6.5 Structure and Dynamics of Pre-Ionized Jets
6.5.1 Bright Pinch
3.7 µs Outline of inner 3.7 µs 3.7 µs 3.7 µs
electrode
gain = 5 gain = 4 gain = 3
gain = 6
Figure 6.13: Imacon camera images of pre-ionized argon jets with successively decreasing ICCD gains, demonstrating that the narrow collimated structure near the base of the jet was many times brighter than the front of the jet. The experiment parameters were: Vmain = 4 kV, Vbias = 80 V, Vgas,RF = 550 V, Vgas,inner = 460 V, andVgas,outer = 750 V.
had Vgas,RF = 0 V and Vgas,inner = 700 V. Although the gas bank voltages were the same in both cases, the initial gas pressure in front of the inner electrode may have been different because the gas delivery piping was not identical for the “inner” and “RF” gas valves12, and the inner valve was triggered earlier relative to the gas travel distance to the electrodes than the RF gas valve was (see Table 1.2). Nevertheless, it appears likely that the pre- ionized jets were in a fundamentally different regime, independent of the amount of gas input. This conclusion is supported by images of the plasma structure, which showed that the pre-ionized jets created with Vgas,inner = 0 V always pinched down to a very narrow radius that was approximately independent of Vgas,RF (see Fig. 6.21). This behavior will be discussed in the following sections.
2.3 µs 2.6 µs 2.9 µs 3.2 µs
3.5 µs 3.8 µs 4.1 µs
2.5 cm
Figure 6.14: Imacon camera movie of the pinching behavior at the base of an argon pre- ionized jet formed withVmain= 4 kV,Vbias = 80 V, Vgas,RF = 650 V, Vgas,inner= 0 V, and Vgas,outer = 750 V.
(see Fig. 6.14) showed that the jet base pinched down to a remarkably narrow radius (r≤ 0.3 cm) and then bounced back over a time interval of ∼ 1µs. The general behavior was similar to that of dense plasma focus [147] and Z-pinch [148] plasmas.
The [Ar III 351.14 nm] / [Ar II 349.13 nm] and [Ar IV 291.30 nm] / [Ar II 294.29 nm]
line ratios shown in Fig. 6.12 rose suddenly at the time of the bright pinch (t= 2.5–4µs), implying that the plasma was heated and became more ionized at this time. The increase in the line ratios occurred later for the more massive pre-ionized jets created with high Vgas,RF than for jets created with lowVgas,RF, consistent with camera images showing that the overall evolution was slower and the pinch occurred later for the heavier jets. After the initial rapid rise, the [Ar IV] / [Ar II] line ratio continued to increase for several µsin all cases, and the [Ar III] / [Ar II] ratio also continued to rise fromt≈4–6µs for the heavier jets. For the low-mass jets withVgas,RF = 525 V or 550 V, on the other hand, the [Ar III] / [Ar II] emission ratio decreased fromt≈4–6µs, at the same time that the [Ar IV] / [Ar II]
ratio was rising, suggesting that the plasma was burning through the Ar III ionization stage (this observation rules out the possibility that the line ratios were increasing solely because Te was rising, while the ionization balance remained approximately constant). Fig. 6.12 therefore confirms that the plasma was not in ionization equilibrium (see Sec. 6.1.5.2 for more discussion). The most significant heating of the electrons probably occurred during
1 2 3 4 5 6 7 8 9 0
2 4 6 8 10 12 14 16
z (cm)
[Ar III 350.36 nm] / [Ar II 347.67 nm]
t = 2.8−3.8 µs t = 3.8−4.8 µs Vgas,RF= 550 V
1 2 3 4 5 6 7 8 9
0 5 10 15
z (cm)
[Ar III 350.36 nm] / [Ar II 347.67 nm]
t = 3.3−4.3 µs t = 4.3−5.3 µs t = 5.3−6.3 µs Vgas,RF= 700 V
Figure 6.15: [Ar III 350.36 nm] / [Ar II 347.67 nm] line intensity ratio as a function of position around the time of the bright pinch for pre-ionized jets with Vgas,outer = 750 V, Vgas,inner = 0 V, and Vgas,RF = 550 V (left) or Vgas,RF = 700 V (right). A collimating lens was used to collected light from a narrow line of sight (diameter ∼ 6 mm) aligned nearly perpendicular to the jet (the z value of each data point corresponds to the location at which the line of sight intersected the jet axis). Although all spectroscopy measurements were line of sight averages, these can be considered to be essentially local measurements with spatial resolution<1 cm because the bright jet column was so narrow. The line ratios were averaged over 3 shots for each data point; the error bars show the standard deviation.
