Plasma Spectroscopy Master's Thesis
Plasma Spectroscopy Master's Thesis
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Or: The Path to the One Plasma Diagnostic to Rule Them All
Or: The Path to the One Plasma Diagnostic to Rule Them All
Or: Dante's Inferno Via Spectroscopy Hell
As any plasma experimentalist will tell you, (one of) the most irritating parts of plasma diagnostics is that diagnostics never provide enough information. Some provide spatial information at a point in time, others vice versa. In most cases, they provide information on different plasma parameters and rarely have good agreement across multiple diagnostics. For my master's thesis, I wanted to develop a plasma diagnostic that alleviated a lot of these issues. My focus became:
As any plasma experimentalist will tell you, (one of) the most irritating parts of plasma diagnostics is that diagnostics never provide enough information. Some provide spatial information at a point in time, others vice versa. In most cases, they provide information on different plasma parameters and rarely have good agreement across multiple diagnostics. For my master's thesis, I wanted to develop a plasma diagnostic that alleviated a lot of these issues. My focus became:
Can I create a single diagnostic that determines the spatio-temporal evolution of plasma parameters critical to understanding the force balance of a flow Z pinch?
Can I create a single diagnostic that determines the spatio-temporal evolution of plasma parameters critical to understanding the force balance of a flow Z pinch?
The answer, it turns out, is somewhat. Let me explain.
The answer, it turns out, is somewhat. Let me explain.
The torus, the staple shape of all plasma physics. This specific one is apparently significant to some folks.
I had learned line-radiation spectroscopy up to that point in my plasma physics career and wanted to keep working in that area. Spectroscopy (in this flavor), is data-rich and non-intrusive, characteristics that experimentalists love. With a small number of modifications to an existing diagnostic, I could get temporal evolution of temperature and magnetic field strength.
I had learned line-radiation spectroscopy up to that point in my plasma physics career and wanted to keep working in that area. Spectroscopy (in this flavor), is data-rich and non-intrusive, characteristics that experimentalists love. With a small number of modifications to an existing diagnostic, I could get temporal evolution of temperature and magnetic field strength.
To lay out the various paths I could go down in configuring my diagnostic to get these measurements, I wrote a literature review that weighed all the possible paths and chose one in the end that would involve the least amount of modifications, give the highest SNR, and be doable within the time frame. You can read that document here.
To lay out the various paths I could go down in configuring my diagnostic to get these measurements, I wrote a literature review that weighed all the possible paths and chose one in the end that would involve the least amount of modifications, give the highest SNR, and be doable within the time frame. You can read that document here.
Once I knew how I wanted to configure my diagnostic and measure temperature and magnetic field strength, I set about testing some of the diagnostic parts, calibration schemes, and code needed for the new setup on an existing diagnostic.
Once I knew how I wanted to configure my diagnostic and measure temperature and magnetic field strength, I set about testing some of the diagnostic parts, calibration schemes, and code needed for the new setup on an existing diagnostic.
I started with an existing diagnostic, a Pi-Max gated single-frame ICCD coupled to an Acton SpectraPro 500i. One of the spectroscopy phenomena I was hoping to measure is Zeeman splitting, an incredibly sensitive change in line centroid. Calibration of pixel location on the ICCD to wavelength was therefore critical, and I developed a calibration scheme of moving a known reference line across the image sensor. For each image, the expected centroid location of each line is subracted from the actual location of the line. These errors are then fit with a 3 dimensional surface in image sensor space and the equation is saved to use for corrections of experimental data.
I started with an existing diagnostic, a Pi-Max gated single-frame ICCD coupled to an Acton SpectraPro 500i. One of the spectroscopy phenomena I was hoping to measure is Zeeman splitting, an incredibly sensitive change in line centroid. Calibration of pixel location on the ICCD to wavelength was therefore critical, and I developed a calibration scheme of moving a known reference line across the image sensor. For each image, the expected centroid location of each line is subracted from the actual location of the line. These errors are then fit with a 3 dimensional surface in image sensor space and the equation is saved to use for corrections of experimental data.
Pardon the weird perspective. This plot shows the red shift of spectra due to the spectrometer optics off-axis over the entire ICCD sensor. A best fit surface of these red shift points was used for correcting the red shift in the experimental data.
I took my data on this device, ZaP-HD! (Ross, 2016)
Once I figured out the calibration, and took some data at various times in the plasma pulse, I felt confident that I could swap the working ICCD setup for the new Kirana setup and still get the clear data I was getting with the ICCD setup.
