Direct measurement of the ionization source rate and closure of the particle balance in a helicon plasma using laser induced fluorescence

Heating a plasma with radio frequency (RF) electromagnetic waves in the helicon regime is an attractive method for producing high density, low temperature plasmas. Electron densities as high as 10²⁰ m⁻³ have been achieved in helicon sources using only a few kilowatts to tens of kilowatts of power.^1,2 The efficiency with which helicon waves can convert RF power into electron density is both its most sought after and poorly understood property.³ The ultimate density achieved in helicon plasma sources is tightly coupled to both the power and particle balance present during the discharge. In particular, the observation of neutral depletion underscores the importance of the particle balance.^4,5 In trying to explain the neutral depletion, multiple hypotheses have been proposed to explain the transport processes in effect. Chen et al. have suggested that electron ion pairs are predominantly lost radially and that axial losses are negligible.⁶ Similarly Magee et al. concluded that the depletion of neutrals in helicon plasmas was due to expulsion, e.g., by collisional processes, not simply ionization alone.⁵ Despite multiple theories regarding the transport processes taking place, only a few studies have been done to study the flows present, definitively conclude whether axial or radial losses dominate, and identify the source and sink terms of neutral particles.^7,8 Answering these questions is the focus of this work.

To better understand the ionization source strength and distribution, laser induced fluorescence (LIF) was used to measure spatially resolved ion and neutral atom fluxes in the MARIA helicon device at several axial and radial locations. From these fluxes, a clear picture of the ion and neutral flow dynamics can be attained. Additionally, taking the divergence of the flux yields a direct measurement of the ionization source strength and distribution. While these measurements do not answer the question of how the RF wave energy is converted into electron-ion pairs, it represents the best observation of the actual ionization source distribution which is itself a direct result of the RF to ionization coupling mechanism.

The measurements presented in this work were taken on the MARIA helicon device, shown in Fig. 1, in the 3DPSI group at the University of Wisconsin—Madison.⁹ MARIA is 2.4 m long with an inner chamber diameter of 14 cm. The antenna is an 18 cm long helical antenna designed to couple to the m = +1 mode. The magnetic field is generated by eight water cooled pancake magnets and generates a peak magnetic field strength of 943 G at 938 A of total current. A water-cooled solid state RF generator provides up to 10 kW of RF power and is typically operated at constant power (CW). A single RF compensated Langmuir probe, of the same type proposed by Chen et al.,¹⁰ is the baseline diagnostic for electron temperature and density measurements. Electron densities in the range of $5×1018$ m⁻³ are typical at neutral pressures in the range of 2 mTorr, with 700 W of RF power, and a magnetic field strength of 700 G.

The LIF system follows the master oscillator power amplifier (MOPA) design championed by Severn et al.,¹¹ and is designed around a 40 mW tunable single mode diode laser and a tapered amplifier, which can produce 500 mW of maximum laser power. This system can be tuned to pump the 3D $4F$ 7/2 to 4p $4D$ 5/2 singly ionized argon absorption transition at 668.614 nm, or the 4s $2[3/2]$ 1 to 4p $2[1/2]$ 0 neutral argon absorption transition at 667.912 nm. The ion and neutral pumping strength, which is proportional to the density of atoms in the lower atomic level and incident laser power, is monitored via the fluorescence intensity at 442.6 nm and 750.6 nm, respectively. More details of the LIF system and the typical analysis steps to extract flow measurements are provided in a paper by Green et al.¹² 

The optical configuration is different when making measurements with the laser injected axially along the chamber as compared to radial laser injection. The difference lies in the polarization of the laser light and its interaction with the atoms of interest. As a result of the interaction between the angular momentum of an atom's electrons and the background magnetic field, certain transitions are associated with light emitted or absorbed with a specific polarization. Specifically, when the projection of an atom's angular momentum along the z-axis, labeled with the quantum number m, either increases or decreases by one unit during a transition, called a σ transition, it either emits or absorbs circularly polarized light. When the z-projection of angular momentum does not change during a transition, called a π transition, the emitted or absorbed light is linearly polarized in the direction of the magnetic field. To account for this, the laser light is circularly polarized by placing a linear polarizer and quarter wave-plate at the output of the fiber. In the case of radial laser injection, only the linear polarizer is used. Condon and Shortley showed that the intensity of the σ and π transitions of the Zeeman Effect differed by a factor of 2 in their book Atomic Spectra.¹³ 

