I've posted new SXR temperature profiles calculated using errors proportional to the filter ratios rather than a single constant error value for all ratios. The results have not changed drastically, even though I found that the method of calculation used can have a noticeable effect on temperatures calculated for individual shots.

I've posted some results from a non-Maxwellian simulation in which I had PrismSPECT calculate a spectrum out to 500 eV. It turns out that although high energy emission lines are sparse, those that are present dominate the spectrum. It's definitely very important that we include these energies in our SXR calculations--in fact, I think I should be calculating spectra all the way up to 1000 eV, because PrismSPECT identifies oxygen and carbon lines at energies as high as 790 eV. I'm worried about the effect that the C V and C VI lines at 300+ eV will have on our standard SXR results with Maxwellian distributions--I have a feeling it will be substantial.

I've recalculated the SXR filter responsivites again, this time for energies up to 1000 eV. I found an "interpolate" tool in Origin that works as long as the desired grid of energies is evenly spaced and gives much better results than the spline interpolation in IDL.

My long SXR simulation with copper (T ranging from 5 to 100 eV) finally finished running, and I've posted results. The temperature profiles I was getting looked strange, and at first I thought something was wrong with my code, but I've determined that everything is working properly. I think we can interpret these results as evidence that a 1% copper impurity in SSX is far too high (not all that surprising). The results do confirm that if there were a lot of copper in SSX, the effect on SXR analysis would be quite significant.

Analyzing this example has made me concerned about the way that my code determines best-fit temperatures. Lacking a good way to estimate errors for individual SXR filter ratios, I simply assumed that all uncertainties were equal to 1 for the purpose of chi-squared calculations, so my code minimizes the total squared deviation of the simulated ratios from the data. I realize now that relative (fractional) differences between simulated and measured filter ratios are probably more relevant than absolute differences. For example, if we had the following data: [Ratio A = 1, Ratio B = 20], and two simulations gave the following ratios: [Simulation 1: A = 1, B = 40], [Simulation 2: A = 5, B = 5], my code would decide that Simulation 2 best fit the data, while it seems pretty obvious that Simulation 1 was actually a better match. I'm going to try changing this and see whether our results are affected substantially.

I also posted plots of the C III 97.7 nm / Cu VIII 90.0 nm and C III 97.7 nm / Cu VIII 93.8 nm ratios as a function of temperature. These are the strongest two copper lines in the VUV range, and the ratios are of order unity between 20 eV and 60 eV in simulations with equal concentrations of carbon and copper. If we can't detect these lines with the monochromator, we can conclude that the copper concentration is at least a factor of several less than the carbon concentration. However, we can probably already make this inference from the SXR results discussed above.

Finally, went back to a simulation without copper and recalculated temperatures for several shots by assuming that the SXR filter ratios have errors proportional to their magnitude, rather than constant errors for all ratios. I've posted these results as well.

I met with David and Doc today to talk about our paper. We may submit it to Physics of Plasmas, but I'm going to check to see whether other papers with this much spectroscopy have been published previously. If not, we may go for the Journal of Applied Physics. We talked about a number of other details, and David made some suggestions for improvements on what I've written so far. I'm working on implementing the changes, and I'm going to continue writing and cleaning up the necessary figures. I also emailed Jason today to find out where he saved the data that went into the azimuthal flow figure in his thesis.

Pam from Prism-CS sent us a new version of PrismSPECT today (version 3.5.1Beta). The bug that made the electron distribution string not read in correctly has been fixed; I succesfully ran a simulation with a flat electron tail out to 500 eV and will post the results soon.

I'm running one more simulation with copper in order to be able to make some conclusive statements about the magnitude of the possible effects on SXR signals. The simulation is identical to a simulation called "SXRden5e14FullHModel" that I ran on 3-23-07, except that I included a 1% copper impurity in addition to the standard carbon and oxygen impurities. The actual amount of copper in the plasma is unlikely to be that high, but this will give us an upper limit on the effect that it could have on SXR measurements and temperature calculations. When it finishes running, I'll post comparisons of the filter signals produced with and without copper.

I finished my letter to Joe today, and I've been working on doing more writing. Doc, David, and I are going to meet on Wednesday to discuss the paper, choose a journal, etc. I realized that one of the figures in my thesis was based on an old simulation that used flawed atomic models, didn't have planar geometry, and didn't cover a wide enough range of temperatures, so I'm re-running it (we'll probably use it in the paper).

I chatted with Doc and David briefly today about simulations with non-Maxwellian electrons. Doc thinks that having 10% high energy electrons is probably too many (I suspected as much), but will allow us to place a useful upper limit on the effect they could have. David also suggested that I calculate the numerical effects on SXR signals of including copper in the plasma.