Once I figured out the calibration, and took some data at various times in the plasma pulse, I felt confident that I could swap the working ICCD setup for the new Kirana setup and still get the clear data I was getting with the ICCD setup.
The Kirana's imaging sensor only senses visible light, and part of the literature review/configuration document I wrote above was dedicated to acknowledging this limitation. Fortunately, because the apparent Zeeman split is proportional to the center wavelength of the split line squared, moving into the visible range -- as opposed to the UV range that most of ZaP-HD's spectroscopy takes place in (normally due to the high ionization states from the high energy plasma which have higher energy (more UV) transitions) -- makes it possible to use the Kirana without any modifications.
The Kirana's imaging sensor only senses visible light, and part of the literature review/configuration document I wrote above was dedicated to acknowledging this limitation. Fortunately, because the apparent Zeeman split is proportional to the center wavelength of the split line squared, moving into the visible range -- as opposed to the UV range that most of ZaP-HD's spectroscopy takes place in (normally due to the high ionization states from the high energy plasma which have higher energy (more UV) transitions) -- makes it possible to use the Kirana without any modifications.
To couple the Kirana to our 250 cm spectrometer, I removed the ICCD camera and its mounting hardware. I then placed the Kirana aligned with the spectrometer's output port with no lens on the Kirana. The lens is uneeded since the spectrometer creates its own imaging plane that the camera sensor needs to be aligned with. Unfortunately with the Kirana, the image sensor is located deep enough within the camera body that one of the lens attachment rings on the camera needed to be removed so the Kirana would fit far enough into the spectrometer.
To couple the Kirana to our 250 cm spectrometer, I removed the ICCD camera and its mounting hardware. I then placed the Kirana aligned with the spectrometer's output port with no lens on the Kirana. The lens is uneeded since the spectrometer creates its own imaging plane that the camera sensor needs to be aligned with. Unfortunately with the Kirana, the image sensor is located deep enough within the camera body that one of the lens attachment rings on the camera needed to be removed so the Kirana would fit far enough into the spectrometer.
Focusing was completed in a similar fashion to the ICCD setup: a calibration lamp illuminated the fibers and the FWHM of the resulting spectra on the Kirana was monitored while the Kirana was moved slightly towards and away from the spectrometer until the FWHMs of the spectra were minimized.
Focusing was completed in a similar fashion to the ICCD setup: a calibration lamp illuminated the fibers and the FWHM of the resulting spectra on the Kirana was monitored while the Kirana was moved slightly towards and away from the spectrometer until the FWHMs of the spectra were minimized.
Two of the spectroscopy telescopes on ZaP-HD. The imaged light is carried back to the spectrometer through fiber bundles clad in very bright yellow plastic.
A snippet of my test plan. Note the lack of checkmarks in the "Completed" column.
Once focused, calibration with the Kirana setup was completed the same way the ICCD calibration was performed. A known wavelength from the calibration lamp was "swept" across the image sensor by varying the center wavelength on the spectrometer. The spectra at multiple sensor locations were recorded for later calibration analysis (let's put a pin in that).
Once focused, calibration with the Kirana setup was completed the same way the ICCD calibration was performed. A known wavelength from the calibration lamp was "swept" across the image sensor by varying the center wavelength on the spectrometer. The spectra at multiple sensor locations were recorded for later calibration analysis (let's put a pin in that).
Now ready to go, it was time to test with ZaP-HD's plasma. I had written up a test plan (see left), but testing, of course, did not go to plan -- I couldn't see anything! After debugging every piece of hardware in the spectroscopy system (mainly power-cycling everything with an on switch and hooking up scopes to monitor the triggers and frame monitor from the Kirana), I arrived at the terrible conclusion that the Kirana's bare sensor was not nearly sensitive enough to pick up any signal. I'd need to add the intensifier, which I was not looking forward to.
Now ready to go, it was time to test with ZaP-HD's plasma. I had written up a test plan (see left), but testing, of course, did not go to plan -- I couldn't see anything! After debugging every piece of hardware in the spectroscopy system (mainly power-cycling everything with an on switch and hooking up scopes to monitor the triggers and frame monitor from the Kirana), I arrived at the terrible conclusion that the Kirana's bare sensor was not nearly sensitive enough to pick up any signal. I'd need to add the intensifier, which I was not looking forward to.
Although one might be led to believe that an intensifier built by the same company as the camera it is designed to connect to would work well with said camera, the further could not be the truth for the SIL3 intensifier built by Specialized Imaging. The Kirana and intensifier use different software, do not communicate to each other, do not take the same number of frames, and most infuriatingly, won't image at the same time even with the same trigger signal hooked up to both! I found this out in the process of debugging why my signals were so dim -- I ended up having to time the difference in starting frame time between the two systems using a scope hooked up to the frame monitors on both, then manually add that timing difference in the triggering software so the two systems would be synced in real life.
