lines for density and the 447:588 lines for temperature. The CRM only considers states in the triplet manifold up to n = 5. Interactions that can cause electron state transfers between the singlet and triplet states are ignored.^14,15 This results in a total of 15 states and thus a set of 15 differential equations that describe changes in the atomic states due to electronic processes, ionic processes, and atomic processes. The CRM is then run for multiple different electron density, electron temperature, and pressure conditions. Polynomial fits are then used to relate the LCIF line ratios to electron density and temperature as discussed in the Appendix of White et al.¹⁴ The fits were found using the robust linear least squares fitting method in MATLAB with 95% confidence bounds.¹⁴ Using the CRM to solve for the electron density is dependent on the 588:389 ratio being nearly independent of electron temperature. Solving for the electron temperature is dependent on the 447:588 ratio being nearly linear with respect to temperature. These conditions give this method lower and upper bounds of n_e of about 5 × 10⁸ and 5 × 10¹² cm⁻³, respectively. Lower and upper bounds of about 0.4 and 10 eV are set for T_e. More information about the CRM can be found in Barnat and Frederickson.¹⁵ 

Having knowledge of the rate coefficients is key to obtaining useful information from the measurements. The CRM assumes a Maxwellian distribution for the electrons.^14,15 This allows for simultaneous measurement of $ne$ and $Te$⁠. In Fig. 5, the key rate coefficients leading to emission at 588 and 447 nm by LCIF are given. The 588 nm state is approximately independent of temperature. This allows the ratio of 588:389 to be used in order to calculate the electron density. Once the density is known, the temperature independent 588 nm line can be used with the temperature dependent 447 nm line in order to calculate the electron temperature.

To study the effect of a magnetic cusp field on a SRR plasma, a parametric study was carried out. This was performed by operating at three powers, three pressures, and four magnetic field cases. The result of this was 36 different experimental cases. For each case, five two-dimensional (2D) images were acquired for different positions of the SRR with respect to the laser light sheet. The images are oriented perpendicular to the SRR surface and spaced 16.7 mm apart. 1D plots were created by taking the regions of highest density and temperature and taking an x- and y-slice through the region as shown in Fig. 6(c). As it is not possible to display results from every case in this paper, only a portion of the data is presented here. The results and trends presented here are consistent for all cases tested. The rest of the data is available as the supplementary material.

Powers of 10, 11, and 12 W were used to drive the SRR, and LCIF was used to measure the electron density and electron temperature. The 1D x- and y-slice results for the low field case at 250 mTorr are given in Fig. 7. As the power is increased, the electron density increases, but the overall profile of the plasma stays the same. This is seen by the widths and shapes of the curves staying the same. As the power is increased, the energy supplied to the system increases. This results in more ionization and thus a higher density. This trend holds for all cases with a constant pressure and magnetic field. Looking at Fig. 7(b), it can be seen that the peak density in the y-direction occurs about 8 mm away from the surface of the SRR. This behavior agrees with previous Langmuir probe measurements that were taken for the SRR in no magnetic field.⁸ The peak electric field of the SRR is highest at the surface; however, the peak ionization rate does not occur there. Peak electron densities occurring away from the surface seems to indicate that secondary ionization occurs after the initial ionization at the surface. A possibility is that the electric field that causes the primary ionization results in the electrons being accelerated away from the surface of the SRR. These excited electrons could then collide with neutral species in the plasma and result in further ionization.

Pressures of 250, 500, and 1000 mTorr were considered next. Figures 6 and 8 show the 2D and 1D electron density profiles for these different background pressures at the low field case at 11 W. The 2D images appear to have crisp edges for the plasma boundary. It should be noted that these edges are not indicative of the actual “plasma edge.” Rather they represent the edge of where the electron density was high enough to produce a LCIF signal that was high enough to detect. The crisp nature of the edges is due to thresholding that was implemented to remove noise. More info on the thresholding process can be found in the  Appendix. The most obvious change between the different pressures is in the volume of the discharge. As expected, increasing the pressure reduced the volume of the plasma. Furthermore, the peak density location in the y-direction moves closer to the surface of the SRR as shown in Fig. 8(b). This is due to the increased pressure reducing the mean free path of the electrons. As previously mentioned, the peak density location is some distance away from the location of the primary ionization and is possibly due to the electrons being excited and accelerated. These excited electrons then collide with neutrals and result in further ionization and the release of electrons. If the mean free path of the electrons is reduced by increasing the pressure, the collisions responsible for the secondary ionization will occur closer to the surface of the SRR as is observed.

