Bidirectional vortex stabilization of a supersonic inductively coupled plasma torch

Radio-frequency (RF) inductively coupled plasma (ICP) torches using a supersonic nozzle have many industrial materials processing applications and have also been proposed as novel electrothermal plasma thrusters for space propulsion. The gas injection method in plasma torches plays an important role in both gas heating dynamics and overall discharge stabilization. Here, we investigate reverse vortex gas injection into a supersonic ICP torch for RF powers up to 1 kW, argon mass flow rates between 15 and 180 mg s−1, and plasma torch pressures from ∼270 Pa to ∼50 kPa. In this configuration, gas is injected tangentially just upstream of the nozzle inlet. This produces a bidirectional vortex flow field where gas first spirals upwards along the outer edge of the plasma torch walls, before then reversing direction at the torch end and spiralling back down through the central plasma region towards the nozzle exit. Results are compared to a more conventional forward vortex configuration where gas is instead injected tangentially from the upstream end of the torch, and which forms a unidirectional vortex that spirals towards the downstream nozzle. While performance is similar for gas flows below 80 mg s−1, we show that at higher mass flow rates both the effective torch stagnation temperature and thermal efficiency can be increased by almost 50% with reverse vortex injection. Considering that the measured RF antenna-plasma power transfer efficiency is similar for both configurations, this enhancement occurs because of the unique bidirectional vortex flow field which leads to reduced gas-wall heat losses and consequently an increased enthalpy flow leaving the torch.


Introduction
An inductively coupled plasma (ICP) torch is a device that is used to heat a gas to very high temperatures. It consists of a coil wrapped around a hollow dielectric tube (often made of quartz or a technical ceramic), and which is supplied with a radio-frequency (RF) current. The gas to be heated is injected from one end of the tube while the other end is either open or terminated by a subsonic/supersonic nozzle. The RF current produces inductive time-varying electric fields inside the tube that couple power to electrons and sustain a high-density partially ionized plasma through electron-gas impact ionisation [1]. In order to obtain high gas temperatures (which can be in excess of 10 000 K), ICP torches are typically operated at relatively high pressures (often atmospheric pressure) since gas heating depends on the collision frequency [2,3]. This leads to the system being in local thermal or quasi-thermal equilibrium with a gas temperature that is of the order of the plasma electron temperature itself.
The significant gas heating obtained with a plasma torch makes it a very useful device for a number of different industrial applications. This includes materials processing where it is used for the spheroidization and synthesis of nanopowders, the formation of metal-matrix composites, and thinfilm deposition of metals and ceramics [4][5][6][7][8][9][10][11]. Plasma torches are also widely used in analytical chemistry where they act as a source to ionize or atomize material samples which are then subsequently analysed with optical or mass spectrometry techniques [12][13][14][15][16][17][18][19][20]. Because of the high gas temperatures that are possible, ICP torches have found use as high-enthalpy flow generators to simulate atmospheric re-entry of hypersonic or space vehicles, and aerothermodynamics studies for the testing and development of thermal protection materials [21][22][23][24]. They have also been proposed as novel electrothermal plasma propulsion systems. Here, volume-heating of a propellant by a high-density plasma enables much higher gas temperatures and exhaust velocities to be obtained compared with heating by chemical combustion or physical electrical heating elements [25][26][27][28]. In all of these applications, ICP torches offer several unique advantages because they are essentially electrodeless discharges (with little or no erosion and any consequent process contamination or lifetime limitations), and can be used with a wide range of gases (including reactive gases).
Some important considerations when designing and operating ICP plasma torches are associated with gas flow dynamics, plasma discharge stabilisation, and torch thermal management [1,29]. Flow stabilization is necessary to ensure stable operation of the torch and is usually achieved through control of the gas-plasma flow dynamics through specific gas injection configurations [1]. Here there are two main configurations: single flux and double flux injection. In single flux designs, gas is injected at the upstream end of the torch directly into the plasma heating region with an injection port creating a single axial gas stream, or a gas stream that is tangential to the axis of tube, as seen in figure 1(a) [30]. The tangential gas injection, sometimes referred to as forward vortex stabilization, was first proposed in 1961 by Reed and is still widely used today [1]. In double flux designs, gas is injected via two different streams separated by a dielectric tube that typically ends just upstream of the RF coil and main plasma region, and which is concentric with the torch discharge tube. The outer gas stream, called the sheath gas, flows along the inner walls of the torch tube, while the inner or central gas stream flows directly towards the centre of the plasma discharge [20,[31][32][33]. The gas injection configuration can also play an important role in protecting the torch discharge tube from thermal damage. For some gas injection configurations or power levels however, special high-temperature torch materials (such as technical ceramics) or dedicated water cooling designs are needed [30,34,35].