My first simulation with a dual Maxwellian electron energy distribution has finished running. There are a lot more lines in the spectrum than for a simulation with no high energy electron population, and the SXR filter signals are different too. However, it's not apparent to me that the dual Maxwellian model spectrum fits the SXR data any better than the single Maxwellian spectra did. I have also looked at the C III 97.7 nm / C III 229.7 nm line strength ratio--it is still ~22, just as it was in the old simulations, so the presence of high-energy electrons doesn't seem to play a role in the 229.7 nm line anomaly.

I still can't get the analytic expression option to work--PrismSPECT crashes no matter what f(E) I choose. Perhaps the feature hasn't been fully implemented in the code after all. I'm going to try a couple of more things this afternoon, and if it still doesn't work I'll probably email Joe MacFarlane.

On another note, while I was reading through old email exchanges with Joe, I came upon a discussion of optical depth in SSX--specifically whether the plasma could become optically thick in some lines, which might explain some of our outstanding mysteries. He pointed out that the spectral viewer in PrismSPECT can display optical depths, but I don't think I ever actually tried this before. Today I looked back at the simulations I used for my thesis, and it looks like optically thick lines should not be a problem at SSX temperatures--at T > 20 eV no lines have optical depths above 0.1.

My time-dependent simulation with copper has finished running, and I've posted some results. It appears that although the Cu ionization balance takes longer to equilibrate than carbon does, by the time the plasma is observed by the VUV monochromator and SXR the spectrum is similar to the steady-state spectrum.

I tried to set up a simulation with a non-Maxwellian electron energy distribution today. At first I used PrismSPECT's "Analytic expression" option, setting up a simulation with 90% of the electrons in a 30 eV Maxwellian and 10% in a constant "slide-away" distribution extending out to 1000 eV. However, PrismSPECT crashed when I tried to run the simulation. I think it didn't like the fact that there was no energy dependence in my analytic expression for f(E). I decided instead to run a simulation with dual Maxwellian, with a large population of electrons at 30 eV and a smaller population at 100 eV. I'll report on the results tomorrow.

I printed out final versions of my thesis and summary for the Apker award, and Doc is going to mail everything off today. I've also found a bunch of papers that relate to non-Maxwellian electron distributions, and I'm browsing through them to see if any offer guidance for our simulations. The simulation with copper that I was running yesterday unfortunately got interrupted, so I had to start over. It looks like it's going to take 25-30 hours to run; it will probably be done by tomorrow afternoon.

I finished fixing up my TfromSXR code today. I'll have to get a few people to test it out and see how clear the instructions are.

Doc and Chris suggested that the copper ionization balance in SSX would likely take longer to reach equilibrium than the carbon ionization balance does, since so many electrons have to be stripped off to reach the dominant copper ionization stages (Cu IX and Cu X). If the equilibrization time scale isn't short compared to the lifetime of the SSX plasma, we might expect to see strong lines from lower ionization stages (in the event that copper is present at all). I'm going to run a time-dependent simulation to look into this.

Contrary to my initial conclusion, I've discovered that it is possible to specify an arbitrary electron velocity distribution using the current version of PrismSPECT. I'm going to try a test simulation sometime later this week. Doc suggested adding a flat tail of "runaway electrons" with energies up to 100-1000 eV on top of the standard Maxwellian distribution. I'm going to see if I can find any papers with other examples of non-Maxwellian velocity distributions that people have used.

My simulation with copper from yesterday has finished running, and I've posted the results. As I suspected, there are a number of strong lines at high energies (mostly between 50 and 100 eV). This means that if there is a substantial Cu impurity in SSX, we would not be able to detect it with the VUV monochromator, but it would still have a significant effect on the interpretation of SXR data.

I've started a new "To Do" list for the summer and will try to keep it updated over the next few weeks.

The simulation discussed above had a strange looking copper ionization balance, so I created a new Cu atomic model with 50 energy levels for every ionization stage up to fully ionized. When I re-ran the simulation using this new atomic model, the ionization balance had changed considerably. At this point I don't to get exact results for copper, so it's not a big deal, but if we ever want to understand the emission that copper produces with any precision we'll have to evaluate whether PrismSPECT is handling this situation correctly.

For some reason yesterday I was thinking that the SSX plasma gun was made of titanium, but I realized today that it's actually coated with tungsten, while the new flux conserver will eventually be coated with titanium. In the simulations I ran yesterday, I found several relatively strong Ti lines between 62-72 nm (resonance lines for Ti VII, VIII, IX, and X) but a notable absence of strong Cu lines. I ran a new simulation with only Cu and C impurities today in order to reduce the complexity of the spectrum and make it easier to find the copper lines, and the results were the same--it seems that if the carbon and copper impurity concentrations were equal, we wouldn't be able to detect any copper lines with the VUV monochromator. This concerns me, because there may still be strong copper lines at higher energies that would effect SXR measurements. I'm running a new simulation with a spectral energy range of 10-150 eV to see if this is true.

