High-Speed Tomography—A New Approach to Plasma Bulk Velocity Measurement

Abstract

The plasma bulk velocity is one of the key parameters describing the behavior of a plasma jet and is relevant for applications such as plasma spraying or electric propulsion. Therefore, different measurement techniques to determine the velocity were developed in the past. This paper presents a novel, non-invasive method for spatially resolved velocity measurements. The method is based on tracking of characteristic features in tomographic reconstructions of the plasma plume. A high-speed image recording system combined with tomographic acquisition is therefore the backbone of this method. The proposed setup captures the object under study from six different directions at a frame rate up to one million frames per second, providing high spatial and temporal resolution. The tomographic reconstructions are then calculated using the ART algorithm to track features in the plasma fluctuations, from which the bulk velocity is determined. The setup was tested with a DC plasma torch operated at reduced pressures in the range of tens of millibars. For the analyzed parameters, the axial velocity reached a maximum of 1061 m/s at a distance of three centimeters from the plasma torch exit and decreased to 919 m/s further downstream at a distance of seven centimeters, which is in good accordance with previous work. Therefore, the proposed diagnostic method can serve as a non-invasive alternative to velocity measurements, providing additional information in the form of a 3D model of the plasma bulk.

1. Introduction

In the field of thermal plasma diagnostics, a wide range of different measurement techniques exist that allow for a qualitative and quantitative description of the plasma under investigation. The techniques can be divided in general into invasive and non-invasive methods. The former provide quantitative results and are often used to determine electron properties or flow velocities. The latter can provide quantitative and qualitative results alike. Quantitative non-invasive methods are typically used for the identification of plasma constituents, the determination of species density or gas and electron temperatures. These methods include optical emission spectroscopy, photometry or laser-based diagnostics. Qualitative non-invasive methods are usually camera-based and include techniques such as high-speed imaging, schlieren optics, or emission tomography. Depending on the technique chosen, simplifying assumptions are often required for a quantitative description of the plasma under investigation [1,2,3,4,5,6].

The presented high-speed tomography diagnostic combines two of the above non-invasive methods: high-speed imaging and emission tomography. While in previous works these tools have been used separately to determine the behavior or, in the case of tomography, to measure the temperature of the plasma, the techniques were combined in this work to assess the bulk velocity of the plasma. The bulk velocity is one of the key parameters for determining the heat transfer from the plasma to the particles (relevant for thermal spraying applications) [7] and the fluxes of mass, thrust, and energy (relevant for electric propulsion applications) [8]. Previous studies have measured the plasma velocity invasively using electronic probes or optically using laser light scattering and spectroscopy [3,4,6]. In contrast to electronic probes, high-speed tomography offers the advantage of non-invasive diagnostics and a three-dimensional reconstruction of the object, which is not possible with other optical methods. A reconstructed model provides additional information, such as the shape and expansion of the plume, which can be used for further analysis. However, this is beyond the scope of this paper. The measurement of the plasma bulk velocity is the focus of this work.