As background pressure is increased, the peak electron density increases. This is due to an increase in pressure corresponding to an increase in the number of neutrals in a given volume. Ionization of neutrals acts as the source of electrons in this sytem. By increasing the density, the likelihood of a neutral atom experiencing a collision resulting in ionization in a given region increases. Another interesting characteristic is the uniformity of the density profile. At 250 mTorr, the density profile is fairly uniform across the plasma volume as shown in Fig. 8. As the pressure is increased, it can be seen in Fig. 8(a) that the peak density region becomes more and more isolated in the x-direction while the density falls off more sharply from the peak location in the y-direction as shown in Fig. 8(b). The localization of the high density region in the x-direction is due to the increase in background pressure raising the energy required for breakdown. As shown in Fig. 1, the peak electric field is located at the gap. When the pressure is raised, the regions of lower electric field do not have enough energy to cause breakdown, unlike at lower pressures. This results in the primary ionization being more localized to the region around the gap. The effect of this is exaggerated with the addition of the magnetic field, which limits cross field transport of the electrons and isolates transport primarily to the direction parallel to the magnetic field.

Four different magnetic field cases were considered. The electron temperature is given in Fig. 9. This provides evidence of the electrons becoming trapped along the magnetic field lines. In the x-slice, the no magnet case has a fairly uniform temperature of about 0.8 eV while the magnet cases have a temperature of about 1.5 eV on the edges that rises to about 3 eV in the center of the discharge. This is an expected trait of plasma where the electrons have become magnetized. Since electron transport is mainly confined along the magnetic field lines, the electrons establish their own Maxwell–Boltzmann equilibrium with separate temperatures along each magnetic field line.¹⁶ The temperatures will tend to be higher along magnetic field lines that cross the electron heating region of the plasma source,¹⁶ which for the SRR coincides with the high electric field regions that result in high density regions.

As with the electron temperature figures, the electron density profile figures show magnetic-field effects on the plasma. Figure 10 shows the 2D electron density map for the four different cases at 11 W and 500 mTorr. The no magnet case has a relatively uniform shape and distribution. This is due to electron transport being dominated by diffusion. When magnetic fields are added to the system, the overall shape of the plasma volume becomes elongated and the uniformity starts to be replaced by structures that appear in the plasma. These structures impact not only the overall shape of the volume plasma but also how the high-density regions are distributed throughout the plasma. This is due to electrons becoming trapped along the magnetic field lines. It is hard for the electrons to move perpendicular to the magnetic field lines, but easy to move parallel. This restricts electron transport mainly to the y-direction. Due to how ionization occurs with the SRR, there will be localized regions with higher densities of electrons. This is corroborated by referring back to the electron temperature results. The 1D electron temperature data presented in Fig. 9 are the same data that were used for the 2D density plot given in Fig. 10. Comparing the two figures shows that the high temperature regions appear in the same regions as the high electron density regions for the magnetic field cases.

The structures that appear in the magnetized cases appear to occur directly below the rings and in the region in the center of the SRR. The structures occurring below the SRR rings appear to support the idea that the electrons become magnetized and follow the magnetic field lines. As shown in Fig. 2, the magnetic field lines are isosymmetric radially. As previously explained, the peak electric field occurs along the rings of the SRR in the region of the gap. This results in peak electron densities occurring below the surface of the ring. These electrons then become trapped in the magnetic field lines. Due to the isosymmetric nature of the field, the trapped electrons can easily move azimuthally, but not radially, which results in the structures that appear in the 2D image. This is further supported by Fig. 11, which shows 2D cross sections as in Fig. 10, but the images are acquired at step 2 that does not lie directly below the SRR rings. This results in less structures appearing in the images.