I finished a couple of iterations of my Apker award summary today, and I'll post the final version when it's ready. I've made most of the changes to my thesis that I'm planning to make, although I make tweak a couple of more things after I talk to David and Doc. I've also begun working on cleaning up some of my IDL code to make it more user friendly.

One of the issues I'd like to address this summer is whether or not the gun and flux conserver materials (titanium and copper) contribute significantly to the impurities in the plasma. Back when Slava was here, they looked for some copper lines with the VUV monochromator but didn't find them. However, they did not have access to a tool like PrismSPECT to guide their searching, so I'm going to run a few simulations to determine which Cu and Ti lines can be expected to be strong under SSX conditions. Today I created new Cu and Ti atomic models. For both elements, I decided to use 50 energy levels for each of the first 10 ions and ground states for the remaining ions. This should be sufficient since the strongest lines will almost certainly be transitions to the ground state out of relatively low-energy excited states, and we don't expect very high ionization stages to be present at SSX temperatures. Later, if it turns out we need to include Cu and Ti in simulations for SXR modeling, I may create more detailed atomic models. As a first pass, I ran a single simulation with typical SSX parameters (T = 30 eV, n = 5e14 cm^-3), and 1% concentrations of C, Cu, and Ti.

In other news, yesterday I started over and reformatted my thesis, abandoning the template I had been using, and after a couple of hours of tweaking, everything looks good and the automatic numbering of my bibliography entries is finally working. Thank goodness. As part of this process, I created a Bibtex file with all of my references, which should make doing the reference section of any papers I write a breeze.

The results of my simulation are in, and it turns out I underestimated how ionized the Ti and Cu would be. At 30 eV, the dominant ionization stages are Cu IX and Ti VIII, and there are appreciable fractions of ions as high as C XIII and Ti XII. I'm going to make a new atomic model that includes 50 energy levels for all ions that had non-zero populations in the original simulation and then run a new one.

Lots more writing has been done this week, and the end is in sight--I just need to finish the section on the lollipop test, write up the results from SXR temperature calculations, write the conclusion, and make energy level diagrams for the appendix. I ran two PrismSPECT simulations for SXR, one with an oxygen atomic model with 100 energy levels per ion and one with a simpler model with 50 levels for OIII through OVII and just ground states for the other ions. The simpler simulation has finished running, but the other one was interrupted twice, so I'm having to run it again. Hopefully it will be done by tomorrow evening; in the meantime I'm going to go ahead and process the results from the finished simulation.

Based on the strengths of lines observed with the VUV monochromator, we decided to use a carbon to oxygen ratio of 1000/1 for the SXR simulations. The CIII 97.7 nm / OV 63.0 nm line ratio from these simulations is of order unity for most temperatures, matching the experimental data, so it appears that this ratio is approximately accurate.

Since I got somewhat surprising results for the CV and CVI fractions at 60 eV during my simulations last week, I made one more atomic model in which I increased the number of CV energy levels from 200 to 296 (the maximum possible). My old model (C200each11_6) already had the maximum possible number of levels for CVI (60). I ran a new simulation with varying density and T = 60 eV: the ionization stage fractions look identical to those derived previously, so I am concluding once and for all (I hope) that my 200-levels-per-ion carbon atomic model is complex enough.

In the next day or two I plan to use my final carbon atomic model to set up some time-dependent simulations to re-determine the equilibrization time and make sure using steady-state simulations is still a safe bet (similar to the tests I did back in June).

David and I have figured out how to examine the atomic model files using a text editor, and we are reasonably convinced that the newest carbon models are correct. The strange density dependences must then be a function of the fact that CIII and CIV are trace ions in the SSX plasma (CV is dominant). The next step is to try to figure out which energy levels that are important to the density dependence were left out of the 304-level atomic model (when no density dependence was observed) but included in the 200-level per ion model.

I worked on writing some this afternoon. I'm almost done with Chapter 4, but I need to finish the simulations soon if I'm going to have time to finish writing everything up.

Today I'm using the new simulation results to re-calculate temperature profiles for the data from 8-2-06 (counter-helicity) and 8-3-06 (single spheromak). For the August 2 data, I used run 9 as a baseline shot, averaged over runs 20-44 for the 97.7 nm line strength, and averaged over runs 63-87 for the 155 nm line strength. For the August 3 data, I used run 38 as a baseline shot, averaged over runs 40-64 for the 97.7 nm line, and averaged over runs 73-97 for the 155 nm line. I made separate plots for each of the 3 densities we tried (1e14, 5e14, and 2e15 ions/cm^3), but the big news for today is that density doesn't seem to matter anymore now that we are using atomic models with fine structure included. Although we were able to justify the density-dependent line ratios and ionization fractions by invoking a legitimate breakdown of coronal equilibrium in the SSX density regime, it appears that previous results were instead simply an artifact of our accidentally using atomic models that weren't detailed enough. This is good news not only because it simplifies my research problem, but also because it provides solid evidence that we actually set up the atomic models the way we meant to this time.