The plasma velocity of DC plasma spray torches has been measured using several different methods. Some authors have determined the velocity by means of electronic probes [9,10]. Axial velocities of 100–550 m/s under atmospheric pressure at different currents and argon gas flow rates can be found in [9]. In [10], the velocities for different nozzle designs and pressure values of a DC plasma torch operated at 400 A with a gas mixture of argon and hydrogen were determined. The results presented show that the plasma jet velocity can reach up to 1200 m/s depending on the nozzle design and operating pressure. Brossa and Pfender used enthalpy probes to investigate the influence of the argon flow rate and current on the velocity of the plasma jet. The commercially available DC plasma torch used by the authors reached velocities in excess of 100 m/s while operating at atmospheric pressure [11]. A different approach was taken by Johnson and Murphree in [12], who determined the velocity of a super-sonic argon plasma stream in a low-vacuum environment by Langmuir probe measurements. Depending on the gas flow rate, velocities in the range of Mach number 1.12–1.18 were measured [12]. A comparison of probe and optical velocity measurement techniques for different kinds of plasma is presented in [13]. A pulsed DC non-equilibrium atmospheric plasma bullet generator operated with helium was used as a test object. Plasma plume velocities of about 50–60 km/s were assessed with probe measurements, while the optically determined velocities were about 80–85 km/s [13]. Chen et al. also combined probe and optical measurements and showed that a plasma jet from a DC torch operated at 800 A with argon and helium as plasma forming gases at atmospheric pressure under the assumption of local thermal equilibrium (LTE) can reach up to 1000 m/s [14]. Couder, Planche, and Fauchais measured the plasma velocity optically by observing arc fluctuations [15,16]. The authors examined a plasma torch fed with direct current in the range of 300–900 A and argon or nitrogen under atmospheric conditions. To measure the velocity, an image of the plasma jet was split into two planes so that a distance between them could be determined. Depending on the current, voltage, gas type, gas flow and nozzle shape, velocities up to 1600 m/s were measured [15,16]. Plasma velocity can also be determined by means of laser-induced fluorescence [17,18]. MacDonald et al. used this method, for example, to examine an electromagnetic propulsion thruster in a vacuum. The authors recorded axial ion velocities of a straight cylindrical cusp field thruster in the range of 15.6 km/s [17]. The same diagnostics were also used to measure the ion velocity in a DC plasma sheath. Values of up to 21 km/s are reported in [18]. Another non-invasive technique, laser scattering, was used to determine the plasma velocity of a DC plasma torch operated with argon and current values between 300 and 900 A in ambient air. Values of up to 1100 m/s have been observed under these operating conditions [19]. Laser scattering was also used in another work involving a DC plasma generator operated at pressures lower than atmospheric. In [20], velocities of up to 2.6 km/s were achieved using argon and 600 A at 100 mbar operating pressure. In [21], on the other hand, laser absorption as well as fluorescence and emission spectroscopy were used to measure plasma velocity of a modified 4 kW cutting torch operated with argon and hydrogen in a vacuum chamber. The torch was used as a low-pressure plasma spraying source. Values of up to 7 km/s were reported by the authors [21]. An invasive approach was used by Bowman in [22] to measure the plasma velocity of a high power DC arc. The horizontal deflection of dropped ball bearings has been recorded, resulting in values in the range of 1500 m/s [22].

Tomography is used to detect the temporal behavior of the local emissions of the plasma jet, as done in [23]. In combination with spectroscopic diagnostics as in [24] or two-color pyrometry as in [25], tomography is also applied for temperature determination. In order to obtain a tomographic reconstruction, it is necessary to observe the studied object from a number of different viewing directions. This can be achieved with a single camera by rotating it around the object, as presented in [26], but at the same time this approach implies that the object does not change significantly during the recording. For temperature measurements, this assumption is usually acceptable due to the more statistical behavior. For other applications, it can be circumvented by using a set of mirrors that simultaneously image the object onto the camera’s sensor plane, creating the required number of viewing directions. Such an approach provides an instantaneous image of the object and is therefore better suited to evaluate the temporal behavior of the object under study. For example, it was used to assess the asymmetries of a plasma jet in [27].

The spatial resolution of a tomographic reconstruction is determined by the number of images from different directions of view. The more complex the shape of the measured object, the more different viewing angles that are needed for an accurate reconstruction. Feasibility studies on how many directions of view are needed to reconstruct complex shapes were presented in [28]. According to the results, only four viewing directions are sufficient for a reconstruction calculation using the Algebraic Reconstruction Technique (ART) [28]. Four directions of view have also been used for a time-resolved temperature measurement of a thermal plasma jet [29]. In this study, the plasma torch was operated at atmospheric pressure with a current of 200 A and argon as the plasma carrier gas. The filtered back-projection was then used for the reconstruction [29].

As discussed above, there are many diagnostics for determining the plasma velocity of different measurement objects. Here, the tomographic diagnostic tool coupled with high-speed imaging is used for velocity measurements. One advantage of this approach is that it is a non-invasive measurement technique. In addition, compared to laser or spectroscopic diagnostics, the used method promises low complexity. The combination with a high-speed imaging system enables the detection of fluctuations of the plasma plume in the range of microseconds and the tracking of these fluctuations in the reconstructed images to determine the velocity of the plasma. The aim of this work is therefore to determine the velocity of the plasma bulk with such a high-speed tomographic system. To validate the proposed setup, a DC plasma spray torch operated at a pressure of 20 mbar was used as the measurement object. However, the proposed setup can be used for other applications such as electric propulsion. In order to achieve the highest possible spatial resolution and, on the other hand, due to geometrical limitations, the torch under study was observed from six directions of view. As a result, a reconstructed three-dimensional model of the plasma plume was delivered.