Although one might be led to believe that an intensifier built by the same company as the camera it is designed to connect to would work well with said camera, the further could not be the truth for the SIL3 intensifier built by Specialized Imaging. The Kirana and intensifier use different software, do not communicate to each other, do not take the same number of frames, and most infuriatingly, won't image at the same time even with the same trigger signal hooked up to both! I found this out in the process of debugging why my signals were so dim -- I ended up having to time the difference in starting frame time between the two systems using a scope hooked up to the frame monitors on both, then manually add that timing difference in the triggering software so the two systems would be synced in real life.
But first, getting the intensifier-Kirana combo aligned and focused with the spectrometer was another pain. Similarly to before, the intensifier is moved in and out relative to the spectrometer opening until the FWHM of the spectra as seen on the Kirana screen is minimized. The intensifier must also be on at the same time (it will turn itself off after a few minutes, because it hates me). Once the intensifier sensor is in position relative to the spectrometer, the lens connecting the Kirana to intensifier must also be focused. Dear reader, you might be asking, "why is there a lens that must be focused even though it connects two pieces that are designed to be connected together?" Well I'll tell you, I don't know (of course there's not going to be perfect alignment and having adjustability makes sense, but not the full adjustability of a zoom lens, which is what the coupling lens is). Once that focus is also found, the process is repeated both between the intensifier and spectrometer and intensifier and Kirana since the image will now be clear enough that more focusing can occur. Calibration spectra were taken and stored the same way as previously (leave that pin in still).
But first, getting the intensifier-Kirana combo aligned and focused with the spectrometer was another pain. Similarly to before, the intensifier is moved in and out relative to the spectrometer opening until the FWHM of the spectra as seen on the Kirana screen is minimized. The intensifier must also be on at the same time (it will turn itself off after a few minutes, because it hates me). Once the intensifier sensor is in position relative to the spectrometer, the lens connecting the Kirana to intensifier must also be focused. Dear reader, you might be asking, "why is there a lens that must be focused even though it connects two pieces that are designed to be connected together?" Well I'll tell you, I don't know (of course there's not going to be perfect alignment and having adjustability makes sense, but not the full adjustability of a zoom lens, which is what the coupling lens is). Once that focus is also found, the process is repeated both between the intensifier and spectrometer and intensifier and Kirana since the image will now be clear enough that more focusing can occur. Calibration spectra were taken and stored the same way as previously (leave that pin in still).
Left to right: the spectrometer, intensifier, and Kirana, respectively. Alignment was iteratively with each element focused on the next as best as possible, then focused again after the other elements had been focused as much as possible.
The C IV doublet as recorded by the ICCD setup over a few micro-seconds at a specific point in the plasma pulse.
This time, I saw actual spectra while imaging ZaP-HD's plasma. After completing my test points and collecting what appeared to be sufficient data, I called my data collection campaign over and went about to data analysis. Simultaneously, I removed my spectroscopy setup since it would no longer be needed and ZaP-HD was brought offline for vacuum system maintenance (store these nuggets beside the pin). I now had a quarter of un-interrupted time to do my data analysis and write and defend my thesis.
This time, I saw actual spectra while imaging ZaP-HD's plasma. After completing my test points and collecting what appeared to be sufficient data, I called my data collection campaign over and went about to data analysis. Simultaneously, I removed my spectroscopy setup since it would no longer be needed and ZaP-HD was brought offline for vacuum system maintenance (store these nuggets beside the pin). I now had a quarter of un-interrupted time to do my data analysis and write and defend my thesis.
My first step was analyzing the ICCD data. After spending a few weeks writing, testing, and crying over my deconvolution algorithm, I finally got it up and running and managed to get plots of the ICCD data. Notably, the algorithm could not deconvolve the signals unless the signals had a very high SNR. While the the raw image data on the lab computer looked quite good SNR-wise using the Mk. 1 signal analy-eye-zer, the actual 1D-binned spectra the algorithm was injecting were notably less clear. While I had sensical results with this algorithm and the ICCD data, I was not feeling confident for the Kirana data.
My first step was analyzing the ICCD data. After spending a few weeks writing, testing, and crying over my deconvolution algorithm, I finally got it up and running and managed to get plots of the ICCD data. Notably, the algorithm could not deconvolve the signals unless the signals had a very high SNR. While the the raw image data on the lab computer looked quite good SNR-wise using the Mk. 1 signal analy-eye-zer, the actual 1D-binned spectra the algorithm was injecting were notably less clear. While I had sensical results with this algorithm and the ICCD data, I was not feeling confident for the Kirana data.
