mode (assuming Te≈2 eV, so cs ≈2.2 km/s). After 120µs, the plasma would have filled the region within∼20 cm of the center electrode, and it would have been a good time to trigger the main capacitor bank. However, the actual behavior observed was very different from this. Examples for three different RF plasma source configurations are shown in Figs.
4.1, 4.2, and 4.3.
In all three image series, the plasma expansion into the chamber appears to be unsteady, with two or more phases in which different behaviors are evident. A region of bright emission appears in front of the RF plasma source tube output within 50µs after RF turn-on—the spatial extent of this region is greater for cases with the bias coil and solenoid turned on1 (Figs. 4.1 and 4.2) than for the case shown in Fig. 4.3 with no magnetic field. It appears in frames 2–3 of Figs. 4.1 and 4.2 that the emitting region is expanding away from the source tube and into the chamber; however, around t = 150 µs it rapidly dims. In Fig. 4.1, in which the RF power was turned off att= 200µs, a new cloud of plasma emerges from the source tube at around this time, expanding far into the chamber roughly following the bias magnetic field lines and gradually dimming at late times. In Fig. 4.2, on the other hand, in which the RF power was left on until t = 400 µs, no plasma expansion is visible from t= 200–400µs—the expansion appears to be inhibited somehow by continued application of RF power back at the antenna region. Meanwhile, in Fig. 4.3, which also used a 400µs RF pulse but hadB = 0, an expanding cone of plasma is readily visible fromt= 200–300µs.
In both Figs. 4.2 and 4.3, an additional relatively dim puff of plasma appears to emerge from the source tube soon after the RF power is turned off. In all cases in which a cloud of plasma appears be expanding into the chamber, the velocity inferred from the images is on the order of 1 km/s.
Figure 4.1: Fast camera images of RF plasma expansion into the main vacuum chamber for shots with the RF power on for 200µs and the bias field coil and solenoid turned on. False color is used to indicate overall light intensity, with the brightest regions shown in white and dimmer areas in red. The orientation of the images is flipped with respect to the source schematic in Fig. 2.2—here the RF source tube and antenna are located to the right of the field of view. The images were each taken on separate shots, but since the discharge behavior was extremely consistent and reproducible for a given set of experimental parameters, they can be interpreted as a movie of RF plasma expansion. The images suggest that there are two phases to plasma expansion: at early times there is bright emission near the source tube output, but this dims before the RF source is turned off att= 200µs, and only after RF turn-off does the plasma fully expand into the chamber. However, as discussed in Sec.
4.2, Langmuir probe measurements (see Fig. 4.4) revealed that the brightness of optical emission by the plasma was not always proportional the local plasma density; in fact, some aspects of the images are highly deceiving.
Figure 4.2: Fast camera images of RF plasma expansion into the main vacuum chamber for shots with the RF power on for 400 µs and the bias field coil and solenoid turned on.
The 1” diameter RF plasma source tube output is visible toward the right side of each frame—it appears as a bright narrow oval due to the nearly side-on camera viewing angle.
The two bright dots directly to the lower left of the source tube output are an artifact due to a damaged portion of the ICCD detector. These images are identical to those in Fig.
4.1 for t <200µs, as expected; however, from t= 200–400µs, very little light emission is seen in the chamber. Only after RF turn-off at t= 400µs does plasma appear to expand unimpeded into the chamber. Once again, however, some features of these images are deceptive—see Sec. 4.2 for a detailed analysis.
Figure 4.3: Fast camera images of RF plasma expansion into the main vacuum chamber for shots with the RF power on for 400 µs and the magnetic field coils turned off. The exposure time for these images and those in Figs. 4.1 and 4.2 was 10 µs. The axially moveable Langmuir probe shown in Fig. 3.4 is visible along the center axis of the chamber in some frames here and in Figs. 4.1 and 4.2; the probe tip was located atz= 6 cm in front of the jet experiment electrodes. Compared to Figs. 4.1 and 4.2, the size of the initial emitting region at early times is much smaller with B = 0, and in stark contrast to the case in Fig.