2. Materials and Methods

2.1. Experimental Setup

As stated in the previous section, a DC plasma torch (described in Section 2.1.1) operated at about 20 mbar was used as a test object for the proposed setup. In order to minimize possible influences on the gas flow caused by the chamber walls, the plasma torch was mounted in a vacuum chamber with a volume of about 0.77 m³. A Duo 120 A rotary valve pump and a PCR 260 pressure sensor with matching controller, all from Pfeiffer Vacuum, Asslar, Germany, were used to evacuate the chamber. The vacuum pump has a volume flow of 120 m³/h.

The relevant components of the experimental setup are shown in Figure 1. For clarity reasons, the vacuum chamber is shown as a sectional view. The plasma gun is mounted on a linear traversing unit, which is used to adjust its horizontal position. In addition, the tomographic setup, which consists of a set of smaller mirrors providing six different directions of view of the plasma jet and a larger mirror that redirects the projections to the image recording system, was also mounted in the chamber. A detailed description of this setup is given in Section 2.1.2. In contrast, the image recording system, which is described in detail in Section 2.1.3, was mounted outside the chamber.

2.1.1. Plasma Generator

The plasma generator F4-MBX, manufactured by OC Oerlikon Corporation AG, Pfäffikon, Switzerland, was used as the measurement object. Figure 2 shows the generator in operation. In this figure, the set of mirrors can be seen in the background, providing the different viewing directions for the tomographic reconstruction.

The plasma generator has a simple design, with a finger-shaped cathode with a tungsten core casted in copper and a tungsten anode with an outlet diameter of six millimeters. Argon was used as the plasma forming gas in all experiments. The gas flow was set to 35 slpm. The nozzle of the plasma generator had a diameter of 6 mm [30]. The necessary cooling water for the plasma generator was provided by a glanded pump. The electrical power for igniting the plasma was provided by three TopCon Quadro power supplies, arranged in such a way to provide a voltage of 200 V and a current of 600 A. These devices were manufactured by Regatron AG, Rorschach, Switzerland. A 1559A mass flow controller from MKS Instruments, Andover, MA, USA, was used to control the gas flow.

2.1.2. Tomography Setup

As mentioned above, the tomographic system consisted of a set of six smaller plane mirrors and another larger mirror to redirect the projected images of the plasma plume through a chamber window to the image recording system mounted outside the chamber. The six smaller mirrors were arranged cylindrically in 30-degree increments on a metal carrier plate, as shown in Figure 3.

The mirror arrangement was offset by 15° from the horizontal plane. All deflection mirrors were manufactured by Edmund Optics Inc., Barrington, NJ, USA with an enhanced aluminum coating with an average reflectance of >95% at 450–650 nm at an angle of 45°. The surface flatness amounted to 4–6 λ and the surface quality to 60–40. The six small ones had a size of 50 mm × 75 mm and the larger one had a size of 250 mm × 350 mm.

Furthermore, all mirrors were mounted on kinematic holders that allowed for vertical and horizontal fine adjustment. These kinematic mirror holders were manufactured by OWIS GmbH, Staufen, Germany.

2.1.3. Image Recording System

The image acquisition was realized with a self-developed system, shown in Figure 4, consisting of a rotating mirror, an image intensifier and a high-speed camera.

The rotating mirror with an electric motor is a self-assembled component. It consists of a brushless motor controlled by a microcontroller using pulse width modulation to drive the motor shaft. A trigger wheel with a light barrier is responsible for triggering the system at the moment when the mirror is in the desired position for recording. The rotation speed can be adjusted up to 20,000 rpm. The recording technique is described as follows.

