WEBVTT 00:00:00.000 --> 00:00:10.510 align:middle line:84% [SQUEAKING] [RUSTLING] [CLICKING] 00:00:10.510 --> 00:00:14.800 align:middle line:84% JACK HARE: All right, so welcome back, been a bit of a break. 00:00:14.800 --> 00:00:16.845 align:middle line:84% You may be-- yes, exactly, why are we here? 00:00:16.845 --> 00:00:18.220 align:middle line:84% What are we doing with our lives? 00:00:18.220 --> 00:00:19.887 align:middle line:84% We're learning about plasma diagnostics. 00:00:19.887 --> 00:00:22.330 align:middle line:84% And you may remember, before we went away, 00:00:22.330 --> 00:00:24.040 align:middle line:84% we spent a very enjoyable lecture 00:00:24.040 --> 00:00:27.190 align:middle line:84% drawing all sorts of diagrams, like this, where 00:00:27.190 --> 00:00:29.440 align:middle line:90% we had some energy levels here. 00:00:29.440 --> 00:00:32.270 align:middle line:84% Maybe this is a ionization energy level. 00:00:32.270 --> 00:00:34.720 align:middle line:84% This is maybe some lower energy level. 00:00:34.720 --> 00:00:36.670 align:middle line:90% And something happened. 00:00:36.670 --> 00:00:38.860 align:middle line:90% Photons were flying around. 00:00:38.860 --> 00:00:40.495 align:middle line:90% Electrons were flying around. 00:00:40.495 --> 00:00:43.480 align:middle line:90% 00:00:43.480 --> 00:00:46.930 align:middle line:84% And we said that if we want to understand what the ionization 00:00:46.930 --> 00:00:50.260 align:middle line:84% state is in our plasma and also the excitation state, which 00:00:50.260 --> 00:00:53.840 align:middle line:84% would be if you have some intermediate level here, 00:00:53.840 --> 00:00:55.600 align:middle line:84% which I guess I've already used I. 00:00:55.600 --> 00:00:58.510 align:middle line:84% So I'll have to come up with some other notation for it, N, 00:00:58.510 --> 00:00:59.440 align:middle line:90% like that. 00:00:59.440 --> 00:01:02.380 align:middle line:84% Maybe we want to know how many electrons 00:01:02.380 --> 00:01:05.750 align:middle line:84% are in this intermediate level, in the lower level, 00:01:05.750 --> 00:01:06.620 align:middle line:90% in the upper level. 00:01:06.620 --> 00:01:08.578 align:middle line:84% Because at the end of the day, in spectroscopy, 00:01:08.578 --> 00:01:11.130 align:middle line:84% what we're detecting is photons, which are being emitted. 00:01:11.130 --> 00:01:14.060 align:middle line:84% And the photons are being emitted when the electron drops 00:01:14.060 --> 00:01:17.810 align:middle line:84% down either from being a free electron into a bound state 00:01:17.810 --> 00:01:19.678 align:middle line:90% or between two bound states. 00:01:19.678 --> 00:01:21.470 align:middle line:84% And we went through all of these processes. 00:01:21.470 --> 00:01:23.930 align:middle line:84% And we said, if we really want to understand the plasma, 00:01:23.930 --> 00:01:25.970 align:middle line:84% we need to model all of these processes. 00:01:25.970 --> 00:01:27.900 align:middle line:84% And obviously, that's an awful lot. 00:01:27.900 --> 00:01:29.390 align:middle line:84% So today, I'm going to go through. 00:01:29.390 --> 00:01:31.910 align:middle line:84% And I'm going to present some simplified 00:01:31.910 --> 00:01:34.130 align:middle line:84% equilibria in which we do not need to include 00:01:34.130 --> 00:01:35.203 align:middle line:90% all of these processes. 00:01:35.203 --> 00:01:36.620 align:middle line:84% And these are the equilibria which 00:01:36.620 --> 00:01:38.453 align:middle line:84% we tend to have a better chance of modeling. 00:01:38.453 --> 00:01:41.240 align:middle line:84% Anyone remember what this process was called here? 00:01:41.240 --> 00:01:45.770 align:middle line:84% This is my personal favorite, when 00:01:45.770 --> 00:01:50.960 align:middle line:84% you have two electrons in an excited state, and one of them 00:01:50.960 --> 00:01:53.060 align:middle line:84% drops down, and that provides enough energy 00:01:53.060 --> 00:01:54.850 align:middle line:84% for the other electrons to ionize itself. 00:01:54.850 --> 00:01:55.850 align:middle line:90% STUDENT: Autoionization. 00:01:55.850 --> 00:01:59.960 align:middle line:84% JACK HARE: Autoionization, yes, absolute favorite. 00:01:59.960 --> 00:02:00.515 align:middle line:90% That's crazy. 00:02:00.515 --> 00:02:06.470 align:middle line:90% 00:02:06.470 --> 00:02:08.460 align:middle line:90% OK, good stuff. 00:02:08.460 --> 00:02:11.840 align:middle line:84% So now, let's go through some equilibria most of which 00:02:11.840 --> 00:02:13.640 align:middle line:90% do not involve autoionization. 00:02:13.640 --> 00:02:16.500 align:middle line:90% 00:02:16.500 --> 00:02:18.780 align:middle line:84% And the reference for all of this-- 00:02:18.780 --> 00:02:22.230 align:middle line:84% there are many textbooks on plasma spectroscopy. 00:02:22.230 --> 00:02:25.140 align:middle line:90% A very famous textbook is Griem. 00:02:25.140 --> 00:02:26.940 align:middle line:90% That's the name of the author. 00:02:26.940 --> 00:02:29.733 align:middle line:84% And the title of the book is Plasma Spectroscopy. 00:02:29.733 --> 00:02:31.650 align:middle line:84% Griem is not actually a particularly good book 00:02:31.650 --> 00:02:32.640 align:middle line:90% for learning spectroscopy. 00:02:32.640 --> 00:02:33.882 align:middle line:90% It's a pretty good reference. 00:02:33.882 --> 00:02:35.340 align:middle line:84% But you will find all of this stuff 00:02:35.340 --> 00:02:37.020 align:middle line:84% in here, if you want to know more. 00:02:37.020 --> 00:02:39.970 align:middle line:84% Hutchinson has some of it in a slightly more fragmented 00:02:39.970 --> 00:02:40.470 align:middle line:90% fashion. 00:02:40.470 --> 00:02:43.620 align:middle line:84% So I've been taking most of this material from Griem. 00:02:43.620 --> 00:02:48.420 align:middle line:84% So the most simple equilibrium is an equilibrium 00:02:48.420 --> 00:02:51.608 align:middle line:84% where we're in complete thermodynamic equilibrium. 00:02:51.608 --> 00:02:59.430 align:middle line:90% 00:02:59.430 --> 00:03:01.620 align:middle line:84% If we're in a thermodynamic equilibrium, 00:03:01.620 --> 00:03:05.320 align:middle line:84% this implies straight away that we have a Boltzmann occupation 00:03:05.320 --> 00:03:05.820 align:middle line:90% of states. 00:03:05.820 --> 00:03:10.610 align:middle line:90% 00:03:10.610 --> 00:03:13.460 align:middle line:84% So our Boltzmann occupation of states 00:03:13.460 --> 00:03:16.710 align:middle line:84% is something like the occupation of the i-th state, 00:03:16.710 --> 00:03:18.200 align:middle line:84% whether that's an ionization state 00:03:18.200 --> 00:03:21.110 align:middle line:84% or it's an excited state within an ion, 00:03:21.110 --> 00:03:25.580 align:middle line:84% is proportional to exponential of minus 00:03:25.580 --> 00:03:28.550 align:middle line:84% the energy of that state over the temperature. 00:03:28.550 --> 00:03:31.970 align:middle line:84% And the electrons, and the ions, and the radiation all 00:03:31.970 --> 00:03:33.960 align:middle line:90% share the same temperature. 00:03:33.960 --> 00:03:42.790 align:middle line:84% So there is only one temperature for electrons, the ions, 00:03:42.790 --> 00:03:43.915 align:middle line:90% and the photons. 00:03:43.915 --> 00:03:48.040 align:middle line:90% 00:03:48.040 --> 00:03:50.350 align:middle line:84% The other thing about a thermodynamic equilibrium 00:03:50.350 --> 00:03:51.865 align:middle line:84% is that all the processes balance. 00:03:51.865 --> 00:03:55.520 align:middle line:90% 00:03:55.520 --> 00:03:58.370 align:middle line:84% So all of the up processes that excite the system 00:03:58.370 --> 00:04:00.590 align:middle line:84% are exactly balanced by their counterparts 00:04:00.590 --> 00:04:02.160 align:middle line:90% that de-excite the system. 00:04:02.160 --> 00:04:04.280 align:middle line:84% This is how we get into a steady state here. 00:04:04.280 --> 00:04:06.350 align:middle line:84% That's actually not true in other equilibria. 00:04:06.350 --> 00:04:09.230 align:middle line:84% There can be processes which excite and different processes 00:04:09.230 --> 00:04:09.913 align:middle line:90% that de-excite. 00:04:09.913 --> 00:04:12.330 align:middle line:84% As long as the rate is the same, you're in an equilibrium. 00:04:12.330 --> 00:04:14.700 align:middle line:84% And we'll talk about some of those later on. 00:04:14.700 --> 00:04:16.310 align:middle line:84% But for thermodynamic equilibrium, 00:04:16.310 --> 00:04:20.524 align:middle line:84% all processes balance with their opposite process. 00:04:20.524 --> 00:04:30.600 align:middle line:90% 00:04:30.600 --> 00:04:31.200 align:middle line:90% OK. 00:04:31.200 --> 00:04:34.470 align:middle line:84% Now, how often do we think we get a thermodynamic equilibrium 00:04:34.470 --> 00:04:37.158 align:middle line:90% in a plasma? 00:04:37.158 --> 00:04:38.589 align:middle line:90% STUDENT: [INAUDIBLE]? 00:04:38.589 --> 00:04:43.840 align:middle line:90% 00:04:43.840 --> 00:04:46.135 align:middle line:84% JACK HARE: Maybe in space, probably getting closer. 00:04:46.135 --> 00:04:47.830 align:middle line:84% I mean, a thermodynamic equilibrium 00:04:47.830 --> 00:04:52.100 align:middle line:84% is an infinite in the system, which is not changing in time. 00:04:52.100 --> 00:04:54.970 align:middle line:84% So of course, in reality, we can never realize it. 00:04:54.970 --> 00:04:56.770 align:middle line:84% The space plasma, you might get close 00:04:56.770 --> 00:04:58.790 align:middle line:90% to thermodynamic equilibrium. 00:04:58.790 --> 00:05:00.940 align:middle line:84% But this also implies that you have 00:05:00.940 --> 00:05:04.060 align:middle line:84% to have your photons in thermal equilibrium with your gas, which 00:05:04.060 --> 00:05:05.890 align:middle line:84% means that your system is optically thick. 00:05:05.890 --> 00:05:07.720 align:middle line:90% And space plasma is-- 00:05:07.720 --> 00:05:09.970 align:middle line:84% at least plasma in space, in outer space, 00:05:09.970 --> 00:05:11.830 align:middle line:90% is rarely optically thick. 00:05:11.830 --> 00:05:14.113 align:middle line:84% Maybe inside some astrophysical body, 00:05:14.113 --> 00:05:15.280 align:middle line:90% it could be optically thick. 00:05:15.280 --> 00:05:18.140 align:middle line:84% So this we don't really get very often. 00:05:18.140 --> 00:05:20.035 align:middle line:90% So this is rare. 00:05:20.035 --> 00:05:25.660 align:middle line:90% 00:05:25.660 --> 00:05:26.380 align:middle line:90% OK. 00:05:26.380 --> 00:05:36.260 align:middle line:84% Next one I want to talk about is local thermodynamic equilibrium, 00:05:36.260 --> 00:05:39.110 align:middle line:90% which I'll write as local TE. 00:05:39.110 --> 00:05:44.690 align:middle line:84% So people will often call this LTE, like this. 00:05:44.690 --> 00:05:45.380 align:middle line:90% OK. 00:05:45.380 --> 00:05:47.690 align:middle line:84% Now, in local thermodynamic equilibrium, 00:05:47.690 --> 00:05:54.620 align:middle line:84% we make the assumption that our plasma is optically thin, 00:05:54.620 --> 00:05:58.330 align:middle line:84% which means that we can ignore the processes that 00:05:58.330 --> 00:06:02.110 align:middle line:84% involve photons being absorbed and emitted in terms 00:06:02.110 --> 00:06:03.950 align:middle line:90% of changing the levels. 00:06:03.950 --> 00:06:06.610 align:middle line:90% So we have no-- 00:06:06.610 --> 00:06:08.440 align:middle line:84% I guess I'll call it radiative processes. 00:06:08.440 --> 00:06:13.500 align:middle line:90% 00:06:13.500 --> 00:06:15.240 align:middle line:84% The range of processes still occur. 00:06:15.240 --> 00:06:18.030 align:middle line:84% We can still observe the lines coming from them 00:06:18.030 --> 00:06:19.350 align:middle line:90% and do spectroscopy on them. 00:06:19.350 --> 00:06:21.390 align:middle line:84% But they don't dominate the balance 00:06:21.390 --> 00:06:25.560 align:middle line:84% of what determines what states are excited and what are not. 00:06:25.560 --> 00:06:28.440 align:middle line:84% In fact, that balance is then obviously dominated 00:06:28.440 --> 00:06:29.890 align:middle line:90% by the non-radiative processes. 00:06:29.890 --> 00:06:32.190 align:middle line:84% So these are collisional processes. 00:06:32.190 --> 00:06:41.400 align:middle line:90% 00:06:41.400 --> 00:06:43.240 align:middle line:84% The collisional proceses dominate is. 00:06:43.240 --> 00:06:47.850 align:middle line:90% 00:06:47.850 --> 00:06:50.130 align:middle line:84% So this is collisional processes which 00:06:50.130 --> 00:06:53.240 align:middle line:84% excite from a lower state to an upper state, 00:06:53.240 --> 00:06:55.140 align:middle line:84% but also collisional processes which 00:06:55.140 --> 00:06:57.690 align:middle line:84% de-excite from the upper state back down to the lower state. 00:06:57.690 --> 00:06:59.648 align:middle line:84% So our occupation of the upper and lower states 00:06:59.648 --> 00:07:02.620 align:middle line:84% is set purely by these collisional processes. 00:07:02.620 --> 00:07:07.220 align:middle line:84% However, we don't need to know the cross-section 00:07:07.220 --> 00:07:11.670 align:middle line:84% for these processes, which we would do in our more 00:07:11.670 --> 00:07:12.690 align:middle line:90% detailed full model. 00:07:12.690 --> 00:07:15.090 align:middle line:84% Remember, this sigma ij is the cross-section 00:07:15.090 --> 00:07:18.060 align:middle line:84% for a process that takes us from state i to state j. 00:07:18.060 --> 00:07:24.130 align:middle line:84% But they are unimportant in LTE, due to the balance. 00:07:24.130 --> 00:07:27.580 align:middle line:84% So we keep the feature of a thermodynamic equilibrium. 00:07:27.580 --> 00:07:29.780 align:middle line:84% But the processes balance the opposite process. 00:07:29.780 --> 00:07:34.010 align:middle line:84% So the actual cross-section of the process is not important. 00:07:34.010 --> 00:07:36.655 align:middle line:84% That's what makes it a local thermodynamic equilibrium. 00:07:36.655 --> 00:07:43.090 align:middle line:90% 00:07:43.090 --> 00:07:47.220 align:middle line:84% And if you look at what this means and you 00:07:47.220 --> 00:07:52.680 align:middle line:84% work through the mathematics of your population balance, 00:07:52.680 --> 00:07:55.810 align:middle line:84% you come up with the famous Saha equilibrium. 00:07:55.810 --> 00:08:03.960 align:middle line:84% So a Saha equilibrium, named after its discoverer, 00:08:03.960 --> 00:08:06.420 align:middle line:84% has a form that says that the electron density 00:08:06.420 --> 00:08:13.080 align:middle line:84% times the ionization density for state z in its ground state 00:08:13.080 --> 00:08:18.100 align:middle line:84% over z minus 1 in its ground state-- 00:08:18.100 --> 00:08:21.480 align:middle line:84% so this is the density of atoms in ionization state 00:08:21.480 --> 00:08:25.260 align:middle line:84% z and their ground state atoms in ionization state z minus 1 00:08:25.260 --> 00:08:29.010 align:middle line:84% in their ground state times by the electron density-- 00:08:29.010 --> 00:08:34.340 align:middle line:84% is equal to, most importantly, a factor 00:08:34.340 --> 00:08:38.610 align:middle line:84% to do with the ionization potential. 00:08:38.610 --> 00:08:41.210 align:middle line:84% So this chi z here is the ionization 00:08:41.210 --> 00:08:45.620 align:middle line:90% to go from z minus 1 to z. 00:08:45.620 --> 00:08:51.510 align:middle line:90% 00:08:51.510 --> 00:08:54.870 align:middle line:84% So the change in energy there over the temperature. 00:08:54.870 --> 00:08:56.933 align:middle line:84% And then there's a few other factors out front 00:08:56.933 --> 00:08:58.350 align:middle line:84% that come from the fact that we're 00:08:58.350 --> 00:09:01.470 align:middle line:84% going to be assuming the populations are Maxwellian. 00:09:01.470 --> 00:09:09.330 align:middle line:84% There's an ion mass temperature over 2 pi h-bar squared, 00:09:09.330 --> 00:09:10.500 align:middle line:90% the 3/2. 00:09:10.500 --> 00:09:12.330 align:middle line:84% And then there's also a factor that's 00:09:12.330 --> 00:09:15.143 align:middle line:84% to do with the degeneracy of these levels. 00:09:15.143 --> 00:09:16.560 align:middle line:84% And we talked about the degeneracy 00:09:16.560 --> 00:09:19.470 align:middle line:84% as being different ways to arrange electrons and still get 00:09:19.470 --> 00:09:22.120 align:middle line:90% out the same energy. 00:09:22.120 --> 00:09:25.890 align:middle line:84% So this is gz, for the z ionization state, 00:09:25.890 --> 00:09:32.770 align:middle line:84% 1 over the degeneracy of the lower ionization state. 00:09:32.770 --> 00:09:34.570 align:middle line:84% So the Saha equilibrium doesn't tell you 00:09:34.570 --> 00:09:37.900 align:middle line:84% about how the excitation states are distributed within each ion, 00:09:37.900 --> 00:09:40.570 align:middle line:84% but it does tell you what the ionization is. 00:09:40.570 --> 00:09:43.360 align:middle line:84% And so this tells you, for a given temperature, 00:09:43.360 --> 00:09:46.930 align:middle line:84% how many particles you expect to be in each ionization state. 00:09:46.930 --> 00:09:49.275 align:middle line:84% And because of this exponential factor here, 00:09:49.275 --> 00:09:51.400 align:middle line:84% which comes from a sort of Boltzmann-like argument, 00:09:51.400 --> 00:09:53.400 align:middle line:84% we're going to end up with most of our particles 00:09:53.400 --> 00:09:57.180 align:middle line:84% still being in lower ionization states. 