Further proof of magnetization of the electrons can be found by estimating the mean free path and collision frequency of the electrons, and comparing that to calculations for the Larmor radius and gyrofrequency of the electrons in the magnetic fields. As the neutral density is several orders of magnitude higher than the electron density, and thus the ion density assuming quasineutrality, the electrons mainly collide with neutrals and thus only the mean free path and collision frequency for electron–neutral collisions is calculated. An electron temperature of 3 eV is used based on the LCIF measurements. The cross section is then found to be 6.67 × 10⁻¹⁶ based on the data from Belmonte et al.¹⁷ This results in mean free paths of 1.8, 0.9, and 0.5 mm and collision frequencies of 637, 1274, and 2548 MHz for the 250, 500, and 1000 mTorr cases, respectively. By using the electric field strengths at the gap that were found from the FEMM simulation given in Sec. II, Larmor radii of 0.03, 0.03, and 0.02 mm are found for the low, medium, and high field cases, respectively. This corresponds to gyrofrequencies of 5878, 6717, and 8117 MHz. The gyrofrequencies are much larger than the collision frequencies, which indicates that the electrons are magnetized. As the pressure is increased, this difference decreases, especially at higher pressures. As the two frequencies get closer, the effect of magnetization reduces, which could explain why the low field case has density profiles more similar to the no magnet case at 500 and 1000 mTorr as depicted in Fig. 12.

The electron temperature and electron density results along with the mean free path and Larmor radius calculations support that the magnetic field magnetized the electrons. This results in restrictions on the electron transport due to magnetic field effects, which results in elongated high density, high temperature regions in the plasma.

It was believed that by introducing a cusp field around the SRR, the electron density could be increased due to the cusp-field reducing the rate of electron diffusion and increasing ionization. However, the introduction of the cusp field did not increase the electron density as evidenced by Fig. 12. In every case, the no magnet case outperformed every one of the magnetic cases. The no magnet case had peak electron densities ranging from 1.3 × 10¹¹ to 1.9 × 10¹¹ cm⁻³ while the different magnetic field cases had peak densities ranging from 5.0 × 10¹⁰ to 1.7 × 10¹¹ cm⁻³ with the highest peak densities occurring at higher pressure. The likely cause of this behavior is that the introduction of the permanent magnets results in interference with the magnetic resonance of the SRR, thereby changing the power coupling. In the work by Hu et al.,¹⁸ ANSYS HFSS is used to simulate a permanent magnet placed behind a SRR with a field perpendicular to the SRR surface. In that work, various magnet thicknesses corresponding to higher magnetic field strengths were simulated in order to look at the effect of the magnet field on the S parameters of SRRs. It was found that the S11 parameter, also known as the reflection coefficient, had an optimal magnetic field strength that resulted in a maximized S11 parameter.¹⁸ This shows that the addition of a permanent magnet to a SRR system does in fact affect the magnetic resonance of the SRR. Thus, it is likely that even if the cusp fields do reduce diffusion and increase ionization, this effect is overridden by a lower initial ionization due to the coupling of the SRR being affected by the permanent magnets. Further work would need to be done to see how the addition of the cusp magnetic field affects the electric field on the SRR and thus the ionization, and how the geometry of the SRR field affects this result. Unfortunately, that was outside the scope and timeline of this experimental effort at SNL.

While the no magnet case always had the highest density, an interesting relationship between the magnetic field strength and pressure was observed. In Fig. 12, it is observed that at 250 mTorr the high magnetic field case has the highest density of all the magnet cases. However, as the pressure increases, the low magnet case starts to perform better and the high magnet case starts to perform worse relative to the other magnet cases. This could possibly indicate that at low enough pressure and a high enough magnetic field strength, it would be possible to have a magnetically confined SRR plasma that could have a higher electron density than the no magnet case.

A SRR is used as a plasma source for a helium discharge. Permanent magnets were introduced to the system in order to create a magnetic cusp-field with the intent to increase the electron density through reduction in the rate of electron diffusion, similar in concept to magnetized RF plasma. A parametric study was performed with varying power, pressure, and magnetic field strength in order to observe the effect of the magnetic fields. LCIF was used to acquire electron density and electron temperature in order to compare the different cases. It was found that increasing the power and pressure results in increased electron density and negligible effect on electron temperature. Increasing the pressure also results in decreased plasma volume. The addition of magnetic fields was found to magnetize the electrons as evidenced by changes in the shape of the discharge, which was caused by reduced electrons cross field diffusion. This finding was further supported by the electron temperature measurements, which showed that different Maxwell–Boltzmann distributions form along the magnetic field lines. This resulted in the magnetized cases having a higher peak electron temperature of ∼3 eV while the no magnet case had a more uniform electron temperature profile and a peak temperature of ∼0.8 eV. Contrary to expectations, the introduction of the magnetic fields resulted in a decrease in the electron density. This could possibly be due to the permanent magnets affecting the electromagnetic resonance of the SRR and resulting in a decreased electric field along the surface of the SRR.