A particularly novel stabilization technique is the reverse vortex, which is illustrated in figure 1(b). In contrast with conventional designs, gas is injected tangentially from the downstream end of the ICP torch just ahead of an exit nozzle. Due to its initial angular momentum, the gas first spirals up along the inner surface of the ICP tube towards the upstream torch end, before reversing and spiralling back down towards the downstream end through the centre of the tube. Thus, the gas injection method essentially creates two vortices travelling in different directions: an outer vortex spiralling towards the closed torch end, and an inner vortex spiralling in the opposite direction towards the open torch end [1,36]. Since the axial gas velocity in the inner and outer vortices are in different directions, there is a radial location where the axial velocity goes to zero. This zero-velocity region along the length of the tube is called the mantle. The reverse vortex configuration has been used previously in both microwave and ICP plasma torches, where it offers a number of advantages over conventional gas injection methods [37][38][39][40]. For example, the outer vortex creates a layer of cool gas that shields the walls of the plasma torch and reduces heat losses. Additionally, because of the inner vortex, almost all of the input gas passes through the hot central plasma region before exiting. The vortex flow fields also effectively increase the gas residence time and promote better gas mixing [38,41]. Experiments with a microwave plasma torch showed that the reverse vortex can lead to a decrease in heat losses to the torch walls from 26%-42% to 4%-7% of the discharge power compared to the forward vortex, while with an ICP torch, similar experiments showed that the torch thermal efficiency can be increased from about 40% to 60%, while also resulting in a significantly higher jet enthalpy (depending on the mass flow rate and input power) [38,40].
While the reverse vortex has been used in several subsonic ICP torches, there have been very few fundamental investigations with supersonic ICP torches. Compared with subsonic nozzles, compressible flow effects become particularly important in supersonic nozzles, and the dimensions and geometry of the nozzle itself (such as the inlet and throat diameters compared with the size of the vortex mantle) may strongly influence the resulting vortex flows [42,43]. Supersonic ICPs have a number of practical industrial applications however, such as plasma assisted supersonic jet deposition, where improved thermal efficiency when using reverse vortex injection offers a number of benefits in terms of reduced gas or input power consumption, or even the possibility of different torch construction materials [44,45]. Additionally, as reverse vortex injection is extremely promising for reducing heat losses to the torch walls, this may be an enabling technology for high-performance applications, such as electrothermal ICP plasma thrusters, where heat losses currently represent a strong technical barrier [28,46,47].
Independent of research within the plasma physics community, reverse vortex gas injection has been studied extensively in the field of gas dynamics where it forms the basis of several devices such as cyclone separators and swirl gas injectors, and is referred to instead as a bidirectional vortex [48][49][50]. Here it has also been used together with supersonic nozzles in liquid propellant rocket engines, notably NASA's vortex injection hybrid rocket engine, which produced marketed improvements in efficiency [51,52]. Bidirectional vortex injection has been seen as a very promising technology for future NASA and commercial liquid rocket engine development due to the numerous benefits offered by such unique flows. This includes the removal of traditional engine cooling methods and hardware, enhanced propellant mixing and combustion processes, relatively high regression burning rates, the use of cheaper engine construction materials, and smaller more lightweight engines [51]. Since supersonic ICP plasma torches share many similarities to chemical rocket engines, the use of bidirectional vortex gas injection may offer many similar benefits for different plasma technologies and applications.
In this paper, we perform an experimental investigation studying the effect of reverse vortex gas injection in a supersonic ICP plasma torch and perform a direct comparison with conventional forward vortex injection. We measure the effective gas stagnation temperature and torch thermal efficiency and demonstrate the strong advantages of this promising technology in terms of overall system operation and performance.

RF ICP
A schematic of the ICP plasma torch used in this study is shown in figure 2. The torch consists of a 7-turn RF antenna made from 3 mm diameter hollow copper tubing wrapped around two concentric alumina tubes. The outer tube has an outer diameter of 30 mm and a length of 77 mm, while the inner tube has an outer diameter of 24 mm and a length of 105 mm. Both tubes connect to top and bottom aluminium end caps by a series of o-rings.
Water is injected through an inlet in the bottom end cap and then flows between the inner and outer alumina tubes before exiting through an outlet in the top end cap. This water serves to efficiently cool the plasma torch enabling it to operate safely and stably without overheating. The temperature increase of the water between the inlet and outlet also allows calorimetry measurements to be performed (see section 2.4 below).
A modular stainless steel nozzle is attached to the bottom end cap downstream of the RF antenna. The convergingdiverging nozzle has a throat diameter of 2 mm and an exit diameter of 20 mm. The half-angle of the converging section is 45 • , while the divergence half-angle is approximately 26.5 • .