00:09:57.180 --> 00:09:57.930 align:middle line:90% OK. 00:09:57.930 --> 00:09:59.160 align:middle line:90% Any questions so far? 00:09:59.160 --> 00:10:00.568 align:middle line:90% Yeah? 00:10:00.568 --> 00:10:02.578 align:middle line:90% STUDENT: [INAUDIBLE]? 00:10:02.578 --> 00:10:04.120 align:middle line:84% JACK HARE: The radiation doesn't have 00:10:04.120 --> 00:10:05.935 align:middle line:84% to be the same because it's optically thin. 00:10:05.935 --> 00:10:07.060 align:middle line:90% And we don't care about it. 00:10:07.060 --> 00:10:10.292 align:middle line:84% But the ions and the electrons are the same temperature, yes. 00:10:10.292 --> 00:10:13.600 align:middle line:90% STUDENT: [INAUDIBLE]? 00:10:13.600 --> 00:10:18.160 align:middle line:84% JACK HARE: Yeah, so this notation here, this lower number 00:10:18.160 --> 00:10:24.070 align:middle line:84% here, is like if you have a series of levels within an atom, 00:10:24.070 --> 00:10:28.180 align:middle line:84% that atom has a charge of plus z. 00:10:28.180 --> 00:10:33.430 align:middle line:84% And then I've got these levels, which I could label 1, 2, 3, 4, 00:10:33.430 --> 00:10:34.730 align:middle line:90% and so on like that. 00:10:34.730 --> 00:10:37.630 align:middle line:84% This 1 refers to the energy level 00:10:37.630 --> 00:10:40.270 align:middle line:90% with an atom with charge plus z. 00:10:40.270 --> 00:10:44.570 align:middle line:84% And the z here refers to that charge. 00:10:44.570 --> 00:10:47.588 align:middle line:84% So these are atoms with different ionization states, 00:10:47.588 --> 00:10:49.630 align:middle line:84% which means, in general, their energy levels will 00:10:49.630 --> 00:10:51.010 align:middle line:90% have different energies. 00:10:51.010 --> 00:10:54.250 align:middle line:84% But here, we're taking the ratio of the atoms of ionization state 00:10:54.250 --> 00:10:57.670 align:middle line:84% z in the ground state, level 1, and the atoms of ionization 00:10:57.670 --> 00:10:58.690 align:middle line:90% state z minus 1. 00:10:58.690 --> 00:11:00.220 align:middle line:90% So they have one more electron. 00:11:00.220 --> 00:11:01.990 align:middle line:84% And they're in their ground state, 1. 00:11:01.990 --> 00:11:04.172 align:middle line:84% And the energy of that ground state 00:11:04.172 --> 00:11:06.130 align:middle line:84% will not, in general, be the same as the energy 00:11:06.130 --> 00:11:08.210 align:middle line:84% of the ion with one fewer electron 00:11:08.210 --> 00:11:10.210 align:middle line:84% because all the energy levels will shift when we 00:11:10.210 --> 00:11:11.650 align:middle line:90% reduce the number of electrons. 00:11:11.650 --> 00:11:15.610 align:middle line:90% 00:11:15.610 --> 00:11:16.587 align:middle line:90% Yeah? 00:11:16.587 --> 00:11:17.581 align:middle line:90% STUDENT: [INAUDIBLE]? 00:11:17.581 --> 00:11:24.050 align:middle line:90% 00:11:24.050 --> 00:11:24.824 align:middle line:90% JACK HARE: Yeah. 00:11:24.824 --> 00:11:26.246 align:middle line:90% STUDENT: [INAUDIBLE]? 00:11:26.246 --> 00:11:31.934 align:middle line:90% 00:11:31.934 --> 00:11:33.930 align:middle line:90% JACK HARE: Ah, yes. 00:11:33.930 --> 00:11:36.450 align:middle line:84% Yeah, but you could skip that by just 00:11:36.450 --> 00:11:39.660 align:middle line:84% taking ratios of this equation with an ionized argon. 00:11:39.660 --> 00:11:41.730 align:middle line:84% And then you get out the ionization 00:11:41.730 --> 00:11:43.240 align:middle line:84% to get the fifth ionization level. 00:11:43.240 --> 00:11:44.295 align:middle line:84% So you don't actually have to do it recursively. 00:11:44.295 --> 00:11:45.880 align:middle line:90% You can do it all in one go. 00:11:45.880 --> 00:11:47.880 align:middle line:84% You could also do it that way, if you wanted to. 00:11:47.880 --> 00:11:50.130 align:middle line:84% But yeah, in general, these ionization potentials 00:11:50.130 --> 00:11:51.000 align:middle line:90% are tabulated. 00:11:51.000 --> 00:11:53.670 align:middle line:84% They're things that people know from experiments. 00:11:53.670 --> 00:11:56.280 align:middle line:84% It's 13.6 electron volts for hydrogen. 00:11:56.280 --> 00:12:00.550 align:middle line:84% It's less for every subsequent element. 00:12:00.550 --> 00:12:02.850 align:middle line:84% And so you need to put in the temperature, of course, 00:12:02.850 --> 00:12:03.820 align:middle line:90% of your plasma. 00:12:03.820 --> 00:12:05.950 align:middle line:84% But then you can calculate this pretty quickly. 00:12:05.950 --> 00:12:07.440 align:middle line:90% So this is a nice and simple-- 00:12:07.440 --> 00:12:09.150 align:middle line:90% relatively simple equilibria. 00:12:09.150 --> 00:12:12.810 align:middle line:84% And so for example, if you're doing spectroscopy and you see 00:12:12.810 --> 00:12:17.250 align:middle line:84% a line which has an energy which corresponds to the z ionization 00:12:17.250 --> 00:12:20.445 align:middle line:84% state-- you see a line that corresponds to argon 5+, 00:12:20.445 --> 00:12:23.490 align:middle line:84% then you know you have to be at least the temperature that 00:12:23.490 --> 00:12:24.780 align:middle line:90% produces argon 5+. 00:12:24.780 --> 00:12:26.280 align:middle line:84% You can't be at a temperature where 00:12:26.280 --> 00:12:28.830 align:middle line:84% argon is completely neutral or only singly ionized. 00:12:28.830 --> 00:12:30.990 align:middle line:84% So straight away, this sort of equilibrium 00:12:30.990 --> 00:12:34.300 align:middle line:84% is like if I see that line, it must be at least this hot. 00:12:34.300 --> 00:12:37.660 align:middle line:84% And that's often good enough for spectroscopy. 00:12:37.660 --> 00:12:40.210 align:middle line:84% We'll talk about more advanced tactics for using spectroscopy 00:12:40.210 --> 00:12:41.630 align:middle line:90% later on. 00:12:41.630 --> 00:12:42.130 align:middle line:90% OK. 00:12:42.130 --> 00:12:42.815 align:middle line:90% Other questions? 00:12:42.815 --> 00:12:43.315 align:middle line:90% Any online? 00:12:43.315 --> 00:12:49.440 align:middle line:90% 00:12:49.440 --> 00:12:51.080 align:middle line:90% OK. 00:12:51.080 --> 00:12:58.086 align:middle line:84% Next equilibrium is something called corona equilibrium. 00:12:58.086 --> 00:13:05.240 align:middle line:90% 00:13:05.240 --> 00:13:07.550 align:middle line:84% Coronal equilibrium is called coronal 00:13:07.550 --> 00:13:10.580 align:middle line:84% because it was first derived in the case of the solar corona. 00:13:10.580 --> 00:13:16.070 align:middle line:90% 00:13:16.070 --> 00:13:20.180 align:middle line:84% Sometimes, this is also called a collisional radiative 00:13:20.180 --> 00:13:21.267 align:middle line:90% equilibrium. 00:13:21.267 --> 00:13:24.470 align:middle line:90% 00:13:24.470 --> 00:13:29.435 align:middle line:84% And that name, radiative, is much more descriptive. 00:13:29.435 --> 00:13:30.560 align:middle line:90% And I wish we used it more. 00:13:30.560 --> 00:13:32.268 align:middle line:84% But you'll still find most people calling 00:13:32.268 --> 00:13:34.020 align:middle line:90% it coronal equilibrium instead. 00:13:34.020 --> 00:13:37.250 align:middle line:84% So it's called a collisional radiative equilibrium 00:13:37.250 --> 00:13:42.060 align:middle line:84% because we consider the excitation going 00:13:42.060 --> 00:13:44.100 align:middle line:84% from a lower state to an upper state 00:13:44.100 --> 00:13:46.110 align:middle line:90% only collisional processes. 00:13:46.110 --> 00:13:49.880 align:middle line:90% 00:13:49.880 --> 00:13:52.490 align:middle line:84% But for any de-excitation going from an upper state 00:13:52.490 --> 00:13:54.740 align:middle line:84% back down to a lower state, we consider 00:13:54.740 --> 00:13:57.190 align:middle line:90% only radiative processes. 00:13:57.190 --> 00:14:00.950 align:middle line:90% 00:14:00.950 --> 00:14:05.540 align:middle line:84% So this is a slightly seemingly contrived setup 00:14:05.540 --> 00:14:07.610 align:middle line:84% that actually occurs a great deal of the time. 00:14:07.610 --> 00:14:10.700 align:middle line:84% It's a setup in which our system is optically thin. 00:14:10.700 --> 00:14:16.690 align:middle line:90% 00:14:16.690 --> 00:14:19.710 align:middle line:84% And so we are very unlikely to have a photon wander by 00:14:19.710 --> 00:14:22.170 align:middle line:84% and suddenly excite our system because the photons 00:14:22.170 --> 00:14:25.390 align:middle line:84% mostly just stream through the plasma without being absorbed. 00:14:25.390 --> 00:14:26.550 align:middle line:90% So this is optically thin. 00:14:26.550 --> 00:14:27.383 align:middle line:90% The, photons escape. 00:14:27.383 --> 00:14:33.340 align:middle line:90% 00:14:33.340 --> 00:14:35.320 align:middle line:84% And yet, it's also so collisionless-- 00:14:35.320 --> 00:14:37.510 align:middle line:84% the collisions happen so rarely-- 00:14:37.510 --> 00:14:39.970 align:middle line:84% that, although they are responsible for excitation, 00:14:39.970 --> 00:14:43.840 align:middle line:84% before you have chance to have a collision de-excite your system, 00:14:43.840 --> 00:14:46.670 align:middle line:84% it will spontaneously emit a photon. 00:14:46.670 --> 00:14:50.290 align:middle line:84% So it instead will have spontaneous emission taking us 00:14:50.290 --> 00:14:50.950 align:middle line:90% back down. 00:14:50.950 --> 00:15:00.870 align:middle line:90% 00:15:00.870 --> 00:15:05.275 align:middle line:84% So this works very well for low density plasmas. 00:15:05.275 --> 00:15:11.760 align:middle line:90% 00:15:11.760 --> 00:15:12.330 align:middle line:90% Yeah? 00:15:12.330 --> 00:15:13.680 align:middle line:90% STUDENT: [INAUDIBLE]? 00:15:13.680 --> 00:15:16.380 align:middle line:90% 00:15:16.380 --> 00:15:18.858 align:middle line:90% JACK HARE: Yes, exactly. 00:15:18.858 --> 00:15:21.150 align:middle line:84% But we're not dealing with any radiative processes that 00:15:21.150 --> 00:15:23.025 align:middle line:84% rely on there being a large number of photons 00:15:23.025 --> 00:15:24.180 align:middle line:90% like stimulated emission. 00:15:24.180 --> 00:15:25.630 align:middle line:90% Those will never happen. 00:15:25.630 --> 00:15:29.130 align:middle line:84% It's just imagine you've got your ion floating around. 00:15:29.130 --> 00:15:30.630 align:middle line:90% Lots of photons stream by. 00:15:30.630 --> 00:15:32.040 align:middle line:84% They will never interact with it. 00:15:32.040 --> 00:15:33.623 align:middle line:84% Occasionally, a collision will happen. 00:15:33.623 --> 00:15:34.440 align:middle line:90% It excites. 00:15:34.440 --> 00:15:36.240 align:middle line:84% And so now, it's an excited state. 00:15:36.240 --> 00:15:37.443 align:middle line:90% Then the clock is ticking. 00:15:37.443 --> 00:15:38.610 align:middle line:90% Two things could happen now. 00:15:38.610 --> 00:15:41.790 align:middle line:84% Another collision could de-excite it and nonradiatively 00:15:41.790 --> 00:15:43.050 align:middle line:90% take that energy away. 00:15:43.050 --> 00:15:45.630 align:middle line:84% Or spontaneous emission could occur. 00:15:45.630 --> 00:15:47.700 align:middle line:84% And we've chosen-- or this system 00:15:47.700 --> 00:15:50.040 align:middle line:84% works in a regime where the density is low enough. 00:15:50.040 --> 00:15:52.800 align:middle line:84% Remember, these processes, the collisional processes, 00:15:52.800 --> 00:15:55.293 align:middle line:84% all depend on density, like that. 00:15:55.293 --> 00:15:57.960 align:middle line:84% We've chosen a density which is low enough that there will never 00:15:57.960 --> 00:16:00.240 align:middle line:84% be a second collision more quickly than we 00:16:00.240 --> 00:16:01.900 align:middle line:90% have spontaneous emission here. 00:16:01.900 --> 00:16:06.120 align:middle line:84% This occurs a lot in tokamaks and other plasmas. 00:16:06.120 --> 00:16:08.020 align:middle line:84% And it's also relatively easy to solve for. 00:16:08.020 --> 00:16:12.630 align:middle line:84% So this is a very favorite model in plasma spectroscopy. 00:16:12.630 --> 00:16:13.860 align:middle line:90% OK. 00:16:13.860 --> 00:16:19.030 align:middle line:84% So if you have that, we can also write down the occupation 00:16:19.030 --> 00:16:20.830 align:middle line:90% of the excited states. 00:16:20.830 --> 00:16:23.860 align:middle line:84% So this is some upper excited state, number 00:16:23.860 --> 00:16:26.595 align:middle line:84% of atoms in that state, compared to the ground state. 00:16:26.595 --> 00:16:28.720 align:middle line:84% Everything is being driven back to the ground state 00:16:28.720 --> 00:16:29.980 align:middle line:90% by spontaneous emission. 00:16:29.980 --> 00:16:32.260 align:middle line:84% Even if it takes multiple steps, you'll eventually 00:16:32.260 --> 00:16:33.280 align:middle line:90% get the ground state. 00:16:33.280 --> 00:16:36.410 align:middle line:84% And you'll get there long before any collision occurs. 00:16:36.410 --> 00:16:39.033 align:middle line:84% So we are going to end up mostly in this ground state here. 00:16:39.033 --> 00:16:40.450 align:middle line:84% And this ratio here is going to be 00:16:40.450 --> 00:16:44.560 align:middle line:84% equal to the number of electrons doing the collisions to pump it 00:16:44.560 --> 00:16:48.160 align:middle line:84% up to an excited state times by the cross section 00:16:48.160 --> 00:16:54.370 align:middle line:84% to go from the ground state to this excited state averaged 00:16:54.370 --> 00:16:55.220 align:middle line:90% over the velocity. 00:16:55.220 --> 00:16:58.420 align:middle line:84% So that's our standard reaction rate here. 00:16:58.420 --> 00:17:04.000 align:middle line:84% And it's going to be divided by the rate at which any process 00:17:04.000 --> 00:17:09.260 align:middle line:84% takes it from the upper state down to the lower state here. 00:17:09.260 --> 00:17:12.290 align:middle line:84% And this could be by a chain of multiple processes. 00:17:12.290 --> 00:17:14.380 align:middle line:84% So for example, if this is the upper state, 00:17:14.380 --> 00:17:15.880 align:middle line:84% and there's some intermediate state, 00:17:15.880 --> 00:17:17.800 align:middle line:84% and this is the lower state, we'd 00:17:17.800 --> 00:17:20.349 align:middle line:84% have to add up the processes that go straight down 00:17:20.349 --> 00:17:24.099 align:middle line:84% and the processes that go via some intermediate. 00:17:24.099 --> 00:17:26.740 align:middle line:84% And any chain of these processes will happen more quickly 00:17:26.740 --> 00:17:27.770 align:middle line:90% than other collisions. 00:17:27.770 --> 00:17:31.537 align:middle line:84% So this is the balance between these two here. 00:17:31.537 --> 00:17:34.120 align:middle line:84% And we can write it very easily for this collisional radiative 00:17:34.120 --> 00:17:36.340 align:middle line:90% equilibrium. 00:17:36.340 --> 00:17:37.870 align:middle line:84% But the up processes are no longer 00:17:37.870 --> 00:17:39.340 align:middle line:90% balanced by the down processes. 00:17:39.340 --> 00:17:40.600 align:middle line:90% They're completely separate. 00:17:40.600 --> 00:17:43.360 align:middle line:84% That's a big break from our local thermodynamic 00:17:43.360 --> 00:17:46.170 align:middle line:84% and our thermodynamic equilibria. 00:17:46.170 --> 00:17:47.010 align:middle line:90% OK. 00:17:47.010 --> 00:17:49.580 align:middle line:90% Questions on that? 00:17:49.580 --> 00:17:51.080 align:middle line:90% Mm-hmm? 00:17:51.080 --> 00:17:52.080 align:middle line:90% STUDENT: [INAUDIBLE]? 00:17:52.080 --> 00:17:59.082 align:middle line:90% 00:17:59.082 --> 00:18:00.790 align:middle line:84% JACK HARE: That won't happen in this case 00:18:00.790 --> 00:18:03.410 align:middle line:84% because, before the second collision happens, 00:18:03.410 --> 00:18:05.050 align:middle line:90% it will have decayed, right? 00:18:05.050 --> 00:18:08.620 align:middle line:84% Because we're saying that these collisions are so infrequent. 00:18:08.620 --> 00:18:13.630 align:middle line:84% Yeah, really, we just have collisions going up. 00:18:13.630 --> 00:18:16.350 align:middle line:84% If the collision only took us up to here, then, 00:18:16.350 --> 00:18:18.970 align:middle line:84% before a second collision could occur, 00:18:18.970 --> 00:18:21.340 align:middle line:84% we'd have spontaneous emission and decay. 00:18:21.340 --> 00:18:24.070 align:middle line:84% If it goes up to here, then there could be multiple pathways 00:18:24.070 --> 00:18:25.147 align:middle line:90% back down, yeah. 00:18:25.147 --> 00:18:27.645 align:middle line:90% 00:18:27.645 --> 00:18:28.145 align:middle line:90% OK. 00:18:28.145 --> 00:18:29.416 align:middle line:90% STUDENT: [INAUDIBLE]? 00:18:29.416 --> 00:18:34.840 align:middle line:90% 00:18:34.840 --> 00:18:36.250 align:middle line:90% JACK HARE: I'm sorry? 00:18:36.250 --> 00:18:37.180 align:middle line:90% STUDENT: [INAUDIBLE]? 00:18:37.180 --> 00:18:43.042 align:middle line:90% 00:18:43.042 --> 00:18:43.750 align:middle line:90% JACK HARE: Right. 00:18:43.750 --> 00:18:45.458 align:middle line:84% So this is one of these things, like when 00:18:45.458 --> 00:18:46.660 align:middle line:90% is this model valid, right? 00:18:46.660 --> 00:18:49.130 align:middle line:84% And so then there will be a dimensionless parameter, 00:18:49.130 --> 00:18:51.010 align:middle line:84% which will be the ratio of those time scales. 