 And I'm going to ask for your suggestions about what to do. It's not a test. You don't have to answer if you don't want to. If you don't answer, I'll do it myself, but it'll be more fun if you make suggestions. So, first, one thing we need to know is what is the X-ray source? You're a computational physicist, you've been sitting back in your office. Someone walks in your door and hands you this spectrum and says, tell me what's in this spectrum. So one of the first things you would ask is what is the X-ray source? What materials were in the X-ray source? Was it copper, krypton, tungsten? And then secondly, what spectrometer recorded that spectrum? What are the properties, the capabilities of that spectrometer? So here's the answer to those first two questions. That spectrum was recorded at a laser facility. It was the Titan laser at the Lawrence Livermore National Laboratory in California. And the target was a gallium arsenide wafer. So what does that tell you about these spectral lines? Where there are two groups of spectral lines, they look kind of similar, similar patterns. So we're looking for pattern recognition. So one group is probably gallium, the other group is arsenic. And if you have your this chart, gallium is atomic number 31, and arsenic is atomic number 33. So gallium has a lower atomic number. Those spectrum, those transitions would have lower photon energy from the lower atomic number. And arsenic, so if we had an energy scale, we could say one is gallium and the other is arsenic, but we don't have an energy scale. So here's the answer to what spectrometer? The spectrometer was a transmission crystal spectrometer and it covered 9 to 11 kilovolt energy range. And this spectrometer was high resolution, so it was called the high resolution crystal spectrometer, very original. Here's a photograph of the inside of the target chamber at the Titan laser in California. The laser beam comes in through this port into the vacuum chamber. The gallium arsenide target is here. And then here's the high resolution transmission crystal spectrometer. And the size of this chamber is about one meter or so. So now we know the spectral lines are from gallium and arsenic and the energy range is 9 to 11 kilovolts. And it turns out energy increases to the right. So now we can say these are lines from gallium and these are lines from arsenic. Fairly close in atomic numbers, so these are probably the same type of transitions, but just from the two different elements and shifted in energy. Okay, now we need an energy scale. So how do we establish the energy scale? Remember, the first thing you do is you look for the spectral lines you know. So what spectral lines did we talk about during the first hour? We talked about the helium-like resonance lines, the lithium-like satellites, and the characteristic X-ray lines from the neutral or singly ionized atoms. So let's look for those. The helium-like, lithium-like transitions are higher energy than the transitions from the neutrals. So if energy goes from left to right increasing, these are from the high energy charge states, probably lithium-like, helium-like on this side of the distribution. And then the characteristic X-ray lines will be on the lower side of the distribution. So let's make a guess. Let's guess that the lower strong transitions are the characteristic X-ray lines from gallium, and the K-alpha 1 and K-alpha 2 should have a ratio of 2 to 1. So that looks pretty good. And then over here, maybe these two are the same transitions in arsenic. So we have the K lines in gallium. Let's look for the K-batas. So there are probably the K-batas of 1 and 2, which also should have a relative line ratio of roughly 1 to 2. So here's what we are guessing so far, but we still don't have an energy scale. So let's use the very well-known, accurately known transition energies of the characteristic transitions to establish the energy scale. So we're going to use these two K lines from gallium, gallium K-batas, and the arsenic K-alphas, and let's calculate the energy scale. So now we have what we think is a good energy scale. And it does go from roughly 9 to 11 kilovolts, like we were told. So now that we know the K-alpha lines and what we think are the lithium and helium-like lines, we know these transition energies, so that's probably good. What are the other features? So if we know these are neutral or singly ionized, and if we know these are two electron ions, three electron ions, let's just count. Four electron, five, six, seven, eight, nine, ten. So perhaps these features are from the lithium-like to the neon-like charge states, and similarly in arsenic. But what's the difference between the gallium spectral line distribution and the arsenic? What do you notice? Something is missing from the arsenic. So the arsenic is a higher Z element. It's somewhat less ionized because it's higher Z. So the helium-like and the lithium-like lines appear to be missing from the arsenic spectrum, and that's what you would kind of expect. So things are looking good so far. To go further, we have to simulate a spectrum. We have to use a code to simulate the spectrum because we think we know what the charge states are, so we're ready to simulate the spectrum. And then we can check