The operation principle of the image recording system is depicted in Figure 5. The image intensifier is operated in multiple exposure mode while the high-speed camera integrates the respective exposures on its chip. The exposure time of the high-speed camera is set to 1.2 ms. The image of the measurement object is shifted by the rotating mirror so that the exposures do not overlap. Thus, it is only necessary to ensure that the exposure time of the high-speed camera is longer than the sum of all exposures of the image intensifier and delays between each of them. To achieve this, the components have to be synchronized. The Quantum Leap image intensifier, manufactured by Stanford Computer Optics, Munich, Germany, can capture up to twenty exposures when operated in multiple exposure mode. The lowest delay value between two exposures can be set to one microsecond and exposure time can be set between one nanosecond and one millisecond. Since the image intensifier is the determining element for the multiple exposure, a frame rate up to one million frames per second can be achieved with this image recording system. The measurement object was reproduced on the photocathode of the image intensifier using a wide-angle AF Nikkor 24 mm F/2.8 D lens manufactured by Nikon, Tokyo, Japan. The output of the image intensifier, on the other hand, was reproduced on the Dimax HS4 high-speed camera from Excelitas PCO GmbH, Kehlheim, Germany, with a Laowa CA-Dreamer 100 mm F/2.8 macro lens manufactured by Venus Optics-Laowa, Tsuen Wan, Hong Kong. The high-speed camera is capable of recording 2277 frames per second at full resolution of 2000 × 2000 pixels.

The challenge is to trigger the image amplifier and the high-speed camera when the rotating mirror is in the recording position, so that the measurement object is displayed on the camera chip and the area of the chip is filled with exposures as best as possible.

Figure 6 depicts the trigger scheme for the experiment. The plasma generator was running continuously during the image acquisition. The image recording system is self-triggering. The rotating mirror and a flywheel with a small hole are both mounted on the motor shaft. A light barrier emits a trigger signal when the rotating mirror, or more specifically the hole of the flywheel, is in the light barrier. The flywheel can be adjusted to a desired position with respect to the mirror. The emitted signal triggers both the image amplifier and the high-speed camera.

Due to the multiple exposures of the measurement object on the camera chip, the recording system has limitations. Optical imaging must ensure that multiple exposures are placed within the size of the camera chip. To obtain a higher resolution of the object, the temporal resolution has to be reduced, because a longer delay between the exposures is necessary to avoid overlapping of each other, while a high sampling rate of the measurement object limits the spatial resolution. Therefore, a balance has to be found between achieving the highest possible sampling rate without losing too much spatial resolution.

2.2. Experimental Procedure

In this section the entire procedure for the experiment is described, from activating the peripheral devices to recording the data. First, the entire setup needs to be adjusted precisely. During installation of the plasma torch, care has to be taken to ensure that the torch is positioned along the axis of rotation of the chamber. An adjustment tool is used to ensure that the measurement object is located in the center of the tomography mirror assembly.

The CAD model of this adjustment tool is shown in Figure 7a. It consists of a small one-millimeter pin and a bracket for attaching the tool to the plate on which the mirrors are mounted. Once attached, the pin is positioned exactly in the center of the circle of the six deflection mirrors. Afterwards each mirror is adjusted horizontally and vertically, so that the image of the pin on each mirror is positioned as shown in Figure 7b. After adjusting the mirrors, the tip of the plasma torch is positioned at the top of the pin. Subsequently, the experiment can start.

Figure 8 shows the basic process flow of the experiment. The first step is the ignition of the plasma generator. Once the plasma plume is stable, the vacuum pump is turned on. After reaching a constant vacuum level of about 20 mbar, the data acquisition is initiated. Afterwards the data processing starts, as described in the next section.

2.3. Data Processing

Before describing the processing of the recorded data, a brief summary of the theoretical background of the computed tomography used for the reconstruction in the present work is given. For a successful reconstruction, it was assumed that the expanded plasma plume is optically thin.