00:18:51.010 --> 00:18:52.385 align:middle line:84% And you would like that parameter 00:18:52.385 --> 00:18:55.180 align:middle line:84% to be very large or very small, depending on whether you write 00:18:55.180 --> 00:18:56.950 align:middle line:90% it one way or the other way up. 00:18:56.950 --> 00:18:58.570 align:middle line:84% What is very large and very small? 00:18:58.570 --> 00:19:00.310 align:middle line:90% 10 is a pretty large number. 00:19:00.310 --> 00:19:02.920 align:middle line:84% 3 can sometimes be large enough, right? 00:19:02.920 --> 00:19:06.970 align:middle line:84% So if you're using this model in a situation where the ratio is 00:19:06.970 --> 00:19:08.852 align:middle line:90% only 3, it will work roughly. 00:19:08.852 --> 00:19:10.060 align:middle line:90% It won't be completely wrong. 00:19:10.060 --> 00:19:12.100 align:middle line:84% There'll be a nice, gentle transition 00:19:12.100 --> 00:19:13.570 align:middle line:90% from being right to being wrong. 00:19:13.570 --> 00:19:15.590 align:middle line:84% And you will be somewhere in the middle there. 00:19:15.590 --> 00:19:18.025 align:middle line:84% And so a lot of the time, we will use this model. 00:19:18.025 --> 00:19:19.900 align:middle line:84% And if you go and look in Hutchinson's book-- 00:19:19.900 --> 00:19:21.820 align:middle line:84% I'm not covering it in the lecture today-- 00:19:21.820 --> 00:19:24.880 align:middle line:84% actually, there's a limit to the energy levels 00:19:24.880 --> 00:19:27.320 align:middle line:90% for which CRE works. 00:19:27.320 --> 00:19:34.510 align:middle line:84% And so we find that transitions between the lower energy levels 00:19:34.510 --> 00:19:35.620 align:middle line:90% tend to be very rapid. 00:19:35.620 --> 00:19:37.660 align:middle line:84% They're very favorable because of the overlap 00:19:37.660 --> 00:19:40.780 align:middle line:84% between the upper electron wave function and the lower electron 00:19:40.780 --> 00:19:41.523 align:middle line:90% wave functions. 00:19:41.523 --> 00:19:43.690 align:middle line:84% And so you can actually use this coronal equilibrium 00:19:43.690 --> 00:19:46.810 align:middle line:84% to describe the first n energy levels. 00:19:46.810 --> 00:19:49.870 align:middle line:84% And then you have to use a different equilibrium, 00:19:49.870 --> 00:19:53.300 align:middle line:84% like maybe LTE, to describe the upper energy level. 00:19:53.300 --> 00:19:54.790 align:middle line:84% So you actually have a transition 00:19:54.790 --> 00:19:57.488 align:middle line:84% between which models are valid even within the same atom 00:19:57.488 --> 00:19:58.780 align:middle line:90% with the same ionization state. 00:19:58.780 --> 00:20:02.230 align:middle line:84% So this stuff can get complicated. 00:20:02.230 --> 00:20:06.460 align:middle line:84% Yeah, that was probably too much information, but still. 00:20:06.460 --> 00:20:07.480 align:middle line:90% Any questions online? 00:20:07.480 --> 00:20:11.450 align:middle line:90% 00:20:11.450 --> 00:20:12.020 align:middle line:90% OK. 00:20:12.020 --> 00:20:18.440 align:middle line:84% And then the final thing, after we've done coronal equilibrium, 00:20:18.440 --> 00:20:23.450 align:middle line:84% is really just having to actually solve those equations. 00:20:23.450 --> 00:20:32.110 align:middle line:84% So this is what we call non-local thermodynamic 00:20:32.110 --> 00:20:33.160 align:middle line:90% equilibrium. 00:20:33.160 --> 00:20:36.040 align:middle line:84% For many years, I thought there was a hyphen here 00:20:36.040 --> 00:20:39.057 align:middle line:84% and this was non-local thermodynamic equilibrium. 00:20:39.057 --> 00:20:40.640 align:middle line:84% So we had a thermodynamic equilibrium, 00:20:40.640 --> 00:20:42.130 align:middle line:90% which mediated non-locally. 00:20:42.130 --> 00:20:43.640 align:middle line:90% It turns out I was wrong. 00:20:43.640 --> 00:20:47.180 align:middle line:84% This is just not a local thermodynamic equilibrium, 00:20:47.180 --> 00:20:50.470 align:middle line:84% which is a much less descriptive name, but is much more valid. 00:20:50.470 --> 00:20:55.730 align:middle line:84% And you'll often see this written as lowercase nLTE. 00:20:55.730 --> 00:21:00.050 align:middle line:84% So in general, you have to solve all of the different processes, 00:21:00.050 --> 00:21:01.460 align:middle line:90% exciting and de-exciting. 00:21:01.460 --> 00:21:04.310 align:middle line:84% But for a specific nLTE model for a specific plasma 00:21:04.310 --> 00:21:05.780 align:middle line:84% you're interested in, you may still 00:21:05.780 --> 00:21:08.203 align:middle line:84% be able to restrict what those processes are. 00:21:08.203 --> 00:21:09.620 align:middle line:84% So what you need to do is actually 00:21:09.620 --> 00:21:13.600 align:middle line:84% consider all the relevant processes 00:21:13.600 --> 00:21:16.910 align:middle line:84% because, even in these models, other processes are happening. 00:21:16.910 --> 00:21:18.770 align:middle line:84% It's just we think the rate is very small. 00:21:18.770 --> 00:21:20.900 align:middle line:84% And so those processes are not relevant. 00:21:20.900 --> 00:21:22.540 align:middle line:84% So if you're doing an nLTE model, 00:21:22.540 --> 00:21:25.833 align:middle line:84% you simply have to calculate what processes are relevant 00:21:25.833 --> 00:21:26.500 align:middle line:90% and what aren't. 00:21:26.500 --> 00:21:28.340 align:middle line:84% So I'll give you an example here, 00:21:28.340 --> 00:21:30.385 align:middle line:84% if we're dealing with a photo-ionized plasma. 00:21:30.385 --> 00:21:34.480 align:middle line:90% 00:21:34.480 --> 00:21:39.610 align:middle line:84% For example, I've got a gas cell, a chamber filled with gas. 00:21:39.610 --> 00:21:42.880 align:middle line:84% And I've got windows on it, which are transparent to X-rays. 00:21:42.880 --> 00:21:44.650 align:middle line:84% And I have an X-ray source outside. 00:21:44.650 --> 00:21:46.930 align:middle line:90% Those X-rays will stream in. 00:21:46.930 --> 00:21:49.000 align:middle line:84% And they will photoionize the gas. 00:21:49.000 --> 00:21:51.070 align:middle line:90% The photons will be absorbed. 00:21:51.070 --> 00:21:53.470 align:middle line:90% And we'll have photoionization. 00:21:53.470 --> 00:21:56.890 align:middle line:84% And then the occupation levels will 00:21:56.890 --> 00:21:59.260 align:middle line:84% be set by those photoionization processes. 00:21:59.260 --> 00:22:01.660 align:middle line:84% We won't have to consider collisional processes 00:22:01.660 --> 00:22:04.990 align:middle line:84% because the photon field, the strength of the X-ray drive, 00:22:04.990 --> 00:22:07.810 align:middle line:84% is so strong that the photons are much more likely to be 00:22:07.810 --> 00:22:09.890 align:middle line:90% involved than any collisions. 00:22:09.890 --> 00:22:12.520 align:middle line:84% And so for a photonionized system, 00:22:12.520 --> 00:22:15.840 align:middle line:84% for example, we can neglect collisional processes. 00:22:15.840 --> 00:22:18.120 align:middle line:84% So that reduces the number of equations 00:22:18.120 --> 00:22:20.050 align:middle line:90% that you need to solve. 00:22:20.050 --> 00:22:22.170 align:middle line:84% And so you may be able to get away with a smaller 00:22:22.170 --> 00:22:23.040 align:middle line:90% set of equations. 00:22:23.040 --> 00:22:25.600 align:middle line:90% 00:22:25.600 --> 00:22:28.320 align:middle line:84% But if you calculate it and all your processes are roughly 00:22:28.320 --> 00:22:31.080 align:middle line:84% equal, then you really do have to solve that big equation I put 00:22:31.080 --> 00:22:36.300 align:middle line:84% up on the board last time that was effectively 0, because we're 00:22:36.300 --> 00:22:40.380 align:middle line:84% in steady state, equals the sum over all processes. 00:22:40.380 --> 00:22:43.910 align:middle line:90% 00:22:43.910 --> 00:22:45.877 align:middle line:84% And as I mentioned, people spend their lives 00:22:45.877 --> 00:22:47.710 align:middle line:84% writing code to calculate these coefficients 00:22:47.710 --> 00:22:49.630 align:middle line:90% and to solve this balance. 00:22:49.630 --> 00:22:52.860 align:middle line:84% And it can get very, very messy indeed. 00:22:52.860 --> 00:22:56.290 align:middle line:84% But that's all I'm really going to say on nLTEs. 00:22:56.290 --> 00:23:01.040 align:middle line:84% So in general, if we're trying to do spectroscopy, 00:23:01.040 --> 00:23:04.260 align:middle line:84% there was a workflow that we might need to do. 00:23:04.260 --> 00:23:06.920 align:middle line:84% So this is modeling spectroscopy. 00:23:06.920 --> 00:23:16.410 align:middle line:90% 00:23:16.410 --> 00:23:19.590 align:middle line:84% So first of all, we're going to model the spectra 00:23:19.590 --> 00:23:24.750 align:middle line:84% from a blob of plasma, a little cube like this. 00:23:24.750 --> 00:23:28.070 align:middle line:84% It's got some mass density, which is what spectroscopists 00:23:28.070 --> 00:23:29.450 align:middle line:90% often work in, rho. 00:23:29.450 --> 00:23:32.330 align:middle line:90% And it has some temperature. 00:23:32.330 --> 00:23:34.100 align:middle line:84% Occasionally, your spectroscopists 00:23:34.100 --> 00:23:37.580 align:middle line:84% might work in terms of ion density instead. 00:23:37.580 --> 00:23:41.840 align:middle line:84% Obviously, these are same up to the ion mass here. 00:23:41.840 --> 00:23:45.890 align:middle line:84% Then you need to determine what equilibrium is appropriate. 00:23:45.890 --> 00:23:50.930 align:middle line:90% 00:23:50.930 --> 00:23:54.120 align:middle line:84% This could be a Saha-type equilibrium 00:23:54.120 --> 00:23:57.520 align:middle line:84% or a collisional radiative equilibrium. 00:23:57.520 --> 00:24:01.307 align:middle line:84% So maybe you know this by back of the envelope calculations. 00:24:01.307 --> 00:24:03.390 align:middle line:84% Maybe you go through and calculate a load of rates 00:24:03.390 --> 00:24:05.230 align:middle line:84% and determine what's most important. 00:24:05.230 --> 00:24:08.170 align:middle line:84% But you have to determine what your equilibrium is. 00:24:08.170 --> 00:24:14.710 align:middle line:84% So then you need to calculate the ionization states. 00:24:14.710 --> 00:24:18.830 align:middle line:84% What organizations are present in your system here? 00:24:18.830 --> 00:24:23.830 align:middle line:84% So these are the density of ions with charge z, 00:24:23.830 --> 00:24:25.030 align:middle line:90% all the different z's. 00:24:25.030 --> 00:24:27.220 align:middle line:84% In some cases, you may be very weakly ionized. 00:24:27.220 --> 00:24:28.630 align:middle line:90% You may have a lot of neutrals. 00:24:28.630 --> 00:24:30.610 align:middle line:84% And you may have just a few atoms 00:24:30.610 --> 00:24:33.220 align:middle line:90% which have an ionization of 1. 00:24:33.220 --> 00:24:35.920 align:middle line:84% In other cases, you may go all the way from neutrals 00:24:35.920 --> 00:24:37.983 align:middle line:90% to fully stripped. 00:24:37.983 --> 00:24:39.400 align:middle line:84% For something like tungsten, which 00:24:39.400 --> 00:24:44.200 align:middle line:84% has 74 electrons, 76 electrons, that's an awful lot of energy. 00:24:44.200 --> 00:24:46.840 align:middle line:84% But you may well be able to get a plasma [INAUDIBLE]. 00:24:46.840 --> 00:24:50.080 align:middle line:84% So then you'd have to take into account all the other ionization 00:24:50.080 --> 00:24:51.970 align:middle line:90% states. 00:24:51.970 --> 00:24:57.580 align:middle line:84% Then you have to calculate the excited states. 00:24:57.580 --> 00:25:00.760 align:middle line:84% And you have to calculate the excited states for each nz. 00:25:00.760 --> 00:25:09.070 align:middle line:84% So for all nz, you need nz, and then whatever the excitation is. 00:25:09.070 --> 00:25:13.450 align:middle line:90% 00:25:13.450 --> 00:25:15.970 align:middle line:84% Then you need to calculate the line strengths. 00:25:15.970 --> 00:25:20.900 align:middle line:90% 00:25:20.900 --> 00:25:26.340 align:middle line:84% So these are these coefficients a, i, j. 00:25:26.340 --> 00:25:30.330 align:middle line:84% And you'll remember that these had some hand-wavy relevance 00:25:30.330 --> 00:25:35.520 align:middle line:84% to the overlap integral with the dipole operator 00:25:35.520 --> 00:25:38.280 align:middle line:84% between the upper and the lower state. 00:25:38.280 --> 00:25:40.530 align:middle line:84% So this is the dipole operator, which 00:25:40.530 --> 00:25:47.640 align:middle line:84% is radiating away a photon of energy, h-bar omega ij. 00:25:47.640 --> 00:25:50.560 align:middle line:84% And that process has some probability to occur. 00:25:50.560 --> 00:25:54.398 align:middle line:84% And so this tells you how many photons with that energy 00:25:54.398 --> 00:25:55.440 align:middle line:90% that you're going to see. 00:25:55.440 --> 00:25:57.930 align:middle line:84% And you need to do that for every transition 00:25:57.930 --> 00:26:00.840 align:middle line:84% between every set of excited states 00:26:00.840 --> 00:26:05.080 align:middle line:90% for every ion in your system. 00:26:05.080 --> 00:26:07.280 align:middle line:90% So this is hard. 00:26:07.280 --> 00:26:13.130 align:middle line:90% 00:26:13.130 --> 00:26:15.935 align:middle line:84% Once you've done that, you can now predict the spectra. 00:26:15.935 --> 00:26:18.690 align:middle line:90% 00:26:18.690 --> 00:26:24.120 align:middle line:84% So this is predicting the intensity of radiation 00:26:24.120 --> 00:26:31.450 align:middle line:84% with frequency omega for the very specific density 00:26:31.450 --> 00:26:33.745 align:middle line:84% and temperature that you started out with. 00:26:33.745 --> 00:26:36.700 align:middle line:90% 00:26:36.700 --> 00:26:39.840 align:middle line:84% Now, if you're very, very lucky, your system 00:26:39.840 --> 00:26:43.650 align:middle line:84% is optically thin, so tau less than 1. 00:26:43.650 --> 00:26:45.980 align:middle line:90% Life is good. 00:26:45.980 --> 00:26:47.960 align:middle line:84% If tau is greater than 1, now you 00:26:47.960 --> 00:26:52.158 align:middle line:84% need to consider radiation transport or the fact 00:26:52.158 --> 00:26:54.200 align:middle line:84% that some of the radiation will be absorbed as it 00:26:54.200 --> 00:26:56.780 align:middle line:90% moves through your plasma. 00:26:56.780 --> 00:26:58.730 align:middle line:84% And actually, for both of these as well, 00:26:58.730 --> 00:27:00.900 align:middle line:84% you'll have to consider things like reflections. 00:27:00.900 --> 00:27:03.140 align:middle line:84% So the fact you've got metal walls on your tokamak, 00:27:03.140 --> 00:27:06.920 align:middle line:84% or whatever it is, means that some light going the other way 00:27:06.920 --> 00:27:08.675 align:middle line:90% will bounce back. 00:27:08.675 --> 00:27:10.880 align:middle line:90% I've got my plasma here. 00:27:10.880 --> 00:27:13.760 align:middle line:84% Some of the light from this bit of plasma 00:27:13.760 --> 00:27:17.210 align:middle line:90% is going to be emitted this way. 00:27:17.210 --> 00:27:20.720 align:middle line:84% And then it will bounce back into your detector. 00:27:20.720 --> 00:27:22.660 align:middle line:84% And although it's being emitted from here, 00:27:22.660 --> 00:27:25.160 align:middle line:84% it will look like it's being emitted along the line of sight 00:27:25.160 --> 00:27:25.440 align:middle line:90% here. 00:27:25.440 --> 00:27:27.523 align:middle line:84% So if you don't take into account the reflections, 00:27:27.523 --> 00:27:30.830 align:middle line:84% you will be thinking you've got lines from one bit of plasma 00:27:30.830 --> 00:27:33.580 align:middle line:84% when they're, in fact, from another bit of plasma. 00:27:33.580 --> 00:27:37.460 align:middle line:84% You'll also need to model the response of your detector. 00:27:37.460 --> 00:27:41.730 align:middle line:84% But there are no perfect spectrometers out there. 00:27:41.730 --> 00:27:45.950 align:middle line:84% And they, in general, have a response curve to them, 00:27:45.950 --> 00:27:49.090 align:middle line:84% which is like response as a frequency of omega. 00:27:49.090 --> 00:27:49.855 align:middle line:90% They're not flat. 00:27:49.855 --> 00:27:51.730 align:middle line:84% They treat different frequencies differently. 00:27:51.730 --> 00:27:56.040 align:middle line:84% They absorb infrared photons more than visible photons. 00:27:56.040 --> 00:27:58.860 align:middle line:84% And then finally, you need to compare this 00:27:58.860 --> 00:28:00.750 align:middle line:90% to your experimental data. 00:28:00.750 --> 00:28:05.260 align:middle line:90% 00:28:05.260 --> 00:28:10.830 align:middle line:84% So for example, if you had a spectrum that 00:28:10.830 --> 00:28:14.890 align:middle line:84% has two lines in it like that, and you've 00:28:14.890 --> 00:28:17.170 align:middle line:84% done all of this process, and you get out 00:28:17.170 --> 00:28:21.570 align:middle line:84% a spectrum that looks like this, you'll have a choice. 00:28:21.570 --> 00:28:23.810 align:middle line:84% You can either say, it's close enough for today. 00:28:23.810 --> 00:28:26.638 align:middle line:84% Or you iterate and you do all of this again. 00:28:26.638 --> 00:28:28.430 align:middle line:84% And you pick a new density and temperature. 00:28:28.430 --> 00:28:31.460 align:middle line:84% And you do some sort of gradient descent type thing 00:28:31.460 --> 00:28:36.680 align:middle line:84% until eventually your model spectra matches up 00:28:36.680 --> 00:28:38.510 align:middle line:90% with your experimental spectra. 