A cylindrical coordinate system is adopted with the $ẑ$ axis colinear with the chamber axis and parallel to the magnetic field as indicated in Fig. 1. The “downstream” direction is in the direction of the magnetic field. This direction points away from the antenna toward the blind end of the chamber. The reference point for axial position measurements is a part of the structure supporting the LIF collection optics. The center of the 18 cm long antenna is located at 21 cm and the downstream plasma boundary is located at 168.4 cm. Positive and negative flow velocities discussed in this work match the coordinate system, i.e., positive axial flow velocity is a flow in the +Z direction and positive radial flow is away from the chamber axis.

In this work, the source and sink terms of the mass conservation equation are the quantities of interest. By operating the plasma CW, the temporal component of the conservation equation can be neglected and the mass conservation equation simply balances the particle source and flux divergence,

Here, V is the flow velocity, n is the number density, and S(x) is the ionization rate.

No particle flux variation is expected in the azimuthal direction of the coordinate system discussed previously. Separating Eq. (1) into its axial and radial components, and dropping the azimuthal component, yields

Here, V_z and V_r are the axial and radial flow velocity components, respectively, and r is the radial position.

It is clear that an ionization source results in a positive value of flux divergence. Negative terms are indicative of an ion sink. The objective then is to measure the particle flux, $Γ=Vn$⁠, in both the radial and axial directions and calculate the divergence, thereby measuring the ion source and sink rate. By measuring the Doppler shift of the velocity distribution function using the LIF system, the flow velocity, V, can be measured directly. However, the LIF intensity itself only yields information about the density of the atomic state being pumped. To determine the ionization source rate for a singly ionized ion population, the total ion density is the desired quantity. In principle, a collisional radiative (CR) model might be used to infer total ion density and thus total electron density. However, failure to accurately capture all the relevant atomic processes in the CR model would make it quite difficult to interpret the results. In this work, an empirical calibration between singly ionized argon LIF intensity and electron density is made from experimental measurements directly.

The minimum flow velocity uncertainty is limited by the absolute laser wavelength uncertainty. Previously, the wavelength of a molecular iodine transition near 668.614 nm was reported as 668.6144 nm by Keesee et al.,¹⁴ 668.6126 nm by Woo et al.,¹⁵ and 668.6128 nm by Green et al.¹² The wavelength of this iodine peak was further refined in this work by identifying the offset from the v = 0 transition wavelength of the 3D $4F$ 7/2 to 4p $4D$ 5/2 singly ionized argon absorption transition.

To perform this calibration, 9% of the laser power was passed through the iodine reference cell, while 81% of the initial laser power was injected into the plasma chamber via a 50 μm fiber optic cable. The remaining 10% of the laser power was shone on a photodiode to monitor and correct for laser power. As the laser wavelength was scanned, the laser power, iodine fluorescence signal, and argon fluorescence spectrum were recorded simultaneously by a digital storage oscilloscope. More details of the laser optical arrangement and LIF analysis methodology can be found in Green et al.¹² 

The key to the calibration measurement lies in the simultaneous capture of argon fluorescence from atoms with velocity, V, aligned with the laser wave vector, k, and anti-aligned. In this way, no assumption was made about the flow velocity. By assuming steady state conditions, the flow velocity at a single point can be assumed to be constant. So, the aligned, $k·V$⁠, and anti-aligned, $−k·V$⁠, fluorescence signals must yield the same velocity with opposite sign. The midpoint between the two signals is therefore the $|V|=0$ point. Thermal line broadening of the fluorescence spectrum tends to blend the two peaks together and thus, performing the measurement at locations where the velocity is high makes the fitting process more definitive.