4.2 with the magnetic field on, it appears that a cone of plasma successfully expands out into the chamber between t= 150–300 µs, while the RF power is still on. However, Langmuir probe measurements (see Fig. 4.4 and Sec. 4.2) ultimately told a different story about the relative conditions with the magnetic field on and off. In these images, the emission dims rapidly betweent= 300–350µs, and after RF turn-off another cloud of plasma appears to emerge from the source tube, as in Fig. 4.2.
−100 0 100 200 300 400 500 600 700 800 900
−0.2 0 0.2 0.4 0.6 0.8 1 1.2 1.4
Time (µs)
Ion saturation current (mA)
RF on 200 µs, B on RF on 400 µs, B on RF on 400 µs, B off
Figure 4.4: Ion saturation current measured with Vprobe = −15.3 V at z = 6 cm during the discharges photographed in Figs. 4.1, 4.2, and 4.3 (the probe tip may be seen glowing just to the right of the center of the first image in each series). The negative current collected at t= 20–60 µs in the “RF on 400 µs, B off” case indicates that the probe was collecting some electron current at this time because the plasma was hotter than usual at the probe location; at later times, however, the current measured should truly be ion saturation current, proportional ton√
Te. The electron temperature is expected to change drastically only immediately after RF turn-off—at other times, changes in Isat. should closely correspond to variations in the plasma density.
the images was not at all straightforward. In essence, due to the existence of several differ- ent regimes for atomic processes producing visible and infrared line emission in a partially ionized plasma, the images were a relatively poor indicator of “where the plasma was” at a given time.
Because the gas pressure was>100 mTorr for these experiments, ion-neutral collisions in the pre-sheath reduced the ion saturation current collected by the Langmuir probe to below the value predicted by collisionless theories, and the magnitude of the ion density could not be measured accurately (see Sec. D.2 for details). However, for experiments at a given gas pressure, the measuredIsat. still scaled linearly withni, so using Isat. measurements to track temporal variations in density or compare densities between different discharges was still a valid approach.
Fig. 4.4 shows Isat.(t) in front of the electrodes (at z = 6 cm) during the discharges shown in the image series in Figs. 4.1, 4.2, and 4.3. Consider first the initial 100 µs of
Figure 4.5: Fast camera images of the emission in front of the source tube output at t = 100 µs for five different argon fast gas valve delays. From left to right: tgas,RF = [−4.5 ms,−5.0 ms,−5.5 ms,−6.0 ms,−6.5 ms], wheret= 0µs is the time at which the UV flashlamp was triggered and the RF was turned on. For longer fast gas valve delays, the neutral gas had propagated further into the chamber by t = 0 µs, and thus the emitting region, which corresponded mostly to the neutral gas glowing as it was bombarded by fast electrons accelerated near the RF antenna, was larger. The small black circle to the lower left of the brightest part of each image is an artifact caused by a damaged portion of the ICCD detector.
each discharge. During this time interval in Figs. 4.1 and 4.2 (the first three frames), there is a bright cloud of emission in front of the source tube that reaches the location of the probe tip. However, Fig. 4.4 shows that the plasma density at the probe was low at this time (with the highest early spike in density in fact measured for the case with B = 0, corresponding to Fig. 4.3). This implies that the emission was produced mostly by neutral gas that was already present in front of the source tube output at t = 0, not by plasma that flowed into the chamber from the antenna region. Further evidence is provided by the images in Fig. 4.5, which show that the size of the emitting region varied when the fast gas valve delay relative to RF turn-on was adjusted to be longer or shorter than the usual tgas,RF =−6.0 ms.