00:28:38.510 --> 00:28:41.670 align:middle line:84% And then you say, aha, now I finally 00:28:41.670 --> 00:28:47.010 align:middle line:84% know the density and temperature of my plasma. 00:28:47.010 --> 00:28:49.590 align:middle line:90% 00:28:49.590 --> 00:28:52.700 align:middle line:84% It's a fair bit of work to do spectroscopy. 00:28:52.700 --> 00:28:53.390 align:middle line:90% Questions? 00:28:53.390 --> 00:28:57.540 align:middle line:90% 00:28:57.540 --> 00:28:58.910 align:middle line:90% Yeah? 00:28:58.910 --> 00:28:59.890 align:middle line:90% STUDENT: [INAUDIBLE]? 00:28:59.890 --> 00:29:06.543 align:middle line:90% 00:29:06.543 --> 00:29:07.710 align:middle line:90% JACK HARE: Yeah, so you can. 00:29:07.710 --> 00:29:10.680 align:middle line:84% I will show you some tricks to narrow this parameter 00:29:10.680 --> 00:29:11.520 align:middle line:90% space in a moment. 00:29:11.520 --> 00:29:12.863 align:middle line:90% This is the most general case. 00:29:12.863 --> 00:29:14.280 align:middle line:84% I had whole page of notes on this, 00:29:14.280 --> 00:29:15.822 align:middle line:84% and then my iPad hasn't updated them. 00:29:15.822 --> 00:29:17.400 align:middle line:84% But I wrote the word line ratios. 00:29:17.400 --> 00:29:19.605 align:middle line:84% And I'm going to try and reconstruct the memory what 00:29:19.605 --> 00:29:20.730 align:middle line:90% exactly I was going to say. 00:29:20.730 --> 00:29:22.350 align:middle line:90% So we'll see how it goes. 00:29:22.350 --> 00:29:23.830 align:middle line:90% Yes? 00:29:23.830 --> 00:29:24.830 align:middle line:90% STUDENT: [INAUDIBLE]? 00:29:24.830 --> 00:29:32.420 align:middle line:90% 00:29:32.420 --> 00:29:34.520 align:middle line:84% JACK HARE: Well, other diagnostics 00:29:34.520 --> 00:29:37.460 align:middle line:84% can be expensive they can be limited to certain parameter 00:29:37.460 --> 00:29:38.420 align:middle line:90% ranges. 00:29:38.420 --> 00:29:39.890 align:middle line:84% If you're doing astrophysics, you 00:29:39.890 --> 00:29:42.350 align:middle line:84% can't do Thomson scattering on your black hole corona. 00:29:42.350 --> 00:29:46.210 align:middle line:84% So you're stuck with this sort of thing. 00:29:46.210 --> 00:29:49.000 align:middle line:84% Spectroscopy does provide extremely detailed information 00:29:49.000 --> 00:29:50.703 align:middle line:90% on all of the atomic kinetics. 00:29:50.703 --> 00:29:52.120 align:middle line:84% This is what people call this sort 00:29:52.120 --> 00:29:54.820 align:middle line:84% of distribution of different states, the atomic kinetics. 00:29:54.820 --> 00:29:57.550 align:middle line:84% So if you're far from local thermodynamic equilibrium, 00:29:57.550 --> 00:29:59.890 align:middle line:84% say you're looking at fast electrons in a tokamak, 00:29:59.890 --> 00:30:02.650 align:middle line:84% the spectrum may provide information 00:30:02.650 --> 00:30:05.500 align:middle line:84% on those fast electrons that something like Thomson 00:30:05.500 --> 00:30:07.690 align:middle line:84% scattering doesn't because Thomson scattering may 00:30:07.690 --> 00:30:11.110 align:middle line:84% be as sensitive just to the bulk of the plasma. 00:30:11.110 --> 00:30:14.200 align:middle line:84% So this is a time-honored time honored diagnostic. 00:30:14.200 --> 00:30:16.270 align:middle line:84% We have a lot of knowledge about how to do it. 00:30:16.270 --> 00:30:18.362 align:middle line:84% It's just that it turns out to be very hard. 00:30:18.362 --> 00:30:20.320 align:middle line:84% I've presented this in a slightly flippant way. 00:30:20.320 --> 00:30:22.060 align:middle line:84% But this is what you need to do if you actually 00:30:22.060 --> 00:30:23.320 align:middle line:90% want to solve all these things. 00:30:23.320 --> 00:30:25.750 align:middle line:84% Some of these steps have already been done for you, right? 00:30:25.750 --> 00:30:28.208 align:middle line:84% I mean, a lot of this is now included in computer packages. 00:30:28.208 --> 00:30:31.000 align:middle line:84% And so if you know what your equilibrium is-- 00:30:31.000 --> 00:30:35.290 align:middle line:84% for example here, this rho t getting out some spectra here, 00:30:35.290 --> 00:30:37.690 align:middle line:84% there are large codes PrismSPECT is 00:30:37.690 --> 00:30:38.980 align:middle line:90% a commercially available code. 00:30:38.980 --> 00:30:41.950 align:middle line:84% You give it a density at a temperature 00:30:41.950 --> 00:30:43.390 align:middle line:84% and the size of your plasma and it 00:30:43.390 --> 00:30:44.800 align:middle line:84% will do radiation transport through it 00:30:44.800 --> 00:30:46.220 align:middle line:84% and tell you what the spectra is. 00:30:46.220 --> 00:30:49.700 align:middle line:84% You run that for a few different rhos and t's and you create 00:30:49.700 --> 00:30:51.740 align:middle line:84% a table of spectra for different rho and t, 00:30:51.740 --> 00:30:54.660 align:middle line:84% you can very quickly fit that to your experimental spectra. 00:30:54.660 --> 00:30:56.618 align:middle line:84% So none of this stuff is impossible. 00:30:56.618 --> 00:30:58.410 align:middle line:84% It's just, if you're doing it from scratch, 00:30:58.410 --> 00:30:59.570 align:middle line:90% it can be very hard. 00:30:59.570 --> 00:31:02.190 align:middle line:84% Yeah, I'll just take Nicola's question. 00:31:02.190 --> 00:31:03.190 align:middle line:90% STUDENT: [INAUDIBLE]? 00:31:03.190 --> 00:31:18.442 align:middle line:90% 00:31:18.442 --> 00:31:20.150 align:middle line:84% JACK HARE: Yeah, that's a great question. 00:31:20.150 --> 00:31:23.480 align:middle line:84% So what we talked about here is that there 00:31:23.480 --> 00:31:25.400 align:middle line:84% is some photon with some energy, right? 00:31:25.400 --> 00:31:27.800 align:middle line:84% So if we think that that is true, 00:31:27.800 --> 00:31:32.090 align:middle line:84% our spectrum should look like a set of delta functions, right? 00:31:32.090 --> 00:31:37.415 align:middle line:84% And those delta functions should sit at omega ij. 00:31:37.415 --> 00:31:39.290 align:middle line:84% And I know that delta functions are infinite. 00:31:39.290 --> 00:31:40.760 align:middle line:84% But they should have a height that 00:31:40.760 --> 00:31:46.050 align:middle line:84% is related to the strength of the transition here. 00:31:46.050 --> 00:31:48.700 align:middle line:84% What we'll talk about next lecture is line broadening. 00:31:48.700 --> 00:31:52.260 align:middle line:84% So that is when these lines are broadened by other processes. 00:31:52.260 --> 00:31:54.670 align:middle line:84% And we may be able to, in some circumstances, 00:31:54.670 --> 00:31:56.670 align:middle line:84% learn more about the plasma from the broadening. 00:31:56.670 --> 00:31:58.080 align:middle line:84% For example, if there's Doppler broadening, 00:31:58.080 --> 00:31:59.497 align:middle line:84% we'll learn about the temperature. 00:31:59.497 --> 00:32:02.310 align:middle line:84% If there's Stark broadening, we'll learn about the density. 00:32:02.310 --> 00:32:04.623 align:middle line:84% And then there are other Zeeman splitting and things 00:32:04.623 --> 00:32:06.790 align:middle line:84% like that may even be related to the magnetic field. 00:32:06.790 --> 00:32:08.400 align:middle line:90% But we'll get on to that later. 00:32:08.400 --> 00:32:08.960 align:middle line:90% Yeah? 00:32:08.960 --> 00:32:10.280 align:middle line:90% STUDENT: [INAUDIBLE]? 00:32:10.280 --> 00:32:22.525 align:middle line:90% 00:32:22.525 --> 00:32:24.150 align:middle line:84% JACK HARE: I would say yes, in general. 00:32:24.150 --> 00:32:26.160 align:middle line:84% And the worst the case of this is the fact 00:32:26.160 --> 00:32:27.660 align:middle line:90% that this is line integrated. 00:32:27.660 --> 00:32:29.485 align:middle line:84% So we're going through the plasma 00:32:29.485 --> 00:32:31.360 align:middle line:84% here when we're collecting all of that light. 00:32:31.360 --> 00:32:35.520 align:middle line:84% And so if the plasma-- for example, rho or t-- 00:32:35.520 --> 00:32:40.530 align:middle line:84% changes along that curve, then you 00:32:40.530 --> 00:32:43.710 align:middle line:84% can't say exactly how that density changes because there 00:32:43.710 --> 00:32:47.860 align:middle line:84% are lots of different solutions that give you the same result. 00:32:47.860 --> 00:32:50.520 align:middle line:90% So definitely not unique. 00:32:50.520 --> 00:32:53.235 align:middle line:84% People do inverted spectroscopy and very cool 00:32:53.235 --> 00:32:55.860 align:middle line:84% techniques like that, where they measure lots of lines of sight 00:32:55.860 --> 00:32:57.110 align:middle line:90% and have symmetry assumptions. 00:32:57.110 --> 00:32:59.575 align:middle line:90% But that's quite tricky. 00:32:59.575 --> 00:33:00.450 align:middle line:90% Any questions online? 00:33:00.450 --> 00:33:09.120 align:middle line:90% 00:33:09.120 --> 00:33:11.220 align:middle line:84% OK, I'm going to try and do the line ratio thing. 00:33:11.220 --> 00:33:12.220 align:middle line:90% Let's see how this goes. 00:33:12.220 --> 00:33:27.630 align:middle line:90% 00:33:27.630 --> 00:33:38.630 align:middle line:84% So you may have a spectrum with some very well-isolated lines. 00:33:38.630 --> 00:33:43.110 align:middle line:84% So these lines could be ones that are some distance apart 00:33:43.110 --> 00:33:44.790 align:middle line:90% from any other lines. 00:33:44.790 --> 00:33:46.140 align:middle line:90% They stand by themselves. 00:33:46.140 --> 00:33:49.620 align:middle line:84% It's very clear what their wavelength is 00:33:49.620 --> 00:33:51.690 align:middle line:90% or the frequency is. 00:33:51.690 --> 00:33:53.710 align:middle line:84% There's no confusing it as anything else. 00:33:53.710 --> 00:33:55.890 align:middle line:84% An example of a poorly separated line 00:33:55.890 --> 00:34:00.990 align:middle line:84% would be if you have three lines all on top of each other, 00:34:00.990 --> 00:34:02.220 align:middle line:90% like this. 00:34:02.220 --> 00:34:06.720 align:middle line:84% Because these lines are probably adding together in some way, 00:34:06.720 --> 00:34:09.550 align:middle line:84% you can't exactly tell what the intensity of each of these is. 00:34:09.550 --> 00:34:11.460 align:middle line:84% But if you have nice, well-separated lines, 00:34:11.460 --> 00:34:15.239 align:middle line:84% then you have some intensity coefficients for this one, 00:34:15.239 --> 00:34:17.800 align:middle line:84% some intensity coefficient for this one here. 00:34:17.800 --> 00:34:30.150 align:middle line:84% So this line ratio technique, you need to have strong, 00:34:30.150 --> 00:34:35.389 align:middle line:90% isolated, and identified. 00:34:35.389 --> 00:34:39.790 align:middle line:84% You need to know what these lines correspond to. 00:34:39.790 --> 00:34:42.190 align:middle line:84% So identified, in this case, means 00:34:42.190 --> 00:34:47.820 align:middle line:84% we need to know what the ionization state is for it. 00:34:47.820 --> 00:34:52.909 align:middle line:84% And we also need to know what upper level and lower level 00:34:52.909 --> 00:34:55.949 align:middle line:84% it corresponds to within that ionization state. 00:34:55.949 --> 00:34:57.850 align:middle line:90% So we need to know the-- 00:34:57.850 --> 00:35:00.860 align:middle line:84% I guess we technically need to know the density 00:35:00.860 --> 00:35:03.960 align:middle line:90% of the upper state here. 00:35:03.960 --> 00:35:06.530 align:middle line:84% And so an example of this would be 00:35:06.530 --> 00:35:12.380 align:middle line:84% if I have a line that comes from aluminum that is twice ionized 00:35:12.380 --> 00:35:16.280 align:middle line:84% and aluminum which is three times ionized 00:35:16.280 --> 00:35:19.190 align:middle line:84% or something like that, these two ions 00:35:19.190 --> 00:35:21.650 align:middle line:84% will have very strong lines for certain transitions. 00:35:21.650 --> 00:35:24.320 align:middle line:84% You'll often have a very strong transition 00:35:24.320 --> 00:35:29.270 align:middle line:84% from some upper state, the lowest lying upper state, back 00:35:29.270 --> 00:35:32.090 align:middle line:84% down to the ground state because, 00:35:32.090 --> 00:35:34.160 align:middle line:84% in general, that's where you're going to end up. 00:35:34.160 --> 00:35:36.720 align:middle line:84% And also, in general, you have a large energy gap here. 00:35:36.720 --> 00:35:38.120 align:middle line:90% So this is pretty favorable. 00:35:38.120 --> 00:35:40.670 align:middle line:84% So maybe you've got some well-isolated lines 00:35:40.670 --> 00:35:44.630 align:middle line:84% that you know correspond from emission from an upper level 00:35:44.630 --> 00:35:45.980 align:middle line:90% down to the ground level here. 00:35:45.980 --> 00:35:47.930 align:middle line:84% And you can measure their intensity very well. 00:35:47.930 --> 00:35:51.320 align:middle line:84% So we now know the intensity of omega 1. 00:35:51.320 --> 00:35:54.350 align:middle line:84% And we know the intensity of omega 2. 00:35:54.350 --> 00:35:55.910 align:middle line:84% And this is what I mean by strong. 00:35:55.910 --> 00:35:58.070 align:middle line:84% You don't want to be doing this on little lines 00:35:58.070 --> 00:36:01.340 align:middle line:84% that are down here in the noise because we can't measure 00:36:01.340 --> 00:36:04.270 align:middle line:90% their intensity very well. 00:36:04.270 --> 00:36:06.640 align:middle line:84% So what you do with these lines is you say, 00:36:06.640 --> 00:36:18.335 align:middle line:84% OK, I know that the intensity of this line-- 00:36:18.335 --> 00:36:21.590 align:middle line:90% 00:36:21.590 --> 00:36:25.370 align:middle line:84% so the intensity at some frequency corresponding 00:36:25.370 --> 00:36:28.070 align:middle line:84% to the transition from the upper state to the lower state here 00:36:28.070 --> 00:36:33.910 align:middle line:84% is equal to the number of ions in the upper state 00:36:33.910 --> 00:36:36.460 align:middle line:84% times by the probability of transition 00:36:36.460 --> 00:36:38.530 align:middle line:84% from the upper state to the lower state. 00:36:38.530 --> 00:36:42.730 align:middle line:84% And then because this intensity often has units of energy here-- 00:36:42.730 --> 00:36:43.840 align:middle line:90% this is like a power-- 00:36:43.840 --> 00:36:45.770 align:middle line:84% we obviously need to have an energy unit here. 00:36:45.770 --> 00:36:49.820 align:middle line:84% So this is h-bar omega upper lower. 00:36:49.820 --> 00:36:53.650 align:middle line:84% So if we have two lines here, we can take the ratio of these. 00:36:53.650 --> 00:36:57.760 align:middle line:84% So we can have intensity of omega 00:36:57.760 --> 00:37:03.110 align:middle line:84% z upper lower over intensity of omega z 00:37:03.110 --> 00:37:05.980 align:middle line:90% minus 1 upper lower like that. 00:37:05.980 --> 00:37:06.480 align:middle line:90% And 00:37:06.480 --> 00:37:12.600 align:middle line:84% We can see then that we're going to get out a z upper over n 00:37:12.600 --> 00:37:20.210 align:middle line:84% to the z minus 1 upper a upper lower a upper lower-- 00:37:20.210 --> 00:37:22.080 align:middle line:84% I'll put little superscripts on these, 00:37:22.080 --> 00:37:24.260 align:middle line:84% so we remember that these are different coefficients 00:37:24.260 --> 00:37:26.120 align:middle line:84% for our different ionization states. 00:37:26.120 --> 00:37:28.170 align:middle line:90% And then the h-bars will cancel. 00:37:28.170 --> 00:37:32.000 align:middle line:84% So we'll have an omega z upper lower omega z 00:37:32.000 --> 00:37:34.494 align:middle line:90% minus 1 upper lower. 00:37:34.494 --> 00:37:37.380 align:middle line:90% 00:37:37.380 --> 00:37:43.430 align:middle line:84% But these are things that we can calculate, 00:37:43.430 --> 00:37:46.325 align:middle line:90% look up in our atomic database. 00:37:46.325 --> 00:37:47.950 align:middle line:84% These are things that we have literally 00:37:47.950 --> 00:37:50.380 align:middle line:84% measured because our spectrometer is well-calibrated. 00:37:50.380 --> 00:37:54.670 align:middle line:90% 00:37:54.670 --> 00:37:57.010 align:middle line:84% This line ratio we've also just measured. 00:37:57.010 --> 00:38:00.570 align:middle line:90% 00:38:00.570 --> 00:38:08.350 align:middle line:84% So that means we can infer the ratio between the number 00:38:08.350 --> 00:38:13.690 align:middle line:84% of atoms in one ionization state and another ionization state. 00:38:13.690 --> 00:38:15.940 align:middle line:84% Here, I've done them as neighboring ionization states. 00:38:15.940 --> 00:38:17.920 align:middle line:84% This could be like z minus 2, z minus 3. 00:38:17.920 --> 00:38:18.980 align:middle line:90% It doesn't really matter. 00:38:18.980 --> 00:38:20.320 align:middle line:84% You don't generally get that because, 00:38:20.320 --> 00:38:22.870 align:middle line:84% for a certain temperature, you only have a few ionization 00:38:22.870 --> 00:38:25.510 align:middle line:90% states active at a time. 00:38:25.510 --> 00:38:27.510 align:middle line:84% And because you've now inferred this quantity, 00:38:27.510 --> 00:38:35.390 align:middle line:84% you can then use an equilibrium, such as Saha. 00:38:35.390 --> 00:38:38.010 align:middle line:84% And you can get out the temperature. 