Overestimation of Mach number due to probe shadow

The lifetime of plasma facing components (PFCs) in a tokamak is primarily governed by material erosion, migration, and redeposition.¹ The effect of material migration is especially important because net erosion is what essentially governs the PFC lifetime.² Prior research has shown evidence of impurity entrainment in background plasma flows in linear devices³ and the scrape-off-layer (SOL) of tokamaks.^2,4–8 As large flows in the SOL are common,^5,8 accurate measurements of the SOL flow are essential in order to properly model and understand material migration.^1,7

These studies are complicated because diagnostic access to the SOL plasma flows can be difficult. The flow pattern is complex, and the multi-point measurements of the flow are not always available.⁸ Measurements of the flow in the scrape-off-layer are generally made with Mach probes (MPs),¹ but there has been some debate over how exactly to interpret the results from these probes.^9–11 Ion fluorescence methods of measuring the velocity in hydrogen are of course not available because the ion is fully stripped of electrons. However, the velocities of higher Z ions, such as argon, can be measured using non-invasive, optical techniques. Because laser induced fluorescence (LIF) is a technique that has been used to measure ion flows successfully in argon plasmas,^9,12–23 we used an argon plasma as a platform to compare Mach probe measurements to the well-established LIF technique.

In this paper, we present results for measurements of the mean fluid flow of an argon plasma performed with both Mach probes and LIF. Previous comparisons between Mach probe measurements and LIF have been made in weakly ionized plasmas,⁹ low density ECR discharges,¹⁹ in a weakly collisional discharge,²⁰ and in a helium discharge using the neutral pressure as an experimental knob.¹⁸ Our experiment is unique because changing the magnetic field allows us to adjust the perpendicular diffusion coefficient in the plasma without greatly affecting the other global plasma parameters (T_e, T_i, and n_e). All experiments were performed in the Controlled Shear Decorrelation eXperiment (CSDX) helicon plasma device. We show results for the plasma flow measured on-axis. The results show that the probe's own shadow perturbs the measurements when the ion-neutral mean free path (⁠$λi−n$⁠) is shorter than the characteristic length of the geometric shadow. We then discuss the differences between the two diagnostic measurements and introduce a geometric probe shadow model to account for the differences between the measurements. The model also provides a correction factor which accounts for this shadowing effect and provides for accurate, probe-based, Mach number measurements.

The experiments described in this paper were performed on the upgraded Controlled Shear Decorrelation eXperiment (CSDX),²⁴ a linear plasma device 2.8 m long and 0.2 m in diameter. A schematic of CSDX is shown in Figure 1. The insulators are placed on both ends of the device so that the plasma flux terminates on an insulating boundary.^25,26 The plasma is produced using a 13.56 MHz, 1.8 kW, m = 1 RF antenna. The m = 1 helical antenna is placed over a 15 cm diameter bell jar that is mated to the end of the vacuum chamber. The plasma is confined radially by a series of 28 axisymmetric magnetic coils capable of creating axial magnetic fields up to 2400 G.

Argon was used as the working gas; it is injected radially from a port located at the wall of the device at the source end of the device, and a mass flow controller (MFC) maintains a constant influx of neutral argon gas at a rate of 25 sccm. A 1000 l/s turbomolecular pump at the far axial end of the machine maintains a neutral pressure of 4.2 mTorr at the source end and 3.2 mTorr at the pump when the RF antenna is off. When the antenna is on, the plasma acts as a sink for the neutrals and the pressure at the wall is approximately 1 mTorr along the length of the device. Typical electron temperatures and densities are 4 eV and 10¹³cm⁻³ as measured by an RF-compensated Langmuir probe. The plasma parameters do not vary by more than 50% over the range of magnetic fields used in these experiments.²⁴ 

A Mach probe was used to measure the plasma velocity parallel to the magnetic field. The location of the Mach probe is shown in Figure 1. The probe was constructed from an alumina shaft, approximately 0.45 cm in diameter, with 14 bore holes. Tungsten rods housed in each of the holes act as electrodes. A small window was cut azimuthally around the circumference of the rod to expose the tungsten electrodes to the plasma. This gave each tip an ion acceptance angle of approximately 4π/7 rad, as shown in Figure 2. The tungsten rods were negatively biased at V_bias = −80 V with respect to the chamber wall, which is about 50 V below the floating potential,²⁴ to collect only the ion saturation current.