Gas inlet configuration
Gas is injected into the plasma torch via inlets in the top and bottom end caps that allow two different gas injection configurations to be studied: a forward vortex and a reverse or bidirectional vortex. With the forward vortex, gas is injected tangentially through four identical inlets in the top end cap spaced 90 • apart. With the reverse vortex, gas is injected tangentially through four similar inlets in the bottom end cap located just upstream of the nozzle. When in the reverse vortex configuration, or vice versa, the forward vortex gas inlets are sealed. A schematic of both injection configurations can be seen in figure 3.

Experimental setup
A schematic of the complete experimental set up is shown in figure 4. The plasma torch is mounted vertically onto a vacuum chamber such that the plasma/gas flows downwards. The vacuum chamber is pumped to a base pressure below 1 Pa with a Peiffer ACP 15 pump that has a maximum pumping speed of about 14 m 3 h −1 . A glass window on the side of the vacuum chamber allows visual observation of the downstream plume. Figure 5 shows two example photographs of the plume during operation with the reverse vortex.
An ENI ACG-10 air-cooled RF generator operating at 13.56 MHz supplies power to the plasma torch antenna via a custom pi-type impedance matching network. To prevent electromagnetic interference, an RF shield made of perforated aluminium sheeting surrounds the plasma torch and is attached to the matching network. An AlphaPower 4520 digital meter is placed between the RF generator and the matching network, and monitors the forward power, the reflected power, and the voltage standing wave ratio.
For both the forward and reverse vortex configurations, argon gas is injected into the plasma torch via standard Swagelok connectors and the mass flow rate is controlled using a digital Kofloc DF-350C mass flow controller (corrected for argon).

Diagnostics
Because of the high gas temperatures obtained in the plasma torch during operation, and to prevent any possible interference that could alter the vortex flow fields, all diagnostics used are non-invasive. The pressure inside the plasma torch is measured with a Thyracont VSC43MV piezoresistive pressure sensor attached to the top end cap. A second identical pressure sensor is connected to the vacuum chamber, together with a Granville-Phillips 275 Convectron gauge for lower pressure measurements.
The stagnation temperature of the gas inside the plasma torch is determined using an indirect method. Assuming choked flow at the nozzle throat, the mass flow rate is related to the upstream stagnation pressure and temperature froṁ where p s is the stagnation pressure, T s is the stagnation temperature, A t = πR 2 t is the cross-sectional area of the nozzle throat with R t the throat radius, k B is Boltzmann's constant, M is the atomic mass of the gas, and γ is the ratio of specific heats (equal to about 1.67 for argon). Experimental measurements (with no plasma; i.e. cold conditions) of the stagnation pressure and input mass flow rate show that equation (1) is well satisfied. The normalized root mean square error for the forward and reverse vortex configurations is 4.8% and 4.7% respectively, indicating a discharge coefficient close to unity. Additionally, this is found to be relatively constant with nozzle throat Reynolds number (which varied between 1000-6000).
Thus, viscous boundary layer effects in equation (1) are expected to be small and are neglected.
Fixing the mass flow rate and measuring the pressure when a plasma is present (i.e. hot conditions) then allows the stagnation temperature to be determined from Thus, the ratio of the hot-to-cold stagnation temperature is proportional to the square of the hot-to-cold pressure ratio. Thermocouple measurements give T s,cold of approximately 20 • C. Note that the gas stagnation temperature is an effective average temperature within the torch (and a more appropriate value to use when estimating some torch performance metrics), whereas the actual maximum gas temperature (which typically peaks on, or close to, the torch central axis) is expected to be about 3 times higher [53]. Once the stagnation temperature is determined from equation (2), the enthalpy flow and thermal efficiency of the plasma torch can be estimated from where c p is the specific heat at constant pressure (and equal to 520 J kg −1 K −1 for argon) and P abs is the power transferred from the RF antenna into the plasma. The RF current in the plasma torch antenna is measured with an Ion Physics current probe placed around the low-voltage leg of the antenna. The probe is connected to a digital oscilloscope with a 50 Ω input impedance via a BNC cable. Measurement of the forward power and reflected power to the antenna (denoted P fwd and P rev respectively), as well as the antenna peak current given as I RF , allows the effective resistance of the antenna to be obtained from When no plasma is present, the resistance is labelled R vac and is largely due to the finite resistance of the antenna itself. When plasma is present, the resistance is labelled R eff and now includes both the antenna resistance and the effective resistance due to the plasma as seen by the antenna. The RF antennaplasma power coupling efficiency, η RF , is given by With the plasma torch design used here, the coupling efficiency is typically between 90%-93%, with the remaining power dissipated in the antenna