The refined wavelength for one of the iodine transitions near 668.614 nm of 668.61272 ± $3.13×10−5$ nm was found from the standard error of the mean of 7 repeated measurements. The uncertainty of the 668.614 nm transition was taken from the measurement of 14956.32 ± 0.0004 cm^–1 (668.61380 ± $1.8×10−5$ nm) by Whaling et al.,¹⁶ which itself is the source of the data held in the NIST ASD database.¹⁷ 

The prominent I₂ peak near the 667.9125 nm Ar I transition was measured in a similar way. Unfortunately, the very low flow velocity, V, meant that the LIF signals obtained with the laser wave vector aligned parallel and anti-parallel were not sufficiently separated to follow an analysis procedure identical to the argon ion transition. Instead, the laser was passed through the plasma radially such that the beam could be reflected off an external mirror for the second, counter propagating, pass through the plasma. One set of data was taken with a laser beam dump in place of the mirror such that only the $k·V$ component is first acquired. This is plotted as the red trace in Fig. 2. The beam dump is then replaced with a mirror and an LIF signal with both the forward and backward components is acquired; the teal trace is shown in Fig. 2. The red trace can then be subtracted from the teal trace to reveal the $−k·V$ component, plotted as the black dashed-dotted trace. The midpoint between the $k·V$ and $−k·V$ curves which corresponds to the $V=0$ transition frequency of 667.9125 provided by NIST could then be more easily identified. The NIST transition wavelength was again sourced from Whaling et al.¹⁸ who reported the transition wavenumber as 14972.0217 ± 0.0006 cm^{– 1} (667.9125 ± $2.67×10−5$ nm).

The wavelength of the I₂ peak near 667.9125 nm was determined in the same way as the 668.6128 nm line, with multiple samples. The final value of 667.91687 ± $3.10×10−5$ nm was found from the standard error of the mean of eight measurements.

It is important to note that the I₂ peak wavelengths were essentially calculated as offsets from well-known argon lines. The minimum uncertainty in the I₂ wavelength is then at least as large as the wavelength uncertainty of the argon line to which it is compared. This lower limit leads to a minimum absolute velocity uncertainty of 17 m/s and 11 m/s for the neutral and singly ionized argon species, respectively.

To correlate the LIF intensity with the electron density, LIF and Langmuir probe measurements were made at the Langmuir probe axial location and at radial locations r/a = 0, 0.2, and 0.4. The magnetic field strength was then scanned over the same range as was used for the measurements presented below. Plotting the electron density as a function of LIF intensity, shown in Fig. 3 for the axial and Fig. 4 radial case, yields the scaling required to infer electron density from LIF intensity measurements.

Performing the measurements at several radial locations was done in an effort to verify the scaling under the different plasma conditions found at different locations during a discharge. A robust scaling was found for all plasma conditions, and for both axial and radial laser injection cases. The LIF signal was found to strongly increase as the electron density rose while scanning the magnetic field strength between 450 G and 850 G. The electron temperature did not scale significantly with magnetic field strength. Figure 5 shows the typical radial electron temperature profiles at several of the magnetic field strengths used in this work.

The particular non-linear scaling observed in Figs. 3 and 4 requires some interpretation. The metastable state being pumped is an excited state of singly ionized argon. The excitation rate due to electron impact excitation is therefore at least proportional to the density of electrons, n_e, and the density of ions, n_i. Indeed, in a similar experiment, Sun et al. have shown a scaling $ILIF=ne2Te1/2$ to match their data well.¹⁹ However, we note that the electron temperature in Sun's work is in the range of 6 eV, which is more than double those experienced in MARIA. Ultimately, the LIF intensity is proportional to the actual density of the atomic level, not just the population rate. In the low temperature, moderate density, plasmas relevant to this work, the ultimate density is a very complex function of several atomic processes such as metastable quenching, decays from higher levels, electron impact excitation, etc. Fully understanding the mechanism underlying the strong density dependence would require detailed investigation with collisional radiative modeling codes.