The Mach probe was inserted radially into the center of the plasma at a rate of ∼3 cm/s using a stepper motor under computer control. The ion saturation current was measured with a current following amplifier connected to a 0.5 MHz bandwidth data acquisition (DAQ) system. The Mach number is determined from the measured upstream and downstream current densities of the probe using the method from Shikama²⁷ 

where $α$ is the acceptance angle of the probe tip, $θ$ is the angle of the tip normal with respect to the magnetic field line, j_θ and j_θ+π are the ion saturation current densities collected π radians apart, and k is a calibration constant. The probe was rotated through 2π rad in 14 equal increments to obtain independent measurements of the Mach number from each tip and eliminate effects due to differing probe tip areas. Since we used the rotation method of measurement, we used the collected ion current directly without needing to take a precise measurement of the probe tip area.

Different plasma parameters and different models for the ion current collection call for different values of the calibration constant, k.^10,28 Simulations approximating ion current to a sphere with a collisional presheath have been performed by Patacchini and Hutchinson previously.²⁹ In these studies, the flow was parallel to the magnetic field and the level of magnetization was represented by the parameter $β=eBRp( 2πmiTi )12$⁠. Over a range of $β$ = 0 to 1, these simulations showed an increase in the value of the calibration factor, k, with increasing magnetic field for weakly magnetized plasmas. Our experiments run over a range of β from 0.2 to 0.7, the calibration factor increases by ∼30%. As will be shown below, this is significantly less than the effect that can be attributed to ion-neutral collisions.

In addition to the work described above, collisionless simulations over a wider range of magnetic fields were performed³⁰ with flows including components both parallel and transverse to the magnetic field. However, these calibration factors represent even higher values for the Mach numbers with a given ratio of upstream-downstream ion currents. Thus, for our experiments, we use the unmagnetized calibration factor of k = 1.34 from Hutchinson's previous work.²⁸ The same value has been used in the past for weakly magnetized plasmas.²⁷ 

The ion saturation current signals were averaged over 100 ms periods, giving a ∼3 mm spatial resolution, and averaging out short period fluctuations (>10 Hz). Although data were taken for the full radial profiles, only the on-axis data are shown here for comparison with the LIF data measurements. The full radial profiles of the uncorrected Mach number were published previously.²⁴ 

An LIF system was also used to measure the absolute parallel velocity for comparison with the Mach probe measurements. The three level scheme originally described by Severn¹⁵ was used, which stimulates a transition from the Ar-II metastable 3d⁴F_7/2 state to the 4p⁴D_5/2 state causing a photon to be re-emitted through a transition back to the 4s⁴P_3/2 state as shown in the diagram in Figure 3. The magnetic field causes this transition to broaden into one group of linearly polarized $π$ transitions with $ΔM$ = 0 and two orthogonal, circularly polarized groups of $σ$ transitions with $ΔM$ = ±1 due to the Zeeman effect, where M is the magnetic quantum number (the z projection of the total angular momentum).

A diagram of the optical setup for the LIF system is shown in Figure 4. The laser used was a Toptica TA100 tunable diode laser with a linewidth of 1 MHz and a mode hop free range of up to 30 GHz. One 8% beam splitter was used to redirect a portion of the beam into a Bristol Instruments 621-VIS wavemeter, which measured the wavelength with an absolute accuracy of ±0.0001 nm; this corresponds to an uncertainty in ion velocity of approximately ±45 m/s. A second 8% beam splitter was used to redirect a portion of the beam through an iodine cell. The measurements of the iodine fluorescence spectrum confirm the measurements from the wavemeter and are consistent with two other independent measurements.^15,16 A more detailed description of the iodine spectrum is given in the  Appendix, which will be beneficial for future groups using this technique.

Laser light centered at 668.6139 nm was injected on axis, parallel to the magnetic field, from the pump end of the plasma device as shown in Figure 1. The laser frequency was scanned over 10–20 GHz to capture the full ion velocity distribution function (IVDF). A quarter wavelength plate was inserted in the beam path after the splitters to change the polarization of the laser light from linearly to circularly polarized. By rotating the quarter wave plate and monitoring the emitted light, we are able to isolate the individual, circularly polarized sigma branches. The circularly polarized, $ΔM$ = 1 component of the transition was used for our LIF experiments. The spectrum showing the $π$ and both sets of $σ$ transitions is shown in Figure 5 with the $ΔM$ = 1, $σ$ excitation branch used in our experiments shown in blue. The emitted florescence is collected through a side port at the measurement location using a focusing optic and 1 nm width bandpass filter centered at 443 nm in front of a photomultiplier tube (PMT). This isolates the 4p⁴D_5/2 to 4s⁴P_3/2 transition from any nearby transitions in the plasma.