Modern computed tomography is based on the radon transform of a two-dimensional function $f(x,y)$. In order to obtain a 3D reconstruction, all projections have to be calculated first. A projection is defined as an integral over $f(x,y)$, which is formed by all straight lines $g$ with a path length $l$ going through the measurement object at the same angle $\theta$ and at different distances $s$ from the origin [31,32], as illustrated in Figure 9. The entirety of all projections is represented by the function $p(s,\theta )$. The transformation of $f(x,y)$ into $p(s,\theta )$ is carried out using the radon transform, which can be mathematically expressed as

$$p(s,\theta )=R\{f(x,y)\}={\int }_{g}f(x,y)dl.$$

(1)

According to the above, the recorded projections of the object under study from each angle of view ${\theta }_i$ (with $i=1\dots 6$) are the radon transforms $p(s,{\theta }_i)$. The straight line $g$ can be described as follows, where $l$ is perpendicular to $s$ [33,34],

$$g=s\left(\begin{array}{c}\cos \theta \\ \sin \theta \end{array}\right)+l\left(\begin{array}{c}-\sin \theta \\ \cos \theta \end{array}\right).$$

(2)

The six projections of the measurement object originated from the six deflection mirrors shown in Figure 3. Thus, for a 3D reconstruction the inverse radon transform has to be computed, with

$$f\left(x,y\right)=R^{-1}\left\{p\left(s,\theta \right)\right\}.$$

(3)

Since digital camera recordings were used, the given function $f(x,y)$ is discrete. Therefore, the discrete version of the radon transform was applied. In this case each projection-value $p_i$ is multiplied by a weighting factor $w_{i,j}$ introduced in Equation (4), which represents the influence of a single pixel value on the projection $i$.

$$p_i={\sum }_{i,j=1}^N{w}_{i,j}\times f_i.$$

(4)

The two-dimensional image $f(x,y)$ is summarized in the vector $f_i$ with $N\times N$ elements, which represents the image size. A linear equation system results by summarizing the given projections to the vector $\overrightarrow{p}$ and the weights to the matrix $W$, which is formulated as

$$\overrightarrow{p}=W\times \overrightarrow{f}.$$

(5)

With the calculated values of $\overrightarrow{p}$ and the known weighting matrix $W$, $\overrightarrow{f}$ as a sum of the $N\times N$ values has to be computed. Due to the six directions of view, the system of equations is underdetermined. To solve the system of linear equations, the ART was used in this work. A detailed description of the ART can be found in [35,36].

In the following, the data processing procedure is explained, starting from the recorded image to the reconstructed 3D model. The process is described using a recorded image as an example, shown in Figure 10.

As can be seen in Figure 10, nine exposures were recorded on a single image of the high-speed camera. The temporal sequence of exposures goes from top to bottom of the image, with an interval of 10 µs between each exposure. The first and the second exposure with their appropriate six viewing directions are marked with green and yellow boxes respectively.

Since the proposed setup consists of an image intensifier and a high-speed camera and both devices are triggered by the rotating mirror (see Figure 6), the frame rate of the setup is determined by the rotation speed of the mirror. The exposure time of the high-speed camera has to be long enough to capture all the desired exposures displayed by the image intensifier (see Figure 5). In the case of the example presented in Figure 10, a minimum exposure time of about 82 µs (8 delays of 10 µs between 9 exposures of 0.2 µs each plus a few µs for camera sensor read out) is required to capture 9 exposures of the measurement object. Consequently, the exposure time of the high-speed camera is set arbitrarily as long as it exceeds the required minimum exposure time mentioned above. Then, the delay between trigger edges (one full rotation of the trigger flywheel) should be also taken into account. The maximum rotation speed of the mirror in the proposed setup was around 20,000 revolutions per minute and the diameter of the trigger wheel was 80 mm. This means that the high-speed camera was triggered at 3 ms intervals and therefore every trigger edge was recorded in the above example. However, since each image captured by the high-speed camera consists of several exposures displayed by the image intensifier, a frame rate can be defined for each individual image. This frame rate is determined by the delay between two successive exposures of the image intensifier. In the case of the example shown in Figure 10, a delay of 10 µs corresponds to a frame rate of 100,000 frames per second. This “individual image frame rate” is considered by the authors to be more relevant for the proposed setup than the frame rate of the high-speed camera.

For further processing, six contours (corresponding to the six viewing directions) of the first exposure are cut out and are shown side by side in Figure 11.

The contours of the measurement object were obtained using a well-known algorithm called marching squares [37]. In the next step, cross-sectional images based on these six directions of view were computed.