For the argon ion axial LIF data, the laser was aligned with the axis of the chamber and the collection optics were traversed along the axis of MARIA, collecting fluorescence photons emitted perpendicular to the laser beam. The LIF spectra intensities were converted to electron density using the axial calibration data shown in Fig. 3. The calculated electron density at several magnetic field strengths and plotted as a function of axial position along the plasma chamber is shown in Fig. 6. At magnetic field strengths below approximately 600 G, e.g., the 500 G trace, the electron density is relatively evenly distributed between the antenna and the downstream boundary plate. As the magnetic field strength is increased further, the electron density does not increase significantly near the antenna at 210 mm and appears to hit an upper limit near 700 G at an axial location of 680 mm. With further downstream however, near 1200 mm, the electron density continues to increase with increasing magnetic field strength. The result of this asymmetric density scaling with magnetic field strength is a downstream shift in location of the maximum electron density. This shift suggests a change in the fueling and ionization equilibrium reached at different magnetic field strengths.

The argon ion flow velocity measurements, shown in Fig. 7, are extracted directly from the LIF data by measuring the Doppler shift of the absorption spectrum. The flow velocity is negative near the antenna, crosses the horizontal axis at 900 mm, and transitions to a strong positive velocity near 1500 mm. Not much can be said about the cause from these data alone, but the sharp increase in velocity beyond 1600 mm is likely the velocity increase that occurs in the presheath to satisfy the Bohm criterion.²⁰ The sound speed for the 2.5 eV plasmas in this case is 2461 m/s, and the closest measurement was approximately 4 mm from the sheath boundary. If this is indeed the case, the lack of any velocity scaling with magnetic field strength may indicate near constant electron temperature and thus constant ion sound speed.

The shape of the axial ion flux profile shown in Fig. 8, which is a product of the density and velocity data, is most strongly influenced by the ion velocity profile and thus has a very similar shape. The flux is negative (upstream flow) near the antenna, crosses the horizontal axis near 900 mm, and transitions to a strong positive flux (downstream flow) near 1500 mm. The flux is augmented up or down depending on the electron density. Ignoring the exponential region likely due to the presheath, the slope of the ion flux measurements clearly suggests an ionization source distributed along the axis of the device.

Taking the divergence of just the axial flow data, the contribution of axial flux divergence to the ionization source rate can be determined. These data alone represent a lower bound for the ionization source rate. The divergence of the axial flux data is shown in Fig. 9. The rapid flux increase in the presheath region near 1650 mm results in a significant ionization rate there. However, in the main plasma region between 450 mm and 1500 a distinctly positive ionization source rate of $∼1021$ m⁻³ s⁻¹ is also evident. Despite some scatter in the data, a fairly clear scaling with magnetic field strength is also evident at 1250 mm. This suggests an ionization rate that scales similarly to the helicon dispersion relation, with a dependence on magnetic field strength. However, the downstream shift in the location of maximum electron density can also affect the divergence calculation. A slight dip at 1650 mm in the ionization rate calculated from the axial data suggests an ion sink in this region. However, the radial contribution must be included before any conclusion regarding this possible sink is drawn.

The radial ion flux measured at radial positions of r/a $≤0.05$⁠, 1/3, and 2/3, and the same axial locations as for the axial data is shown in Fig. 10. At all positions, there is a consistent outward radial flux on the order of $2.5×1020$ m⁻² s⁻¹ with slightly higher values at an axial position of 680 mm. Despite a fairly consistent flux, the density of ions in the 3D $4F$ 7/2 state able to absorb laser photons was significantly lower at greater radii leading to a decreased signal to noise ratio. Signals below a certain threshold could not be fit reliably and hence were not plotted in the figure leading to the sparsity of data points at r/a = 2/3. The radial flux between $2.5–5×1020$ m⁻² s⁻¹ is comparable to the axial flux measured between 680 mm and 1400 mm. This already means that over the bulk plasma domain, neither the axial nor radial flux dominates the loss channel.