and see if these line identifications are correct or not. So there are many codes. There's the Cowan code. There's the FlightCheck and GrantGrasp code, Q-Lack back. Lots of codes. Me being an experimentalist, I'm going to look for the easiest to use code. So it turns out that Cowan code and FlightCheck are quite accessible on websites, easy to use, even an experimentalist can use these codes. So let's just look at the GF values from the Cowan code website. So these sticks represent the GF values, which gives an indication of the relative line, spectral line intensities. And so here are the GF values convolved with a 10-EV Gaussian to kind of simulate the experimental spectrometer resolution for the gallium-like transitions. And here's the experimental spectrum. So with this 10-EV shift, you can kind of see the matching starting to emerge. And here are the gallium-brillian-like transitions and the arsenic-carbon-like transitions. So it looks like the assignments of all of those spectral features, it looks good. So now that we are confident of the line identifications, let's really use another code to simulate the spectral line intensities using a kinetics code, and let's see if we can determine the temperature and density of the plasma region. So what code should be, what kinetics code should be used? One that's easy to use, accessible, and that would be the fly check code. Well, first of all, if we're going to calculate a spectrum, we need to start out with a temperature and a density. We have to plug that into the code. So what temperature and density should we use? We have to have a guess to start out with. Earlier in the week, it was mentioned a couple of times that the most abundant charge state in a thermal plasma has ionization potential from that most abundant charge state. Ionization potential is roughly three times the temperature or five times the temperature. So here's a plot of the ionization potentials versus charge state of the various ions in gallium and arsenic. So when you start out with the neutral, it's got a small ionization potential. As you ionize up, you come to the neon-like closed shell, very tightly bound closed shell. So there's a jump in the ionization potential at that neon-like tin electron ion. And then you continue ionizing, and now you get to the helium-like closed shell. So from the lithium-like weakly bound charge state to the helium-like tightly bound charge state, there's a big jump in ionization potential. And here are the ionization potentials on a log scale in kilovolts. So if our temperature is about a factor of three less than the ionization potential, and we know that we have ions between neon and lithium and also some weak abundance of helium-like, let's pick an ionization potential, let's say six. That's kind of in this range of ionization. Let's divide it by three and we get two kilovolts. So that's a reasonable electron temperature to plug into the code. Now the density is a little bit more difficult, but we start out with a solid gallium arsenide target. So solid densities, 10 to the 23, 24, whatever. But we know that plasma expands as it blows off from that solid surface. So the density is going to be some orders of magnitude below solid density. If it expands, you know, a factor of 10 to 100, it's going to go down by several orders of magnitude at least. So let's pick a density of 10 to the 19. So now we run a flight check simulations for a fixed electron density because we have confidence that that's in the ballpark. We have less confidence in the density. We have confidence in the temperature. So we'll fix the temperature at two kilovolts, which we think is correct, and we'll vary the density. So here are the ion abundances for a fixed two kilovolt temperature and a variable density where we vary the density from five times 10 to the 18, which is these curves, this curve, and one times 10 to the 19 is very close. And then there's a shift in ionization when we go up in density to five times 10 to the 19. So you see the density dependence is weak until you get over, up to say, five times 10 to the 19. Certainly above one 10 to the 19, below the density dependence is weak. When you go higher, it becomes stronger. So here are the calculate, this is the calculated spectrum for five times 10 to the 19, one 19, five 18. So take a look at this spectral distribution and if you recall the experimental spectrum, let's see how they match up. Do you recall the largest, the most intense charge state for gallium is carbon-like? So let's see which density gives us the most intense carbon-like. And also notice also that the lithium-like, helium-like are weaker and neon-like is weak, fluorine, oxygen-like are stronger. So just kind of keep that pattern in mind and let's see which density is best. So here's the carbon-like and one 19, five 18, carbon-like is strongest. Higher density, the higher charge state becomes comparable to carbon so it's probably going to be somewhere in this density range. But when you go to lower density, the lower charge states come up and they're a little bit too strong here. And also you'll see a subtle change in the lithium-like transitions. If you recall from earlier in the week, the lithium-like satellite transitions, those are