5.2 Plasma Density Peak in the Afterglow
5.2.1 Experimental Observations
0 200 400 600 800 1000
−0.2 0 0.2 0.4 0.6 0.8 1 1.2
Time (µs)
Ion Saturation Current (mA)
700 µs RF 600 µs RF 500 µs RF 400 µs RF B on
z = 6.7 cm
Figure 5.7: Langmuir probe ion saturation current measured at z = 6.7 cm for discharges with the RF amplifier turned off at four different times. The fast gas valve was used with Vgas,RF = 550 V, and the bias field coil and solenoid were turned on.
forpAr &50 mTorr, although the predicted pressure dependence is gentler than what was
observed. Although one might have expected the excited state population densities, and consequently the radiated power, to be higher in discharges with high pAr and ne, this was not the case in the simulation—the electron temperature was lower at higher pressures, partially negating the effect of higherne on the collisional excitation rates, and the balance of collisional and radiative populating and depopulating processes (see Eqs. 4.32, 4.33, and 4.34) ultimately causednm,nr, andnp to be nearly independent of pressure in the 30–300 mTorr range.
500 550 600 650 700 750 800 850 900 0
1 2 3 4 5 6 7 8x 1018
Ion Density (m−3)
Time (µs)
500 550 600 650 700 750 800 850 9000 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6
Electron Temperature (eV)
ni
Te
z = 0.0 cm
500 550 600 650 700 750 800 850 900 0
2 4 6 8 10 12x 1017
Ion Density (m−3)
Time (µs)
500 550 600 650 700 750 800 850 9000 0.2 0.4 0.6 0.8 1 1.2
Electron Temperature (eV)
Te
z = 6.0 cm ni
Figure 5.8: ni(t) andTe(t) atz= 0.0 cm (left) andz= 6.0 cm (right) during the afterglow, measured by analyzing the full Langmuir probe I-V curve. The RF power was turned off at t= 500µs. The fast gas valve was used with Vgas,RF = 550 V, and the bias field coil and solenoid were turned on.
ne√
Te should decrease monotonically in the afterglow of an RF discharge. However, it was apparent from the probe data that some exotic process not considered in these models was important in our pre-ionization source. The effect is illustrated in Fig. 5.7, which showsIsat.(t) atz= 6.7 cm (out in the main vacuum chamber in front of the jet experiment electrodes) measured during discharges with four different RF pulse lengths. After an initial burst of ionization at the initiation of the discharge, the plasma density was low at the probe location until t∼220µs, when the bulk of the expanding plasma reached the probe. After the main density peak,Isat.decayed, but in all four cases it rose again after RF turn-off to 20–40% of its original peak value.
Fig. 5.8 confirms that the afterglow Isat. rise was due to an increase in the ion density rather than the electron temperature—Te fell rapidly to <0.5 eV in the first∼30µs after RF turn-off and did not rise again. For the case with a 500µs RF pulse shown in Fig. 5.8, the density atz= 6.0 cm increased by more than a factor of 5 from its minimum value at t= 500µs. The relative increase at z= 0.0 cm (at the output of the RF source tube) was smaller, but the absolute magnitude of the density increase was ∼ 1×1018 m−3 at both locations4.
4Given that we found in Sec. 5.1 that the gas pressure in the antenna region waspAr≈460 mTorr when the fast gas valve was used withVgas,RF = 550 V, it seems likely that the pressure was greater than 60 mTorr atz = 0.0 cm, and possibly at z = 6.0 cm as well. Therefore, the Langmuir probe measurements may have underestimatedni due to collisional effects (see Sec. D.2), so the density values shown in Fig. 5.8
0 100 200 300 400 500 600 700 800
−0.2 0 0.2 0.4 0.6 0.8 1 1.2
Time (µs) Isat./ Isat.,peak
B on
z = −5.7 cm
z = 6.7 cm
z = 0.4 cm
0 100 200 300 400 500 600 700 800
−0.2 0 0.2 0.4 0.6 0.8 1 1.2
Time (µs) Isat./ Isat.,peak
B off
z = 6.5 cm
z = −5.5 cm
z = 0.5 cm
Figure 5.9: Ion saturation current near the RF antenna (blue), at the end of the discharge tube (green), and out in the main chamber (red), normalized to its peak value at each location, for discharges with the bias and solenoid fields on (left) and off (right). The RF power was turned on from t = 0–500µs, and the fast gas valve was used with Vgas,RF = 550 V.
There are two basic possible explanations for the observed behavior: either plasma was confined deep in the discharge tube during the main discharge period and then released when the RF power was turned off, or new plasma was created during the afterglow. The confinement interpretation was initially favored, based in part on the fast camera images shown in Figs. 4.2 and 4.3, which gave the impression that plasma was flowing out of the discharge tube after RF turn-off, and also on the apparent lack of an energy source to power new ionization. However, we showed in Sec. 4.2 that the camera images could be deceptive, and indeed, no confinement mechanism could be identified that was consistent with the data. Furthermore, there was in fact a substantial amount of energy stored in excited neutral atoms—potentially enough to account for the observed density rise, as we will see in Sec. 5.2.2.
One candidate process that could have caused confinement was the ponderomotive force [4, p. 501], a nonlinear effect that pushes plasma away from regions where there is a high RF electric field. If for some reason there had been a peak in the RF field near the front of the discharge tube (at the end of the antenna, for example), then the plasma might have been confined in the tube while the RF power was on, and then allowed to escape once the power was turned off. Ponderomotive plasma confinement has been used to reduce axial losses in
should be taken as a lower limit on the true density.