00:38:38.010 --> 00:38:40.153 align:middle line:84% So you can say your Saha equilibrium says, 00:38:40.153 --> 00:38:41.570 align:middle line:84% at a certain temperature, I should 00:38:41.570 --> 00:38:45.950 align:middle line:84% have twice as many ions in the lower ionization state 00:38:45.950 --> 00:38:47.480 align:middle line:90% as the upper ionization state. 00:38:47.480 --> 00:38:48.620 align:middle line:90% That's what I see. 00:38:48.620 --> 00:38:50.720 align:middle line:84% Therefore, that is my temperature. 00:38:50.720 --> 00:38:53.000 align:middle line:84% So just simply from looking at line ratios 00:38:53.000 --> 00:38:55.280 align:middle line:84% without doing all of this complicated modeling, 00:38:55.280 --> 00:38:57.470 align:middle line:84% you may be able to get a handle on the temperature. 00:38:57.470 --> 00:38:59.780 align:middle line:84% And that could be a first step that you then feed back 00:38:59.780 --> 00:39:01.280 align:middle line:84% into your algorithm where you say, 00:39:01.280 --> 00:39:03.280 align:middle line:84% I know what the starting temperature roughly is. 00:39:03.280 --> 00:39:06.720 align:middle line:84% So let's only look in the solution space surrounding that. 00:39:06.720 --> 00:39:08.355 align:middle line:84% So this is quite a powerful technique. 00:39:08.355 --> 00:39:09.980 align:middle line:84% And often, this is as far as people go. 00:39:09.980 --> 00:39:11.180 align:middle line:90% They'll do a line ratio. 00:39:11.180 --> 00:39:12.560 align:middle line:90% They'll get a temperature out. 00:39:12.560 --> 00:39:15.200 align:middle line:84% And I mentioned earlier the even simpler thing to do is just be 00:39:15.200 --> 00:39:20.390 align:middle line:84% like, hey, I've got a line that corresponds to aluminum 3+ ions. 00:39:20.390 --> 00:39:22.580 align:middle line:84% That only happens when the temperature in the plasma 00:39:22.580 --> 00:39:25.610 align:middle line:84% is like 10 electron volts, maybe 12, maybe 8. 00:39:25.610 --> 00:39:27.990 align:middle line:84% But that means my plasma is probably 10 electron volts. 00:39:27.990 --> 00:39:28.490 align:middle line:90% Perfect. 00:39:28.490 --> 00:39:32.580 align:middle line:84% And that's good enough for a lot of purposes. 00:39:32.580 --> 00:39:33.080 align:middle line:90% OK. 00:39:33.080 --> 00:39:33.950 align:middle line:90% Questions on this? 00:39:33.950 --> 00:39:42.360 align:middle line:90% 00:39:42.360 --> 00:39:43.689 align:middle line:90% Yes? 00:39:43.689 --> 00:39:45.066 align:middle line:90% STUDENT: [INAUDIBLE]? 00:39:45.066 --> 00:39:58.480 align:middle line:90% 00:39:58.480 --> 00:40:00.440 align:middle line:84% JACK HARE: Yeah, so no, so absolutely. 00:40:00.440 --> 00:40:01.570 align:middle line:90% I say you're measuring it. 00:40:01.570 --> 00:40:02.950 align:middle line:90% But you know it, right? 00:40:02.950 --> 00:40:03.700 align:middle line:90% It's close enough. 00:40:03.700 --> 00:40:05.825 align:middle line:84% Yes, there may be some Doppler shift involved to it 00:40:05.825 --> 00:40:07.810 align:middle line:84% or some of these other line broadening 00:40:07.810 --> 00:40:10.490 align:middle line:84% mechanisms, which means you don't know exactly where this 00:40:10.490 --> 00:40:10.990 align:middle line:90% is. 00:40:10.990 --> 00:40:13.615 align:middle line:84% You may also have uncertainties in your atomic code, especially 00:40:13.615 --> 00:40:15.190 align:middle line:90% when you're working with X-rays. 00:40:15.190 --> 00:40:18.070 align:middle line:84% The X-ray spectroscopy models can be 00:40:18.070 --> 00:40:20.360 align:middle line:90% quite inaccurate to within 20%. 00:40:20.360 --> 00:40:21.880 align:middle line:90% And that's still pretty good. 00:40:21.880 --> 00:40:25.890 align:middle line:84% And so you'll say, OK, I thought it was going to be here. 00:40:25.890 --> 00:40:28.770 align:middle line:84% There's nothing anywhere near here, apart from this line. 00:40:28.770 --> 00:40:30.080 align:middle line:90% So that is probably this line. 00:40:30.080 --> 00:40:32.960 align:middle line:84% So making a line identification is very tough. 00:40:32.960 --> 00:40:34.940 align:middle line:84% And especially in a plasma in the laboratory, 00:40:34.940 --> 00:40:37.505 align:middle line:84% you think my plasma is made out of aluminum because that's 00:40:37.505 --> 00:40:38.630 align:middle line:90% what you've made it out of. 00:40:38.630 --> 00:40:40.430 align:middle line:84% But then you forget that the lenses are 00:40:40.430 --> 00:40:42.078 align:middle line:90% coated with magnesium fluoride. 00:40:42.078 --> 00:40:44.120 align:middle line:84% And so there may be magnesium fluoride absorption 00:40:44.120 --> 00:40:46.610 align:middle line:84% lines when the X-rays from your experiment photoionizing. 00:40:46.610 --> 00:40:49.222 align:middle line:84% Or your electrode is made out of copper. 00:40:49.222 --> 00:40:50.930 align:middle line:84% And now, you've got copper lines as well. 00:40:50.930 --> 00:40:53.960 align:middle line:84% Or someone left their thumbprint on one of the electrodes. 00:40:53.960 --> 00:40:55.790 align:middle line:84% And now, you have hydrocarbons and salt. 00:40:55.790 --> 00:40:58.130 align:middle line:84% So you have sodium lines on there as well. 00:40:58.130 --> 00:41:00.560 align:middle line:84% All of this has happened to me very recently. 00:41:00.560 --> 00:41:01.880 align:middle line:90% So actually, it's a nightmare. 00:41:01.880 --> 00:41:03.715 align:middle line:84% You think, my plasma is made out of this. 00:41:03.715 --> 00:41:04.590 align:middle line:90% And the answer is no. 00:41:04.590 --> 00:41:06.257 align:middle line:84% Your plasma is made out of whatever crap 00:41:06.257 --> 00:41:08.600 align:middle line:84% there is in the machine, so yeah. 00:41:08.600 --> 00:41:09.100 align:middle line:90% OK. 00:41:09.100 --> 00:41:09.979 align:middle line:90% Yeah? 00:41:09.979 --> 00:41:11.162 align:middle line:90% STUDENT: [INAUDIBLE]? 00:41:11.162 --> 00:41:17.800 align:middle line:90% 00:41:17.800 --> 00:41:20.530 align:middle line:84% JACK HARE: Yes, and preferably negligible, right? 00:41:20.530 --> 00:41:22.900 align:middle line:84% So yeah, this is definitely a technique that works best 00:41:22.900 --> 00:41:24.610 align:middle line:90% if it's optically thin. 00:41:24.610 --> 00:41:28.270 align:middle line:84% You could use it if you have very strong priors about what 00:41:28.270 --> 00:41:30.160 align:middle line:84% the density and temperature are so that you 00:41:30.160 --> 00:41:31.300 align:middle line:90% can calculate the opacity. 00:41:31.300 --> 00:41:32.800 align:middle line:84% But if you have those strong priors, 00:41:32.800 --> 00:41:34.090 align:middle line:84% then you don't need to do this technique. 00:41:34.090 --> 00:41:36.160 align:middle line:84% You can use it to confirm post-hoc afterwards 00:41:36.160 --> 00:41:38.424 align:middle line:84% that your technique was right, yeah. 00:41:38.424 --> 00:41:39.412 align:middle line:90% STUDENT: [INAUDIBLE]? 00:41:39.412 --> 00:41:44.723 align:middle line:90% 00:41:44.723 --> 00:41:46.640 align:middle line:84% JACK HARE: Well, I mean, that's really tricky. 00:41:46.640 --> 00:41:47.990 align:middle line:84% If you're able to do an experiment where 00:41:47.990 --> 00:41:49.940 align:middle line:84% you can increase the depth of your plasma, 00:41:49.940 --> 00:41:51.747 align:middle line:84% that would be one easy way to do it. 00:41:51.747 --> 00:41:53.330 align:middle line:84% But of course, if you're in a tokamak, 00:41:53.330 --> 00:41:55.330 align:middle line:84% you can't just make the plasma twice as big just 00:41:55.330 --> 00:41:56.930 align:middle line:84% to see what would happen to the lines. 00:41:56.930 --> 00:42:01.010 align:middle line:84% And so in some experiments, you could use that technique. 00:42:01.010 --> 00:42:03.710 align:middle line:84% Otherwise, yeah, you'll have to use maybe other diagnostics 00:42:03.710 --> 00:42:05.720 align:middle line:84% to give you ideas of density and temperature 00:42:05.720 --> 00:42:07.700 align:middle line:84% that you can then check how optically thick 00:42:07.700 --> 00:42:11.270 align:middle line:84% the various lines are, and then iterate from there. 00:42:11.270 --> 00:42:14.840 align:middle line:90% 00:42:14.840 --> 00:42:16.970 align:middle line:84% Or simulation as well gives us some hints 00:42:16.970 --> 00:42:18.140 align:middle line:90% as to what the answer is. 00:42:18.140 --> 00:42:21.460 align:middle line:90% 00:42:21.460 --> 00:42:22.660 align:middle line:90% Any other questions? 00:42:22.660 --> 00:42:26.680 align:middle line:90% 00:42:26.680 --> 00:42:27.430 align:middle line:90% What are we doing? 00:42:27.430 --> 00:42:30.160 align:middle line:84% Ah, X-ray spectroscopy, very good. 00:42:30.160 --> 00:42:34.800 align:middle line:90% 00:42:34.800 --> 00:42:37.800 align:middle line:84% So the reason I'm talking about X-ray spectroscopy in particular 00:42:37.800 --> 00:42:40.380 align:middle line:84% is that quite a few people doing plasma physics 00:42:40.380 --> 00:42:42.300 align:middle line:90% end up using X-ray spectroscopy. 00:42:42.300 --> 00:42:45.630 align:middle line:84% And also, it's got its sort of niche nomenclature 00:42:45.630 --> 00:42:47.260 align:middle line:84% that I wanted to introduce you to 00:42:47.260 --> 00:42:49.110 align:middle line:84% so that when people start talking about it, 00:42:49.110 --> 00:42:51.510 align:middle line:84% you have some vague idea of what's going on. 00:42:51.510 --> 00:42:55.062 align:middle line:90% 00:42:55.062 --> 00:42:57.020 align:middle line:84% Of course, all forms of spectroscopy are valid. 00:42:57.020 --> 00:42:59.450 align:middle line:84% A lot of people do visible spectroscopy, infrared, 00:42:59.450 --> 00:42:59.990 align:middle line:90% ultraviolet. 00:42:59.990 --> 00:43:01.910 align:middle line:84% But if you're working with plasmas 00:43:01.910 --> 00:43:04.970 align:middle line:84% at fusion conditions, which are like kiloelectron volt plasmas, 00:43:04.970 --> 00:43:07.430 align:middle line:84% then you're going to be getting kiloelectron volt photons, 00:43:07.430 --> 00:43:07.970 align:middle line:90% right? 00:43:07.970 --> 00:43:10.310 align:middle line:84% And so that means they're in the X-ray regime. 00:43:10.310 --> 00:43:13.252 align:middle line:84% And X-ray spectroscopy can be a little bit different. 00:43:13.252 --> 00:43:22.910 align:middle line:90% 00:43:22.910 --> 00:43:26.485 align:middle line:84% So X-ray spectroscopy has very strong characteristic lines. 00:43:26.485 --> 00:43:34.100 align:middle line:90% 00:43:34.100 --> 00:43:38.920 align:middle line:84% So these lines tend to have a high transition 00:43:38.920 --> 00:43:41.260 align:middle line:90% probability, aij. 00:43:41.260 --> 00:43:45.250 align:middle line:90% And they tend to be narrow. 00:43:45.250 --> 00:43:47.380 align:middle line:84% So they show up very, very strongly. 00:43:47.380 --> 00:43:48.710 align:middle line:90% They're easy to identify. 00:43:48.710 --> 00:43:49.940 align:middle line:90% They're easy to work with. 00:43:49.940 --> 00:43:53.980 align:middle line:84% And these lines correspond to transitions often 00:43:53.980 --> 00:43:57.290 align:middle line:84% between some of the lowest energy levels inside our atom. 00:43:57.290 --> 00:44:02.220 align:middle line:84% So here, this 1 is not referring to some abstract concept here. 00:44:02.220 --> 00:44:05.550 align:middle line:90% This is literally n equals 1. 00:44:05.550 --> 00:44:08.220 align:middle line:84% So this is the lowest energy level down there, 00:44:08.220 --> 00:44:10.410 align:middle line:84% the energy level that your ground state hydrogen 00:44:10.410 --> 00:44:12.360 align:middle line:90% atom occupies here. 00:44:12.360 --> 00:44:14.490 align:middle line:84% And these are the other excited states. 00:44:14.490 --> 00:44:17.940 align:middle line:84% Because we're dealing with relatively high energy systems 00:44:17.940 --> 00:44:19.530 align:middle line:84% when we're doing X-ray spectroscopy, 00:44:19.530 --> 00:44:22.080 align:middle line:84% an ion may be almost completely stripped. 00:44:22.080 --> 00:44:25.655 align:middle line:84% There may be only two, or three, or one electrons here. 00:44:25.655 --> 00:44:28.640 align:middle line:90% 00:44:28.640 --> 00:44:31.700 align:middle line:84% And people start referring to these ions as helium-like 00:44:31.700 --> 00:44:32.810 align:middle line:90% or lithium-like. 00:44:32.810 --> 00:44:37.910 align:middle line:84% So a helium-like, unsurprisingly, 00:44:37.910 --> 00:44:39.320 align:middle line:90% has two electrons. 00:44:39.320 --> 00:44:44.410 align:middle line:84% And a lithium-like has three electrons. 00:44:44.410 --> 00:44:47.343 align:middle line:84% What they mean is this could be something like tungsten, 00:44:47.343 --> 00:44:49.010 align:middle line:84% or aluminum, or anything else like that. 00:44:49.010 --> 00:44:51.110 align:middle line:84% But it's so ionized that there's only two 00:44:51.110 --> 00:44:52.510 align:middle line:90% or three electrons left. 00:44:52.510 --> 00:44:56.050 align:middle line:84% And that means that you can use all of the spectroscopy, all 00:44:56.050 --> 00:44:58.180 align:middle line:84% of the quantum physics that you do on helium, which 00:44:58.180 --> 00:45:01.570 align:middle line:84% is a relatively simple system to solve compared to something more 00:45:01.570 --> 00:45:02.200 align:middle line:90% complicated. 00:45:02.200 --> 00:45:03.910 align:middle line:84% And all you have to do is replace 00:45:03.910 --> 00:45:07.570 align:middle line:84% the atomic charge, the nucleus charge, from 2 00:45:07.570 --> 00:45:09.830 align:middle line:84% to whatever your actual nuclear charge is. 00:45:09.830 --> 00:45:13.630 align:middle line:90% So you just take z from 2 to-- 00:45:13.630 --> 00:45:18.200 align:middle line:90% I don't know-- 13 for aluminum. 00:45:18.200 --> 00:45:20.638 align:middle line:84% But it means that you have a pretty good idea of what 00:45:20.638 --> 00:45:22.430 align:middle line:84% these energy levels are because the quantum 00:45:22.430 --> 00:45:24.920 align:middle line:84% physics of low atomic number elements 00:45:24.920 --> 00:45:27.130 align:middle line:90% is pretty well understood. 00:45:27.130 --> 00:45:29.040 align:middle line:84% So these characteristic lines will 00:45:29.040 --> 00:45:33.330 align:middle line:84% occur when there is some vacancy in a lower energy level. 00:45:33.330 --> 00:45:36.320 align:middle line:84% So for example, if we have an electron up here 00:45:36.320 --> 00:45:38.900 align:middle line:84% in the n equals 2 level and there's 00:45:38.900 --> 00:45:41.150 align:middle line:84% space in the n equals 1 level to drop down, 00:45:41.150 --> 00:45:44.500 align:middle line:90% it will emit a photon here. 00:45:44.500 --> 00:45:48.390 align:middle line:84% Now, why would there be space in this lower energy level? 00:45:48.390 --> 00:45:51.670 align:middle line:84% I'd updated my notes and that was also not updated as well. 00:45:51.670 --> 00:45:55.183 align:middle line:84% This may be because of collisions, or photoionization, 00:45:55.183 --> 00:45:56.350 align:middle line:90% or something else like that. 00:45:56.350 --> 00:45:58.475 align:middle line:84% If we're in a very hot plasma, it's very reasonable 00:45:58.475 --> 00:46:06.030 align:middle line:84% to have hot electrons flying around that collisionally 00:46:06.030 --> 00:46:08.610 align:middle line:84% ionize us or, indeed, just collisionally exciters 00:46:08.610 --> 00:46:11.690 align:middle line:84% up to some very high energy level, like 7. 00:46:11.690 --> 00:46:13.200 align:middle line:90% And that leaves a hole here. 00:46:13.200 --> 00:46:16.100 align:middle line:84% And because this is energetically unfavorable, 00:46:16.100 --> 00:46:18.050 align:middle line:84% to have a lower energy level unfilled, 00:46:18.050 --> 00:46:20.570 align:middle line:84% one of these electrons in one of the higher energy levels 00:46:20.570 --> 00:46:23.550 align:middle line:84% will very rapidly drop down into here. 00:46:23.550 --> 00:46:26.510 align:middle line:84% And these different transitions from down to the ground state 00:46:26.510 --> 00:46:29.280 align:middle line:84% from 2 and 3 and so on have different names. 00:46:29.280 --> 00:46:32.510 align:middle line:84% So first of all, we have what are 00:46:32.510 --> 00:46:34.160 align:middle line:90% called the K-shell transitions. 00:46:34.160 --> 00:46:38.010 align:middle line:90% 00:46:38.010 --> 00:46:40.530 align:middle line:90% This is transitions from-- 00:46:40.530 --> 00:46:44.070 align:middle line:90% or down to n equals 1. 00:46:44.070 --> 00:46:51.220 align:middle line:84% We have the K alpha, which is from n equals 2 to n equals 1. 00:46:51.220 --> 00:46:52.660 align:middle line:90% That's the one I've drawn here. 00:46:52.660 --> 00:46:56.040 align:middle line:90% You have K beta. 00:46:56.040 --> 00:47:00.150 align:middle line:90% That's n equals 3 to n equals 1. 00:47:00.150 --> 00:47:03.520 align:middle line:84% And so on, K gamma, all that sort of thing. 00:47:03.520 --> 00:47:06.030 align:middle line:84% Now, it turns out that the K alpha is always 00:47:06.030 --> 00:47:07.350 align:middle line:90% the strongest transition. 00:47:07.350 --> 00:47:12.980 align:middle line:90% 00:47:12.980 --> 00:47:15.500 align:middle line:84% So you'll typically get an electron dropping down 00:47:15.500 --> 00:47:18.270 align:middle line:84% from 2 to 1 rather than from 3 to 1 more quickly. 00:47:18.270 --> 00:47:20.030 align:middle line:84% And this line will show up more strongly. 