and matching network. The power absorbed by the plasma is then found from P abs = η RF P RF (7) where P RF is the input power from the RF generator. Calorimetry measurements of the torch cooling water provide a second means to estimate the stagnation temperature and torch thermal efficiency. The temperature of the water was measured using two k-type thermocouples which were inserted directly into the water near the inlet and outlet using a T-piece adaptor. The thermocouples are connected to a digital meter with an accuracy of ±0.3% of a reading between 0 • C-600 • C plus 1 • C and with a resolution of 0.1 • C. During operation, heat transfer to the water occurs resulting in a change in temperature given by where T 1 is the water outlet temperature and T 2 is the water inlet temperature. The power absorbed by the water is calculated from Here c p,w = 4184 J kg −1 K −1 is the specific heat of water, ρ = 998.2 kg m −3 is the mass density of water, and Q is the measured water volumetric flow rate. The torch thermal efficiency can then be estimated by subtracting the power dissipated in the water from the absorbed power The above equation assumes that heat conduction from the ends of the torch to the vacuum chamber and pressure gauge, as well as any radiated power, is negligible (see section 3 below). Substituting equation (10) into equation (3) also allows a second estimate of the gas stagnation temperature to be obtained Finally, the specific enthalpy increase of the torch gas is equal to the measured enthalpy flow per unit mass flow rate

Results and discussion
For both the forward and reverse vortex, the plasma was initially ignited at low gas mass flow rates of approximately 2 mg s −1 (corresponding to a torch pressure of around 270 Pa). The RF power was then steadily increased until a forward power of 800 W was obtained, after which the torch pressure was increased further by increasing the mass flow rate. Experimental measurements were taken until the plasma discharge extinguished, which at some conditions occurred because of the presence of an instability (see below). For all operating conditions, the matching network was tuned to minimize the reflected power, which was typically less than 1%. In the plots below, the shaded regions indicate stagnation pressure measurement uncertainty which is associated with variations in the pressure observed at each mass flow rate. Figure 6 shows the RF current and antenna-plasma power transfer efficiency as a function of mass flow rate. The RF current, and thus the power absorbed, for both the forward and reverse vortex show near identical results. Consequently, any differences in torch performance with gas injection configuration are due solely to the plasma-gas flow dynamics. At low mass flow rates below 50 mg s −1 , the RF current decreases slightly going from about 19 A to 17.5 A. Then at mass flow rates above 50 mg s −1 , the current starts to slowly increase back up to 19 A. At higher mass flow rates, the uncertainty in the current measurements (represented by the shaded regions) increases due to an instability present in the gas flow. In general, the RF antenna efficiency is found to vary very little with increasing mass flow rate and the efficiency is consistently between 90%-93%. The uncertainty in the RF antenna efficiency is relatively low due to the accuracy of the current measurements. Figure 7 shows the hot-to-cold stagnation pressure ratio as a function of mass flow rate. As mentioned previously in section 2.4, the hot pressure corresponds to conditions when a plasma is present (and hence when plasma-gas heating can occur), while the cold pressure corresponds to conditions when no plasma is present (and hence when no gas heating occurs). Figure 7(a) compares the observed pressure ratio when using forward and reverse vortex gas injection at an RF power of approximately 800 W. The horizontal black dashdot line indicates a pressure ratio equal to one. Since the gas flow chokes at the nozzle throat, the stagnation temperature must have increased if the pressure ratio increases for a given mass flow rate (see equation (2)). For both forward and reverse vortex gas injection, it is found that the pressure ratio is well above 1, indicating strong gas heating. For forward vortex gas injection, the pressure ratio is higher than for reverse vortex gas injection for mass flow rates below about 80 mg s −1 .
For higher mass flow rates however, the forward vortex pressure ratio saturates at approximately 2.7 (and even slightly decreases for mass flow rates above 100 mg s −1 ), while the reverse vortex pressure ratio continues to increase monotonically, reaching a maximum of 3.3 at approximately 150 mg s −1 . At mass flow rates above this, the plasma extinguishes.
The power absorbed by the torch cooling water as a function of mass flow rate is shown in figure 7(b) for an RF power of 800 W. For both forward and reverse vortex gas injection, the dissipated power is relatively constant and between 720-740 W for mass flow rates below about 30 mg s −1 . Firstly, this shows that about 60-80 W of power is lost in the RF antenna and matching network, and hence that the RF antennaplasma power transfer efficiency is between 90%-93% (consistent with the independent RF antenna electrical efficiency measurements made in figure 6(b)). As the mass flow rate is increased however, the power dissipation decreases for both the forward and reverse vortex gas injection.