I've posted the new temperature profiles. Another problem/mystery that the new simulations have solved concerns the magnitudes of the temperatures derived from the August data. Previously I had found temperatures rising to as high as 80 eV during counter-helicity shots. While we can't rule this out entirely given the uncertainty that remains in various aspects of the calculation, temperatures that high seemed unlikely given evidence from previous studies at SSX, my SXR measurements, and temperatures observed at other spheromaks.

I did some more writing last night, and today I finished the "experimental" chapter of my thesis. Like all the previous thesis updates, it can be found on my files page. Amazingly, I've made it to October break without falling behind on my writing schedule (well, I fell behind, but I caught back up). Maybe I should try actually working on applying to grad school.

I also talked to David today about resuming work on our PrismSPECT simulations. He's running some simple simulations to try to figure out whether our atomic models are right (i.e. are we actually using the most detailed calculations possible, and does it make a difference?), and I'm going to modify my VUV line ratio temperature fitting code to find best-fit models in a 2D parameter space where both temperature and density can vary.

I apologize for the last of journal entries recently--I'm now officially switched over to my new, faster computer in Eric's lab, so I will be able to resume updating my site as usual. Last week I finished up my poster, which took a bit longer than I had hoped, but I was happy with the end product and the Sigma Xi poster session went well. The final version has been posted, and a hard copy can be found hanging in the hall outside the SSX lab.

I did a lot more work on my thesis this afternoon and evening. I wrote several pages about magnetic reconnection on the sun--the introductory section is now finished except for one figure that I need to create. I'll post a new version within the next couple of days.

This morning I emailed my finished summer research summary to the provost and also worked on my presentation about the ionization fraction density dependences. It's almost ready to send off to Joe MacFarlane.

I backed up all my files today, so I'm no longer gambling on the state of this creaky old computer. I also have begun working on the excitation kinematics section of my thesis.

David now believes that the density dependent ionization state fractions that we see in PrismSPECT simulations are real. Basically, the coronal equilibrium approximation (requiring that collisional ionization and spontaneous emission are the dominant atomic processes) may break down at even at densities many orders of magnitude lower than those necessary for LTE. In particular, PrismSPECT transition rate tables from my simulations show that collisional deexcitation becomes an important process at densities as low as 1e13 ions/cm^3, right about where the ionization state fractions and line ratios start to change with density.

I've added a new page of photos from the lab to my website. This will hopefully compliment the descriptions offered on other pages and give people who are less interested in the technical details of my project something cool to look at.

This morning I updated my homepage and worked on editing my research summary for the provost. I'm going to include some photos and simplify the descriptions somewhat, as David suggested. David and I ran a number of simulations with simplified atomic models in a continued effort to solve the problem of density dependent ionization fractions. We discovered that the density dependence exists even when using an atomic model with only 1 excited state (the upper level of the transition that produces the CIII 97.7 nm line), but the level fractions are constant below densities of around 1e13 ions/cm^3. On a related note, it turns out that spontaneous emission was not the cause of our difficulties. Turning it off doesn't solve the problem, it simply lowers the threshold density where the dependence kicks in, so I didn't see the effects before when I was only running simulations at densities between 5e13 and 5e15 ions/cm^3.

Doc and I also removed the lollipop from the SSX machine today, so that part of the experiment is officially done.

This morning I wrote a two page summary of my research to turn in to Swarthmore. I modified my temperature-from-line-ratios code to calculate error using formal error propogation, because Chris suggested that the method I was using before might be significantly overestimating the error. However, the difference was marginal--the uncertainty on the temperature is still around ± 15 eV.

I think I've gotten to the root of the problem with density dependent line ratios and ionization state fractions in my PrismSPECT simulations. Joe MacFarlane suggested that I try using small but non-zero atomic rate coefficient multipliers when I want to turn off certain atomic processes so that the coupling between different energy levels in a given ion isn't lost. I tried using multipliers of 1e-9 instead of 0 for processes I want to turn off, and this seemed to solve the problem I was having with the ionization/populations viewer. It seems that the density dependence of the ionization state fractions is caused by spontaneous emission--when I turned this off but kept all the other atomic processes, the dependence went away.

This morning I spent some more time processing and displaying VUV monochromator data from last week and also put together a wavelength calibration curve for the monochromator based on the observations I've made this summer. Last week, in the process of investigating the density dependence of the 97.7 nm / 155 nm line ratio in PrismSPECT simulations, I stumbled upon a setup that caused PrismSPECT to display ionization state fractions greater than one for a number of carbon ions. Today I emailed Joe MacFarlane with my workspace file and a powerpoint presentation explaining the problem.