The collection optics were chosen so that the focal point is on the plasma axis. The overlap between the focusing optics and the laser beam forms a collection volume of approximately 3 mm³. Optical layout and collection area is illustrated in Figure 6. Since this transition can also be collisionally excited by electron impact, phase synchronous detection was performed by modulating the beam intensity with a beam chopper at 1 kHz and using a lock-in amplifier in order to increase the signal to noise ratio. For the data points shown here, the minimum signal to noise ratio (defined as $SNR=Aσnoise$⁠, where A is the amplitude of the fit and $σnoise$ is the rms of the residual) is 3.5 and the maximum is 80. A histogram of the signal-to-noise ratio for the LIF data points presented in this paper is given in Figure 7.

The natural broadening of the line is on the order of 0.08 GHz,¹⁵ and the collisional broadening is on the order of 0.05 GHz.²⁴ Therefore, the dominant contributions to the line width are the contribution due to Zeeman splitting, given in Table I, and the Doppler broadening which is given by $Δν=ν08kTiln(2)mc2$ (given in Ref. 15). The Doppler broadening is on the order of 3.5 GHz for the ion temperatures in these experiments (T_i = 0.4 eV).

For interpretation of the LIF results a Maxwellian IVDF is assumed. Since the natural and collisional broadening is negligible compared to the Doppler and Zeeman broadening, only the latter two are considered for the fitting model. The relative magnitudes and the Zeeman splitting of the lines can be calculated from quantum mechanical considerations. These calculations are given in detail in a West Virginia University internal report³¹ and are reproduced in Table I. The breadth due to the Doppler broadening is approximately 3.5 GHz, and the spreading due to the Zeeman splitting is approximately 1 GHz per kG. Since the Zeeman splitting and Doppler broadening are of the same order, each individual Zeeman split transition needs to be fit with a Doppler broadened Maxwellian function. The fitting function in its most general form is

For the sigma transitions, this gives the fitting function as the sum of six Maxwellian functions of different weights. The $νn$ terms represent the shift due to Zeeman splitting (given in Table I). The $δν$ term represents the Doppler shift of the IVDF due to the mean velocity parallel to the magnetic field. The variable $κν$ is a constant with the value 0.092495 (eV/GHz²).³¹ The relative amplitude of each transition is given by $In$⁠, and the values are reproduced in Table I. The parameters $δν$ and T_i are then adjusted to give a best fit of I(⁠$ν$⁠) to the measured spectrum.

Figure 8 shows an example of the raw LIF data with the fit from Equation (2) that is used to determine the Ar-II parallel velocity. Similar results were obtained across a variety of magnetic fields and were compared to Mach probe measurements. The results of the Mach probe (MP) analysis (Figure 9) indicate that the ion velocity parallel to the magnetic field at the plasma center increases monotonically as the magnetic field increases. The Mach number measured was converted to velocity using measurements of electron temperature published previously²⁴ and is shown in Figure 10. At 400 G, the analysis shows a Mach number of 0.1 (350 m/s), and at the highest magnetic field, the Mach number is approximately 0.8 (2800 m/s). The error bars used represent the standard deviation of multiple measurements as well as an uncertainty in the acceptance angle of ∼13°.

The LIF measurements show that the plasma velocity remains constant at about 300 m/s from 400 to 1600 G, which is a Mach number of ∼0.1. This result that stands in stark contrast to the measurements made with the Mach probe, as can be seen in Figure 10, suggests that the Mach probe interpretation model is not correct.

The theory underlying LIF interpretation is simple; it relies only on knowledge of the electronic transitions of the ion (or atom) and the Doppler shift. However, the methods of Mach probe interpretation have been disputed and often rely heavily on the plasma parameters.¹⁰ The LIF diagnostic is precise; however, operating the laser and accurately monitoring the wavelength provide some difficulty. In these experiments, we are confident of our wavemeter accuracy (wavelength uncertainties represent ±45 m/s), and, as discussed in the  Appendix, the measurement of a fiducial iodine spectrum provides further confirmation that we are returning accurate measurements of the Doppler shifted Ar-II ion velocity distribution function (IVDF). So, the most reasonable conclusion is that LIF has given an accurate measurement of the parallel ion velocity. It then follows that the velocity inferred from the Mach probe data becomes progressively more incorrect as the magnetic field is increased.