In section 2.4 it was briefly discussed that power losses due to heat conduction to the vacuum chamber flange and pressure gauge are not included in the calorimetry measurements. At low mass flow rates the heat loss to the flange via conduction was estimated and found to be below the resolution of the temperature reader and hence considered negligible. Additionally, tests connecting the torch to the flange via a thick o-ring (to further increase thermal insulation) showed no effect. Similarly, removing the pressure gauge also produced no change. Consequently, any heat conduction losses are expected to be very small. Furthermore, due to the design of the torch which uses alumina tubes (that are partially opaque), heat loss due to radiation is also expected to be small. Although light emission from the torch is observed during operation, the intensity is very low because radiation is partially absorbed/reflected by the alumina tubes and water cooling layer. Since the RF antenna-plasma power transfer efficiency is similar at all mass flow rates (see figure 6(b)), the power change observed in figure 7(b) therefore corresponds to power carried away by the gas flow leaving the torch. This is also visually observed in the intensity of the plume at the nozzle exit. Above around 100 mg s −1 , the dissipated power for the forward vortex is higher than that for the reverse vortex, indicating that for the reverse vortex more power leaves the torch with the gas for the same initial RF power and mass flow rate. Or stated differently: heat losses to the torch walls are lower with reverse vortex gas injection. For a mass flow rate of 150 mg s −1 , the dissipated power is approximately 550 W for the forward vortex and 470 W for the reverse vortex.
Using the equations in section 2.4, the torch stagnation temperature and thermal efficiency can be estimated from both the gas stagnation pressure and the water calorimetry measurements. Figure 8(a) shows the stagnation temperature with mass flow rate, where it is seen that the temperature with the forward vortex is initially higher than the reverse vortex for mass flow rates below 80 mg s −1 (similar to the pressure ratio measurements in figure 7(a)). This behaviour at low mass flow rates with the reverse vortex has been observed before by Gutsol et al [54] in a subsonic ICP torch. They found that at low mass flow rates a re-circulation zone is formed in the closed region of the torch tube and this leads to increased heat losses. Above mass flow rates of 80 mg s −1 in figure 8(a), the forward vortex temperature initially plateaus at about 2000 K and then begins to slowly decrease as the mass flow rate is further increased. This plateau and slow decrease occurs because a larger amount of gas flows through the torch and insufficient power is available to further increase the temperature of this gas. This can easily be seen from equation (3) where if the enthalpy flow is fixed (because of a fixed absorbed power), the gas temperature change must decrease as the mass flow rate rises. The forward vortex plasma eventually extinguishes at a mass flow rate of 170 mg s −1 . Other conventional gas injection configurations, such as single or double flux axial injection at the upstream end of the torch, have been previously studied and found to produce similar stagnation temperatures as the forward vortex [53]. By contrast, the stagnation temperature with the reverse vortex continues to increase for mass flow rates above 80 mg s −1 , reaching approximately 3200 K at 155 mg s −1 before the plasma extinguishes. As discussed in section 2.2, the reverse vortex is formed from injecting the gas tangentially at the nozzle end of the RF ICP. This forms a slightly higher pressure region at the plasma source edge and the gas is initially heated as it travels upwards (the outer vortex), while a lower pressure region exists in the torch centre where the already pre-heated gas can flow back down towards the nozzle (the inner vortex). This gives rise to higher stagnation temperatures with the reverse vortex configuration, since not only does almost all of the input gas pass through the hot plasma region, but also heat losses to the torch walls are reduced because of the cooler outer vortex. We highlight again that the stagnation temperature in figure 8(a) represents an effective spatial average within the torch, and the maximum peak gas temperature is expected to be as much as 3 times higher.
Power transfer from the RF generator to the gas is a multistep process within the torch. Initially, some of the applied RF power (approximately 7%-10%) is lost due to Ohmic electrical heating in the RF antenna and matching network. The remaining power is then coupled into the plasma and primarily absorbed by electrons. In argon, electron-neutral elastic collisions are expected to be the dominant gas heating mechanism [53], which is a volumetric process. Collisional quenching of excited argon states (formed for example through electron-neutral excitation or resonant radiation absorption) may also contribute. As the electron-neutral collision frequency depends on the gas density, plasma-gas heating is expected to be enhanced at higher pressures and mass flow rates. Similarly, the electron temperature decreases at higher flow rates which reduces the inelastic collision rate coefficients relative to the elastic scattering rate coefficient [53]. Therefore, as the mass flow rate increases, more power is transferred to the gas. Finally, heat conduction/radiation from the gas to the torch walls results in some power losses, and any remaining power is carried away by the gas as it exits the torch.