It is also interesting to note that the perpendicular flux is comparable to Bohm-like diffusion. The Bohm diffusive flux, J, is calculated by $J=DB dne/dr$ and $DB=ckTe/16eB$⁠, where c is the speed of light, k is Boltzman's constant, T_e is the electron temperature, B is the magnetic field strength, and e is the charge of an electron. Taking the density gradient in the radial direction from Langmuir probe measurements gives a radial flux between $1–4×1020$ m⁻² s⁻¹. After comparing the results of numerical simulations to experimental density data, Rapp et al. concluded that radial losses are due to Bohm diffusion and these data seem to support that conclusion.²¹ Taking LIF data with higher spatial resolution might result in an even better comparison with the numerical data of Rapp et al.

Calculating the contribution of the radial flux divergence to the ionization source rate is complicated by the sparse data. No differentiable radial trend can be identified to perform the necessary calculations. However, assuming a constant flux yields an axially peaked ionization source, but one that blows up at r = 0 which is not physical. Calculating an approximate flux gradient based on the r/a = 1/3 and r/a = 2/3 data, and assuming a linear trend between these two data points, yields an ionization source rate of 10²² m⁻³ s⁻¹. However, this calculation carries an uncertainty of ∼200%. The ionization rate of 10²² m⁻³ s⁻¹ is comparable to the ionization rate calculated from the axial flux data in front of the boundary plate. This suggests a bulk plasma ionization rate between $0.5–1×1022$ m⁻³ s⁻¹. Higher spatial resolution in the radial direction is needed to better constrain the radial flux profile and ionization source rate.

Where there is an ion source via ionization in a singly ionized plasma, there must necessarily be a neutral sink. Fortunately, the diode laser used in this work can be re-tuned to lase at 667.912 nm to pump the 4s $2[3/2]$ 1 to 4p $2[1/2]$ 0 neutral argon absorption transition. The neutral LIF intensity is directly proportional to the density of the 4s $2[3/2]$ 1 excited atomic level of neutral argon. This level is directly populated from the neutral argon ground state via electron impact excitation. So, while its connection to the neutral ground state makes it a decent measure of the ground state population, the level density is also very sensitive to the electron density. Unfortunately, no other diagnostics that could measure localized neutral densities were available to create an LIF signal to neutral density calibration. However, as shown below, the mass conservation equation can be used to estimate the neutral atom density using the axial neutral argon LIF data alone.

The neutral argon intensity profile taken with the laser aligned along the axis of the device, shown in Fig. 11(a), is nearly an inverse of the ion density profile. This is generally expected as a high electron density suggests a high ionization rate and thus rapid conversion of neutrals into ions. At low magnetic field strength, $B≤400$ G, the neutral LIF intensity is fairly broad and extends along a significant length of the MARIA chamber. Between 500 G and 600 G or so, the neutral intensity profile increases and is concentrated near an axial position of 1400–1700 mm. However, below 1400 mm the neutral LIF intensity is significantly reduced indicating a reduced density of neutral atoms in that region. Above 600 G, the neutral intensity is still concentrated in the same axial location, but the intensity decreases with further magnetic field strength increase.

The neutral flow velocities, shown in Fig. 11(b), are much slower, around 50 m/s, in contrast to the argon ion flow velocities, which exceeded 1000 m/s in the presheath region. The velocity measurement closest to the boundary plate at 1680 mm, which was 4 mm away from the plate, is negative for all magnetic field strengths. The flow velocity is positive between axial locations of 1400 and 1650 mm. Between 600 and 1400 mm, the flow appears to be positive, but a low signal to noise ratio means many data points are missing and data that could be analyzed carry larger uncertainty. The apparent flow velocity reversal between 1650 mm and 1680 mm is a curious feature that could support the theory of Magee et al. that collisional neutral expulsion is playing a role in the bulk plasma neutral depletion.

The neutral intensity and flow velocity evolution is intuitive in the context of strong ion flux toward the boundary plate. Ions impinging on the boundary plate are neutralized and are necessarily recycled back into the plasma volume as neutral atoms. These recycled neutral atoms are then exposed to the flux of ions and electrons and can undergo ionization and experience collisional momentum transfer. The flow reversal is possibly an indication of the collisional momentum transfer, while the strong buildup and then decay of the LIF intensity are an indication of the electron impact excitation and ionization process.