0 100 200 300 400 500 600 700 800
−5 0 5 10 15 20 25 30 35 40 45
Time (µs)
Ion Saturation Current (mA)
26 mTorr 64 mTorr 112 mTorr 240 mTorr z = −7.3 cm
26 mTorr
240 mTorr
0 100 200 300 400 500 600 700 800
−1 0 1 2 3 4 5 6
Time (µs)
Ion Saturation Current (mA)
29 mTorr 78 mTorr 131 mTorr 224 mTorr z = 6.0 cm
29 mTorr
224 mTorr
0 100 200 300 400 500 600 700 800
0 0.5 1 1.5 2
Time (µs)
Ion Saturation Current (mA)
Vgas,RF= 500 V Vgas,RF= 525 V Vgas,RF= 550 V Vgas,RF= 575 V z = 6.0 cm
500 V 575 V
Figure 5.10: Left and Center: Ion saturation current inside the RF antenna (z=−7.3 cm) and out in the main chamber (z = 6.0 cm) during experiments with a uniform argon gas pressure. Right: Isat(t) atz= 6.0 cm during experiments with the fast gas valve used. In all cases, the RF power was turned on fromt= 0–500µs, and the bias magnetic field was applied (Vbias = 80 V, Vsol. = 0 V).
open-ended magnetic confinement fusion devices such as mirror machines (the technique is often called “RF plugging”) [115, 116]. The expression for the ponderomotive force for each species in a magnetized plasma has a resonance near ω = ωcσ [117], so the effect can be quite strong if the applied RF frequency is chosen to be near the cyclotron frequency. In our experiment, however, the RF frequency ω ≈8.5×107 rad./s was near neither the ion (∼ 2.4×105 rad./s) nor the electron (∼ 1.8×1010 rad./s) cyclotron frequency (assuming B ≈ 0.1 T near the center of the bias field coil), so the resonant effect was not expected to play a role. The Langmuir probe was used to look for a peak in the RF electric field by measuring the amplitude of the RF signal (as in Fig. 3.5) at many different axial locations;
however, no obvious peak was found, so ponderomotive confinement was ruled out as a likely cause of the observed downstream density rise after RF turn-off.
Several observed trends were relevant for understanding the cause of the afterglow den- sity rise. Fig. 5.9 shows a subset of the data from Fig. 4.10, rescaled to show the magnitude of the afterglow density rise (if present) relative to the peak density obtained at each lo- cation while the RF power was on. The relative size of the density rise was larger out in the main vacuum chamber (positive z) than inside the discharge tube (negative z), and Isat.(t) near the antenna region (blue curves in Fig. 5.9) decreased monotonically after RF turn-off. A slight afterglow density rise was visible at z = 6.5 cm in the unmagnetized discharges shown in the right panel, but it was much smaller than the corresponding effect in discharges with the bias field turned on (left panel).
0 100 200 300 400 500 600 700 800
−0.5 0 0.5 1 1.5 2 2.5 3
Time (µs)
Ion Saturation Current (mA)
Vgas,RF= 450 V Vgas,RF= 500 V Vgas,RF= 550 V Vgas,RF= 600 V z = 6.0 cm
550 V
500 V 450 V 600 V
Helium
0 100 200 300 400 500 600 700 800
−0.5 0 0.5 1 1.5 2 2.5
Time (µs)
Ion Saturation Current (mA)
Vgas,RF= 500 V Vgas,RF= 550 V Vgas,RF= 600 V Vgas,RF= 650 V z = 6.0 cm
500 V 650 V Neon
0 100 200 300 400 500 600 700 800
−0.5 0 0.5 1 1.5 2 2.5
Time (µs)
Ion Saturation Current (mA)
Vgas,RF= 500 V Vgas,RF= 550 V Vgas,RF= 600 V Vgas,RF= 650 V
650 V
500 V z = 6.0 cm
Krypton
Figure 5.11: Ion saturation current at z = 6.0 cm for helium (left), neon (center), and krypton (right) plasmas. In all cases, the RF power was turned on fromt= 0–500µs, the fast gas valve was used, and the bias magnetic field was applied (Vbias = 80 V,Vsol. = 0 V).
No clear afterglow density increase was measured in experiments with a uniform gas pressure in the chamber, as shown in Fig. 5.10. Apparently the nonuniform pressure dis- tribution set up by the fast gas valve was critical for enabling the phenomenon to occur.
The right panel of Fig. 5.10 shows Isat.(t) during discharges with a range of fast gas valve voltages used, for comparison with the uniform pressure data5.
When the fast gas valve was used, an afterglow density peak could also be seen in plasmas formed using helium, neon, or krypton gas instead of argon. Examples are shown in Fig. 5.11. Interestingly, in helium the effect was only visible for low Vgas,RF, while the opposite was true for the other gases (high Vgas,RF was required). Experiments were also carried out with hydrogen, deuterium, and nitrogen, but a high-density plasma could not be created when the fast gas valve was used, as noted in Sec. 3.4.4, and thus no afterglow density increase was observed. It is possible that the same physical process responsible for the afterglow density peak was also critical for allowing the discharge to transition from its initial low-density mode of operation to a high-density inductively coupled mode (see Sec.
3.4.1), and this process may have occurred only in noble gases.
5Although the lowest gas bank voltage shown in the right panel of Fig. 5.10 (Vgas,RF = 500 V) produced a pressurepAr ∼380 mTorr in the RF discharge tube (see Fig. 5.3), which is higher than any of the uniform pressures tested, the pressure out in the main chamber atz= 6.0 cm was almost certainly less than half of this value due to radial expansion of the gas puff exiting the discharge tube. Therefore, comparison between the data shown in the center and right panels of Fig. 5.10 is justified.