The data points in the right panel have been offset slightly in time so that the error bars do not overlap.
the rapid pinch, although the Ohmic power input was also expected to increase in time as the main discharge current ramped up (see Fig. 6.9, for example). Fig. 6.12 shows that the mean ionization state of jets formed without pre-ionization also increased gradually throughout the shot.
Additional information about the temperature and ionization balance is contained in the spatially resolved [Ar III 350.36 nm] / [Ar II 347.67 nm] line ratio measurements shown in Fig. 6.15. These plots confirm that the relative level of Ar III emission increased rapidly at the time of the bright pinch. The mean ionization state was highest at the base of the jets and decreased moving away from the electrodes. The electrons were expected to be approximately isothermal in the axial direction due to the high field-aligned heat flux (see Eq. 4.20), but Table 6.1 shows that only a small gradient inTe may have been necessary to produce a large variation in the ionization balance at different locations.
The time-dependent electron density of the jets atz= 2.0 cm, derived from the measured
1 2 3 4 5 6 7 0
2 4 6 8 10 12 14 16 18x 1022
Time After Breakdown (µs) Electron Density (m−3)
No pre−ionization Vgas,RF= 700 V Vgas,RF= 550 V
z = 2 cm
1 2 3 4 5 6 7
0 5 10 15
Time After Breakdown (µs)
Ion Temperature (eV)
No pre−ionization Vgas,RF= 700 V Vgas,RF= 550 V
z = 2 cm
Figure 6.16: Electron density (left) and ion temperature (right) calculated from Voigt profile fits to the Ar II 372.931 nm line. A collimating lens was used to collected light from a narrow line of sight (diameter∼6 mm) that intersected the jet axis at z= 2.0 cm in front of the electrodes. The spectrometer entrance slit width was 50µm, and the ICCD exposure time was 1 µs. The ne and Ti values were averaged over 3 shots for each data point; the error bars show the standard deviation. There were additional possible sources of systematic error that could have caused ne and/or Ti to be overestimated—see the discussion in the text. The data points on the plots have been offset slightly in time so that the error bars do not overlap. Vgas,outer = 750 V was used for all shots. The shots labeled “No pre-ionization”
had Vgas,inner = 700 V and Vgas,RF = 0 V, while the pre-ionized shots hadVgas,inner= 0 V and Vgas,RF = 550 V or 700 V, as noted in the plot legends.
Stark broadening of the Ar II 372.931 nm line, is shown in the left panel of Fig. 6.16. While ne for non-pre-ionized jets13 was approximately constant at 1–2×1022m−3, the density of the pre-ionized jets increased by a factor of 5–10 at the time of the bright pinch, reaching a peak value of ∼1.6×1023 m−3 in the Vgas,RF = 550 V case. ne subsequently appeared to oscillate between high and low values, possibly due to additional contractions and expansions of the jet radius; however, the errors bars for these points mostly overlapped, so the apparent pattern may not be significant. In these measurements the ICCD was exposed for 1 µs, which was the shortest achievable shutter time with the current triggering circuitry14—in the future the exposure window should be shortened in order to better resolve the time
13Higher electron densities exceeding 1×1023m−3 have been measured for nitrogen jets formed without pre-ionization in the original Caltech MHD-Driven Jet Experiment [130, 139], which had twice the neutral gas input capability and twice the main bank capacitance of the new pre-ionized jet experiment.
14The trigger signals for the spectrometer were transmitted optically, as described in Sec. 6.1.5, and the circuit for converting the optical signal back to an electrical signal had a slow fall time that limited the minimum exposure time. The issue has not yet been investigated in detail, but the explanation may have been the slow turn-off of transistors operating in saturation, as discussed in Sec. A.2.2. In this case, the Baker clamp circuit shown in Fig. A.4 would be helpful.
dependence of the electron density.
There are two possible sources of error in the density measurement. At the times when the Ar II emission was brightest (at t= 1.3–3.3µs for the pre-ionized jets and during the entire interval shown in Fig. 6.16 for the non-pre-ionized jets), the best-fit Voigt profile for the 372.931 nm line had a non-zero continuum level, but inspection of the full∼6 nm wide spectral window (like those shown in Fig. 6.7 for two other wavelength ranges) showed that there was in fact no measurable continuum emission. The apparent need for a continuum in the profile fit was almost certainly due to re-absorption that reduced the intensity at the line center (see Sec. 6.1.5.3). An example of a spectral line suffering from this problem is shown in the left panel of Fig. 6.6. Fixing the continuum level to be 0 in the profile fitting procedure had only a small effect on the calculated Stark and Doppler FWHMs, so it is likely that the error introduced by re-absorption was small, but it is possible that the densities for non-pre-ionized jets and those measured att <3.3µs for pre-ionized jets were overestimated.