The stagnation temperature can also be estimated from the water calorimetry measurements, which are shown as the closed data markers in figure 8(a). The displayed error bars are largely due to temperature sensor resolution and water flow meter measurement uncertainties. The calorimetry results are less reliable for mass flow rates below 50 mg s −1 because the dissipated power is close to the power absorbed by the plasma (see figure 7(b)) and the gas jet power is therefore low. For both forward and reverse vortex gas injection, the stagnation temperatures determined by calorimetry are in reasonable quantitative and qualitative agreement with the gas pressure measurements. Nonetheless, calorimetry gives lower temperatures for mass flow rates below 50 mg s −1 and slightly higher temperatures for mass flow rates above approximately 80 mg s −1 . For the forward vortex, calorimetry gives a maximum stagnation temperature of 2400 K, which is about 400 K higher than that obtained by the pressure measurements. For the reverse vortex, calorimetry gives a maximum temperature of 3300 K, which is much closer to that obtained with the pressure measurements. Since the calorimetry misses any power transferred by conduction through the torch bottom end cap to the vacuum chamber flange (particularly at higher mass flow rates where stronger heat transfer to the nozzle and end cap may occur), as well as any emitted radiation power, the stagnation temperature is expected to be slightly overestimated with this method. Figure 8(b) shows the torch thermal efficiency as a function of mass flow rate. For the calorimetry measurements, both forward and reverse vortex gas injection give similar thermal efficiencies up until about 80 mg s −1 . Above this mass flow rate, the thermal efficiency of the forward vortex increases slower than the reverse vortex, and reaches a maximum efficiency of approximately 24% at 170 mg s −1 , while the maximum efficiency for the reverse vortex is 33% at 155 mg s −1 . The reverse vortex produces a higher maximum thermal efficiency due to a reduction in heat losses to the walls compared with the forward vortex. The thermal efficiency can also be estimated from the torch stagnation pressure measurements (see section 2.4). Generally, the efficiency determined by calorimetry and pressure measurements are in reasonable agreement for both the forward and reverse vortex, although for flow rates above 80 mg s −1 calorimetry gives a slightly higher efficiency than the pressure measurements. As mentioned above however, since the calorimetry may miss some power loss contributions, the thermal efficiency is likely to be slightly overestimated.
The torch stagnation temperature and thermal efficiency can also be evaluated at different RF powers, as shown in figure 9, where results have been obtained using the stagnation pressure method. For powers between 400-1000 W, the highest mass flow rate achievable is limited by the presence of an instability (see below) that causes the plasma to extinguish. By contrast, at 200 W the plasma extinguishes because the torch pressure becomes too high and the applied power can no longer sustain the discharge.
In both figures 9(a) and (b), a clear trend is seen where higher RF powers correspond to higher stagnation temperatures, as expected. In general, the plasma discharge can be sustained at higher mass flow rates as the RF power increases. The highest stagnation temperature observed is about 3500 K, and occurs for the reverse vortex at an RF power of 1000 W and a mass flow rate of 170 mg s −1 . By contrast, the highest temperature with the forward vortex is only 2400 K at a mass flow rate of 120 mg s −1 . For both forward and reverse vortex gas injection, the maximum stagnation temperatures obtained do not scale linearly with power. For example, at an applied power of 200 W for the reverse vortex, the stagnation temperature is 1500 K, while for the same mass flow rate at 1000 W, it is 2500 K. Thus, the RF power is 5 times higher but the temperature is only 1.7 times higher. The reason for this non-linear temperature increase is largely associated with conductive heat losses to the walls. Because of the torch water cooling, the temperature of the torch walls is relatively constant and equal to about 300 K. This can be seen from the heat flow equation for a hollow cylinder where Q h is the heat transfer, k is the thermal conductivity of alumina (30 W m −1 K −1 ), L is the length of the tube (105 mm), r i and r o are the inner and outer radii of the tube (9.5 mm and 12 mm respectively), T i is the inner wall temperature, and T o is the outer wall temperature (293.15 K). For a maximum inputted power of 1000 W, and for argument sake assuming a worst case where all of this power is lost through conductive heat transfer, the maximum inner wall temperature is only approximately 305 K. Thus, as the gas temperature increases, the gas-wall temperature difference also increases and so to does the conductive heat flux. In addition, the thermal conductivity of argon rapidly increases with temperature. Taken together, these factors result in heat losses that quickly grow non-linearly with gas temperature [53]. Figures 9(c) and (d) show that for all RF powers, the torch thermal efficiency tends to increase monotonically with mass flow rate. For the forward vortex, the highest thermal efficiency is 24% for 400 W and a mass flow rate of 170 mg s −1 . At the same RF power, the maximum thermal efficiency for the reverse vortex is 34% at 120 mg s −1 . In fact, for the reverse vortex, a similar maximum thermal efficiency is observed for all RF powers between 200-800 W. For a given mass flow rate, there is a clear trend whereby higher RF powers lead to lower thermal efficiencies. For example, at a mass flow rate of 75 mg s −1 , the thermal efficiency is approximately 18% at 200 W and 7% at 1000 W for the forward vortex. Likewise, for the reverse vortex at 75 mg s −1 the thermal efficiency is 25% at 200 W and 7% at 1000 W. This again largely relates to the non-linear increase of the conductive heat flux with temperature.