sensitive to both temperature and density. So there's a very subtle change here, I don't know if you could notice it, but this ratio of the helium-like Y transition to the lithium-like Q transition, see there's a subtle change there. It's kind of flat here, slightly skewed and then cannot really resolve the two there. So this is what the spectrum actually looks like. So let's pick one times 10 to the 19 and vary the temperature. So we're fixing the density at 119 and we're varying the temperature from 1.5 kilovolts, 2 kilovolts, 2.5 kilovolts. Now there's a huge change in the ion, the abundances of the ions in the plasma. There's a very large change with temperature so this is very sensitive to temperature. It was rather insensitive to density but it's very sensitive to temperature so we should be able to determine the plasma temperature accurately and the plasma density somewhat less accurately. So which one looks most similar to the data? Well, it's this one where the carbon emission is highest. When you go to a lower temperature, the lower charge states, neon-like, fluorine-like are way too strong compared to the higher charge states, much too intense. When you go to higher temperature then the lower charge states are way too intense. So it looks like around 2 kilovolts is a good guess for the plasma temperature, a good guess so far. Also you see the satellite line ratios are changing drastically, in particular the y to q ratio. So now we know that a ballpark guess for the temperature is 2 kilovolts and a guess for the density is 1 times 10 to the 19. But there are these subtle changes in the lithium-like satellite so we need to really do some more detailed calculations for those lithium-like satellite transitions. So here's the experimental spectrum and once again these are the Kallin code GF values for these letter designations which were in that previous table. I would like for you to remember the M and T satellite transitions. So fix this in your memory, M and T. To proceed we need to think about the hotter electron component. In laser produced plasmas the laser intensity is very high. We can have a thermal distribution like we've found is about 2 kilovolt temperature but laser radiation is very intense. Electrons can be accelerated during the time of the laser pulse to much higher energy than 2 kilovolts. In some cases it can be 100 kilovolts or 500 kilovolts if the laser is extremely intense. So we need to think about the possibility of a super thermal hot electron component much higher energy than the 2 kilovolt thermal plasma. We know that's present because we see the characteristic gallium and arsenic characteristic X-ray lines that are in the spectrum. The energy to produce those lines to produce a 1s vacancy that is as high as almost 12 kilovolts. So we have to have an abundance of at least 12 kilovolt electrons to produce those characteristic X-ray lines. Moreover, in the plasma we think the temperature is about 2 kilovolts in the plasma so those neutrals and singly ionized ions that produce the characteristic X-ray lines they should not be present in this 2 kilovolt plasma because we know from the ionization potentials those neutrals low ionization stages they have very low ionization potential. So the ionization at 2 kilovolt should be very rapid so there should be practically no abundance of the very low charge states which produce the characteristic X-ray lines. But we see them in the spectrum. So how can this happen? So if this is our gallium arsenide wafer and this will be millimeters in size and the laser is focused to about 100 microns or .1 millimeter so this is very hot plasma which is blowing off from the board and this is a intense laser so the plasma is about 2 kilovolts but yet we think there are much higher energy electrons present somewhere so high energy electrons are accelerated during the laser pulse to very high energy and those high energy electrons propagate out from the focal spot so high energy electrons propagate to this cold gallium arsenide material which surrounds the hot plasma so the characteristic X-rays are coming from the neutrals in the surrounding gallium arsenide wafer they're not present in the hot plasma they're coming from the colder material outside the focal spot and it turns out to propagate some distance from the focal spot through this solid density material the electron energy has to be at least tens of kilovolts to have that range in the solid gallium arsenide material so from previous studies and this has been studied quite a bit there's a rule of thumb formula where the super thermal electron energy called t-hot is given by this formula it's proportional to i lambda squared i lambda squared is proportional to the so-called quiver energy that oscillatory energy that the electron has in that strong laser field that's called the quiver energy and if that oscillating electron collides with a nucleus then it will fly off with that quiver energy so that's how the fast electrons fly off and propagate outside the focal spot i lambda squared is a quantity you'll see quite often where i has real units of watts per centimeter squared that should be not one third but I think ten to the seventeen watts per centimeter squared the laser wavelength of