But first, I needed to do my calibration analysis with the Kirana data.
But first, I needed to do my calibration analysis with the Kirana data.
I had planned to just run the same ICCD calibration scripts, but with a self-generated wavelength scale. In the case of the ICCD and spectrometer, they communicate through one software since they're built by the same company -- imagine that, crazy right? As a result, the software automatically creates the wavelength scale you can see on the x-axis of the above image since Princeton Instruments, who made the camera and spectrometer, knew the FOV, image sensor size, and a bunch of other image parameters and calculated what wavelength the spectrometer and ICCD would see in software. While not perfect, it would give close enough wavelength results that could then be refined with the calibration scripts I had built.
I had planned to just run the same ICCD calibration scripts, but with a self-generated wavelength scale. In the case of the ICCD and spectrometer, they communicate through one software since they're built by the same company -- imagine that, crazy right? As a result, the software automatically creates the wavelength scale you can see on the x-axis of the above image since Princeton Instruments, who made the camera and spectrometer, knew the FOV, image sensor size, and a bunch of other image parameters and calculated what wavelength the spectrometer and ICCD would see in software. While not perfect, it would give close enough wavelength results that could then be refined with the calibration scripts I had built.
In the case of the separate imaging systems, I needed to do this myself, and had assumed that sweeping my one single-wavelength calibration line across the image sensor would give me that. To my horror, I realized it didn't.
In the case of the separate imaging systems, I needed to do this myself, and had assumed that sweeping my one single-wavelength calibration line across the image sensor would give me that. To my horror, I realized it didn't.
This whole write up has been quite dense and drab. Here's some cobra lillies to pretty things up.
A visualization of the "virtual line" idea. The dashed line is the spectrometer "center" where the virtual line exists in pixel space on the image. The wavelength of the virtual line is the spectrometer's center wavelength. The other line is the Cd I calibration line, which of course exists in pixel and known wavelength space. Subtracting the two wavelengths (virtual and calibration line) and dividing by the difference in their corresponding pixel locations would give an incorrect wavelength per pixel value.
To explain, let me demonstrate how we get our wavelength scale: the wavelength scale is a set of values created (in our limited case) as a function of the spectrometer grating, spectrometer center wavelength, and associated optics parameters that I'll leave as a constant for now. In practice, we can look at where the known-wavelength calibration line is on our image system's sensor (think which pixel the center of the line is located) and the current center wavelength of our spectrometer, and back out a pixel location to wavelength conversion. If we change the center wavelength of the spectrometer, our calibration line moves across the image sensor, but the wavelength of that line is the same.
To explain, let me demonstrate how we get our wavelength scale: the wavelength scale is a set of values created (in our limited case) as a function of the spectrometer grating, spectrometer center wavelength, and associated optics parameters that I'll leave as a constant for now. In practice, we can look at where the known-wavelength calibration line is on our image system's sensor (think which pixel the center of the line is located) and the current center wavelength of our spectrometer, and back out a pixel location to wavelength conversion. If we change the center wavelength of the spectrometer, our calibration line moves across the image sensor, but the wavelength of that line is the same.
In essence, I have a wavelength per pixel value of zero because the wavelength I'm measuring from the calibration line hasn't changed. That's pretty bad! However, if I create a "virtual line" at the center wavelength of the spectrometer and subtract that from the calibration line's wavelength, I could have two unique wavelengths with different pixel values that give a wavelength per pixel value. While this sounds good in theory, it absolutely can't work: the second "wavelength" I'm measuring (the spectrometer center wavelength), isn't a comparable wavelength to the first wavelength I measured which is a real wavelength -- I'm subtracting apples from oranges and hoping for a nice Grannysmith, preposterous!
In essence, I have a wavelength per pixel value of zero because the wavelength I'm measuring from the calibration line hasn't changed. That's pretty bad! However, if I create a "virtual line" at the center wavelength of the spectrometer and subtract that from the calibration line's wavelength, I could have two unique wavelengths with different pixel values that give a wavelength per pixel value. While this sounds good in theory, it absolutely can't work: the second "wavelength" I'm measuring (the spectrometer center wavelength), isn't a comparable wavelength to the first wavelength I measured which is a real wavelength -- I'm subtracting apples from oranges and hoping for a nice Grannysmith, preposterous!