By applying this hypothesis to the data, we find that a very simple two species exponential decay model fits the axial neutral LIF data quite well. The model used takes the form:

which has the solution

In this very simple model, n₀ is the ground state immediately adjacent to the downstream boundary plate, n₁ represents the neutral argon ground state density, n₂ is the density of the atomic level being pumped in the LIF process, and λ₁ and λ₂ are the decay constants for the two atomic levels, respectively. The physical “decay” mechanism within this model is electron impact excitation from level 1 to level 2 followed by further excitation and ionization from level 2. The factor c is a constant that takes into account the fact that not all excitation out of the ground level ends up in the single excited level. Insufficient data are available to fully constrain the value of c. However, recognizing that it is simply a density scalar for the 4s $[3/2]2$ 1 neutral argon level, its value can temporarily be set to an arbitrary value, c = 1 here, and the data can be fit remarkably well as indicated by the black line in Fig. 11(a).

Despite setting c = 1 in this work, reasonable estimates of the neutral argon ground state density near the boundary plate can be made. As described above, the flux of ions into the boundary plate must reappear as a flux of neutral atoms. To calculate the flux, a recycling velocity must be determined. Unfortunately, the neutral velocity is pretty scattered, but the average recycling velocity for all magnetic field strengths 4 mm in front of the plate was 25 m/s away from the plate. Multiplying the values of n₀ found through fitting Eq. (4) to each of the traces in Fig. 11(a) and matching to the argon ion flux in Fig. 8 indicates n₀ should be scaled by $9.5×1016$ to yield the neutral argon flux in m²/s. The ion and neutral particle flux in close proximity to the boundary plate at each magnetic field strength after scaling n₀ is shown in Fig. 12. The agreement between the two is very good, and both scale with increasing density as expected. A table showing the values obtained by fitting Eq. (4) to the LIF data is shown in Table I.

The level of agreement between the experimental neutral argon LIF data and the relatively simple model used to fit it adds confidence that the underlying physics are being captured to first order. Assuming this is true, the ionization rate can again be calculated as the neutral atom loss rate. In the model presented above, the atoms lost from the ground state population are stepwise excited and ionized. The ionization rate can thus be estimated by calculating the neutral ground state population loss rate. The loss rate can be calculated using the same model as Eq. (3). The ionization rate is thus

Figure 13 shows the ionization rates calculated using Eq. (5) and the data from Table I. For axial positions above 1250 mm, these ionization rates are comparable with those calculated from the ion LIF data. However, the ionization rates calculated from the neutral LIF data do not reflect the 10²² m⁻³ s⁻¹ ionization rates in the presheath region. The neutral ionization rates at axial locations below 1250 mm are significantly lower than the ion LIF data. This suggests that while ionization of axially recycling neutrals is likely still occurring, they represent a minor contribution to the overall ionization rate. The axial location around 1250 mm is therefore likely the transition point between axially dominant fueling and radially dominant fueling.

The radial LIF intensity and flow velocity were measured for neutral argon at the same locations as for the singly ionized argon case. The fluorescence intensity is shown in Fig. 14 as a function of magnetic field strength. The intensity measured just beyond the antenna at 680 mm, shown in Fig. 14(a), is initially quite high on axis and at low magnetic field strength. However, moving away from the axis, increasing the magnetic field strength, and moving further down stream substantially reduce the LIF intensity. For higher magnetic fields, where the electron density is greater, the lower neutral LIF intensity is a result of a lower neutral atom density.