I've finished processing the SXR data from August 1 (our second set of runs with the lollipop); the results are similar to those I reported earlier. The filter signals with UVFS and sapphire blocking the detector are less than 1.5% of the unblocked signals. The Sn filter signal is the strongest, implying that some visible and UV light is getting through, but certainly not enough to explain the unexpectedly strong Sn filter signals that we see during normal runs. I'm not confident that we ever succeeded in making the sapphire lens completely block all three filters, so, unlike last time, I calculated each average filter signal from the subset of shots in which I was most confident that the particular filter of interest was fully obscured. Using this approach, the extra Sn signal that we previously had observed when looking through sapphire as opposed to UVFS disappeared--the difference between the two average signals is now less than the uncertainty on each measurement.

This morning I processed the VUV monochromator data from yesterday's single spheromak runs. The 97.7 nm / 155 nm data looks good; there are solid signals for at least 30 shots looking at each line, and plugging the average line ratios into my temperature fitting code yields somewhat lower temperatures than I calculated for the counter-helicity merging shots from Wednesday. I'm going to hold off on posting these temperature results for a couple of days until I run a couple of more simulations--in particular, I need to make sure the line ratio density dependence problem is worked out, and I may run some simulations at higher temperatures than I have previously, since my current results indicate that the plasma temperature might exceed 60 eV at some points.

I've tabulated the results of my monochromator scans looking for oxygen and nitrogen lines. We observed average signals of 5-10 μA for the OV 63.0 nm line (these are of the same order of magnitude as the signals we observe for the CIII 97.7 nm line), and no measurable signals for the OIV 55.4 nm, OIV 79 nm, and OVI 103.5 nm lines. We were also unable to find the NIV 76.5 nm line, but there were 10+ μA signals for the NV 123.9 nm line, although these may possibly be contaminated by the nearby hydrogen Lyman α line at 121.6 nm.

Chris stopped by yesterday evening and helped us figure out where we were going wrong with the experimental setup, so we should be good to go to take some shots today. I worked on my thesis a bit more in the morning.

This afternoon we took 149 SSX shots taking VUV monochromator and SXR data. I have data from at least 10 shots from all three possible positions of the lollipop, 10 baseline monochromator shots, and 25 shots each looking at the carbon 97.7 nm and 155 nm lines for both counter-helicity merging and single spheromaks. We also looked for the OV 63.0 nm line and the NIV 76.5 nm line. Both appeared fairly weak at first glance, although we measured something when looking for the 63 nm line that was definitely distinguishable from zero. I'll post detailed results within the next couple of days after I process the data and use the carbon line ratio to calculate temperatures.

This morning we had a group meeting and made plans for what will probably be our last week of SSX runs this summer. We're planning to do another set of SXR shots, mostly to confirm the results from Friday and make sure that the sapphire lens was really blocking all four filters, and we also still need to take a large set of VUV monochromator data for the CIII 97.7 nm and CIV 155 nm lines. If we have time I'm also hoping to look for a couple of carbon and nitrogen lines. I processed the SXR data from Friday and posted the results. There were small but non-zero signals for all filters, and the tin filter had the largest response for both types of glass. However, when looking through UVFS and sapphire the average tin filter signals were only about 1.3% and 2.3%, respectively, of the unblocked values for similar shots.

We planned to take some more SXR and VUV data today, but Doc, Jason, and I couldn't figure out how to get the data acquisition software to work, and after several failed attempts to contact Chris we had to give up. Afterwards I finished up my Sweet-Parker reconnection section for my thesis.

Today we inserted the "lollipop" device (as Doc likes to call it) into SSX. It was tricky because the UVFS lense barely fit through the opening under SXR, but we pulled it off, thanks in large part to Chris's steady hands. After closing the machine up and pumping it down to vacuum pressure again, we were ready to try the experiment to see whether the SXR filters have non-zero transmission at energies below 10 eV. Preliminary results suggest that there was essentially no signal through any of the filters using the UVFS lens (low wavelength transmission cutoff of ~170 nm), but the tin and zirconium filters both showed some response when blocked by the sapphire lens (low wavelength transmission cutoff of ~150 nm). The signal strengths using the sapphire lens appeared to be at most 10% of the unblocked filter signals, so these results probably do not fully explain the anomalous signals we have been seeing from the tin filter. I'll run the data through my processing code and post more detailed results on Monday.

I also continued working on the theory section of my thesis today.

