- Conference date: 19-22 March, 2007
- Location: Gaithersburg, Maryland (USA)
Experimental investigations of the ion density and flow as a function of time and space in z‐pinch plasmas are of key importance for improving the understanding of z‐pinch dynamics. For such studies, measurements of emission‐line shapes can be highly useful.
In the present experiment line emission of oxygen ions is used to investigate the ion density and motion in the imploding plasma in a 0.6‐μs, 220‐kA z‐pinch experiment. For the time period studied here (220 – 85 ns before the stagnation on‐axis), the plasma properties have been extensively characterized previously, employing various spectroscopic methods to determine the time‐dependent radial distributions of the ion velocities, the magnetic field, the charge‐state composition, the electron temperature, and the particle densities. In particular, the electron density was determined from the absolute intensities of spectral lines, from the ionization times in the plasma, and from momentum‐balance considerations, based on the previously measured time‐dependent magnetic field radial distribution. The electron density determined was also found to be consistent with energy‐balance considerations, as described in Ref. .
Using the values of the electron density and temperature as a function of the radial coordinate and time, the Stark widths of all emission lines observed (of O II – O VI) were calculated (we note that all lines used are isolated, i.e, their Stark shapes are Lorentzian). For the Stark broadening computations we employed two independent methods, namely, a quantum‐mechanical method based on the Baranger formula and a non‐perturbative semi‐classical method. For the quantum‐mechanical calculations of the line widths performed, we use electron‐collision cross sections calculated using two approaches: the Coulomb‐Born‐Exchange method and the convergent close‐coupling (CCC) method. The latter has been successfully applied to many atomic‐collision experiments, for example for the analysis of spectral‐line broadenings in Li‐ and Be‐like ions. The calculation results of the quantum‐mechanical and of the semi‐classical methods were found to be similar for the purpose of present discussion.
The total widths predicted for each line were then determined by convolving the calculated Stark widths with the Doppler broadening (assuming equal ion and electron temperatures; i.e., Ti= Te) and with the measured instrumental broadening. It was found that these widths are significantly smaller than the observed widths. For example for the 3144.7‐Å line of OV, the calculated Stark width is found to be 0.20 ± 0.08 Å, the Doppler broadening (due to Ti = Te = 13 eV) is 0.42 ± 0.09 Å, and the instrumental broadening is 0.21 Å. The width resulting form the convolution of these three contributions is 0.51±0.13Å. This value is much smaller than the observed width, 0.98 ± 0.03 Å. Similar results were obtained for the other O III – O VI lines.
Since the uncertainties in the Stark‐broadening calculations are believed to be significantly smaller than the difference between the computed and experimental line widths, an additional Doppler broadening is suggested. Energy balance considerations, based on the radial distributions of the electron temperature, electron density, charge state, and magnetic field previously determined (Refs. [8‐11]) allow for demonstrating that an ion temperature much higher than Te is unlikely. For explaining the extra broadening we thus suggest the presence of turbulent ion motion at the outer plasma boundary, which develops in the plasma during the implosion. The spatial scale of the turbulence is believed to be smaller than the spatial resolution of the measurements, which is ≅ 0.5 mm.
Based on this explanation, it is inferred that the ion kinetic energy associated with the turbulence can be up to 70% of the radially‐directed kinetic energy. It should be emphasized that these non‐thermal ion velocities are inferred for the imploding plasma that was observed to be with no geometrical disruptions, i.e, the small‐scale hydrodynamic turbulence here considered results in no spatial distortion of the plasma, to within the 0.5‐mm spatial resolution of the measurements.
- Plasma temperature
- Plasma turbulence
- Spatial resolution
- Doppler effect
- Magnetic fields
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