Spatio-temporal ion temperature and velocity measurements in a Z pinch using fast-framing spectroscopy

Ion Doppler Spectroscopy (IDS) is a technique used to determine the temperature or velocity of radiating ions in a plasma. IDS is a convenient diagnostic for experiments where high temperatures prohibit the insertion of physical probes into the plasma. Data are collected without perturbing the plasma flow. In addition to the benefits of being a passive diagnostic, spectroscopy collection techniques are relatively simple. Plasma radiation can be collected at any optical access point on an experiment. Making additional measurements generally only requires the addition of more optical fibers to the system. The versatility and simplicity of IDS have solidified this tool as an important diagnostic for plasma experiments with a wide range of densities, temperatures, and confinement times.^1–4 

This paper illustrates a new method for measuring time-resolved ion velocity and temperature using ion Doppler emission spectroscopy. The diagnostic was created by implementing an ultra-fast framing camera and ultraviolet intensifier as the detector for a 0.5 m Czerny–Turner spectrometer. The camera records many spectra throughout the plasma pulse as frames in a video. The Doppler broadening and shift are calculated for each spectrum to reconstruct time-resolved ion temperature and velocity profiles. A thorough treatment of line radiation broadening can be found in Refs. 5 and 6. Implementing a fast-framing camera not only shortens the time required to collect time-resolved profiles from several weeks to several minutes but also allows the temperature and velocity profiles to be measured contiguously, rather than be pieced together from many plasma pulses.

The time-resolved emission spectrometer has been developed on the ZaP-HD Flow Z-Pinch Experiment at the University of Washington. The ZaP-HD experimental apparatus is described in Ref. 7. The ZaP-HD machine creates 50 cm-long hydrogen Z-pinch plasmas with radii between 0.2 and 1 cm. Measurements indicate peak ion temperatures of up to 1 keV and peak densities on the order of 10²⁴ m⁻³. Radial shear of the axial velocity in the pinch allows for periods of pinch stability of up to 60 µs, thousands of times longer than the magnetohydrodynamic instability growth time computed for a static plasma. Measuring the pinch velocity and temperature is imperative to characterizing the pinch stability and behavior, as well as understanding how plasma parameters scale with pinch current.

The instrumentation for spectroscopic measurements is described in detail in Ref. 8. Light emitted by the plasma is collected using bundles of optical fibers attached to telecentric telescopes.⁹ Two types of optical fiber bundles are used on the experiment. One is a 20-chord fiber bundle, which collects light at 20 impact parameter locations across a 34 mm span. The second consists of two 10-chord fiber bundles, which collect light at ten impact parameter locations each across a 34 mm span. This bundle can be used to collect light through two different telescopes at up to two axial locations. Two telescopes are mounted at different angles to the plasma to measure Doppler effects from the impurity ion radiation. Both telescopes record Doppler broadening. An oblique telescope mounted at 45° to the z-axis can measure a component of the Doppler shift due to axial plasma flow. A radial telescope mounted at 90° to the z-axis is insensitive to the bulk plasma flow in the axial direction.

Light collected by the optical fibers is directed to a 0.5 m Acton Research Spectra Pro SP500i spectrometer. A 3600 grooves/mm dispersion grating separates the light by wavelength. The spectrometer is calibrated with a cadmium-ion lamp using the Cd I spectral line at 228.802 nm. Ion Doppler measurements use impurity line radiation from the carbon-III ion at 229.687 nm as the hydrogen plasmas in the ZaP-HD device are typically fully ionized. The plasma is seeded with a small percentage of methane (CH₄) to ensure that the intensity of the radiating carbon is large enough for accurate measurements. Carbon can also enter the plasma due to impurities embedded in the wall.

The ∼100 µs lifetimes of the Z-pinch plasmas produced in the ZaP-HD experiment necessitate the use of spectroscopy detectors capable of sub-microsecond resolution. Short detector exposure times can reduce any broadening effects from turbulent motion in the plasma. Spectroscopic measurements on ZaP-HD were previously made¹⁰ with a Princeton Instruments PI-MAX2 intensified charge-coupled device (ICCD) with a 512-by-512 pixel array. Using the 3600 g/mm grating, measurements with a 0.011 nm/pixel resolution could be made. Sub-pixel measurements were possible, for example, when determining emission centroids. Each chord was binned and numerically fitted to a Gaussian distribution to obtain the ion temperature and velocity.

Characterizing the time-evolution of plasma temperature and velocity was limited by the ICCD. Only one radially resolved measurement could be made during a plasma pulse. The plasma temperature and velocity evolve over the duration of the pulse, but contiguous measurements of these profiles could not be made. Instead, spectra from several hundred plasma pulses with the same initial conditions were used to determine the temporal evolution of velocity profiles.¹⁰ Creating a single time-resolved plot required several weeks of data collection, and plots could only be made if the plasma behavior was repeatable.