I did some more calculations using the SXR filter ratios this morning. Yesterday I ran a set of PrismSPECT simulations with a wider range of plasma temperatures (before I had only been considering temperatures up to 40 eV), so I'm using these spectra now for my best-fit T calculations. I modified my code to calculate T at 1 μs intervals throughout a shot, and I've posted a few of these results. They don't look terribly good--they're certainly not in agreement with the temperature profile I calculated using VUV line ratios, and I generally see little to convince me that they might be right. This is not entirely surprising given our concerns about the SXR filters, but it is disappointing nevertheless.

I finished my summary of Abram's thesis, and I've also began working on the reference list for my thesis in Latex.

This morning Chris, Doc, Jason, and I met and discussed our plans for the week. We're going to take a large set of VUV data, probably on Wednesday, and some of the parts have come for the device that Chris is building to insert a piece of glass in front of the SXR detector, so we may be able to try that out to. Everyone was surprised by my finding that the 97.7 nm / 155 nm line ratio depends on density in my simulations; to try to figure out what's going on, I made some plots of the ionization state fractions.

On Friday, I ran a set of steady-state simulations with C, N, and O included as impurities, and today I ran the resulting spectra through my SXR binning code. The results are posted here. Nitrogen has strong lines at low temperatures, but at temperatures above 20 eV the filter signals are almost identical to those from runs with only C and O.

Chris suggested that I run a couple of simulations to determine the density dependence of the 97 nm / 155 nm line ratio that I've been using to determine electron temperature; I posted those results today. Increasing or decreasing the ion density by a factor of 10 has a significant effect on the line ratio, but we're going to take some VUV data next week with the interferometer also running so we'll know precise densities, so I'm hoping I won't have to worry about this much.

I've posted some spectra from the simulation I did yesterday with nitrogen as an impurity. I also calculated an uncertainty range for my temperature calculation from VUV line ratios, and I made a new plot showing the uncertainties. From the plot it is apparent that we need to take more shots at each wavelength in order to lesson the effect of random variance between shots.

This morning I put the finishing touches on my powerpoint presentation and sent it to Joe McFarlane. I've been working out some kinks in code for deriving temperatures from VUV data, and I've posted results using the data from June 20. Averaging over observations from 4 shots looking at the 97.7 nm line and 4 shots looking at the 155 nm line, I find that the electron temperature is around 16-17 eV early in the shot, increases to about 25 eV during reconnection (50-60 μs), and falls back to about 15 eV by t = 90 μs.

I ran my first PrismSPECT simulation with nitrogen as an impurity. There are lots of lines in the range 10 eV < E < 100 eV, the two strongest of which appear to be NIV 76.5 nm (a doublet?) and NV 123.9 nm. Maybe we can look for these with the VUV monochromator. I'll post some spectra tomorrow, and I'm also going to run simulations with carbon, oxygen, and nitrogen together and see what the SXR filter signals look like.

Based on my results posted yesterday, David and I think that even the most complex atomic models I've been using for my simulations, with ~100 levels per ionization state, may not be detailed enough to produce accurate SXR signals, so today I've been investigating the issue more systematically. I ran steady-state, zero-width simulations with 50, 100, and 200 levels per ionization state for both carbon and oxygen and compared the results to a simulation using the most detailed models that can be made with Atomic Model Builder (the simulation took about two hours). I've concluded that 200 energy levels per state is probably sufficient, but 50 and even 100 are not. An unexpected result was that sometimes adding more energy levels led to smaller filter signals--this occured because having additional energy levels enabled electrons to take different paths to the ground state of the atoms, thereby strengthening some emission lines and weakening others.

I edited my APS-DPP abstract today, and it is about ready for submission. I also have been investigating whether or not I can calculate reasonable temperature measurements with 1 μs time resolution by average VUV monochromator data from several identical shots and then comparing it to the simulated 97.7 nm / 155 nm line strength ratio. This is looking promising--preliminary results will be posted soon.

This morning we had our weekly SSX group meeting and talked about our plans for the rest of the summer. We're going to replace one or more of the SXR filters with their supposedly identical alternates and see if the signals change, and we may also rotate the detector in order to get a better idea of how much the different lines of sight affect the signals. It looks like we're not going to have time to incorporate IDS measurements into my project this summer before Chris leaves, so I'm going to concentrate on getting meaningful results from the SXR and VUV data. After the meeting, Chris explained how to use his HeNe interferometer code, so now I can use it to precisely calculate how the density varies during SSX shots.

Last Thursday Doc, Chris, and Jason did a set of 100 single spheromak shots--today I used my IDL code to calculate average SXR signals for 30 of these shots. The ordering of the filter strengths was the same as before, so we've still got a mystery, but at least we know the unexpectedly strong tin signal wasn't caused by some crazy process occuring during reconnection.