00:47:20.030 --> 00:47:22.430 align:middle line:84% And it's strong, again, because of this overlap 00:47:22.430 --> 00:47:29.200 align:middle line:84% between the lowest energy state and the second highest n 00:47:29.200 --> 00:47:30.130 align:middle line:90% equals 2 energy state. 00:47:30.130 --> 00:47:32.230 align:middle line:84% These wave functions look most similar. 00:47:32.230 --> 00:47:33.920 align:middle line:84% As you start getting out to high ends, 00:47:33.920 --> 00:47:35.920 align:middle line:84% these wave functions start to look really weird. 00:47:35.920 --> 00:47:37.462 align:middle line:84% And when you do the overlap integral, 00:47:37.462 --> 00:47:38.740 align:middle line:90% it's not particularly large. 00:47:38.740 --> 00:47:41.230 align:middle line:84% So quantum mechanically, it's much easier for the electron 00:47:41.230 --> 00:47:44.270 align:middle line:84% to transition between these two wave functions here. 00:47:44.270 --> 00:47:46.670 align:middle line:84% So the K alpha is always strongest. 00:47:46.670 --> 00:47:48.940 align:middle line:90% We also then have the L-shell. 00:47:48.940 --> 00:47:51.700 align:middle line:90% 00:47:51.700 --> 00:47:56.400 align:middle line:84% This is transitions down to n equals 2. 00:47:56.400 --> 00:48:02.465 align:middle line:84% And you'll have L alpha, which is 3 to 2, 00:48:02.465 --> 00:48:05.220 align:middle line:90% L beta, which is 4 to 2. 00:48:05.220 --> 00:48:13.240 align:middle line:84% Then you also have the M shell and so on. 00:48:13.240 --> 00:48:15.480 align:middle line:84% But we tend to focus on the K shell 00:48:15.480 --> 00:48:18.257 align:middle line:84% because these lines are the highest energy atomic lines you 00:48:18.257 --> 00:48:20.340 align:middle line:84% can get from a system because you're dropping down 00:48:20.340 --> 00:48:22.660 align:middle line:84% to the lowest energy level from somewhere else. 00:48:22.660 --> 00:48:24.030 align:middle line:90% So these lines are very bright. 00:48:24.030 --> 00:48:26.220 align:middle line:84% And they're very good signatures of what 00:48:26.220 --> 00:48:28.080 align:middle line:90% the plasma conditions are. 00:48:28.080 --> 00:48:35.860 align:middle line:84% So just to give you an example, this is energy here 00:48:35.860 --> 00:48:37.270 align:middle line:90% and this is intensity. 00:48:37.270 --> 00:48:39.880 align:middle line:84% And we have something like copper. 00:48:39.880 --> 00:48:44.200 align:middle line:84% The copper spectrum will have some Bremsstrahlung component 00:48:44.200 --> 00:48:46.810 align:middle line:84% background here that you can never get rid of. 00:48:46.810 --> 00:48:48.435 align:middle line:84% And then at sufficiently high energies, 00:48:48.435 --> 00:48:52.170 align:middle line:84% it will have two peaks, like this. 00:48:52.170 --> 00:48:54.120 align:middle line:90% This one is the K alpha. 00:48:54.120 --> 00:48:56.150 align:middle line:90% This is the K beta. 00:48:56.150 --> 00:48:59.610 align:middle line:84% The K alpha, in this case, is 8.1 kV. 00:48:59.610 --> 00:49:02.700 align:middle line:90% 00:49:02.700 --> 00:49:07.010 align:middle line:90% And the K beta is 8.9 kV. 00:49:07.010 --> 00:49:10.040 align:middle line:90% 00:49:10.040 --> 00:49:12.740 align:middle line:84% And these lines are so narrow and so well-defined 00:49:12.740 --> 00:49:15.870 align:middle line:84% that they form a very strong spectroscopic signature. 00:49:15.870 --> 00:49:17.780 align:middle line:84% So if I'm looking inside my tokamak plasma 00:49:17.780 --> 00:49:20.990 align:middle line:84% that I want to be hydrogen, and I look at these high energy 00:49:20.990 --> 00:49:24.290 align:middle line:84% kiloelectron volt ranges, and I see peaks there, 00:49:24.290 --> 00:49:26.750 align:middle line:84% I can say straight away there is iron in my plasma, 00:49:26.750 --> 00:49:30.140 align:middle line:84% there's tungsten in my plasma, there's molybdenum in my plasma. 00:49:30.140 --> 00:49:32.175 align:middle line:84% And of course, all of those impurities 00:49:32.175 --> 00:49:34.550 align:middle line:84% are radiating very strongly because these transitions are 00:49:34.550 --> 00:49:35.400 align:middle line:90% very strong. 00:49:35.400 --> 00:49:39.667 align:middle line:84% And so that really ruins your power balance in the reactor. 00:49:39.667 --> 00:49:41.750 align:middle line:84% So a lot of spectroscopy, early spectroscopy work, 00:49:41.750 --> 00:49:43.430 align:middle line:84% at least in magnetic confinement fusion, 00:49:43.430 --> 00:49:46.490 align:middle line:84% was looking for these signatures of impurities in the plasma 00:49:46.490 --> 00:49:47.890 align:middle line:90% here. 00:49:47.890 --> 00:49:49.378 align:middle line:90% OK. 00:49:49.378 --> 00:49:50.420 align:middle line:90% Questions on all of this? 00:49:50.420 --> 00:49:52.330 align:middle line:84% The nomenclature thing is basically 00:49:52.330 --> 00:49:55.450 align:middle line:84% knowing that K means transitions to 1 and alpha 00:49:55.450 --> 00:49:58.300 align:middle line:84% and beta mean from the level above and the level above that 00:49:58.300 --> 00:50:01.510 align:middle line:84% and knowing that the K alpha is much stronger than the others 00:50:01.510 --> 00:50:03.560 align:middle line:84% and maybe knowing that sometimes people are like, 00:50:03.560 --> 00:50:06.610 align:middle line:84% this is a K alpha transition in helium, like aluminum. 00:50:06.610 --> 00:50:10.900 align:middle line:90% And you're like, ah, cool, yeah. 00:50:10.900 --> 00:50:12.205 align:middle line:90% But questions? 00:50:12.205 --> 00:50:13.420 align:middle line:90% STUDENT: [INAUDIBLE]? 00:50:13.420 --> 00:50:19.493 align:middle line:90% 00:50:19.493 --> 00:50:20.660 align:middle line:90% JACK HARE: Yeah, absolutely. 00:50:20.660 --> 00:50:23.180 align:middle line:84% Bremsstrahlung is producing those wavelengths as well, 00:50:23.180 --> 00:50:26.750 align:middle line:90% in general, but not lines. 00:50:26.750 --> 00:50:28.640 align:middle line:90% So that's why they're so unique. 00:50:28.640 --> 00:50:32.000 align:middle line:84% And maybe in some system, you could have synchrotron radiation 00:50:32.000 --> 00:50:33.020 align:middle line:90% or something like that. 00:50:33.020 --> 00:50:36.240 align:middle line:84% But in general, these are very specific. 00:50:36.240 --> 00:50:37.370 align:middle line:90% So yeah. 00:50:37.370 --> 00:50:39.060 align:middle line:84% And they're slightly different energies. 00:50:39.060 --> 00:50:42.680 align:middle line:84% So K alpha for helium-like is at a slightly higher energy 00:50:42.680 --> 00:50:44.220 align:middle line:90% than alpha for lithium-like. 00:50:44.220 --> 00:50:48.840 align:middle line:84% And so you may also then have the-- 00:50:48.840 --> 00:50:51.300 align:middle line:84% say these ones are the helium-like. 00:50:51.300 --> 00:50:55.590 align:middle line:84% And this is the K alpha and the beta for the lithium-like 00:50:55.590 --> 00:50:58.290 align:middle line:84% And then because you know exactly what these lines are 00:50:58.290 --> 00:51:00.948 align:middle line:84% because they're so specific, you can do your line ratio trick 00:51:00.948 --> 00:51:02.490 align:middle line:84% that we used before and work out what 00:51:02.490 --> 00:51:06.060 align:middle line:84% the temperature is because this is a lower ionization 00:51:06.060 --> 00:51:08.590 align:middle line:90% state than this one. 00:51:08.590 --> 00:51:09.370 align:middle line:90% Yeah. 00:51:09.370 --> 00:51:11.290 align:middle line:84% Obviously, if you are fully stripped, 00:51:11.290 --> 00:51:13.390 align:middle line:84% if you have got to a temperature where there 00:51:13.390 --> 00:51:15.160 align:middle line:84% are no electrons left in your system, 00:51:15.160 --> 00:51:17.050 align:middle line:90% you no longer have the line. 00:51:17.050 --> 00:51:19.840 align:middle line:84% You would only get a line from recombination. 00:51:19.840 --> 00:51:21.388 align:middle line:84% But the recombination has a spectrum, 00:51:21.388 --> 00:51:23.680 align:middle line:84% as we talked about, with an edge, but still a spectrum. 00:51:23.680 --> 00:51:24.715 align:middle line:90% yeah? 00:51:24.715 --> 00:51:25.930 align:middle line:90% STUDENT: [INAUDIBLE]? 00:51:25.930 --> 00:51:28.870 align:middle line:90% 00:51:28.870 --> 00:51:31.660 align:middle line:84% JACK HARE: No, I believe that is separate. 00:51:31.660 --> 00:51:35.080 align:middle line:84% Yeah, actually, it's been a while since I reminded myself 00:51:35.080 --> 00:51:36.160 align:middle line:90% what Lyman alpha was. 00:51:36.160 --> 00:51:38.670 align:middle line:84% That's the one that's 121 nanometers, right? 00:51:38.670 --> 00:51:39.545 align:middle line:90% STUDENT: [INAUDIBLE]. 00:51:39.545 --> 00:51:40.295 align:middle line:90% JACK HARE: Oh, OK. 00:51:40.295 --> 00:51:41.280 align:middle line:90% Any astrophysicists? 00:51:41.280 --> 00:51:41.780 align:middle line:90% No? 00:51:41.780 --> 00:51:42.290 align:middle line:90% OK. 00:51:42.290 --> 00:51:46.383 align:middle line:90% Yeah, that's like a UV line. 00:51:46.383 --> 00:51:48.300 align:middle line:84% Is there a chance that it is related to these? 00:51:48.300 --> 00:51:49.717 align:middle line:84% Yeah, I think it is an X-ray line, 00:51:49.717 --> 00:51:54.158 align:middle line:84% but I can't remember The most common one. 00:51:54.158 --> 00:51:55.265 align:middle line:90% It makes me think-- 00:51:55.265 --> 00:51:56.140 align:middle line:90% STUDENT: [INAUDIBLE]? 00:51:56.140 --> 00:51:59.020 align:middle line:90% 00:51:59.020 --> 00:52:01.450 align:middle line:84% JACK HARE: It's called the Lyman series or the Lyman-- 00:52:01.450 --> 00:52:02.470 align:middle line:90% there's a Balmer series. 00:52:02.470 --> 00:52:04.066 align:middle line:90% What's the Lyman series? 00:52:04.066 --> 00:52:05.687 align:middle line:90% STUDENT: [INAUDIBLE]? 00:52:05.687 --> 00:52:06.270 align:middle line:90% JACK HARE: OK. 00:52:06.270 --> 00:52:09.420 align:middle line:84% So maybe in hydrogen, they have separate names 00:52:09.420 --> 00:52:11.520 align:middle line:90% that correspond to these. 00:52:11.520 --> 00:52:14.880 align:middle line:84% And I think, historically, people were doing spectroscopy 00:52:14.880 --> 00:52:16.440 align:middle line:84% on astrophysical bodies, which were 00:52:16.440 --> 00:52:19.300 align:middle line:84% the first bodies we could looked at that had these temperatures. 00:52:19.300 --> 00:52:20.842 align:middle line:84% So people were not doing spectroscopy 00:52:20.842 --> 00:52:22.120 align:middle line:90% on copper straight away. 00:52:22.120 --> 00:52:24.400 align:middle line:84% But if you point to your spectrometer at the sun, 00:52:24.400 --> 00:52:27.510 align:middle line:84% then you can get these alphas-- or these Lyman series 00:52:27.510 --> 00:52:28.290 align:middle line:90% imbalances. 00:52:28.290 --> 00:52:29.070 align:middle line:90% I'll look that up. 00:52:29.070 --> 00:52:30.240 align:middle line:90% Good question. 00:52:30.240 --> 00:52:32.070 align:middle line:84% Any questions online or comments if you 00:52:32.070 --> 00:52:34.500 align:middle line:84% know anything about Lyman series and Balmer series? 00:52:34.500 --> 00:52:41.450 align:middle line:90% 00:52:41.450 --> 00:52:41.950 align:middle line:90% OK. 00:52:41.950 --> 00:52:44.260 align:middle line:84% We can use this in reverse to design 00:52:44.260 --> 00:52:46.690 align:middle line:90% filters for our X-ray systems. 00:52:46.690 --> 00:52:50.800 align:middle line:84% So we often want to be able to measure just the light 00:52:50.800 --> 00:52:52.223 align:middle line:90% in a certain region here. 00:52:52.223 --> 00:52:54.640 align:middle line:84% So this would be like taking a picture of just the X-rays. 00:52:54.640 --> 00:52:57.250 align:middle line:84% And so we want to be able to filter out all this other light 00:52:57.250 --> 00:52:59.515 align:middle line:84% and just use the light in this region. 00:52:59.515 --> 00:53:17.940 align:middle line:90% 00:53:17.940 --> 00:53:22.020 align:middle line:84% So this is looking at X-ray filters. 00:53:22.020 --> 00:53:24.900 align:middle line:90% So a filter is a solid object. 00:53:24.900 --> 00:53:27.690 align:middle line:84% It's usually a thin foil made out 00:53:27.690 --> 00:53:30.880 align:middle line:84% of some metal or some non-metal here. 00:53:30.880 --> 00:53:33.420 align:middle line:84% And the idea of the filters is that we still 00:53:33.420 --> 00:53:38.970 align:middle line:84% have these different energy levels here-- n equals 1, n 00:53:38.970 --> 00:53:42.180 align:middle line:90% equals 2, n equals 3 and 4. 00:53:42.180 --> 00:53:46.550 align:middle line:90% But now, this is for z equals 0. 00:53:46.550 --> 00:53:49.820 align:middle line:84% So this is for some solid, like a lump of tungsten or something 00:53:49.820 --> 00:53:50.670 align:middle line:90% like that. 00:53:50.670 --> 00:53:54.350 align:middle line:84% And then if we have a photon coming in, 00:53:54.350 --> 00:53:56.060 align:middle line:84% if there's a possibility that photon 00:53:56.060 --> 00:54:02.350 align:middle line:84% has enough energy, h-bar omega, to excite an electron from one 00:54:02.350 --> 00:54:06.160 align:middle line:84% of the inner shells, from 1 and 2 from 3, 00:54:06.160 --> 00:54:08.270 align:middle line:84% then that process is now favorable. 00:54:08.270 --> 00:54:10.240 align:middle line:84% It's likely that photon will be absorbed. 00:54:10.240 --> 00:54:12.340 align:middle line:84% If it doesn't match with any of these bandgaps 00:54:12.340 --> 00:54:15.620 align:middle line:84% or any of these transitions, then the photon will go through. 00:54:15.620 --> 00:54:20.110 align:middle line:84% But if it does match, then it will get absorbed. 00:54:20.110 --> 00:54:27.540 align:middle line:84% So what we see in our absorption plot for a filter-- 00:54:27.540 --> 00:54:29.990 align:middle line:84% so this is that quantity, alpha, the opacity, 00:54:29.990 --> 00:54:33.880 align:middle line:90% as a function of frequency-- 00:54:33.880 --> 00:54:41.080 align:middle line:84% is we see a series of what are called edges here. 00:54:41.080 --> 00:54:46.820 align:middle line:90% So this is the L edge. 00:54:46.820 --> 00:54:48.840 align:middle line:90% And this is the K edge. 00:54:48.840 --> 00:54:53.210 align:middle line:90% 00:54:53.210 --> 00:54:57.740 align:middle line:84% And what you get is your lines corresponding 00:54:57.740 --> 00:55:03.360 align:middle line:84% to your frequencies corresponding 00:55:03.360 --> 00:55:07.920 align:middle line:84% to K alpha, K beta, all the way up to the highest K, which 00:55:07.920 --> 00:55:11.610 align:middle line:84% is ionizing from whatever the highest occupied state is up 00:55:11.610 --> 00:55:13.170 align:middle line:90% into the continuum. 00:55:13.170 --> 00:55:15.490 align:middle line:90% And same here, you get-- 00:55:15.490 --> 00:55:19.440 align:middle line:84% I'm trying to space these parabolically-- 00:55:19.440 --> 00:55:21.410 align:middle line:90% L alpha, L theta. 00:55:21.410 --> 00:55:24.690 align:middle line:90% 00:55:24.690 --> 00:55:27.350 align:middle line:84% So effectively, you have a sudden increase in absorption 00:55:27.350 --> 00:55:31.100 align:middle line:84% whenever it is possible to do this ionization. 00:55:31.100 --> 00:55:32.510 align:middle line:84% If you have done the homework yet 00:55:32.510 --> 00:55:34.010 align:middle line:84% and you've looked at some of the other filters 00:55:34.010 --> 00:55:35.802 align:middle line:84% that you can generate on the Henke website, 00:55:35.802 --> 00:55:38.330 align:middle line:84% you will have noticed these really weird absorption 00:55:38.330 --> 00:55:38.960 align:middle line:90% features. 00:55:38.960 --> 00:55:40.850 align:middle line:84% Henke normally gives you transmission. 00:55:40.850 --> 00:55:43.100 align:middle line:84% And so you will have seen 1 over this. 00:55:43.100 --> 00:55:44.935 align:middle line:84% The absorption is 1 over the transmission. 00:55:44.935 --> 00:55:47.060 align:middle line:84% But you will have noticed these really sharp edges. 00:55:47.060 --> 00:55:48.443 align:middle line:90% That's not a numerical problem. 00:55:48.443 --> 00:55:50.360 align:middle line:84% When you first see it, you think, oh, the code 00:55:50.360 --> 00:55:51.200 align:middle line:90% is broken here. 00:55:51.200 --> 00:55:55.010 align:middle line:84% No, these correspond to these very strong absorption edges 00:55:55.010 --> 00:55:55.590 align:middle line:90% here. 00:55:55.590 --> 00:56:02.580 align:middle line:84% So if you have a spectrum that has some lines in it 00:56:02.580 --> 00:56:04.960 align:middle line:84% and you put that spectrum through this filter, 00:56:04.960 --> 00:56:08.100 align:middle line:84% this filter would cut out, for example, this highest energy 00:56:08.100 --> 00:56:08.700 align:middle line:90% line here. 00:56:08.700 --> 00:56:12.780 align:middle line:84% And you'd just be left with the spectrum in this region. 00:56:12.780 --> 00:56:15.087 align:middle line:84% So this is how you use X-rays to do filtering. 00:56:15.087 --> 00:56:20.224 align:middle line:90% 00:56:20.224 --> 00:56:23.080 align:middle line:90% Oh, OK. 00:56:23.080 --> 00:56:23.830 align:middle line:90% Questions on that? 00:56:23.830 --> 00:56:27.780 align:middle line:90% 00:56:27.780 --> 00:56:30.260 align:middle line:84% And the position of these edges depends on the element. 00:56:30.260 --> 00:56:33.050 align:middle line:84% So if I use an aluminum filter, or a tungsten filter, 00:56:33.050 --> 00:56:35.940 align:middle line:84% or plastic filter, they'll have edges in different places. 