The new spectroscopy system was designed to create time-resolved temperature and velocity profiles using data from a single plasma pulse. This compresses the required time to make these plots from several weeks to ∼3 min. A Kirana 05M ultra-fast framing camera with a solid-state megapixel uCMOS image sensor¹¹ is used instead of an ICCD to record the spectra during the pulse. The camera is coupled to a Specialized Imaging lens ultraviolet intensifier to record light emitted by the carbon-III impurity ion at 229.687 nm. The ultraviolet intensifier uses a phosphor screen with a 27 line pair/mm resolution to detect light in the UV range,¹² where the plasma ions tend to radiate in the ZaP-HD device. The 300 ns recovery time of phosphor limits the fastest frame rate of the system to 1 MFPS, which is sufficient to record up to 100 frames during the plasma lifetime.

The camera and intensifier are attached to the spectrometer with a series of UV coupling optics. A sketch of the diagnostic setup is shown in Fig. 1. The system is calibrated with cadmium and mercury ion pen lamps. A thorough calibration of the Kirana is paramount to the performance of the system as the camera has no spectral software to identify the wavelength of the line radiation. A calibration curve to convert wavelength to pixels must be established to measure Doppler broadening and shift. This is accomplished by positioning the diffraction grating to move the centroid of several Cd and Hg lines across the detector and recording the centroid position in pixels. Once the pixel-to-wavelength conversion is established, the system can be used to make measurements of the plasma.

The time-resolved spectrometer was fielded on the ZaP-HD device for Z-pinch plasmas made of 90% H₂ and 10% CH₄. Doping the pinch with methane ensured that the carbon impurity ion signal was high enough to accurately measure the plasma ion temperature and velocity. Spectra were recorded at different applied voltages and gas puff settings to measure plasma parameters for a variety of initial conditions.

A raw image from the Kirana can be seen in Fig. 2. The Kirana data contain light from ten chords measured at a 90° angle to the plasma flow and light from ten chords measured at a 45° angle from the plasma flow. In the figure, light only appears in 11 chords, indicating an emission extent of 16 mm. The solid lines bound the location on the detector of chords measuring velocity, while the dashed lines bound chords measuring temperature. The measurements resolve the radial profiles of ion temperature and axial velocity at a location 15 cm downstream of the coaxial accelerator. Both telescopes are positioned to collect light from the same axial position simultaneously.

The raw data are binned and corrected for optical aberrations before being numerically fitted with a Gaussian function. A sample spectrum is shown in Fig. 3. The optics create a slight curve across the 20 chords, resulting in shifted wavelength centroids for each Gaussian. This is corrected with a baseline subtraction at the beginning of the analysis. The temperature and velocity can then be determined from the fit parameters. A Matlab program is used to fit all chords in each frame of the video and produces plots of the temporal evolution of the ion temperature and axial velocity for each plasma pulse.

Two profiles from a single plasma pulse are shown in Figs. 4 and 5. Figure 4 shows the evolution of plasma temperature over time in eV. Any white space indicates a chord where the intensity of the carbon-III line was too dim for an accurate value to be computed. The data show a columnated temperature profile with a peak close to the center of the machine axis. The maximum temperature is ∼300 eV.

The temperature profile at 80 µs is extracted from Fig. 4 and shown in Fig. 6. Error bars indicate a 90% confidence interval in each temperature measurement. The profile is peaked near the machine axis, which could indicate a centered Z pinch with a radius of ∼5 mm.

Velocity data in km/s from the same pulse are shown in Fig. 5. When carbon-III is first seen in the assembly region, the velocities are high and fairly uniform. The velocity tends to decrease in time, and the signal from carbon-III is only seen within 10 mm of the machine axis.

Carbon-III emission recorded on the Kirana is compared to the time-resolved intensity of carbon-III recorded using a photomultiplier tube (PMT). The photomultiplier tube has a higher dynamic range than the Kirana and can thus record smaller fluctuations in intensity of the impurity ion radiation. A comparison of measured intensities between the Kirana data and the PMT indicates that the Kirana tracks the large-scale intensity fluctuations well but may miss smaller changes.

A new method for making time-resolved ion Doppler spectroscopy measurements has been designed and fielded on the ZaP-HD device at the University of Washington. The new IDS system uses an ultra-fast framing camera as a spectroscopy detector to record 100 spectra over the 100 µs lifetime of a Z-pinch plasma. Time-resolved IDS uses two telescopes and two fiber bundles to radially resolve both ion temperature and velocity during the pulse. Plasma ion temperature and velocity have been measured for the ZaP-HD Z pinch by observing the radiation from carbon impurity ions. Additional work is being done to resolve higher ionization states of carbon to measure higher ion temperatures and create time-resolved profiles of velocity shear. The method is currently being used in the ZaP-HD diagnostic suite to characterize plasmas with different initial conditions and pulse energies.

The data that support the findings of this study are available from the corresponding author upon reasonable request.

The information, data, or work presented herein was funded, in part, by the Advanced Research Projects Agency-Energy (ARPA-E), U.S. Department of Energy, under Award No. DE-AR-0000571, the U.S. National Nuclear Security Administration under Grant No. DE-NA0001860, and the U.S. Department of Energy under Grant No. DEFG02-04ER54756.