See the supplementary material for plots and images in the various cases. Due to the amount of data that was collected, it was not possible to show plots and images for every case. The supplementary contains the 2D images and 1D plots for every case. It also contains plots comparing the maximum densities for the various cases.

This material is based upon work supported by the U.S. Department of Energy, Office of Science, Office of Workforce Development for Teachers and Scientists, Office of Science Graduate Student Research (SCGSR) program. The SCGSR program is administered by the Oak Ridge Institute for Science and Education for the DOE under contract No. DE‐SC0014664. This work was supported by Sandia National Laboratories' Plasma Research Facility, funded by the U.S. Department of Energy Office of Fusion Energy Sciences. Sandia is managed and operated by NTESS under DOE NNSA contract No. DE-NA0003525. This work was supported by the NSF EPSCoR RII-Track-1 Cooperative Agreement (No. OIA-1655280). The author would like to thank Dr. Brian Bentz at Sandia National Laboratory for his guidance and support in taking the measurements.

The authors have no conflicts to disclose.

Andrew T. Walsten: Conceptualization (equal); Data curation (equal); Methodology (equal); Writing – original draft (lead). Brian Z. Bentz: Formal analysis (equal); Methodology (equal); Supervision (equal); Writing – review & editing (equal). Kevin Youngman: Resources (equal). Kunning G. Xu: Conceptualization (equal); Project administration (equal); Supervision (equal); Writing – review & editing (equal).

The data that support the findings of this study are available within the article and its supplementary material.

As mentioned in Sec. II, the plasma densities and temperatures that are presented in this work are found through the use of ratios of different lines. In regions where LCIF signal is extremely low, noise can cause issues. For example, if the denominator of the ratio used has a very low noise signal compared to the numerator, it can result in the ratio increasing significantly and creating artificial peak values. For this reason, it was necessary to use thresholds. These thresholds are applied to the individual LCIF lines before the ratios are determined. The thresholds work by setting any pixel to zero that has a value that is a certain percentage below the peak value for the image. This eliminates the noise so that artificial features do not appear in the data. However, due to the different signal levels caused by different acquisition times, accumulation times, location of measurements, and operating conditions, it was necessary to set different thresholds for different steps and different operating conditions. Due to it being necessary to manually decide on these thresholds, it was important to create a consistent approach to deciding on the threshold values so that we were not artificially manipulating the data. This appendix will describe the method by which threshold values were set. An example comparing the electron density calculated using raw data and the post threshold data is shown in Fig. 13. A striking feature of the post threshold data is the “crisp” lines that appear to designate the “edge” of the plasma. It should be noted that this is not the “edge” of the plasma, but rather the boundary at which the density of electrons was high enough to obtain significant LCIF signal. Looking at Fig. 13(a), there are several distinguishing features. There is a relatively “high signal” region that corresponds to the plasma directly below the SRR, a “high density” region to the left of the plasma region, a “high density” region above the plasma where the SRR is located, a horizontal line that appears around the y = 40 mm location, and a large noise region that surrounds all of the other regions. The “high density” region to the left of the plasma is believed to be caused by noise and a reflection of the LCIF signal. Ideally, this region would be removed by the threshold; however, in some cases, the edge of the reflection impinges on the actual plasma region. In these cases, it was not possible to completely remove the reflection without removing part of the plasma region and thus altering the data. In these cases, the effect of the reflection on the edges of the plasma should be ignored. The region above the plasma at y < 0 mm corresponds to light reflecting off the SRR and magnet holder. The SRR was not perfectly centered in the images acquired. However, the reflections on the SRR allowed determination of the center position of the surface of the SRR, defined as the origin in the images. Finally, the most important region in the determination of the thresholding of the raw data is the horizontal line at approximately y = 40 mm. This line corresponds to the edge of the laser sheet that passes through the plasma. Knowing this, it can be said that any signal that occurs below that line is noise and not LCIF signal. Thus, thresholds were set up to the point where they removed this noise signal in the region below the edge of the laser sheet at y < 40 mm without removing any of the signal above it. This line was only visible for the 250 mTorr cases due to a high-density electron region extending low enough to pass the laser edge. At higher pressures, as the location of the laser did not change, the same h < 40 mm region could be used to determine the threshold. For example, if there were any artificial signals that appeared in all images at higher pressures, such as the reflection, the threshold could be set to remove the artificial signal. As the thresholds for the 250 mTorr cases removed the grainy low signal regions, these regions were also removed by the thresholds for the higher-pressure cases.