I'm newly a member of the American Physical Society, which should allow me to submit my abstract smoothly next week, assuming my application is processed in time. The results of my PrismSPECT simulation with oxygen were interesting--I expected the total signals in the SXR filters to increase by roughly a factor of two, but it turns out that oxygen has A LOT of spectral lines, and the increase was more than two orders of magnitude. So now the sizes of our simulated SXR currents (for planar simulations) are finally in approximate agreement with the experimental results. Unfortunately, the simulation took about three hours, so I'm going to have to simplify the atomic models somewhat. Oxygen has more emission lines at energies above 50 eV than carbon does, but I'm still unhappy with the filter ratios we're seeing in SSX. David and I are meeting with Doc and Chris this afternoon to talk about this issue.

This afternoon I read and summarized a paper by G. Cunningham that describes the use of line intensity ratios and computer simulations to derive spheromak properties. I also worked on a summary of the CIII 229.7 anomaly that we have observed to send to Joe MacFarlane.

This morning I finished my summary of the Turner et al. paper and made some changes to my LaTex unit conversion document. After taking a closer look at some of the SXR data from a few weeks ago, I discovered some surprising things. For one thing, the strongest signal is not in the Al filter, as in my simulations, but in the Sn filter, implying that there must be a lot more emission at energies greater than 50 eV than I thought previously. The Zr signal is also almost as strong as the Ti signal, which I wouldn't have expected. Take a look at the filter response curves to see what I mean. These results concerned me enough that I went back into the lab and double-checked which filter signal led to each oscilloscope channel, but I'm convinced now that I had them right.

I've written a first draft of my abstact for the APS-DPP conference in the fall. I'm also running a new PrismSPECT simulation with oxygen included as well as carbon, because I now realize that I can't make a meaningful comparison between the magnitudes of the SXR filter signals calculated in my simulations and the actual currents we see unless I have most of the key impurity ions included.

Today I made some more progress on my SXR code--after talking to Chris yesterday I was able to plug in some numbers for the unit conversion between emissivity and amperes. Although my filter ratios appear to agree with the PrismSPECT spectra (I'll post some evidence of this on my results page Monday), I found that my currents are off by a large factor, around 10^8. Several people have checked my unit conversions, and the problem appears to be with the original emissivity numbers that are coming from PrismSPECT. My average values for emissivity are in the realm of 10^13, while they should be around 10^5. Interestingly, I found some PrismSPECT spectra in Victoria's thesis that have emissivity values approximately in this range. So far I'm not sure what's going on, but I ran a couple of simulations with planar geometry (as opposed to zero width, which I have been using for all my simulations up to this point) and the spectra has changed in interesting ways, so I have a feeling the problem is related to this setting in PrismSPECT and the way that the code handles the units. I wrote up a description of the unit conversion in Latex, and this has been posted.

I spent a long time today talking to David to make sure I get the conversion from emissivity to amperes in my SXR simulation spectral binning code right, and now I've got the code working and producing seemingly reasonable filter ratios. The next step is to compare the output to low resolution spectra that can be produced in the PrismSPECT spectral viewer to make sure that the results I'm getting really match the simulation spectra. Then I can work on writing a program to choose the model that best fits the data from a set of PrismSPECT simulations.

I also ran several new time-dependent PrismSPECT simulations today in an effort to determine how the time taken to reach equilibrium scales with the density of the plasma. From my collision time calculation, I would expect the equilibrization time to be inversely proportional to the density, and the simulations appear to agree with this prediction. I'll post results tomorrow. An additional ramification of these simulations is that the ionization of carbon (and probably other impurities as well) in the plasma is driven by the ionization of hydrogen, so that as long as the hydrogen in the plasma is mostly neutral, almost all of the carbon is in the CI state. This is the case because most of the free electrons in the plasma come from hydrogen, so runaway ionization only occurs when the hydrogen ionization fraction crosses a certain threshold.

I've finished processing the VUV monochromator data from Tuesday, and I've calculated line ratios three different ways (using the peak signal at each wavelength and using the average signal over the time period between 40 and 60 μs at each wavelength for both shots in which we used a current amplifier and shots that we did not). Some of these results have been posted. The ratio of the 229.7 nm line to the 155 nm line was about 1/15, and the ratio of the 97.7 nm line to the 155 nm line was about 1/25, so still not terribly good agreement with my PrismSPECT simulations at 15 eV. I'm going to try some time dependent simulations at other temperatures, but based on the steady-state simulations I ran earlier, I don't expect the simulated ratios will approach the experimentally measured ratios until the plasma temperature becomes quite cold.

Doc, Chris, and Jason ran more SSX shots today--they cleaned the guns with helium plasma beforehand, and the result was that the spectral lines were very bright, particularly the CIII 229.7 nm line, despite the fact that the plasma was less dense than before.

