Schematic of the SSX, shown in cross section. The device is cylindrically symmetric about the horizontal axis in the figure. Spheromak plasmas are formed in the guns on the east and west sides of the vacuum chamber and ejected into the main flux conserver. The lines of sight of the VUV monochromator, the SXR detector, and the ion Doppler spectrometer are at the midplane, aligned with the short axis of the chamber and perpendicular to the long axis, and here are indicated schematically by the white squares (see Fig. 9). Arrays of magnetic probes are shown schematically as six black lines in the figure. The probes are removed when we take spectroscopic data. The contours represent the magnetic field lines of a field-reversed configuration (FRC), the plasma structure that forms when two counterhelicity spheromaks merge.
Model spectra from steady-state simulations with (top) and (bottom). Both simulations assume a uniform 40 cm thick plasma composed of 99% hydrogen and 1% carbon with an ion density of . The temperature dependence of the line ratio is evident. Note also the presence of the Lyman edge at 91.2 nm, indicating that radiative recombination of hydrogen, rather than bremsstrahlung, is the dominant continuum process at work.
Simulated line ratio plotted as a function of temperature for three different plasma densities (given in ). Note the mild density dependence of this line ratio.
Carbon ionization balance vs. electron temperature computed from PRISMSPECT simulations with an electron density of .
Sample VUV monochromator data. Top: a measurement of the C IV 155 nm line intensity during a discharge with counterhelicity spheromak merging in SSX. Bottom: a measurement of the C III 97.7 nm line intensity during a single spheromak discharge.
Line ratios calculated from PRISMSPECT simulations with 0.1% carbon, nitrogen, and oxygen impurities and . The N V 124 nm line is predicted to be at least eight times stronger than the C IV 155 nm line for plausible SSX temperatures (top), and the O V 63.0 nm line is predicted to be over 500 times stronger than the C III 97.7 nm line (bottom). The measured strength of the carbon lines relative to the others is much higher than these predictions, allowing us to estimate the concentrations of nitrogen and oxygen relative to carbon in the SSX plasma.
Electron temperatures for counterhelicity merging (top) and single spheromak discharges (bottom) derived from measurements averaged over 25 discharges for each line. An ion density of was assumed. Dashed lines give the uncertainty range, defined as the temperatures implied by a line ratio one standard deviation above or below the mean.
Thermal Doppler broadening of the C III 229.687 nm line observed with the IDS instrument viewing along a midplane diameter of the plasma during counterhelicity merging (top) and single spheromak discharges (bottom). Each data point is the average of up to ten discharges; data with small signal strength or showing nonthermal (flow profile) effects were dropped from the average.
Location of SXR at the midplane on the SSX machine (see the schematic in Fig. 1). The four wires at the top of the image carry current from the SXR photodiodes. Clockwise from upper left, the diodes are filtered by foils made of Al, Zr, Sn, and Ti. The port for the IDS is visible at the bottom center of this image. Note that hydrogen Balmer series recombination emission is visible through the windows in the vessel in this photograph.
SXR filter responsivities (Refs. 43 and 44). The colored lines show the response function of the filtered diodes in the 10–500 eV range, and the black line shows the response function of the unfiltered diode. Line emission at was negligible at all simulation temperatures. The lower panel shows the same responsivity curves, but zoomed in on the range below 100 eV, where the bulk of the plasma emission is expected.
SXR data from a discharge with counterhelicity merging, smoothed over intervals. Note the onset of strong SXR emission around , when reconnection begins.
Top: SXR data for the Al, Zr, and Ti filters from a discharge with counterhelicity merging, smoothed over intervals. Bottom: time evolution of filter ratios for the discharge. Sn filter data are omitted in order to more clearly show the time evolution of the other three ratios.
Model spectrum from a steady-state simulation with and . Impurity concentrations of 1% carbon, 0.002% oxygen, and 0.003% nitrogen were included. The plasma emits primarily at , but SXR will also measure substantial emission from the C V and C VI resonance lines between 300 and 400 eV. Note that the Zr channel has the lowest responsivity at these energies, which is counter to what is seen below 100 eV.
Illustration of the process used to fit SXR data to model spectra and determine . Channel intensity ratios calculated from models are plotted as a function of temperature (solid lines). Measured ratios at (top panel) and (bottom panel) during a typical single spheromak discharge are plotted as points at the location of the calculated best-fit temperature for the time step. For illustrative purposes, 30% error in the measured ratios is assumed. At , a good fit is achieved at . However, at , all three measured ratios cannot match the models at any one temperature, and the best-fit temperature of 30 eV may not accurately reflect the actual in the plasma.
Impurity emission lines measured with the VUV monochromator.
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