This leaves an open question: what is the cause of the discrepancy between the velocity interpreted from the Mach probe and the absolute velocity determined from LIF? We propose that the discrepancy between the LIF velocity measurements and the Mach probe measurements is due to the combination of two effects: the probe shaft creating a low density geometric shadow on the downstream side and ion-neutral collisions, shortening the presheath length to the order of the ion-neutral mean free path. The remainder of this paper is devoted to deriving an estimate of the magnitude of the probe geometric shadow effect and comparing this theoretical calculation to the experimental data.

Many Mach probe studies^10,32–38 have assumed the presheath length is the “natural” presheath length, $Ln=w2csD⊥$⁠, where w is the probe diameter, c_s is the sound speed, and D_⊥ is the perpendicular diffusion coefficient. This is a valid assumption for the presheath length in a fully ionized plasma with Maxwellian electrons. However, when the ion-neutral mean free path is shorter than L_n, $λi−n<Ln$⁠, then the presheath length is proportional to the ion-neutral collision mean free path.³⁹ As a result, when neutral atoms are present in the plasma, the actual length of the presheath can be shorter than the “natural” length.

Another relevant scale length is the probe geometric shadow length, $Lg=(w2vd)D⊥$⁠, where v_d is the drift velocity of the background plasma ions. This is the length scale of a depleted density region due to the probe acting as a physical obstruction in the plasma. If the plasma presheath length is shorter than the probe geometric shadow length due to ion-neutral collisions, then as shown in the schematic in Figure 11, the ion saturation current collected would represent the lower, perturbed density of the geometric shadow due to the probe shaft at the position of the downstream presheath edge, instead of the density of the unperturbed plasma. The lower ion saturation current on the downstream side would then appear as an artificially high Mach number when naively applying the Shikama method described in Equation (1).

This effect can be demonstrated using a simplified model for the downstream plasma density. The ions are modeled as a fluid, neglecting electrostatic effects. We consider a plasma in slab geometry with transport in the direction parallel to the magnetic field dominated by advection and perpendicular transport dominated by diffusion as described in Equation (3), where v_d is the plasma drift velocity parallel to the magnetic field, D_⊥ is the cross field diffusion, z is the coordinate parallel to the magnetic field, and y is the coordinate perpendicular to the field

The probe geometric shadow creates a low plasma density region downstream of the probe as shown in the schematic in Figure 11. As the magnetic field increases, the perpendicular diffusive transport decreases, which increases the geometric shadow length. The effect of the density reduction can be included in the Shikama analysis method as a correction term, shown below.

To calculate the correction term, it is necessary to know the magnitude of the downstream density at the presheath edge relative to the unperturbed upstream density. Assuming v_d is constant, Equation (3) can be rearranged as

Equation (4) is precisely analogous to the 1-D diffusion equation, $∂tn+D⊥vd∂y2n=0$⁠. For the system under consideration here, the probe is modeled as a boundary condition with $n(y, z=0)={n0, y≥a0,−a<y<an0, y≤−a$⁠, yielding an analytical solution for the density of the plasma downstream (Equation (4))

In both Equations (4) and (5), D_⊥ represents the perpendicular diffusion direction, v_d is the drift velocity, a is the probe radius, and n₀ represents the unperturbed plasma density. The resulting density distribution (n_d/n₀) in the probe shadow calculated from Equation (5) is plotted in Figure 12 for 400 and 1600 G magnetic fields, clearly showing the geometric shadow lengthening as the magnetic field is increased.

This representation of the probe geometric shadow downstream can be used to calculate a correction term for the parallel Mach number using the Shikama method. As shown in Equation (6) (taken from Ref. 27), implicit in the Shikama method is the assumption that the density at the edge of the presheath (y = 0, z = L_ps) is the same on both the upstream and downstream sides of the probe

Here, F_flow(M_||, θ) is the function that depends only on the ion flow Mach number and direction, $Fflow(M||, θ)=exp(−k2 sin αα(M| | cos θ+M⊥ sin θ))$⁠; M_|| is used to represent the physical Mach number of the flow, and M_||,j represents the Mach number inferred from the ratio of the upstream and downstream ion saturation currents. However, the probe will affect the downstream plasma density as shown in the model above (Equation (5)). Since the densities evaluated at the upstream and downstream presheath edges, $nupand ndown$⁠, are not equal, they should be included explicitly in the model