00:56:35.940 --> 00:56:37.415 align:middle line:84% And so by using different filters, 00:56:37.415 --> 00:56:39.813 align:middle line:84% I can image different parts of the spectrum. 00:56:39.813 --> 00:56:41.730 align:middle line:84% So we'll talk about X-ray imaging in a moment. 00:56:41.730 --> 00:56:42.335 align:middle line:90% Yeah? 00:56:42.335 --> 00:56:45.560 align:middle line:90% STUDENT: [INAUDIBLE]? 00:56:45.560 --> 00:56:47.948 align:middle line:84% JACK HARE: Not at all, yeah, just photo-absorbed, yeah. 00:56:47.948 --> 00:56:49.382 align:middle line:90% STUDENT: [INAUDIBLE]? 00:56:49.382 --> 00:56:55.112 align:middle line:90% 00:56:55.112 --> 00:56:57.070 align:middle line:84% JACK HARE: Yeah, so that's a bit that doesn't-- 00:56:57.070 --> 00:56:58.000 align:middle line:90% yeah, yeah. 00:56:58.000 --> 00:57:02.890 align:middle line:84% That's the unique quantum and treating the photon as a wave 00:57:02.890 --> 00:57:04.860 align:middle line:90% in order to get-- 00:57:04.860 --> 00:57:06.527 align:middle line:84% well, you need a quantum treatment of it 00:57:06.527 --> 00:57:07.985 align:middle line:84% in order to get this roll-off here. 00:57:07.985 --> 00:57:10.500 align:middle line:84% Yeah, my explanation only covers why there's a sharp edge. 00:57:10.500 --> 00:57:13.042 align:middle line:84% I haven't seen a nice intuitive explanation for this roll-off 00:57:13.042 --> 00:57:13.950 align:middle line:90% afterwards. 00:57:13.950 --> 00:57:17.010 align:middle line:84% But all materials at high enough energies, 00:57:17.010 --> 00:57:20.070 align:middle line:84% no matter what, their absorption goes down to 0. 00:57:20.070 --> 00:57:24.015 align:middle line:84% So gamma rays will get through anything eventually, Yeah. 00:57:24.015 --> 00:57:26.750 align:middle line:90% 00:57:26.750 --> 00:57:27.870 align:middle line:90% STUDENT: Professor? 00:57:27.870 --> 00:57:28.670 align:middle line:84% JACK HARE: Oh, sorry, I'm just going 00:57:28.670 --> 00:57:29.930 align:middle line:84% to answer another question, Jacob first. 00:57:29.930 --> 00:57:31.140 align:middle line:90% And then I'll get back to you. 00:57:31.140 --> 00:57:33.515 align:middle line:84% So the question was, why the edges get taller and taller? 00:57:33.515 --> 00:57:38.090 align:middle line:84% I think it's due to the likelihood of this interaction, 00:57:38.090 --> 00:57:39.978 align:middle line:90% but I'm not sure, yeah. 00:57:39.978 --> 00:57:40.520 align:middle line:90% Sorry, Jacob. 00:57:40.520 --> 00:57:42.128 align:middle line:90% Your question? 00:57:42.128 --> 00:57:43.670 align:middle line:84% STUDENT: How do you design a material 00:57:43.670 --> 00:57:48.830 align:middle line:84% to specifically change or take out a certain-- like the K 00:57:48.830 --> 00:57:50.595 align:middle line:90% edge or the L edge? 00:57:50.595 --> 00:57:52.220 align:middle line:84% JACK HARE: You don't design a material. 00:57:52.220 --> 00:57:54.930 align:middle line:84% You have a look and see what materials are available. 00:57:54.930 --> 00:57:57.330 align:middle line:84% STUDENT: Yeah, I mean, how do you choose a material? 00:57:57.330 --> 00:57:58.130 align:middle line:84% JACK HARE: How do you choose a material? 00:57:58.130 --> 00:58:00.383 align:middle line:84% Well I choose it by going on the Henke database. 00:58:00.383 --> 00:58:01.550 align:middle line:90% And I generate these curves. 00:58:01.550 --> 00:58:03.625 align:middle line:90% And I see what they are. 00:58:03.625 --> 00:58:05.510 align:middle line:84% And I guess, if you're very experienced, 00:58:05.510 --> 00:58:07.580 align:middle line:84% you just know, for example, that this K ege 00:58:07.580 --> 00:58:09.830 align:middle line:90% is at 1.6 kV for aluminum. 00:58:09.830 --> 00:58:13.070 align:middle line:84% And if you're trying to measure photons of energies below that, 00:58:13.070 --> 00:58:17.120 align:middle line:84% then 1.6, this aluminum, is quite a good filter. 00:58:17.120 --> 00:58:20.430 align:middle line:84% But you can't engineer a material to have a K edge. 00:58:20.430 --> 00:58:21.638 align:middle line:90% It's an atomic process. 00:58:21.638 --> 00:58:23.180 align:middle line:84% So it really depends on the elements. 00:58:23.180 --> 00:58:25.190 align:middle line:84% If, for example, you have a filter made out 00:58:25.190 --> 00:58:26.930 align:middle line:84% of a mixture of two elements, then it's 00:58:26.930 --> 00:58:30.290 align:middle line:84% just the combination of the absorption for those two 00:58:30.290 --> 00:58:31.440 align:middle line:90% different elements. 00:58:31.440 --> 00:58:33.440 align:middle line:90% So yeah. 00:58:33.440 --> 00:58:36.260 align:middle line:84% STUDENT: And you have to get the L edge to do the K edge, right? 00:58:36.260 --> 00:58:37.183 align:middle line:90% Or can you just get-- 00:58:37.183 --> 00:58:37.850 align:middle line:90% JACK HARE: Yeah. 00:58:37.850 --> 00:58:38.350 align:middle line:90% No, no. 00:58:38.350 --> 00:58:41.630 align:middle line:84% The L edge will always be there as well, and the M edge, and so 00:58:41.630 --> 00:58:43.670 align:middle line:84% on, but down to lower and lower energies, right? 00:58:43.670 --> 00:58:47.597 align:middle line:84% So they may not be interesting for your bit of the spectrum. 00:58:47.597 --> 00:58:49.930 align:middle line:84% STUDENT: All right, so you'll still see the bottom ones. 00:58:49.930 --> 00:58:53.800 align:middle line:84% But you just know that they are too low of an energy to-- 00:58:53.800 --> 00:58:56.058 align:middle line:84% JACK HARE: If you think your spectrum looks like this 00:58:56.058 --> 00:58:58.600 align:middle line:84% and you know that there's no interesting features down here-- 00:58:58.600 --> 00:59:00.948 align:middle line:84% it's just Bremsstrahlung with very bright lines 00:59:00.948 --> 00:59:02.740 align:middle line:84% up at high energies-- then you don't really 00:59:02.740 --> 00:59:05.740 align:middle line:84% care what the structure is down here because when you multiply 00:59:05.740 --> 00:59:08.530 align:middle line:84% the transmission via your spectrum, 00:59:08.530 --> 00:59:10.030 align:middle line:84% there'll be like little fluctuations 00:59:10.030 --> 00:59:12.530 align:middle line:84% down here that you don't care about because your spectrum is 00:59:12.530 --> 00:59:14.635 align:middle line:84% going to be dominated by these lines you think. 00:59:14.635 --> 00:59:17.210 align:middle line:90% STUDENT: OK, makes sense. 00:59:17.210 --> 00:59:19.420 align:middle line:90% JACK HARE: Other questions? 00:59:19.420 --> 00:59:21.290 align:middle line:84% OK, let's talk about X-ray imaging, 00:59:21.290 --> 00:59:23.500 align:middle line:84% so why we might want to use a filter. 00:59:23.500 --> 00:59:25.420 align:middle line:84% Obviously, if we're doing spectroscopy, 00:59:25.420 --> 00:59:27.010 align:middle line:84% we don't really care about the filters 00:59:27.010 --> 00:59:28.930 align:middle line:84% because we can just do spectroscopy. 00:59:28.930 --> 00:59:30.623 align:middle line:84% And we can see where the lines are. 00:59:30.623 --> 00:59:32.290 align:middle line:84% But if you don't want to do spectroscopy 00:59:32.290 --> 00:59:33.850 align:middle line:84% and you want to make an image, you're 00:59:33.850 --> 00:59:35.308 align:middle line:84% going to need some of these filters 00:59:35.308 --> 00:59:37.700 align:middle line:84% so that you know what energies you're looking at. 00:59:37.700 --> 00:59:38.950 align:middle line:90% So this is X-ray imaging. 00:59:38.950 --> 00:59:45.110 align:middle line:90% 00:59:45.110 --> 00:59:47.350 align:middle line:84% So one of the facts about X-ray imaging 00:59:47.350 --> 00:59:48.670 align:middle line:90% is that there are no lenses. 00:59:48.670 --> 00:59:52.410 align:middle line:90% 00:59:52.410 --> 00:59:54.150 align:middle line:84% And that is a consequence of the fact 00:59:54.150 --> 00:59:58.580 align:middle line:84% that the refractive index is roughly 1 for X-rays. 00:59:58.580 --> 01:00:01.130 align:middle line:84% And lenses work on having a difference in refractive index 01:00:01.130 --> 01:00:01.768 align:middle line:90% from air. 01:00:01.768 --> 01:00:04.310 align:middle line:84% So if your refractive index of all your materials is about 1, 01:00:04.310 --> 01:00:06.320 align:middle line:90% you can no longer bend the rays. 01:00:06.320 --> 01:00:08.750 align:middle line:84% So the simplest thing that you can do for X-ray imaging 01:00:08.750 --> 01:00:10.010 align:middle line:90% is called pinhole imaging. 01:00:10.010 --> 01:00:16.310 align:middle line:90% 01:00:16.310 --> 01:00:20.000 align:middle line:84% Pinhole imaging is what the first cameras for visible light 01:00:20.000 --> 01:00:21.080 align:middle line:90% used as well. 01:00:21.080 --> 01:00:24.450 align:middle line:84% You have your object, which, in this case, 01:00:24.450 --> 01:00:27.740 align:middle line:84% I'm drawing as like a triangle with very little symmetry 01:00:27.740 --> 01:00:30.470 align:middle line:84% for reasons that might become apparent later on. 01:00:30.470 --> 01:00:36.890 align:middle line:84% You have your pinhole, which is a little opening of diameter 01:00:36.890 --> 01:00:41.540 align:middle line:84% d in some plate, which is otherwise completely absorbing. 01:00:41.540 --> 01:00:43.890 align:middle line:84% And then this is just geometric optics. 01:00:43.890 --> 01:00:49.750 align:middle line:84% So you trace the rays of light from the corners of your object 01:00:49.750 --> 01:00:50.890 align:middle line:90% through the pinhole. 01:00:50.890 --> 01:00:51.993 align:middle line:90% And if you get it right-- 01:00:51.993 --> 01:00:53.660 align:middle line:84% and I'm probably going to get it wrong-- 01:00:53.660 --> 01:00:58.703 align:middle line:84% you get an object which is inverted from the one 01:00:58.703 --> 01:00:59.620 align:middle line:90% that you started with. 01:00:59.620 --> 01:01:00.630 align:middle line:90% So it's upside down. 01:01:00.630 --> 01:01:04.795 align:middle line:84% And it's flipped up-down and flipped left-right as well. 01:01:04.795 --> 01:01:06.170 align:middle line:84% That's not usually a big problem. 01:01:06.170 --> 01:01:10.640 align:middle line:84% You can usually work out what's going on. 01:01:10.640 --> 01:01:12.310 align:middle line:84% The object will also be magnified. 01:01:12.310 --> 01:01:15.790 align:middle line:84% So there's some distance, u, between your object 01:01:15.790 --> 01:01:18.370 align:middle line:84% and your pinhole and some distance, v, 01:01:18.370 --> 01:01:20.605 align:middle line:84% between your pinhole and your detector. 01:01:20.605 --> 01:01:23.060 align:middle line:90% It could be film or some camera. 01:01:23.060 --> 01:01:34.010 align:middle line:84% And so this is also magnified by the ratio of v upon u. 01:01:34.010 --> 01:01:37.250 align:middle line:84% And you can check that out by drawing some lines for yourself. 01:01:37.250 --> 01:01:40.010 align:middle line:84% And you'll see very quickly, from geometric arguments 01:01:40.010 --> 01:01:42.110 align:middle line:84% and similarity of triangles, that you get 01:01:42.110 --> 01:01:44.480 align:middle line:90% out this magnification here. 01:01:44.480 --> 01:01:47.880 align:middle line:90% But this will also be blurred. 01:01:47.880 --> 01:01:50.490 align:middle line:84% So you'll not get a perfect image. 01:01:50.490 --> 01:01:52.960 align:middle line:84% And it will be blurred by two effects. 01:01:52.960 --> 01:01:55.050 align:middle line:84% The first one is geometric blurring. 01:01:55.050 --> 01:02:01.160 align:middle line:90% 01:02:01.160 --> 01:02:04.180 align:middle line:84% The geometric blurring is a function of the fact 01:02:04.180 --> 01:02:07.450 align:middle line:84% that you have to have some finite size pinhole here. 01:02:07.450 --> 01:02:10.540 align:middle line:84% Ideally, this pinhole would be infinitesimally small. 01:02:10.540 --> 01:02:12.100 align:middle line:84% And then all of your rays of light 01:02:12.100 --> 01:02:13.210 align:middle line:84% would have to go through the pinhole 01:02:13.210 --> 01:02:14.543 align:middle line:90% to make it through the detector. 01:02:14.543 --> 01:02:16.840 align:middle line:84% In practice, if your pinhole is very, very small, 01:02:16.840 --> 01:02:18.880 align:middle line:84% then you don't get any light through at all. 01:02:18.880 --> 01:02:20.600 align:middle line:84% And you don't get a very bright image. 01:02:20.600 --> 01:02:23.050 align:middle line:84% So you have to increase the size of your pinhole 01:02:23.050 --> 01:02:25.390 align:middle line:84% to get enough light through to make an image. 01:02:25.390 --> 01:02:27.370 align:middle line:84% The geometric blurring is effectively-- 01:02:27.370 --> 01:02:32.010 align:middle line:84% if you think that your object consists 01:02:32.010 --> 01:02:36.450 align:middle line:84% of two little bright blobs, like this-- so you're looking at it. 01:02:36.450 --> 01:02:39.430 align:middle line:84% And it's just two little LEDs, like that. 01:02:39.430 --> 01:02:44.410 align:middle line:84% The projection of those dots, say a dot here and a dot here, 01:02:44.410 --> 01:02:45.550 align:middle line:90% through the pinhole-- 01:02:45.550 --> 01:02:48.310 align:middle line:90% 01:02:48.310 --> 01:02:52.142 align:middle line:84% I draw one of these for the top side of the pinhole 01:02:52.142 --> 01:02:54.100 align:middle line:84% and one of them the bottom side of the pinhole. 01:02:54.100 --> 01:02:56.320 align:middle line:84% So if this is just a missing light uniformly 01:02:56.320 --> 01:03:01.610 align:middle line:84% in 4 pi steradian, then it will project a circle through here. 01:03:01.610 --> 01:03:05.420 align:middle line:84% So we will end up not with two dots, but with two circles. 01:03:05.420 --> 01:03:06.758 align:middle line:90% So this is purely geometric. 01:03:06.758 --> 01:03:08.050 align:middle line:90% I'm just using ray optics here. 01:03:08.050 --> 01:03:10.450 align:middle line:84% I don't need to think about waves whatsoever. 01:03:10.450 --> 01:03:12.100 align:middle line:84% And the diameter of these circles 01:03:12.100 --> 01:03:18.490 align:middle line:84% here is going to be equal to M plus 1 times the pinhole size. 01:03:18.490 --> 01:03:20.500 align:middle line:84% So we can change how much this blur occurs 01:03:20.500 --> 01:03:22.530 align:middle line:84% by changing our magnification and also 01:03:22.530 --> 01:03:23.530 align:middle line:90% by changing the pinhole. 01:03:23.530 --> 01:03:26.590 align:middle line:84% And in the limit that our pinhole size becomes very small, 01:03:26.590 --> 01:03:28.430 align:middle line:84% our blur also becomes very small. 01:03:28.430 --> 01:03:30.410 align:middle line:84% And we can resolve point objects again. 01:03:30.410 --> 01:03:35.430 align:middle line:90% But like I said, we need-- 01:03:35.430 --> 01:03:38.970 align:middle line:84% well, if we have a very small pinhole diameter, 01:03:38.970 --> 01:03:41.570 align:middle line:90% then we have no light. 01:03:41.570 --> 01:03:44.050 align:middle line:90% So there's a trade-off here. 01:03:44.050 --> 01:03:45.750 align:middle line:84% And if you do photography and you're 01:03:45.750 --> 01:03:48.180 align:middle line:84% aware of f numbers and things like that, some of this 01:03:48.180 --> 01:03:49.450 align:middle line:90% may be very familiar to you. 01:03:49.450 --> 01:03:53.460 align:middle line:84% But for those of you who don't, I think this treatment is valid. 01:03:53.460 --> 01:03:56.910 align:middle line:84% There's another limit, which is the diffraction limit. 01:03:56.910 --> 01:04:00.303 align:middle line:90% 01:04:00.303 --> 01:04:02.720 align:middle line:84% And this is where we need to take the wave nature of light 01:04:02.720 --> 01:04:03.575 align:middle line:90% into account. 01:04:03.575 --> 01:04:06.320 align:middle line:90% 01:04:06.320 --> 01:04:09.805 align:middle line:84% So we have our little pinhole again here. 01:04:09.805 --> 01:04:12.610 align:middle line:90% 01:04:12.610 --> 01:04:14.650 align:middle line:84% But we know, from Huygens principle, 01:04:14.650 --> 01:04:19.160 align:middle line:84% if we got some wavefronts coming in like this, 01:04:19.160 --> 01:04:21.950 align:middle line:84% every point on the wavefront is a source 01:04:21.950 --> 01:04:24.170 align:middle line:90% of spherical wavefronts. 01:04:24.170 --> 01:04:26.910 align:middle line:90% 01:04:26.910 --> 01:04:29.670 align:middle line:84% Normally, when there's no pinhole here, 01:04:29.670 --> 01:04:31.920 align:middle line:84% that doesn't matter because our next wavefront is then 01:04:31.920 --> 01:04:36.120 align:middle line:84% made out of the sum of all of these little spherical 01:04:36.120 --> 01:04:36.960 align:middle line:90% wavefronts. 01:04:36.960 --> 01:04:41.130 align:middle line:84% But when we put our pinhole aperture in the way, 01:04:41.130 --> 01:04:43.840 align:middle line:84% we block out some of those wavefronts. 01:04:43.840 --> 01:04:47.330 align:middle line:84% And instead, we start to get diffraction. 01:04:47.330 --> 01:04:51.220 align:middle line:84% And so we start to get spherical waves coming out from this. 01:04:51.220 --> 01:04:53.250 align:middle line:84% And so if we initially had a point source, 01:04:53.250 --> 01:04:56.740 align:middle line:84% it's now going to be imaged into a blurry source here. 01:04:56.740 --> 01:05:02.760 align:middle line:90% And so the-- which one's-- 01:05:02.760 --> 01:05:03.972 align:middle line:90% OK, I can't remember. 