the Titan laser at Livermore is one micron wavelength so if you plug those numbers into this equation with this correction you'll get 30 kilovolts which is high enough for the electrons to propagate through the solid material outside the focal spot so now we know there's a 30 kilovolt hot electron component and we have to include that in the flight check code simulations but we don't know how many electrons have 30 kilovolts most will have 2 kilovolts and some small percentage of that electron population will have been accelerated, will have scattered outside the focal spot but that fraction of hot electrons is an unknown so now you not only vary temperature and density but you also vary the hot electron fraction so we have kind of three unknowns so we calculate spectra over that phase space of three unknowns and calculate the correlation between the experimental spectrum and each of those calculated spectra and then you can plot on a two-dimensional plot of temperature and density with different fractions of hot electrons this plot, a correlation plot happens to be for 2% of the total electron population 2% having 30 kilovolt energy and the highest correlation is 1100 EV temperature quite narrow in temperature so we can say it's about plus or minus maybe 5% and then it's a little bit broader in density but it's about 3 times 10 to the 19 plus or minus say 50% and then varying the fraction of hot electrons it's about 2.5% plus or minus some small fraction so now we can do fly check calculations with the 1100 EV temperature and the 3 times 10 to the 19 density the 2.5% abundance of 30 kilovolt electrons so we can calculate a more accurate fly check spectrum which is shown here these are the line intensities and this is the experimental spectrum and I've convolved the calculated intensities I've convolved with a profile that simulates the spectral resolution so I've convolved each of these line intensities with a Voight profile Voight profile is a combination of a Gaussian and a Lorentzian convolution and the Gaussian component has a full width half maximum corresponding to the thermal Doppler broadening the 1100 EV broadening but Doppler width is related to the ion temperature not the electron temperature so we know the electron temperature is 1.1 kilovolt and the ion temperature is the same because the equilibration time in this rather dense plasma is about a picosecond so that's fast electron ion equilibration during the longer laser pulse which was several nanoseconds much longer so during that several nanosecond laser pulse the electrons and ions are being heated but they tend to have the same temperature because of the fast equilibration time we add in some detector broadening and we've measured the spatial resolution of our detector in the laboratory as part of our calibration process so we know how much detector broadening to add in to our line profile and it turns out that the detector broadening spatial resolution profile fits a Voight profile very accurately so it has a Gaussian component and a Lorentzian component so we add in the Gaussian component detector broadening and then the crystal broadening intrinsic spectrometer crystal broadening we've also measured in the laboratory and if I have time I'll talk about how we do that later Lorentzian we have the natural lifetime broadening lifetime of the level gives some broadening and energy for these transitions we know what the radio decay rate A is the Einstein coefficient A from that we can calculate the energy broadening so we know that and then we convolve in the detector Lorentzian broadening make a Voight profile and that's our simulated spectrum and keep in mind that this energy scale is determined by the characteristic transitions in gallium and arsenic the characteristic transition energies from the colder region outside the focal spot but our spectrometer has no sensitivity to the position of the X-ray emission in the source it has no sensitivity because our detectors on the rolling circle where the lines are focused regardless of where they come from spatially in the target so this should be a good energy scale as experimentalists we're going to say this is a good energy scale, no question but we have to keep in mind that it comes from the characteristic X-ray lines outside the focal spot so those atoms are fixed in space they should have no Doppler broadening they should have no bulk motion Doppler broadening, they're fixed so this is our energy scale well what do you notice here there's something, there's a mismatch between the calculated spectrum and the experimental spectrum well if that's the helium like resonance line W in gallium and this is the calculated helium like resonance line W there appears to be a shift of about 10EV so the experimental spectrum is shifted by about 10EV to the higher energy which is shorter wavelength shifted to blue so a Doppler blue shift can occur when the radiation source is traveling toward the observer that gives a blue shift so we suspect that this 10EV blue shift is due to the plasma blowing off from that focal spot and traveling somewhat toward the spectrometer and that gives our blue shift well it's 10EV, let's just shift the experimental spectrum by 10EV and this is reasonable because