Taking the natural logarithm of Equation (7) allows us to relate this back to the model shown in Equation (6)

Upstream of the probe there is no shadowing, so the upstream density can be assumed to be the unperturbed density n₀. The density at the edge of the downstream presheath edge, n_down, is calculated with the simplified advection-diffusion model described in Equation (5). Assuming the probe collects the ion saturation current from the downstream presheath region of length $Lps$ downstream from the probe, the analytic solution for the density collected downstream at the midplane of the probe (y = 0, z = L_ps) is given by

The results for the density on axis are shown in Figure 13. This plot shows that as the magnetic field increases the downstream density is reduced for a considerable distance downstream from the probe. The correction for the Mach number accounting for this effect is given in Equation (10) and arises from using the expression for the downstream density, Equation (9), in Equation (8)

All Mach probe measurements were made at the center of the plasma column, r = 0, where the density fluctuations and turbulent particle flux due to drift waves are at a minimum.⁴⁰ Hence, the perpendicular diffusion is treated as classical on axis. The classical diffusion constant is given by $D⊥=D⊥,A1+(ωciνi)2+μiμe(1+(ωceνe)2)$⁠. Here, $ωcβ$ is the cyclotron frequency of the $β$th species, $νβ$ is the total collision frequency of the $β$th species, and $μβ$ is the mobility of the $β$ th species. The perpendicular diffusion coefficient is given by $D⊥,A=VTi2νi(1+TeTi)$⁠, where $νi=νi−e+νi−n$⁠. The electron collision frequency, $νe$⁠, is dominated by the electron-ion momentum exchange frequency.

The collision frequencies for the ions were calculated using the formulas from Choi.⁴¹ The neutral densities were calculated based on the measured neutral pressure at the wall of the device, which was consistently about 1.1 mTorr. Assuming that the neutral temperature is the same as the plasma ion temperature at r = 0 and the neutral pressure is constant across the radius of the chamber, the neutral density is easily modeled as $nr=0=PwallTr=0$⁠. A calculation of the resulting ion-neutral collision frequency is given in Table II. The dominant contribution to the perpendicular diffusion coefficient was found to be from the electron-ion momentum exchange frequency.

It is important to note that the parallel plasma diffusion is neglected in this model. This is appropriate when the parallel probe shadow Péclet number, $Pe=LgvdD||$ > 1. Here, the parallel diffusion coefficient is calculated using the Einstein relation, $D||=VTi2νs$⁠, where $νs$ is the ion-ion momentum exchange frequency. A calculation of the parallel probe shadow Péclet number is shown in Table III. These calculations indicate that the agreement is expected to be poorest under the 400 G conditions, where the Péclet number drops below 1, and we expect the model to break down at magnetic fields at or below 400 G in our device.

Corrected Mach probe data are shown in Figure 14. The presheath length used is approximately the ion-neutral mean free path calculated using $Vthνi−n$⁠, where V_th is the thermal velocity of the ions. The drift velocity used is the velocity measured with LIF, and the perpendicular diffusion is calculated as the classical perpendicular diffusion coefficient using the ion temperature measurements from the LIF experiments.

The corrected Mach probe data show excellent agreement with the measurements from the LIF experiment, with the exception of the data point at 400 G. The analytic model for the probe shadow is expected to break down at this field because the parallel diffusion can no longer be neglected. We consider this to be a strong indication that this enhancement of the Mach number is due to the geometric shadow described in this section.

In this paper, we compared measurements of the velocity parallel to the magnetic field taken with Mach probe and LIF techniques. As can be seen in Figure 10, the LIF technique shows a parallel velocity approximately constant at 300 m/s over the range of magnetic fields used in these experiments, while the Mach probe reports a velocity ranging from 350 to 2800 m/s. The velocity reported by the Mach probe increases monotonically with increasing magnetic field, suggesting that the cause of the discrepancy is proportional to the magnetic field.

In this work, we have presumed the existence of a geometric shadow downstream of the probe. A simple 2-D model of the shadow, consistent with the probe absorbing the plasma as it passes, is presented in Figure 12. In a collisionless plasma, this shadow would be shorter than the presheath length for subsonic flows, and thus, this effect would not apply in that case. However, previous studies have shown that the presheath length in collisional plasmas is proportional to the ion-neutral mean free path. If the ion-neutral mean free path is shorter than the length of the probe geometric shadow, the downstream ion saturation current will be reduced due to the shadow as shown in the schematic in Figure 11.