As with the argon ions, the radial flow of neutral argon atoms was measured with LIF and is shown in Fig. 15 at the same three radial locations as the ion data. At r/a $≤$ 0.05, the flow velocity is nearly zero for all axial locations and magnetic field strengths. At r/a = 0.33, the radial flow velocity for all magnetic field strengths shifts slightly negative (inward) for axial positions below 1200 mm. However, v = 0 is still within the uncertainty bars. For r/a = 2/3, the flow velocity is a bit more negative than at r/a = 1/3, and now v = 0 is not within the uncertainty. The increasingly inward flow velocity suggests that radial fueling of the plasma is indeed taking place for axial positions between 210 mm and 1200 mm. However, the obvious scatter in the data makes conclusive interpretation difficult. A more detailed study is needed for radial neutral flow and is the focus of future research. For axial positions above 1500 mm, the radial flow velocity is not significantly dependent on magnetic field strength or radial position and tends to hover around −10 m/s.

Unfortunately, the radial neutral LIF intensity cannot be converted into a neutral flux. In the axial case, the conservation of mass equation formed a strong relationship between the incident ion flux and the recycling neutral flux. The ability to take measurements very close to the boundary plate, and thus form a realistic control volume was essential to that analysis. In the radial case, refraction through the glass chamber wall and significantly reduced ion LIF intensity meant LIF measurements could not be taken right next to the chamber wall. A realistic control volume cannot therefore be defined to leverage conservation of mass in converting the neutral LIF intensity and velocity into a neutral flux estimate.

The flow measurements for neutral and singly ionized argon in both the axial and radial direction presented above begin to paint a picture of the particle balance in the MARIA helicon device. The flux of ions flowing along the axis of MARIA exhibits clear scaling with magnetic field strength and the greatest ion loss term was due to axial flux near the boundary plate. The radial ion flux of $2.5–5×1020$ m⁻² s⁻¹ between the antenna and the boundary plate is comparable to the axial flux in the same region. The ion loss due to axial flow is therefore dominant near the axial boundaries, but radial and axial ion loss is of similar magnitude throughout the bulk plasma.

The neutral LIF data indicate a substantial buildup of neutral atoms directly in front of the downstream chamber boundary. This buildup of neutral atoms necessarily has an impact on both the ion losses and the neutral fueling of the plasma. The apparent flow velocity reversal is one such impact and strongly suggests ion-neutral momentum exchange is occurring in that region. The radial neutral argon LIF data are less definitive, but clearly indicate a depletion of neutral atoms at higher electron densities. The neutral argon radial flow velocity indicates an inward flow of neutral argon atoms between the antenna and downstream boundary plate, while the radial flow is essentially zero near the boundary plate.

Combining the ion and neutral argon LIF data suggests that a kind of circulatory ionization and recycling process is taking place in MARIA. Ions produced just downstream of the antenna are lost radially and axially in approximately equal proportions. Ions lost in the radial direction are simply recycled after neutralizing on the chamber wall. Ions that continue along the axis possibly exchange momentum with a higher density cloud of neutral atoms before impinging on the axial boundary plate and neutralizing. The neutral atoms recycling off the plate encounter an intense flux of ions and electrons and are either immediately ionized and sent back toward the plate or make their way further upstream before eventually being ionized. This proposed sequence sets up a net flux of ions in the downstream direction and a net flux of neutrals in the upstream direction. The increased inward flow of neutral atoms in the bulk plasma region near the antenna suggests neutral atoms recycling off the axial boundary plate eventually rebound of the radial chamber wall and join the flux of neutral atoms recycling radially.

It is important to note that this particular fueling cycle is likely unique to the chamber geometry on MARIA where the gas source and vacuum pump are located at the same upstream location of the chamber. Different gas source arrangements will likely result in very different flows, especially when the gas is sourced upstream and the vacuum pump is located downstream. The impact of these alternative vacuum arrangements, including the use of a large expansion chamber at the downstream location, on the plasma flows and ultimate density is the subject of future research.

This work was funded by the National Science Foundation under NSF CAREER Award No. PHY-1455210 and by funds of the Engineering Physics Department in the College of Engineering at the University of Wisconsin-Madison. The support and invaluable input and consultation of Professor Noah Hershkowitz on Helicon plasmas and of Professor Greg Severn on laser induced fluorescence are greatly appreciated.