the energy scale is from these fixed gallium arsenide atoms but the spectral lines here are from the hot plasma that's traveling toward the observer so the energy scale is from the fixed atoms and the hot plasma which produces these spectral lines are traveling toward us so there should be a Doppler shift and it looks like it's about 10EV so let's think about what we're going to do next we think we understand our experimental energy scale that can't be wrong because we did it, it's got to be right so could the transition energies in fly check be inaccurate? we always suspect the computations because the experiment is always right so let's look at the transition energies of this helium like gallium resonance line W it's a 2 electron atom, these transition energies can be accurately calculated so the grant code calculation dating back to 1980 for this transition is 9628EV in 2005 the calculation was improved one more significant figure was added so it's 9628.2EV this transition has been measured I think some of the best measurements so from Afimoglitsky from 1984 from a low inductance vacuum spark which is sort of like that pulse power machine it's a very energetic high voltage high current things blowing up and flowing so in 84 he measured 9631 but with large error bars plus or minus 7.5EV because I think you worry about the Doppler shift due to plasma traveling with respect to the spectrometer so in 88 he corrected for the plasma motion 9627.5 plus or minus 0.7 which overlaps with the most accurate calculation and the fly check transition energy is 9628.4 so that's good so the fly check transition energy is very accurate so this indicates that the 10EV blue shift is real and it's due to this plasma flowing and we understand the origin of the 10EV blue shift because we're once again our energy scale in the beginning was from the fixed gallium arsenide atoms and the hot spectral lines are from the flowing plasma so that gives the 10EV shift it all makes sense and if you calculate the flow velocity it's 3 times 10 to the 7 3 times 10 to the 7 is a generic plasma flow velocity it comes from the hydrodynamic simulations of hot flowing plasma so if you had to guess what the expansion velocity would be you would say 3 times 10 to the 7 and in fact that's what we observe so this is all making sense so now we shifted the experimental spectrum to match the fly check spectrum to correct for that plasma flow velocity so now what do you notice? well there's this T-satellite transition there's this bump in the calculated spectrum that does not occur in the experimental spectrum and also the M-satellite calculated is weaker than observed but if you remember what I asked you to keep in mind the T-satellite should be 0.7EV higher energy than the M-satellite so I think it's fair to just move let's just move this T-satellite transition energy to where it appears in the Cowan code and let's see what we get so now this satellite feature agrees pretty well with the experimental data but look there's still this discrepancy here and this feature is the helium like X-transition and it appears to be about a factor of 2 weaker in the calculation than we observe and I suspect this line intensity is kind of hard to calculate maybe so let's just multiply that calculated energy let's just multiply by a factor of 2 and now we have a very good agreement see? okay let's go back okay we move the T-satellite increase X by 2 hey we got good agreement we have good agreement with a few adjustments and that last one is suspect you know because we're just multiplying by a factor of 2 sometimes we multiply by a factor of pi you know for no good reason or a factor of 2 so now I think we've made some new discoveries here about the comparison between the experimental spectrum and the simulated spectrum that should be pursued and it hasn't yet been pursued so I can't really say any more about that so now Yuri Rochenko used his code NOMAD to do very detailed calculations of the down here or the calculated this is experimental very detailed calculations of the features from the lower charge states lithium like, helium like, plane intensities are fairly easy to calculate but when you go to the lower charge states from the Kowanko GF values you saw there are many many lines dozens or hundreds of spectral lines much more difficult to calculate and Yuri has calculated these spectra different thermal temperatures and different hot electron components so we're kind of in the process of matching up those calculations to the experimental spectrum okay could you let me know when the time is up because I don't remember when we started six more minutes, okay so now we understand the spectrum this spectrometer has a very high spectral resolution so we can now study the line shapes of these experimental features the line shapes to do that we need to measure very well the instrumental broadening of our spectrometer so we need to measure that in the lab to do that we use a laboratory tungsten spectrum and we very accurately measure the width of one of these spectral lines or several spectral lines there are also some other features like these very narrow dips in the diffraction which is, we understand where those come from so let's pick a line that's isolated