A more complete picture of the RF plasma expansion is obtained by considering Langmuir probe measurements taken at several different axial locations. These are shown in Fig.
4.10 for discharges with a 500 µs RF pulse. Several interesting features are apparent in the ion saturation current curves. The peak Isat. near the antenna (which was located at z≤ −5.9 cm) was higher for the case withB = 0 (right panel) than for the case with finite B (left panel); this may reflect the relative ion densities in the two cases, or it could be due to the electron temperature being higher in the unmagnetized case, as predicted by Fig.
3.12. Some caution is warranted in interpreting this result and those that follow, given that the gas pressure was a factor of ∼8 too high for collisionless probe theory to be applicable (see Sec. D.2).
Out in the main chamber at z≈6.5 cm, the peakIsat. was surprisingly only marginally higher with a confining field than without one, confirming the impression given by the images in Fig. 4.3 that a substantial amount of plasma was able to make it out of the source tube even withB = 0 (this was also demonstrated in Fig. 4.4). The relatively sharp bump in theB = 0,z= 6.5 cmIsat.curve at its peak (aroundt= 220µs) likely corresponds to the shock-like structure visible at t = 250–300 µs in Fig. 4.3. Understanding the cause of this feature, which only appeared when there was no applied magnetic field, will require further study.
There was a surprising degree of time-dependence in Isat.measured near the antenna—
0 100 200 300 400 500 600 700 800
−10
−5 0 5 10 15 20 25 30 35 40
Time (µs)
Ion saturation current (mA)
z = −5.7 cm z = −2.4 cm z = 0.4 cm (x 1.06) z = 3.5 cm (x 1.80) z = 6.7 cm (x 3.26) B on
0 100 200 300 400 500 600 700 800
−5 0 5 10 15 20 25 30 35 40
Time (µs)
Ion saturation current (mA)
z = −5.5 cm z = −2.5 cm z = 0.5 cm (x 1.07) z = 3.6 cm (x 1.83) z = 6.5 cm (x 3.14) B off
Figure 4.10: Langmuir probe ion saturation current measured at five different locations on axis (r= 0) for cases with the bias field coil and solenoid on (left) and off (right). The RF power was on from t= 0–500 µs, and the fast gas valve was used with the usual settings (Vgas,RF = 550 V, tgas,RF =−6.0 ms). The Isat. curves for locations beyond the end of the
∼1.1 cm inner radius discharge tube (z > 0 cm) have been multiplied by the ratio of the cross-sectional area of the expanding plasma at the axial location of interest to the cross- sectional area at z = 0, in order to facilitate a clear comparison of the amount of plasma present at different axial locations (this rescaling corrects for the ∂Isat./∂z due solely to the fact that the plasma was expanding along a diverging field, allowing us to focus on the changes inIsat. due to diffusion and ionization). The cross-sectional area as a function ofz was determined for the case with finiteBby assuming that the plasma was expanding along the magnetic field lines; the field profile was calculated using an IDL program written by Bao N. Ha. The same scaling function was used for the data taken with no magnetic field, since camera images (Figs. 4.1 and 4.3) indicated that the opening angle of the expanding plasma cone was similar withB on and off.
the dip around t= 150µs in the unmagnetized case is particularly striking. Such features were absent from data taken at lower gas pressures. Note that the power output by the RF amplifier was gradually decreasing during the 500µs interval shown (see Fig. 3.13). Upon RF turn-off att= 500µs,Isat. near the antenna dropped dramatically; as discussed in Sec.
4.2, this feature was probably primarily due to the rapid decrease of Te in the afterglow.
If we interpret the intervals between the times that Isat. first began to rise at each suc- cessive probe location to be indicative of the expanding plasma’s velocity, then both panels of Fig. 4.10 imply that the plasma was accelerating as it moved away from the antenna.
This result is inconsistent with the simple model of expansion at the ion acoustic speed described in the chapter introduction (presumably Te did not increase moving away from the power source), but it is consistent with diffusive transport in a neutral gas background if ∂ng/∂z < 0 (the ambipolar diffusion coefficient is inversely proportional to ng—see Eq.
0 100 200 300 400 500 600 700 800
−10 0 10 20 30 40 50 60
Time (µs)
Ion saturation current (mA)
tgas= −6.5 ms tgas= −6.0 ms tgas= −5.5 ms tgas= −5.0 ms tgas= −4.5 ms z = −7.0 cm
0 100 200 300 400 500 600 700 800
−0.2 0 0.2 0.4 0.6 0.8 1 1.2 1.4
Time (µs)
Ion saturation current (mA)
tgas= −6.5 ms tgas= −6.0 ms tgas= −5.5 ms tgas= −5.0 ms tgas= −4.5 ms z = 6.0 cm
Figure 4.11: Langmuir probe ion saturation current measured at z = −7.0 cm (left) and atz = 6.0 cm (right) during experiments with the fast gas valve triggered at five different times. The bias field coil and solenoid were turned on, and the RF power was on from t= 0–500µs. The rise in Isat. after RF turn-off atz= 6.0 cm is noteworthy; this behavior will be analyzed in detail in Sec. 5.2.
4.12), which was expected to be the case when the fast gas valve was used.
The diffusive nature of the RF plasma expansion will be further established in Sec. 4.4.
A key feature was the importance of continuous ionization in the downstream region. In Fig.
4.11, Isat. measurements at z =−7.0 cm (well inside the RF antenna) and at z = 6.0 cm are shown for experiments with fast gas valve trigger times ranging fromtgas,RF =−6.5 ms to tgas,RF = −4.5 ms. For large |tgas,RF|, the gas had time to fill the entire discharge tube and the region in front of the jet experiment electrodes before the RF discharge was initiated, while with small |tgas,RF| the gas had only barely reached the antenna region at t= 0, and the plasma expanded into a low density gas background (the spatial extent of the neutral gas cloud, which glowed at early times in the discharge, is visible in the images in Fig. 4.5). The left panel of Fig. 4.11 shows that a high density plasma would form inside the antenna with any of the five gas timings tested. However, the peak density in front of the electrodes at z = 6.0 cm (right panel) was low for tgas,RF =−5.0 ms, and negligible for tgas,RF =−4.5 ms. This shows that despite the radial confinement provided by the magnetic field, axial transport of plasma created inside the antenna was insufficient to achieve a reasonable density in front of the electrodes; there also had to be ionization of pre-existing neutral gas in the expansion path to replenish the plasma against losses to the walls of the discharge tube.