In Figure 12 the resulting sinogram (a) and cross-sectional image (b) for one exemplary cut plane are shown. The six cut-out contours were scanned simultaneously pixel line by pixel line. The sinogram and the cross-sectional image respectively are the result of the computation from the identical line of all six contours. When all contours are positioned correctly, a clear sine wave should be visible in the sinogram, as marked by the blue sine wave in Figure 12a. In addition, the cross-sectional image can be used for verification. The back-projection of the six viewing directions should overlap as shown in Figure 12b. The computation of such a cross-sectional image was done for every pixel line of the cut-out contours and finally, these images were stacked on top of each other. This ultimately leads to a three-dimensional reconstruction of the measurement object. The entire procedure was done for each individual exposure (nine, in the case of the example shown in Figure 10) recorded in an image from the high-speed camera.

To determine the velocity, all cross-sectional images of one exposure (as shown in Figure 12b), were analyzed and the mean grey value of each cross-section was calculated and plotted afterwards. The procedure was executed for all other (nine, in the case of the discussed example from Figure 10) exposures. Then, the maximum values of each exposure (more precisely of the mean grey value plots) were fitted, thus specifying the horizontal shift in pixel. Finally, the velocity was calculated using the horizontal pixel shift, a pre-determined scale and the known time interval between each exposure (10 µs in the discussed example).

2.4. Verification of the Used Algorithm

In order to prove the reliability of this approach, an additional verification step was introduced. For this purpose, an algorithm has been developed, which generates a pseudo camera image in which the measurement object is displayed from six different directions of view, similar to the real measurement shown in Figure 10. The tomographic reconstruction algorithm used was thus verified by comparing the reconstructed result with the simulated image source files. Based on a bivariate normal distribution, the probability can be formulated as follows, with a correlation coefficient of zero,

$$f_x\left(x_1,x_2\right)={\displaystyle \frac{1}{2\pi {\sigma }_1{\sigma }_2}}\ast e^{\left(-{\displaystyle \frac{1}{2}}\left[{\displaystyle \frac{{\left(x_1-{\mu }_1\right)}^2}{{\sigma }_1^2}}+{\displaystyle \frac{{\left(x_2-{\mu }_2\right)}^2}{{\sigma }_2^2}}\right]\right)}.$$

(6)

The idea was to create a three-dimensional model based on several layers, which have been generated by the Equation (6). The amplitude of the density function represents the brightness, and the shape of the model can be adjusted by the expectation $\mu$ and the standard deviation $\sigma$. The brightness value has been normalized and the emission distribution of the model can be modified using a desired additional function for scaling the value. For receiving the six directions of view from the simulated three-dimensional model, a radon transformation was performed from each perspective for each layer. Based on the known output functions, a coordinate transformation over the angle $\theta$ has been calculated, which represents the according radon transform for the angle $\theta$.

In Figure 13, the rotation (a) and the corresponding radon transform (b) of a single layer for six directions of view are displayed. To obtain the complete illustration of the three-dimensional model, the procedure described in previous section has been performed for each single layer of the simulated model.

After all the radon transforms have been computed and merged, a simulated pseudo camera image is created, as can be seen in Figure 14. The figure shows three exposures of the simulated model, with the first exposure on top. The different views of the artificial measurement object are arranged in a circular pattern, as was the case with the recorded images of the real measurement object.

3. Results

First, the resulting reconstruction of the simulated camera picture is shown. Then, the results of the calculated velocities from the measurements are shown.

3.1. Verification of the Used Algorithm

Based on the simulated pseudo camera image from Figure 14, the algorithm used was tested. The contours of a single exposure were cut out and processed as described in Section 2.3.

As the comparison of the 3D models in Figure 15 demonstrates, there is a clear similarity between the original data (a) and the reconstruction (b). The basic structure with most of the details has been reconstructed. Only in the upper third of the 3D models can a small deviation be observed. The reconstructed model shows a slightly stronger and larger shaping in this area. One reason for this might be the small number of viewing directions. Since the main features of the original simulated model are clearly recognizable in the reconstruction, and an increased number of viewing directions would add complexity to the setup as well as extend the calculation time, the result is considered a successful verification of the algorithm. Thus, the algorithm is used in the following to evaluate the recorded measurements.