In a more physical intuition, the virtual line is implying that there would be a real line with a wavelength at the correct corresponding pixel location, but we can't be sure of that. Since Zeeman Splitting is such a sensitive measurement, any error in the wavelength per pixel determination would have a dramatic impact on the determined magnetic field strength.
In a more physical intuition, the virtual line is implying that there would be a real line with a wavelength at the correct corresponding pixel location, but we can't be sure of that. Since Zeeman Splitting is such a sensitive measurement, any error in the wavelength per pixel determination would have a dramatic impact on the determined magnetic field strength.
Graduation was rapidly approaching, and so was the deadline to turn in my thesis. My spectroscopy setup had been completely taken down and stowed; taking new calibration data wouldn't be helpful since the setups could have slightly different alignment. All I had at my disposal was the existing unhelpful calibration data and my experimental data. After a healthy amount of panicking, I realized that my experimental data could also be calibration data.
Graduation was rapidly approaching, and so was the deadline to turn in my thesis. My spectroscopy setup had been completely taken down and stowed; taking new calibration data wouldn't be helpful since the setups could have slightly different alignment. All I had at my disposal was the existing unhelpful calibration data and my experimental data. After a healthy amount of panicking, I realized that my experimental data could also be calibration data.
Me, age 24, realizing I was screwed without calibration data. Attribution
The C IV doublet I measured for my experimental data. Since the center chords were only symmetrically shifted from their center wavelengths, I could use their locations to get a wavelength per pixel value for the Kirana setup.
The line (or should I say lines) that I was measuring are a doublet, and were purposefully chosen early on because more data is more better-er. Both lines of the doublet easily fit on the image sensor of the kirana and were therefore simultaneously imaged. The wavelengths are of course known, and all the spectroscopic effects on each line would be symmetric to the nominal center wavelength of each line. With two known lines, I had two known wavelengths and pixel locations I could calibrate off of! I called this method of calibrating from my experimental data I would then analyze with this calibration data, bootstrapping. With the bootstrapped wavelength per pixel calibration complete, I could then apply all the secondary calibrations to the kirana data as I did to the ICCD data using the single line calibration data. I could then analyze my experimental data (this time for physical results rather than for calibration info). Problem solved!
The line (or should I say lines) that I was measuring are a doublet, and were purposefully chosen early on because more data is more better-er. Both lines of the doublet easily fit on the image sensor of the kirana and were therefore simultaneously imaged. The wavelengths are of course known, and all the spectroscopic effects on each line would be symmetric to the nominal center wavelength of each line. With two known lines, I had two known wavelengths and pixel locations I could calibrate off of! I called this method of calibrating from my experimental data I would then analyze with this calibration data, bootstrapping. With the bootstrapped wavelength per pixel calibration complete, I could then apply all the secondary calibrations to the kirana data as I did to the ICCD data using the single line calibration data. I could then analyze my experimental data (this time for physical results rather than for calibration info). Problem solved!
It turns out that using a camera and intensifier not designed for spectroscopy and using spectroscopy analysis techniques that require very high SNRs to pull very sensitive spectroscopy values is not a recipe for success. While the ICCD data yielded physical results post analysis, the Kirana data was another story. If my algorithms gave a non-physical result (i.e. impossibly large temperatures) or couldn't determine the signal from the noisy data, they would not return a result and there would be no corresponding point for it in the resulting plots. The plot on the right is an example of how poor the Kirana's data was: most of the plot is blank! To be clear, there's still some valuable data here, we have temperature evolution over time at some spatial locations while also generally capturing the center of the pinch, but this isn't quite the One Diagnostic to Rule Them All. At least yet. With a better camera and stronger impurity lines from higher impurity doping, I think it would have been possible to capture the evolution of the pinch force balance over an entire pulse. For now, we know that it might be possible!
It turns out that using a camera and intensifier not designed for spectroscopy and using spectroscopy analysis techniques that require very high SNRs to pull very sensitive spectroscopy values is not a recipe for success. While the ICCD data yielded physical results post analysis, the Kirana data was another story. If my algorithms gave a non-physical result (i.e. impossibly large temperatures) or couldn't determine the signal from the noisy data, they would not return a result and there would be no corresponding point for it in the resulting plots. The plot on the right is an example of how poor the Kirana's data was: most of the plot is blank! To be clear, there's still some valuable data here, we have temperature evolution over time at some spatial locations while also generally capturing the center of the pinch, but this isn't quite the One Diagnostic to Rule Them All. At least yet. With a better camera and stronger impurity lines from higher impurity doping, I think it would have been possible to capture the evolution of the pinch force balance over an entire pulse. For now, we know that it might be possible!
Resolved temperature (in eV) over the life of a pulse using the Kirana setup.
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