This morning I finished reading and summarizing the paper on dynamos by Blackman and Ji. Then I talked to Doc about getting started on my SXR code. The first step was calculating the filter response functions using data from the Lawrence Berkeley National Lab Center for X-Ray Optics. I'll also need the response functions of the photodiodes for my calculations.

I spent the rest of the day in the lab doing my first real experiments! After we got everything working properly we did 40 SSX shots while taking data with the VUV monochromator and the soft x-ray detector. We used the monochromator to look at the CIII 97.7 nm line, the CIV 155 nm line, and the CIII 229.7 nm line. On some shots we tried using a current amplifier to get a stronger signal--this somehow led to an electrical feedback loop that distorted the data. However, we should be able to subtract out baseline data from a shot we did with the monochromator entrance slit closed in order to derive meaningful results from these runs, which can then be compared with the runs in which the photocurrent was sent straight to the oscilloscope.

This morning I tried a simulation using Doc's suggestion of letting the plasma cool from an electron temperature of 30 eV to 15 eV as it leaves the gun and expands. The results were fairly predictable--much less CIII and CIV early on than for the simulation with T = 15 eV the whole time, and by 50 μs the ionization state fractions and line strength ratios were within an order of magnitude, although not identical. The ratio of the CIII to CIV line intensities that we have been looking as was even smaller than before, which makes sense since the amount of CIII present falls more than the amount of CIV when the plasma temperature is increased from 15 eV to 30 eV.

I also tried running a simulation with CV energy levels included in the atomic model. Even though CV is by far the dominant ionization state at 15 eV, there are no strong CV lines in the spectrum between 62 nm and 310 nm. This makes sense because CV is a Helium-like ion with few possible transitions and no resonance transitions at low energies. I discovered a new feature in PrismSPECT that gives transition rates for all possible transitions between levels (it can be accessed by right-clicking on a particular electron configuration in the Ionization / Populations Viewer). This could be useful for answering Doc and Chris's questions about the time scale on which things are happening in the plasma, but I'm not sure how to interpret the table yet, or even what the units are.

Now that I've figured out that 500 time steps is ideal for my PrismSPECT runs, I'm going to look into the effect of changing the setting for the initial level populations. I ran simulations with the initial populations set at LTE levels for 1 eV and 5 eV and compared them to my previous simulations with initial populations set at LTE levels at .025 eV. The results were very encouraging--all three simulations converged after about 10 μs, so it appears that we do not need to worry about getting the initial level populations exactly right.

This afternoon I've been comparing the results of time-independent and time-dependent simulations with the same equilibrium plasma temperature and density. They are surprisingly similar, which worries me a bit. When matching line intensity ratios from my steady-state simulation a few weeks ago to experimental data gave a plasma temperature under 5 eV (far lower than Doc and Chris would expect), our explanation was that probably the steady-state simulation wasn't accurately representing what goes on in SSX. However, so far it appears that changing to a time-dependent simulation doesn't make that much difference, although we certainly haven't included all the complexity in the variations of temperature and density that probably exist in the experiment.

Today I've been working on my investigation of the number of time steps necessary for PrismSPECT simulations to give consistent results. I'm making the changes that David suggested to my presentation, including adding plots of the CV fraction for each model, and adding spectra and ionization fraction plots at later times (50 μs). I've also decided to look at line strengths ratios as a way of quantifying how similar the results are from two different runs. The link to the presentation on my results page has been updated, and I also posted many of the plots directly on the page.

PrismSPECT has been crashing whenever I try to make a major adjustment to the y-axis scale on the spectral viewer--these adjustments are often necessary to see the spectra. I discovered today that this problem can be overcome by right-clicking on the plot and choosing graph:rescale. The "axes properties" tool can then be used to change to a log scale without crashing the program. Comparisons of two runs with 1 eV LTE starting populations, one with 4 simulation time steps and one with 101, confirms our suspicion from yesterday that changing the number of steps influences the way calculations are actually run, and not just the way the data is displayed. The two simulations converge at large times, but at 10 μs the spectra and ionization levels are significantly different.

David talked to Joe on the phone this afternoon, and he said that the "simulation time" control actually does set the time steps used for calculations. With this in mind, he suggested using a logarithmic time scale so that there are lots of time steps early on, during the transition from 0.025 to 15 eV. Following this advice seems to have solved the problems we were having with time-dependent simulations. I have compared the results of several simulations with identical input parameters but different numbers of time steps: we've decided that 500 time steps (with the first calculation at .1 ns) is enough to achieve reasonable results. I also ran a simulation with 2500 steps--this took about 30 minutes to complete and gave similar results as 500 time steps (runtime appears to scale fairly linearly with the number of timesteps). This afternoon I also created a new atomic model file so that we can study the CV line at 227 nm. Before I work on this, I'm going to compare the results at large t from our latest time-dependent simulations with the steady-state results I obtained last week.