3.2. Plasma Bulk Velocities

The velocity of the plasma bulk was determined according to the procedure described in Section 2.3. The parameters used in the measurements are listed in

Table 1. Parameters used for the performed measurements.

Current [A]	Gas Flow [slpm]	Exposure Time [ns]	Delay [µs]
40	35	200	10

.

All measurements were performed at about 20 mbar. The time delay between two exposures of the image intensifier was kept constant at 10 µs. After a measurement, the data were divided into six different bins, where one bin corresponded to one centimeter, and the mean and standard deviation of all bins were calculated. This provided a spatial resolution of the velocity along the axis of the plasma generator.

The graph in Figure 16 shows the calculated plasma bulk velocities along the axis of the generator at a distance of 1 cm to 7 cm downstream of the nozzle outlet. The blue-shaded area around the line in Figure 16 marks the standard deviations of the velocity results, which were about 20%. According to the graph, the plasma bulk accelerates to about three centimeters from the nozzle outlet, where an average velocity of 1061 m/s is reached. Further downstream, the velocity decreases slightly and reaches a mean value of 919 m/s at seven centimeters, with a small dip in the curve at four centimeters.

The reconstructed cross-sectional images used to calculate the velocity were also used to generate a rough 3D visualization of the plasma plume, allowing for a spatial study of the plasma plume.

Figure 17 presents a computed 3D reconstruction of the plasma plume at six different points in time (a–f). For a better visualization, a simplified 3D model of the plasma generator is added to each plume reconstruction. The corresponding image used for the calculations is also marked in the figure with colored boxes in each picture (compare Figure 10). Furthermore, distinct features of the plasma plume observed in each image are marked with an arrow. The movement of the marked feature, combined with the known time delay of 10 µs between each exposure of the image intensifier, allows for the calculation of the plasma bulk velocity. Besides the velocity measurement, the 3D models calculated by the proposed method show that the reconstruction based on six viewing directions is sufficient to visualize the elementary shape of the plume with its characteristic features.

4. Discussion

The presented diagnostic method shows that it is possible to record and detect distinct fluctuations of a plasma jet. As previous studies show, a good reconstruction based on the ART algorithm can be realized with four directions of view [27,28]. The two additional directions of view implemented in this study ensure an even more accurate reconstruction by providing more information without significantly increasing computation time. The velocity of the plasma bulk could be resolved locally and non-invasively by detecting the movement of characteristic fluctuations in the axial direction.

Besides these advantages, one disadvantage of the proposed method is that both an image intensifier and a high-speed camera are required, depending on the measurement object. The proposed setup could be realized with just a high-speed camera if the following two conditions are met: the measurement object is bright enough, or conversely, the high-speed camera is sensitive enough to achieve a short exposure time, and at the same time, the frame rate is sufficiently high to resolve the fluctuations of the object. However, in the case of smaller plasma generators and especially electric propulsion thrusters, one of the above conditions cannot usually be met, and thus both devices are required. As a consequence, the spatial resolution, and to a certain degree the temporal resolution, are limited by the physical size of the image intensifier. The decay time of the phosphor screen of the image intensifier could be another limiting factor for the temporal resolution. Depending on the expected shape and fluctuations of the object to be analyzed, the temporal resolution can be increased by reducing the size of the imaged object. This can be done by shortening the focal length of the lens used. However, the spatial resolution should still be high enough so that distinctive features of the object under study can be detected. A compromise must therefore be found between spatial and temporal resolution. In the authors’ experience, however, the proposed setup, as described in Section 2.1.3, has proven to be versatile enough to analyze plasmas of varying power.

The results achieved for the DC plasma generator show that the velocity increases to a maximum value of 1061 m/s at a distance of three centimeters from the plasma outlet (see Figure 16). Further downstream, the velocity decreases non-linearly, showing a small dip at four centimeters before reaching a value of 919 m/s at seven centimeters. Since no external electric or magnetic field was applied, the deceleration observed at a distance of four centimeters from the nozzle outlet seems implausible. Therefore, it is assumed to be an outlier.

For the sake of clarity, the velocities measured in this work, including the associated operating parameters, are compared with previous work in

Table 2. Comparison of results presented in this work with those of previous work.