We present a simple correction term for the Shikama method of Mach probe interpretation taking into account the probe shadow in Equation (10). We also demonstrate that it can correct this method for the reduced downstream density due to shadowing as shown in Figure 14 if the plasma parameters (C_s, T_e, and D_⊥) are known. It is well known that the ion-neutral collisions can affect the presheath length, and we have shown the perturbation due to the probe shadow can dominate the ion saturation current signal.

For future work, it would be useful to probe the shadow region by using either an electrical probe or spectroscopic diagnostic to estimate the plasma density profile in the shadow region and compare to the simple model proposed above. Additionally, this model only addresses the relatively simple condition of uniform flow along the magnetic field with no transverse flow and a correction is made only for the Shikama Mach probe interpretation method. Developing a fully two dimensional model of the probe shadow would be useful for handling the more general case of transverse flow. Finally, there are many different models that can be used to interpret Mach probe data depending on the plasma parameters. It would be useful to develop an appropriate term to correct the reduced plasma density in the probe shadow for each of these models.

For practical purposes, a model for the downstream density should be included in the interpretation methods used by groups using Mach probes to ensure that the effects due to the geometric shadowing of the probe are included whenever the geometric shadow length, $Lg=w2VdD⊥$⁠, is on the order of the ion-neutral mean free path. This could be especially important in regions of a tokamak where the neutral gas pressure is relatively high, such as the divertor. When exact measurements of the ion-neutral mean free path and perpendicular diffusion are not available, the probe shaft should be designed so that the radius is less than a critical radius derived from Equation (10), $acrit=(4.*D⊥*λi−ncs)$⁠, to avoid these probe shadowing effects.

We would like to thank Rollie Hernandez and Leo Chousal for their expert engineering support. This material is based upon work supported by the U.S. Department of Energy Contract No. DE-FG02-07ER54912 and NSF Award Nos. PHY-0611571 and PHY-0918526.

There has been some disagreement in the literature as to the location of the Ar-II excitation line with respect to the iodine cell spectrum.⁴² In our experiments, we find that the unshifted wavelength for the 3d⁴F_7/2 to the 4p⁴D_5/2 transition agrees well qualitatively with the wavelengths reported in the private communication from Severn reported in Keesee's thesis.⁴² Additionally, we have good quantitative agreement with the peak locations reported by Woo¹⁶ for this same Ar-II LIF scheme as shown in Figure 15.

The result in Figure 15 is the result of averaging over 350 LIF runs. The iodine spectrum was measured by diverting 8% of the beam intensity with a beam splitter into an iodine cell. The fluorescence from the iodine cell was detected by a photomultiplier tube (PMT). Both iodine cell and PMT were housed in a dark box, and the high background (∼80% of max signal) is presumed to be scattered laser light. All of the peak measurements agree with those of Woo within one standard deviation with the exception of the smallest, least well-defined peak. The locations of the peaks, labeled 1–4 in Figure 15, were found by fitting a series of Gaussians to each of the 350 iodine spectrum measurements independently. The line positions and uncertainties represent the mean and standard deviations of the fitted parameter for the peak of the Gaussian. Lines 1–4 locations (and uncertainties) are: (1) 668.6174 (±0.0003) nm, (2) 668.6127 (±0.0001) nm, (3) 668.6093 (±0.0003) nm, and (4) 668.6062 (±0.0005) nm.

This measurement is important because as of the date of publication there are only three comparisons of the Ar-II 3d⁴F_7/2 to the 4p⁴D_5/2 transition compared to the iodine spectrum (I₂). Woo's counter-propagating laser beam measurements provide an excellent physical measurement of the unshifted line. Based on both the extraordinary number of data points for the iodine spectrum that we collected over our experimental campaign, the qualitative agreement with the report from Severn, and the report from Woo; we can say, with a very high level of confidence that we are reporting the correct zero velocity location on the iodine spectrum.

Groups wishing to use LIF for Ar-II velocity measurements can use an iodine cell to verify the wavelength with a wavemeter. The unshifted wavelength is precisely located by the low-frequency “shoulder” of the iodine spectrum, shown as the dotted line in Figure 15. This qualitative feature is visible in the iodine spectrum used by Severn and the fourth figure of Woo's results.¹⁶ Our results represent a quantitative verification of the structure of the iodine spectrum in this wavelength range.