The cause of the emission was probably fast electrons streaming out of the antenna region and colliding with the pre-existing neutral gas cloud, exciting the argon atoms, which then produced line radiation. Some of these atoms got ionized, leading to the small density increase measured by the Langmuir probe at very early times in Fig. 4.4. With no magnetic field, the fast electrons were not confined radially and few made it out of the source tube, explaining the smaller size of the initial emitting region in Fig. 4.3 compared to Figs. 4.1 and 4.2. In Fig. 4.6, a series of images taken around the time of RF turn-off with 1µs exposure time demonstrates that the initial emission in front of the source tube dimmed extremely rapidly when the RF was turned off, in only 1–2µs. This is in contrast to the much slower dimming that occurs in the last few frames of Figs. 4.1, 4.2, and 4.3. If this rapid dimming
Figure 4.6: Fast camera images of the initial emitting region in front of the source tube output, taken with a 1 µs exposure time, for magnetized discharges with the RF power turned off at t = 200 µs. The rapid dimming after RF turn-off, which was too fast to be explained by plasma flowing out of the region in front of the electrodes, provides additional evidence that the emission was caused by fast electrons from the antenna region colliding with a pre-existing neutral gas cloud. Note that the RF amplifier was set up differently when these images were taken than it was for Figs. 4.1 and 4.2 (the driver stage battery voltage was lower), and as a result the transition from the initial low-density discharge mode to a high-density inductively coupled (ICP) mode (see Fig. 3.13) occurred later. The different time-evolution in this case meant that the initial emitting region was still glowing brightly at t= 199µs, while in Figs. 4.1 and 4.2 it had begun to dim by t= 150µs for a reason unrelated to RF turn-off, discussed in the text.
were due to plasma flowing out of the region of interest, which had a radius of ∼2 cm, the bulk ion flow velocity would have to have been ∼ 20 km/s; however, since cs ≤ 4 km/s, this is too fast to be feasible based on the energy considerations discussed in the chapter introduction. On the other hand, an electron with enough energy to collisionally excite an argon atom (∼ 10 eV) can travel ∼ 2 m in 1 µs, so these were lost from the system very rapidly after the RF power was turned off, and the glowing neutral gas dimmed accordingly.
In Figs. 4.1 and 4.2, the initial emitting region actually dims and shrinks before RF turn-off, around t = 150 µs. Then at t ≈ 200 µs in Fig. 4.1, a bright cone of plasma emerges from the source tube, expanding into the chamber in the subsequent frames. No such expanding plasma is visible from t = 200–400 µs in Fig. 4.2, but surprisingly, the Langmuir probe data in Fig. 4.4 shows that there in fact was a high density plasma in the chamber at this time! The peakIsat.att≈260µs was actually higher for the case with the RF power still turned on (corresponding to Fig. 4.2) than for the case in which the RF was turned off att= 200µs (corresponding to Fig. 4.1); however, the electron temperature was likely lower for the discharge in which the RF had already been turned off, so we cannot determine which of the two had a higher peak density from the data shown.
Before seeking to explain the observed behavior from t = 200–400 µs, let us consider the reason for the dimming of the emission in front of the source tube at t ≈ 150 µs.
−50 0 50 100 150 200 250 300 350 400 450
−10 0 10 20 30 40 50 60 70 80
Time (µs)
Voltage on inner electrode (V)
Figure 4.7: Voltage (floating potential) measured on the jet experiment’s inner electrode during a discharge with Vbias = 80 V, Vsol. = 60 V, Vgas,RF = 550 V, tgas,RF = −6.0 ms, and the RF power on for 400µs (the same conditions as in Fig. 4.2).
There are two plausible explanations. The mean free path for electron-electron collisions is λee= (neσ90)−1, whereσ90is the effective cross section for 90 degree scattering due to the cumulative effect of small angle colllisions, given by [4, p. 16]:
σ90= 1 2π
e2 0µvR2
2
ln Λ, (4.4)
where µ=me/2 is the reduced mass, vR is the relative velocity between the two colliding particles, and ln Λ≈10. Plugging in the numbers for a 10 eV electron colliding with lower energy thermal electrons, we find thatσ90≈5×10−18m2. Langmuir probe measurements (see Fig. 3.18) showed that the plasma density inside the antenna wasne>5×1019m−3 in experiments atpAr = 30 mTorr, and the data (Figs. 3.17 and 3.18) and the global discharge model (Figs. 3.9 and 3.12) also showed that the density was an increasing function of gas pressure. If we therefore assume that the density upstream of the antenna in experiments with the fast gas valve was at least ne∼1019m−3, then the mean free path of an electron accelerated toward the main chamber from the antenna region with E ∼10 eV was λee. 2 cm. Thus it is possible that the dimming of the emission in front of the source tube output around t = 150 µs was due to the increasing quantity of plasma near the front of
the tube, which prevented most of the primary electrons accelerated at the antenna from making it out of the tube before losing their energy through collisions2.