In addition to the thermal efficiency, a common performance metric is the specific enthalpy of the torch gas-plasma jet. Figure 10(a) shows the specific enthalpy as a function of thermal efficiency (obtained for different mass flow rates) for a fixed RF power of 800 W. For the forward vortex, the specific enthalpy reaches a maximum of 1 MJ kg −1 at a thermal efficiency of approximately 10%, before decreasing to 0.8 MJ kg −1 at 20%. The specific enthalpy of the reverse vortex is initially lower than that of the forward vortex at low thermal efficiencies, but continues to increase monotonically reaching 1.5 MJ kg −1 at an efficiency of 33%. This behaviour is particularly interesting and promising for several applications as it shows that in contrast with conventional gas injection configurations, the reverse vortex enables both high specific enthalpy and high thermal efficiencies. A similar result has previously been observed with subsonic ICP plasma torches using reverse vortex gas injection [54]. Figure 10(b) shows the specific enthalpy as a function of thermal efficiency (obtained for different RF powers between 400-1000 W) for a fixed mass flow rate of 125 mg s −1 . Here there is a clear trend with the specific enthalpy decreasing as the thermal efficiency increases. At a thermal efficiency of approximately 19%, the specific enthalpy of the reverse vortex is around 1.45 MJ kg −1 , while it is almost three times lower at 0.5 MJ kg −1 for the forward vortex.
Although not the primary focus of this study, an instability was observed for some operating conditions for both the forward and reverse vortex. For example, when increasing the mass flow rate of the reverse vortex to reach high pressures and temperatures, a visible flickering of the plume and an audible noise from the flange was observed. For an applied power of 800 W, the instability was first observed for torch pressures of 24 kPa onward and the plume flickered at approximately 100 Hz (as measured with a photodiode connected to an oscilloscope) for pressures between 24-26 kPa. As the torch pressure increased further, the frequency decreased to approximately 80 Hz until the plasma was eventually extinguished. This is inline with visual observations where the plume became visibly more unstable as the pressure and temperature increased. Figures 11(a) and (b) show discharge stability maps for the forward and reverse vortex for applied powers between 200-1000 W. The forward vortex instability occurred at slightly higher mass flow rates compared to the reverse vortex, and consequently the discharge could be sustained at slightly higher mass flow rates in comparison. A further investigation was conducted whereby the vacuum pump was throttled to equalize the pressure between the torch and downstream vacuum chamber (thus preventing supersonic flow through the nozzle). In this case, the discharge was more stable and did not extinguish even for pressures close to atmosphere.
The relatively low frequencies observed suggest that the instability is not directly a plasma phenomenon and that it may be associated with thermal gas flow effects. Such effects could either lead to strong temporal variations in plasma properties (due to oscillations in the neutral gas density) causing instantaneous loss of matching capability (cascading to full plasma extinction), or that result in the discharge being 'blown out' [54]. At present, the cause of the instability is not known, but intense heating leading to gas depletion in the hot plasma region upstream of the nozzle may play an important role. Cooler upstream gas then takes a finite amount of time to travel along the length of the ICP torch to re-fill this region. A somewhat similar instability, known as the breathing mode, is commonly observed in Hall thrusters [55][56][57]. Although the pressures are much lower in such devices (<1 Pa), intense ionization can cause strong gas depletion. Time is then needed for neutral gas to re-fill the thruster discharge channel (with a re-filling frequency in the kHz range due to the much shorter device length and much higher gas velocity). In the present case, the pressure is orders of magnitude higher and the ionization fraction is low, but gas heating due to plasma collisions provides a different mechanism for depletion. Since the pressure in the ICP torch is approximately constant, if the neutral gas is locally strongly heated, the density will drop to keep a constant pressure. But if the density drops too significantly, either changes in plasma impedance can occur affecting antenna-plasma power transfer, or the strong gradients produced within the discharge could excite instabilities. In either case, a finite amount of time may be needed for gas repletion. This re-filling frequency can be estimated using a simple gas transit time model. The axial velocity of the gas can be calculated with v =ṁ Aρ (14) where ρ is the density of argon, and A is the cross-sectional flow area. For the forward vortex, the cross-sectional area is the entire inner tube cross-sectional area, whereas for the reverse vortex, the cross-sectional area is that of the inner vortex which is found from the location of the mantle separating the inner and outer vortex. It is located at approximately 0.707 of the inner tube radius [41]. The density of argon is found using the ideal gas law with the measured stagnation pressure and temperature. The propellant transit time is then found by dividing the length of the inner tube by the velocity estimated above, and the re-filling frequency is calculated as f = v/L. Results show that for an applied power of 800 W, the re-filling frequency ranges from 35-55 Hz and 70-130 Hz for the forward and reverse vortex configurations respectively. These estimates are comparable to the frequencies measured by the photodiode.