and not blended with weaker L transitions so it's not going to be L alpha 1 that's very strong which is nice but it's blended with L alpha 2 this line is isolated but it's kind of weak L beta 1 is very strong but blended L beta 3 is isolated and unblended blended weaker so we pick L beta 3 isolated, unblended and we measure the width of that line so the squares or the data and the solid line between the squares is our fitted Voight profile this is the residual differences so we measure the Lorentzian component of the Voight is 12.8 plus or minus some small value Gaussian is 4.82 so that's the width of the overall broadening contributions to the Lorentzian and the Gaussian components fitted to the experimental spectral line we know that the Lorentzian component has a contribution from the natural lifetime broadening which we know from this reference 12.8 plus or minus rather large uncertainty 1.4 EV detector Lorentzian is smaller the result if we subtract these two from the measured Lorentzian line width is minus 0.8 plus or minus 1.4 so let's call that 0 within the experimental uncertainties let's call that 0 the Gaussian component has a contribution from the Gaussian detector full width half max all of these values are full width half max and a resultant Gaussian width after subtracting in quadrature because this is a Gaussian we're left with 4.75 EV and that represents the intrinsic crystal broadening so we've subtracted out all the contributions and we're left with the intrinsic crystal broadening so this is the intrinsic resolution of our spectrometer we measure the width of the gallium K-alpha 2 line in the spectrum and we get something similar after subtracting out all the contributions we know that's from a fixed atom so there's no Doppler broadening so that's an accurate measurement so now let's measure the width of a spectral line from highly charged ions and let's just pick the lithium like gallium MT where the two satellite lines are very close in energy only 0.7 EV apart and the helium like X transition so here are the measurements and the components for the Lorentzian widths and the Gaussian widths of those two spectral lines so if you take a look here we measure in MT we measure Lorentzian full width half max of 0.41 EV but look X is 0.01 EV practically 0, much smaller and that's because the natural width of the X line which is very is small and the natural width of the satellite line which is a very fast large A value has a much larger natural lifetime Lorentz broadening so we subtract these out within the experiment measurements we get 0 and then Gaussian subtract out all the components the crystal intrinsic broadening which we've measured detector spatial resolution the thermal ion Doppler width and the result is 1.6 EV in one case and 2.55 EV in another case so we're left with some some broadening some Gaussian broadening so it's probably some kind of Doppler broadening of a couple of EV what can that be do to well we think that's due to the spreading turbulent spreading of that streaming velocity so it's streaming at 3.7 3 times 10 to the 7th centimeters per second but there's some turbulence in that plasma as it flows toward us in that turbulence velocity would be say 5 times 10 to the 6 or 8 times 10 to the 6 which is smaller than 3 times 10 to the 7 so it's flowing toward us fast 3 times 10 to the 7 within that there's some turbulence which causes plasma flow bulk motion flowing with some Doppler motion superimposed on that and it's about 5 or 8 times 10 to the 6 I think I'm about finished in time but if I can use one or two more minutes the spectrometer we've been using has about 2,000 resolving power it's about 4 or 5 EV intrinsic crystal broadening that's a 10 kilovolts that ratio is about 2,000 we have now developed a spectrometer in the laboratory with 20,000 resolving power so it's 10 times higher so now we can measure line shapes almost 10 times better but we haven't done the experiment yet we have tested this spectrometer in the lab by measuring the copper K alpha 1 and 2 lines from a laboratory copper X-ray source these are the 2P to 1S single hole transitions but we see these wings on the low energy side and this has been observed before at a synchrotron using days or weeks of taking data we did this in about 5 minutes and these features are double hole transitions so double hole 2P 3D decaying via a 2P to 1S transition with the 3D spectator hole so 3D is high line so the lines are closely blended with the parent single hole transitions if you plot this on a log scale there's this bump and this bump is due to a double hole transition where the spectator is a 2P electron so lower line larger energy shift from the parent line and this has also been observed in synchrotron measurements so this is a double hole transition with the 2P electron that should look very familiar to you because in helium like die electronic satellites to the hydrogen like resonance line most of those satellites are from 2P squared levels and then the satellites with an equal 3 spectator electron are closer to the resonance line just like this correspondence between the transitions in hot plasma from doubly excited levels to transitions in neutrals with 2 holes physics is beautiful thank you