Another possibility is that the importance of capacitive coupling in the RF plasma source operation diminished after t≈100µs, and at later times there were no large electrostatic potentials in the antenna region to accelerate primary electrons to high energies. Evidence supporting this hypothesis is shown in Fig. 4.7. When the jet experiment’s inner electrode and the attached conductors (including the quick-disconnect piece holding the quartz tube—
see Fig. 2.2) were left electrically floating3, they would charge up to ∼ 75 V and then discharge during the first ∼ 100 µs of the RF pulse. This rise and fall of the floating potential indicates that some plasma with a high plasma potential was contacting these conductors during the early part of the discharge, and then the plasma potential fell at later times. This likely happened because of stray capacitive coupling between the antenna and plasma [5, p. 464], which existed even though the source was operating primarily in an ICP mode after t≈ 20 µs. For some reason the capacitive coupling may have become less important at t > 100µs, leading to a decrease in the number of electrons accelerated toE ≥10 eV, and consequently to a drop in the visible light emission in the chamber.
Returning to our discussion of the t = 200–400 µs interval in Figs. 4.1, 4.2, 4.3, and 4.4: emission line intensities measured with the spectrometer provide some clues regarding how to reconcile the images with the probe Isat. measurements. The spectroscopic data was taken with the optical fiber viewing the MHD-driven jet experiment electrodes at a roughly 45 degree angle through a window at the midplane of the vacuum chamber, with a collimating lens used to restrict the line of sight to a narrow column. Initially, the lens was aligned so that the line of sight intersected the chamber axis at z ≈ 5 cm; however, the signals with this setup were too weak to reliably calculate line intensity ratios, so the
2Note that although the mean free path for 90 degree scattering of a 10 eV electron by collisions with neutrals atp= 460 mTorr (ng = 1.5×1022m−3) isλen≈7×10−4m (usingσen≈1×10−19m2 from [5, Figure 3.13]), the time for the electron to lose most of its energy in these collisions is slower than the 90 degree scattering time by roughly a factormi/4me ≈2×104 [4, p.18], so if magnetic confinement keeps it from being lost to the walls, the electron will still have most of its energy when it emerges from the tube after a number of collisions with neutrals, enabling the bright emission seen in the first 100µs of the discharge in Figs. 4.1 and 4.2.
3Conversely, during most other experiments in which only the RF plasma was being studied and the main bank was not fired, the inner electrode was explicitly grounded by attaching a copper short between one of the cable attachments on the re-entrant port and the vacuum chamber (see Fig. 1.8), in order to have a fixed potential reference contacting the plasma for Langmuir probe measurements. Whether or not the inner electrode was grounded had a negligible effect on the time evolution of the RF plasma emission as monitored by camera images.
0 50 100 150 200 250 300 0
0.05 0.1 0.15 0.2 0.25 0.3
Time (µs)
Line Intensity Ratio
[Ar I 703.0 nm] / [Ar I 696.5 nm]
RF off
0 50 100 150 200 250 300
0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08
Time (µs)
Line Intensity Ratio
[Ar II 434.8 nm] / [Ar I 696.5 nm]
RF off
Figure 4.8: Argon emission line intensity ratios measured near the front of the RF source tube (z ≈ −1 cm) with the bias and solenoid fields on and the RF amplifier pulsed for 200µs. The data was averaged over 20 shots for each line and binned in 25µs intervals.
alignment was adjusted so that the line of sight just barely grazed the near side of the 1”
diameter source tube output hole and intersected the r = 0 axis at z ≈ −1 cm. With this setup, the spectrometer may have collected some light that was emitted deeper in the source tube and reflected off of the quick-disconnect piece.