Reference	Measurement Setup	Max Velocity [m/s]	Gas Flow [slpm]	Current [A]	Nozzle Ø [mm]	Operating Pressure [mbar]
This work	DC plasma torch; optical measurement	1061	35	40	6	20
Capetti et al. [9]	DC plasma torch; probe measurement	550	47.2	600	7.88	1013
Coudert et al. [15]	DC plasma torch; optical measurement	1600	45	520	7	1013
Planche et al. [16]	DC plasma torch; time of flight	2200	60	600	6	1013
Hamatani et al. [21]	Arcjet; doppler shift velocimetry	7000	6.7	20	1–2	10.3–100.7
Zhang et al. [38]	Arcjet; laser absorption	2308	7.3	140	2	0.4

.

Comparing the results with the velocities given by Capetti et al. [9], the values obtained in this work are twice as high. Although the used gas flow and current were lower, Capetti et al. used a nozzle with a larger diameter. A possible explanation for the lower velocity values could also be the higher operating pressure and the invasive probe measurement setup, which unavoidably affects the plasma flow and ultimately the measured data. Velocities three times as high as in [9] were optically determined by Coudert et al. in [15] for a slightly smaller nozzle diameter. Considering also the values reported by Planche et al. [16], which were determined non-invasively for a similar operating pressure as in [9,15] but for a higher gas flow rate, the significant increase in velocity appears to be a consequence of the smaller nozzle diameter. The nozzle diameter used by the authors in [16] is identical to that used in this work. As a result, considering the difference in operating pressure, the velocities presented in this work seem plausible despite the lower gas flow and current. Compared to velocity measurements of arcjets, the velocities presented in this work are significantly lower despite a much higher gas flow. The reason for this is the difference in the diameter and geometry of the nozzle [21,38]. Nonetheless, the velocity values of up to 2308 m/s reported Zhang et al. in [38] are in the same order of magnitude as the values determined in this work. It can be thus assumed that the plasma bulk velocity of an arcjet can be measured with the proposed method without significant modifications. A plasma bulk velocity measurement is of particular interest in electric propulsion applications, since the velocity enables the calculation of thrust. In order to resolve higher velocities, such as those presented by Hamatani et al. also for an arcjet [21], the proposed image recording system requires an adaption and further parameter optimization. A higher frame rate can be achieved by using a shorter delay between each exposure. However, this would require a more powerful image intensifier. In addition, the rotation speed of the mirror has to be increased for a higher frame rate to separate the individual exposures from each other. In terms of parameter optimization, the influence of the number of viewing directions can be investigated. This could lead to an improved utilization of the camera chip, allowing for a higher number of exposures to be stored on the chip. In summary, it can be stated that the measured plasma bulk velocities of the DC plasma torch are in the order of magnitude of values reported in previous studies. Therefore, the presented diagnostic setup seems to be suitable for the determination of the plasma bulk velocity.

Nonetheless, further research and validation regarding different operating parameters of the plasma torch is needed. In addition, the data processing and evaluation procedure can be optimized to reduce the standard deviation of the measurements. The proposed diagnostic method allows for the determination of the spatial dimensions of the measured object, which should be explored in future applications. By implementing this feature, the influence of the input parameters such as current or gas flow on the plasma plume expansion can be examined. The proposed setup could also be coupled with spectral filters and thus provide a rough indication of spatial and temporal distribution of the different species in the plasma jet.

5. Conclusions

In this work the plasma bulk velocity of a DC plasma torch was measured non-invasively. For this, a high-speed imaging setup combined with a tomographic acquisition has been presented. The proposed setup observes the measurement object from six directions of view and allows for resolving fluctuations in the plasma plume on the order of microseconds. It also enables the plume to be reconstructed using the ART, and thus the tracking of fluctuations and the calculation of the velocity of these fluctuations, which could be resolved locally in the axial direction. Moreover, the setup provides rough 3D models that visualize the characteristic features of the effluent plasma plume. The calculated velocity results are within the range of values found in other studies. Thus, this diagnostic setup proves to be more than an alternative for measuring velocity as it is non-invasive and provides the temporal characteristic of velocity, as well as a 3D model of the plume that can be used for additional analyses.