No false continuum was present in the Voigt profile fits for pre-ionized jets during and after the bright pinch, consistent with the evidence from Figs. 6.12 and 6.15 that the plasma had become more ionized by this time, and the Ar II concentration had been reduced enough that re-absorption was no longer important for the 372.931 nm line (see Fig. 6.8). However, the fitting procedure had difficulty accurately deconvolving the line profile during the high- density period (t = 3–7 µs): for some shots, the Gaussian FWHM implied by the fit was less than the Gaussian FWHM of the instrument function (Ti was set to 0 eV for these shots in the plot in the right panel of Fig. 6.16), implying that the fit overestimated the contribution from Stark broadening.
Nevertheless, the basic conclusion that the pre-ionized jets became very dense appears to be robust, as the lines were highly broadened and the dominant shape of the profiles was clearly Lorentzian, as shown in the right panel of Fig. 6.6. This result is not surprising based on the intense brightness of the jet column in the camera images, but there is notable irony given that the original stated goal of the pre-ionization project was to produce “lower density jets”. However, it turned out that decreasing the plasma density was not possible due to the radial balance of MHD forces (to be discussed in the next section), nor was
1 2 3 4 5 6 7 0
200 400 600 800 1000 1200 1400
Time After Breakdown (µs)
Continuum Level (ICCD Counts)
No pre−ionization Vgas,RF= 700 V Vgas,RF= 550 V z = 2 cm
Figure 6.17: Continuum emission in the 370–376 nm wavelength range at z = 2.0 cm in front of the electrodes. Vgas,outer = 750 V was used for all shots. The shots labeled “No pre-ionization” hadVgas,inner = 700 V and Vgas,RF = 0 V, while the pre-ionized shots had Vgas,inner= 0 V and Vgas,RF = 550 V or 700 V, as noted in the plot legend.
it necessary in order to produce faster and hotter jets. The total mass of the jet (or equivalently the number of particles per unit length—see Eq. 6.24) was the parameter that actually mattered. It should be noted that a portion of the electron density increase in Fig.
6.16 was due to argon atoms becoming multiply ionized—ni may have been lower than ne by a factor of 2 or more.
Given the difficulty of extracting accurate ion temperatures from line profiles with dom- inant Stark broadening, it is questionable whether firm conclusions can be drawn from the Ti results shown in the right panel of Fig. 6.16. In general, the fits to the nearly Gaussian line shapes obtained when the electron density was≤2×1022m−3 looked good (although there was a spurious continuum offset as discussed above), so the ion temperatures obtained for these cases may be reliable. The typical temperatures measured were Ti ≈ 5–10 eV, which is notably hotter than the lower limit on the electron temperature of 2.5–3 eV calcu- lated in Table 6.1, butTi may have been overestimated due to re-absorption. There was no clear evidence that the ions in the pre-ionized jets were heated in the bright pinch; better Doppler profile measurements are needed for these cases, perhaps utilizing an Ar III or Ar
IV line that has minimal Stark broadening.
A surprising feature of the emission spectrum at the time of the dense pinch was a sudden increase in the continuum brightness, previously undetectable by our spectroscopy system, by a factor of 100 or more (see Fig. 6.17). The line profile shown in the right panel of Fig. 6.6 is one example of this effect; unlike the constant offset in the profile fits due to re-absorption discussed above, this was a true continuum, visible across all wavelengths in the full spectrum. The most obvious source of continuum radiation from the jet was thermal Bremsstrahlung; the emissivity in W/m3 is [138, p. 162]
f f = 1.5×10−38
TeV1/2neniZ2, (6.25)
whereZeis the typical ion charge. Assumingne= 1×1023m−3,ni = 5×1022m−3,Z = 2, T = 5 eV, andV = 10−5 m3 for the dense portion of the jet, we find a total radiated power Pf f = 7×103 W. Based on measurements by Perkins [67, Figure 4.2] of visible radiated power exceeding 105 W from hydrogen plasmas withne≈1021m−3 in the Caltech Arched Flux Rope Experiment, we expect that the visible radiated power from line emission in the denser argon jet plasmas was Pvis. & 106 W. Therefore, the thermal Bremsstrahlung might have been too small to be detectable by comparison. Non-thermal Bremsstrahlung arising from the sudden deceleration of the pinching plasma at the jet axis is an intriguing possibility, but further measurements and analysis are needed to determine whether it could reasonably produce sufficient optical power.