As in Sec. 3.4.2, the Ar I 696.5 nm, Ar I 703.0 nm, and Ar II 434.8 nm lines were observed.
The measured line intensity ratios for experiments with the magnetic fields turned on and the RF amplifier pulsed for 200 µs (corresponding to Fig. 4.1) are shown in Fig. 4.8. In Secs. 3.1.2 and 3.4.2, we saw that the [Ar I 703.0 nm] / [Ar I 696.5 nm] line ratio was an increasing function of electron temperature, while the [Ar II 434.8 nm] / [Ar I 696.5 nm]
was proportional to the plasma density, but also depended on Te. In the right panel of Fig. 4.8, the [Ar II 434.8 nm] / [Ar I 696.5 nm] ratio is roughly constant in time while the RF power is on, then drops rapidly after RF turn-off, consistent with the expectation that the temperature and density should fall after the power source is removed. Analysis of the time-dependent particle and energy balance equations (see Sec. 4.4.2 and in particular Fig.
4.22) shows that Te falls much faster than ne after RF turn-off, so the rapid decrease in the [Ar II 434.8 nm] / [Ar I 696.5 nm] ratio att= 200µs was probably due mostly to the temperature drop.
In light of the expected temperature decrease after RF turn-off, the sudden increase in the [Ar I 703.0 nm] / [Ar I 696.5 nm] ratio at t = 200 µs visible in the left panel of Fig.
4.8 seems surprising4. However, the experimental results can be understood by recalling the distinction between “ionizing phase” and “recombining phase” plasmas [75] discussed in Sec. 3.1.2. When the RF power was turned on, the plasma inside the antenna was in the ionizing phase, which in this context means that the second term in Eq. 3.1 was of dominant importance in determining the atomic energy level population densities, and does not necessarily imply that the ionization balance was changing in time. On the other hand, after RF turn-off the plasma may be categorized as an “afterglow”, expected to be in the recombining phase [104], which means that the first term in Eq. 3.1 was dominant. In general, at a given electron temperature, the population density of high energy levels is much higher in recombining phase plasmas than in ionizing phase plasmas; in particular, above certain density and temperature thresholds, the population density of a level with effective principle quantum numberpscales asn(p)/g(p)∝p−6for an ionizing phase plasma but as n(p)/g(p) ∝ e−E(p)/kBTe (Boltzmann distribution) for a recombining phase plasma [105], whereg(p) is the statistical weight. Thus one cannot compare line ratios measured in the two different phases and draw conclusions about the relative values ofTe—the dominant physical processes populating the energy levels are very different in the two cases, and thus different scalings with temperature apply. Because of the enhanced atomic upper level populations in the recombining phase, some emission lines will be brighter in the afterglow than during the main discharge [105, 106, 107], and if the gas pressure is high enough, the overall visible and infrared light emission after power turn-off may even exceed the main discharge brightness, as we will see in Sec. 5.1.
The rise in optical emission during the afterglow phase explains why the expanding cone of plasma in the magnetized RF discharges was visible in camera images during the 200–400 µs interval when the RF power was turned off at t = 200 µs (Fig. 4.1), but not when it was left on until t = 400 µs (Fig. 4.2), even though the ion saturation current measured by the Langmuir probe (Fig. 4.4) was similar in both cases. Spectroscopy is also helpful for understanding the differences between Figs. 4.2 and 4.3. In Fig. 4.9, the [Ar I 703.0 nm] / [Ar I 696.5 nm] ratio is shown during discharges with a 500 µs RF pulse for
4To confirm the validity of this result, several other line intensity ratios were measured. The Ar I 703.0 nm line is produced by an electron transition from the 6s to 4p level; to rule out some anomaly in the population of the 6s state, three lines with 4dupper levels (Ar I 675.3 nm, Ar I 687.1 nm, and Ar I 735.3 nm) were observed, and their intensities were compared to those of two other lines (Ar I 738.4 nm and Ar I 763.5 nm) that have 4pupper levels like the Ar I 696.5 nm line. For each ratio a similar phenomenon was observed in which the relative intensity of the line with the higher upper level energy increased after RF turn-off.