Conclusions
This experiment has characterized and compared the performance of a supersonic RF ICP torch using forward and reverse vortex gas injection configurations. The RF antenna-plasma power transfer efficiency was found to be approximately constant for both configurations and between 90%-93%. This was confirmed using electrical current probe measurements as well as calorimetric measurements. As a final check, a third independent method was also performed. Here, the antenna current during operation was recorded. Then, with the plasma off, the RF power was adjusted until the same antenna current was observed. In this case, the difference between the measured forward and reflected RF powers must be equal to the power lost in the antenna and matching network. This was found to be consistent with the other electrical and calorimetry measurement methods. As the RF power transfer efficiency does not change significantly between gas injection configurations, the same amount of power is absorbed by the torch plasmagas system. This therefore means that any performance differences occur because of the gas injection method itself. It was found that both configurations show strong gas heating, although the reverse vortex produces superior performance. In particular, the reverse vortex results in a clear reduction in heat losses to the torch walls and a strong increase in power carried away by the gas exiting the nozzle. Results show that for an applied power of 800 W, the reverse vortex reaches a stagnation temperature of 3200 K and a thermal efficiency of 33%, compared with 2000 K and 19% for the forward vortex. Furthermore, calorimetry was consistent with independent measurements based on the torch stagnation pressure confirming these results. The bidirectional vortex flow fields produced with reverse vortex gas injection offer a number of advantages for different applications. Firstly, higher torch temperatures can be obtained compared with conventional gas injection methods for the same input power. Alternatively, less power is needed to produce a given temperature, as was demonstrated in figures 8 and 9. As less power is required, the power and thermal efficiency of certain industrial processes can potentially be greatly improved. For example, at a target temperature of 2000 K, figure 8 shows that at a mass flow rate of 100 mg s −1 the forward vortex requires 800 W, whereas the reverse vortex requires only 400 W. Since less power is needed for torch operation, this also implies that heat losses are lower and so the water cooling flow rate can be decreased. Additionally, torch thermal management may be improved leading to new and innovative torch designs and construction material possibilities. Reduced heat losses can also be an important enabling factor for some applications. For example, RF ICPs have been proposed as novel electrothermal space propulsion systems. However, with conventional gas injection configurations, heat losses to the source walls are currently seen as too high and lead to a much reduced thruster performance [46,47,53]. Reverse vortex gas injection may offer an interesting solution to overcome this challenge. Indeed, such injection schemes have already been successfully applied to liquid propellant chemical rocket engines [51,52] and microwave electrothermal thrusters [58][59][60], which share many similarities with supersonic ICPs.
There are however several important aspects related to bidirectional vortex stabilized supersonic ICPs that require additional study. One such factor is the influence of the nozzle geometry on the vortex flow fields. In this experiment, the nozzle geometry was fixed and the throat diameter of 2 mm is about 10 times smaller than the plasma source tube diameter. The outer and inner vortex regions of the bidirectional vortex flow field are also separated by a mantle region where the gas axial velocity is zero [41]. The nozzle design (i.e. inlet diameter, inlet curvature, and throat diameter) relative to the mantle diameter is expected to have an important effect on the gas flow [43], and consequently the overall plasma torch performance. Also, trying to force a large quantity of very hot gas through a small nozzle is expected to result in increased relative heat losses to the nozzle walls and a decreased thermal efficiency compared with a larger diameter nozzle. This may partially explain why Gutsol et al [38,54] were able to obtain higher thermal efficiencies in argon when using subsonic plasma torches with a larger relative nozzle diameter. In our investigation, we have also only focused on the plasma-gas heating region upstream of the nozzle, and no study of the downstream supersonic flow was conducted. For supersonic flows, the nozzle sizing determines the exit Mach number and the generation of any shock waves within the plume (depending on the background pressure) [42]. As the gas flow chokes at the nozzle throat, the region downstream of the nozzle has little effect on the upstream torch region. However, the downstream plume physics is of course important for a variety of industrial materials processing applications, which would therefore necessitate further studies with lower vacuum chamber pressures and higher pumping speeds.
Finally, due to the presence of an instability, the plasma discharge was unable to be sustained at high mass flow rates (upwards of about 170-180 mg s −1 ) and high temperatures. This instability represents a limiting factor preventing further gas heating: particularly for the reverse vortex configuration where extrapolation of the results to higher mass flow rates indicates that both higher temperatures and thermal efficiencies can be obtained. At the current time, the instability is not yet well understood, but it is absent when the flow is made subsonic (obtained by throttling the vacuum pump) and the discharge is stable even at pressures close to atmosphere. This suggests that the supersonic discharge is not being extinguished simply because the pressure gets too high inside the torch. The low frequency of the instability also precludes direct plasma phenomena and thus it is most likely related to a type of thermal or gas flow effect. Indeed, in other high temperature gas flow devices, such as conventional rocket engines, combustion instabilities are well known and can be relatively common [61,62]. Strong gas heating is expected to cause neutral depletion in the centre of the plasma torch where the temperature is highest (so as to maintain pressure balance), and the formation of strong spatial gradients, together with sonic/supersonic flow at the torch nozzle, may excite or exacerbate perturbations in the discharge. Further research is needed to better understand the nature of this instability.

Data availability statement
The data that support the findings of this study are available upon reasonable request from the authors.