01:05:03.972 --> 01:05:05.430 align:middle line:84% I think it's the Rayleigh criteria. 01:05:05.430 --> 01:05:10.600 align:middle line:84% The Rayleigh criteria says that if you have two dots like this, 01:05:10.600 --> 01:05:14.800 align:middle line:84% for example, that are some distance apart then 01:05:14.800 --> 01:05:22.380 align:middle line:84% we can only distinguish them if their blur is separated 01:05:22.380 --> 01:05:25.650 align:middle line:84% and this separation, which sets the resolution, 01:05:25.650 --> 01:05:31.390 align:middle line:90% is 1.22 lambda over d. 01:05:31.390 --> 01:05:32.380 align:middle line:90% That's an angle space. 01:05:32.380 --> 01:05:37.420 align:middle line:84% So multiply it by v to bring that angle into a real position 01:05:37.420 --> 01:05:38.810 align:middle line:90% on our detector here. 01:05:38.810 --> 01:05:42.580 align:middle line:84% So this 1.22 comes from zeros of the Airy function. 01:05:42.580 --> 01:05:45.760 align:middle line:84% These are actually like little sinks. 01:05:45.760 --> 01:05:48.850 align:middle line:84% And we're trying to make sure that the first zeros are 01:05:48.850 --> 01:05:50.225 align:middle line:84% separated between these two here. 01:05:50.225 --> 01:05:51.683 align:middle line:84% So you may have seen this if you've 01:05:51.683 --> 01:05:53.110 align:middle line:90% done diffraction theory before. 01:05:53.110 --> 01:05:56.918 align:middle line:84% So the geometric blur doesn't care about the wavelength 01:05:56.918 --> 01:05:57.460 align:middle line:90% of the light. 01:05:57.460 --> 01:05:59.200 align:middle line:84% It doesn't care about the energy of the photons. 01:05:59.200 --> 01:06:01.480 align:middle line:84% The diffraction blur does care about the wavelength 01:06:01.480 --> 01:06:03.620 align:middle line:84% of the light because it's a wave effect here. 01:06:03.620 --> 01:06:05.950 align:middle line:84% And so we can make the diffractive blur go away 01:06:05.950 --> 01:06:10.190 align:middle line:84% by having a bigger pinhole or by having a shorter wavelength. 01:06:10.190 --> 01:06:13.750 align:middle line:84% So if we go to a bigger pinhole, then our geometric blur 01:06:13.750 --> 01:06:14.530 align:middle line:90% will be worse. 01:06:14.530 --> 01:06:16.780 align:middle line:84% And so there's actually a trade-off between these two. 01:06:16.780 --> 01:06:18.405 align:middle line:84% There'll be a sweet spot that gives you 01:06:18.405 --> 01:06:20.590 align:middle line:84% the best resolution, where you minimize 01:06:20.590 --> 01:06:23.560 align:middle line:84% the sum of the diffraction and the geometric resolution. 01:06:23.560 --> 01:06:28.030 align:middle line:84% But you need to think about this when you're designing pinholes. 01:06:28.030 --> 01:06:29.115 align:middle line:90% OK. 01:06:29.115 --> 01:06:30.490 align:middle line:84% Oh, the other thing about this is 01:06:30.490 --> 01:06:32.650 align:middle line:84% if you have a source that is emitting lots of light 01:06:32.650 --> 01:06:34.510 align:middle line:84% in lots of different wavelengths, 01:06:34.510 --> 01:06:37.120 align:middle line:84% then the short wavelengths will be distractingly blurred. 01:06:37.120 --> 01:06:39.370 align:middle line:84% And they'll be smeared out over your detector. 01:06:39.370 --> 01:06:41.320 align:middle line:84% And the long wavelength won't be. 01:06:41.320 --> 01:06:43.840 align:middle line:84% But that means that you'll have this blur over 01:06:43.840 --> 01:06:46.360 align:middle line:84% your whole detector from the short wavelengths, which 01:06:46.360 --> 01:06:48.080 align:middle line:90% reduces your signal to noise. 01:06:48.080 --> 01:06:54.420 align:middle line:84% And so this is especially where you want to have a filter. 01:06:54.420 --> 01:06:58.880 align:middle line:84% So you want to filter out the low wavelengths so that they 01:06:58.880 --> 01:07:01.302 align:middle line:90% don't blur out your image. 01:07:01.302 --> 01:07:03.260 align:middle line:84% And you want to just have the high wavelengths, 01:07:03.260 --> 01:07:05.570 align:middle line:84% like these ones here, make an image just 01:07:05.570 --> 01:07:08.240 align:middle line:84% in some of the K alpha emission from the very hot parts 01:07:08.240 --> 01:07:10.830 align:middle line:90% of your plasma. 01:07:10.830 --> 01:07:11.330 align:middle line:90% OK. 01:07:11.330 --> 01:07:12.140 align:middle line:90% Questions? 01:07:12.140 --> 01:07:22.420 align:middle line:90% 01:07:22.420 --> 01:07:23.420 align:middle line:90% Yeah? 01:07:23.420 --> 01:07:24.572 align:middle line:90% STUDENT: [INAUDIBLE]? 01:07:24.572 --> 01:07:29.680 align:middle line:90% 01:07:29.680 --> 01:07:30.400 align:middle line:90% JACK HARE: Yes. 01:07:30.400 --> 01:07:31.364 align:middle line:90% STUDENT: [INAUDIBLE]? 01:07:31.364 --> 01:07:38.600 align:middle line:90% 01:07:38.600 --> 01:07:41.570 align:middle line:84% JACK HARE: Yes, I'm not sure how that 01:07:41.570 --> 01:07:44.810 align:middle line:84% comes into this geometric optics framework. 01:07:44.810 --> 01:07:47.977 align:middle line:90% STUDENT: [INAUDIBLE]. 01:07:47.977 --> 01:07:48.560 align:middle line:90% JACK HARE: OK. 01:07:48.560 --> 01:07:49.850 align:middle line:84% Yeah, I see where that's coming from. 01:07:49.850 --> 01:07:50.933 align:middle line:90% But this is for a pinhole. 01:07:50.933 --> 01:07:52.720 align:middle line:84% It's always going to be inverted. 01:07:52.720 --> 01:07:55.480 align:middle line:84% I guess, theoretically, if you put two pinholes-- no, 01:07:55.480 --> 01:07:57.070 align:middle line:90% that doesn't work. 01:07:57.070 --> 01:07:59.140 align:middle line:90% Nope, it's always inverted. 01:07:59.140 --> 01:08:02.680 align:middle line:84% Yeah, so maybe it's negative in someone's sign convention. 01:08:02.680 --> 01:08:05.230 align:middle line:84% But not in what I'm using here because it's always true. 01:08:05.230 --> 01:08:07.038 align:middle line:90% Yeah, good question. 01:08:07.038 --> 01:08:08.036 align:middle line:90% STUDENT: [INAUDIBLE]? 01:08:08.036 --> 01:08:17.020 align:middle line:90% 01:08:17.020 --> 01:08:17.830 align:middle line:90% JACK HARE: Yeah. 01:08:17.830 --> 01:08:20.319 align:middle line:84% Well, what I've missed out here is, in fact, 01:08:20.319 --> 01:08:24.010 align:middle line:84% that the transmission of as, you know, a thin bit of metal foil 01:08:24.010 --> 01:08:26.149 align:middle line:84% is actually opaque to visible light. 01:08:26.149 --> 01:08:29.170 align:middle line:84% So if I put a very thin bit of aluminum foil in there, 01:08:29.170 --> 01:08:31.029 align:middle line:84% I will definitely block out the light. 01:08:31.029 --> 01:08:33.020 align:middle line:84% And you need like 200 nanometers. 01:08:33.020 --> 01:08:36.069 align:middle line:84% So you can just deposit it on some basically transparent 01:08:36.069 --> 01:08:37.279 align:middle line:90% plastic. 01:08:37.279 --> 01:08:40.115 align:middle line:84% And then you will also get the filtering from the aluminum K 01:08:40.115 --> 01:08:41.130 align:middle line:90% edge, for example. 01:08:41.130 --> 01:08:43.460 align:middle line:84% So yeah, if we haven't gone down to very low energies, 01:08:43.460 --> 01:08:45.660 align:middle line:84% this is kind of like an X-ray regime treatment of it 01:08:45.660 --> 01:08:48.229 align:middle line:84% because, of course, you need X-ray photons in order 01:08:48.229 --> 01:08:50.066 align:middle line:90% to even get the L edge. 01:08:50.066 --> 01:08:54.859 align:middle line:84% In reality, this goes down and some other stuff happens down 01:08:54.859 --> 01:08:57.470 align:middle line:90% at this visible wavelength. 01:08:57.470 --> 01:08:59.838 align:middle line:84% Yeah, but any metal that is sufficiently thick-- 01:08:59.838 --> 01:09:01.880 align:middle line:84% and it doesn't need to be very thick-- will block 01:09:01.880 --> 01:09:03.290 align:middle line:90% all the visible light out. 01:09:03.290 --> 01:09:04.480 align:middle line:90% Yeah? 01:09:04.480 --> 01:09:05.460 align:middle line:90% STUDENT: [INAUDIBLE]? 01:09:05.460 --> 01:09:13.029 align:middle line:90% 01:09:13.029 --> 01:09:16.069 align:middle line:90% JACK HARE: Yes, you're right. 01:09:16.069 --> 01:09:18.800 align:middle line:84% I just constantly get confused between wavelength 01:09:18.800 --> 01:09:19.609 align:middle line:90% and frequency. 01:09:19.609 --> 01:09:22.189 align:middle line:90% 01:09:22.189 --> 01:09:28.630 align:middle line:84% Filter out long wavelengths, which 01:09:28.630 --> 01:09:31.146 align:middle line:90% is visible light, generally. 01:09:31.146 --> 01:09:34.350 align:middle line:90% 01:09:34.350 --> 01:09:35.715 align:middle line:90% OK, good question. 01:09:35.715 --> 01:09:38.779 align:middle line:90% 01:09:38.779 --> 01:09:39.995 align:middle line:90% You also do imaging-- 01:09:39.995 --> 01:09:41.870 align:middle line:84% and I'm not going to talk about it at length. 01:09:41.870 --> 01:09:44.630 align:middle line:84% Pinhole imaging is quite limited. 01:09:44.630 --> 01:09:53.359 align:middle line:84% You can also do imaging with bent crystals. 01:09:53.359 --> 01:09:57.990 align:middle line:84% So if you've ever looked at diffraction of X-rays 01:09:57.990 --> 01:10:01.770 align:middle line:84% from crystals, you'll know that the crystals will diffract 01:10:01.770 --> 01:10:03.640 align:middle line:90% light of certain wavelengths. 01:10:03.640 --> 01:10:05.190 align:middle line:84% And if you have a bent crystal, you 01:10:05.190 --> 01:10:06.520 align:middle line:90% can also do focusing with it. 01:10:06.520 --> 01:10:08.730 align:middle line:84% So people spend a lot of time very gently 01:10:08.730 --> 01:10:10.470 align:middle line:90% bending bits of crystal. 01:10:10.470 --> 01:10:12.330 align:middle line:84% And that makes a reflective lens. 01:10:12.330 --> 01:10:15.000 align:middle line:84% So you can't have a transmissive lens. 01:10:15.000 --> 01:10:17.560 align:middle line:84% But you can have a bent mirror, effectively. 01:10:17.560 --> 01:10:19.380 align:middle line:84% So there are two ways to focus light. 01:10:19.380 --> 01:10:23.820 align:middle line:84% You can have a lens like this that your light goes through. 01:10:23.820 --> 01:10:27.780 align:middle line:84% Or equivalently, you can have a mirror, 01:10:27.780 --> 01:10:30.190 align:middle line:84% like this, that the light reflects off. 01:10:30.190 --> 01:10:32.800 align:middle line:84% And because the mirror is bent, they 01:10:32.800 --> 01:10:34.720 align:middle line:84% will get focused to a different point. 01:10:34.720 --> 01:10:36.430 align:middle line:84% And as you adjust this mirror, it 01:10:36.430 --> 01:10:38.140 align:middle line:84% will depend where this gets focused on. 01:10:38.140 --> 01:10:40.210 align:middle line:84% Now, even a crystal is not a mirror for X-rays. 01:10:40.210 --> 01:10:42.890 align:middle line:84% It's a mirror for a certain wavelength of light. 01:10:42.890 --> 01:10:46.030 align:middle line:84% And so if you put your detector here, 01:10:46.030 --> 01:10:50.200 align:middle line:84% you might have the K alpha focused onto your detector. 01:10:50.200 --> 01:10:52.510 align:middle line:84% But for example, the K beta, which 01:10:52.510 --> 01:10:54.790 align:middle line:84% is coming in the same direction, might 01:10:54.790 --> 01:11:00.050 align:middle line:84% get reflected or diffracted off to a different point, which 01:11:00.050 --> 01:11:01.230 align:middle line:90% is off your detector. 01:11:01.230 --> 01:11:03.690 align:middle line:84% So this is a way of doing monochromatic imaging. 01:11:03.690 --> 01:11:06.140 align:middle line:84% So effectively, your crystal here 01:11:06.140 --> 01:11:08.790 align:middle line:84% acts as both the filter and the focusing element. 01:11:08.790 --> 01:11:10.617 align:middle line:84% So you can make beautiful images. 01:11:10.617 --> 01:11:12.200 align:middle line:84% You don't need to have a tiny pinhole. 01:11:12.200 --> 01:11:14.030 align:middle line:84% So you can get lots and lots of light. 01:11:14.030 --> 01:11:16.760 align:middle line:84% And you can get images with just a single wavelength, which 01:11:16.760 --> 01:11:18.260 align:middle line:84% can be very powerful for saying this 01:11:18.260 --> 01:11:21.140 align:middle line:84% is a very hot bit of my plasma that's producing K alpha. 01:11:21.140 --> 01:11:25.155 align:middle line:84% So bent crystal, you get what's called monochromatic imaging. 01:11:25.155 --> 01:11:37.500 align:middle line:90% 01:11:37.500 --> 01:11:39.730 align:middle line:84% But bending crystals is extraordinarily expensive. 01:11:39.730 --> 01:11:41.105 align:middle line:84% So pinholes are very, very cheap. 01:11:41.105 --> 01:11:43.022 align:middle line:84% And you'll find a lot of people using pinholes 01:11:43.022 --> 01:11:44.370 align:middle line:90% because they work pretty well. 01:11:44.370 --> 01:11:46.650 align:middle line:84% And of course, the bent crystals only 01:11:46.650 --> 01:11:49.590 align:middle line:90% work for individual energies. 01:11:49.590 --> 01:11:51.395 align:middle line:84% And so if you want to try and measure 01:11:51.395 --> 01:11:53.520 align:middle line:84% more broadly what the radiation is from the plasma, 01:11:53.520 --> 01:11:55.750 align:middle line:90% you'll miss out on information. 01:11:55.750 --> 01:11:56.260 align:middle line:90% OK. 01:11:56.260 --> 01:11:56.760 align:middle line:90% Yeah? 01:11:56.760 --> 01:11:57.760 align:middle line:90% STUDENT: [INAUDIBLE]? 01:11:57.760 --> 01:12:14.690 align:middle line:90% 01:12:14.690 --> 01:12:17.105 align:middle line:84% JACK HARE: My last set of notes for today, I promise. 01:12:17.105 --> 01:12:25.310 align:middle line:90% 01:12:25.310 --> 01:12:26.500 align:middle line:90% Sorry, what? 01:12:26.500 --> 01:12:28.730 align:middle line:90% STUDENT: [INAUDIBLE]? 01:12:28.730 --> 01:12:30.886 align:middle line:84% JACK HARE: Yeah, diodes are pretty good, yeah. 01:12:30.886 --> 01:12:33.830 align:middle line:90% STUDENT: [INAUDIBLE]? 01:12:33.830 --> 01:12:34.580 align:middle line:90% JACK HARE: No, no. 01:12:34.580 --> 01:12:36.560 align:middle line:84% It's nice silicon, 50 nanometers thick, 01:12:36.560 --> 01:12:41.120 align:middle line:84% perfectly good for X-rays up to about 10 kV, so nothing wrong 01:12:41.120 --> 01:12:41.750 align:middle line:90% with diodes. 01:12:41.750 --> 01:12:46.950 align:middle line:90% 01:12:46.950 --> 01:12:47.790 align:middle line:90% OK. 01:12:47.790 --> 01:12:53.790 align:middle line:84% So a lot of these detectors are simply film. 01:12:53.790 --> 01:12:56.710 align:middle line:84% If you went to the dentist a decade or so ago, 01:12:56.710 --> 01:12:58.890 align:middle line:84% they would have used film in their X-ray things. 01:12:58.890 --> 01:13:01.500 align:middle line:84% And in fact, most of X-ray film was developed 01:13:01.500 --> 01:13:05.170 align:middle line:90% for medical applications. 01:13:05.170 --> 01:13:06.860 align:middle line:90% And film is really good. 01:13:06.860 --> 01:13:07.360 align:middle line:90% OK. 01:13:07.360 --> 01:13:09.820 align:middle line:90% So film has a huge drawback. 01:13:09.820 --> 01:13:10.990 align:middle line:90% It's time-integrated. 01:13:10.990 --> 01:13:15.130 align:middle line:84% So you have no sense of what the time is. 01:13:15.130 --> 01:13:21.763 align:middle line:84% You have an integral of the intensity over time. 01:13:21.763 --> 01:13:23.430 align:middle line:84% So if you have some filtering, maybe you 01:13:23.430 --> 01:13:26.150 align:middle line:84% have still frequency information left in your image, 01:13:26.150 --> 01:13:28.650 align:middle line:84% because you're like, oh, this is coming all from the K alpha 01:13:28.650 --> 01:13:30.067 align:middle line:84% because I put a special filter in. 01:13:30.067 --> 01:13:31.240 align:middle line:90% But you don't have any time. 01:13:31.240 --> 01:13:32.782 align:middle line:84% So that could be a really big problem 01:13:32.782 --> 01:13:35.310 align:middle line:84% if you're doing something with a rapid implosion, 01:13:35.310 --> 01:13:37.680 align:middle line:84% like in inertial confinement fusion. 01:13:37.680 --> 01:13:39.580 align:middle line:84% But it doesn't have to be a big problem. 01:13:39.580 --> 01:13:43.780 align:middle line:84% For example, if you've got a signal that is very 01:13:43.780 --> 01:13:46.550 align:middle line:90% bursty in time, like an ICF-- 01:13:46.550 --> 01:13:52.450 align:middle line:84% so this could be a few hundred picoseconds across. 01:13:52.450 --> 01:13:54.680 align:middle line:84% And you have an X-ray diode looking at it. 01:13:54.680 --> 01:13:56.440 align:middle line:84% And that diode has time resolution, 01:13:56.440 --> 01:13:57.640 align:middle line:90% but no spatial resolution. 01:13:57.640 --> 01:13:59.140 align:middle line:84% Then you could use that diode signal 01:13:59.140 --> 01:14:00.973 align:middle line:84% to say, well, all of my really bright X-rays 01:14:00.973 --> 01:14:02.660 align:middle line:90% are missing 100 picoseconds. 01:14:02.660 --> 01:14:04.210 align:middle line:84% So although this is time integrated, 01:14:04.210 --> 01:14:07.360 align:middle line:84% I actually know that the time that this was integrating over 01:14:07.360 --> 01:14:12.230 align:middle line:84% was only P to P plus 100 picoseconds. 01:14:12.230 --> 01:14:14.260 align:middle line:84% So you can use a combination of diagnostics 01:14:14.260 --> 01:14:15.850 align:middle line:90% to localize your signal in time. 01:14:15.850 --> 01:14:17.500 align:middle line:90% That might be OK. 01:14:17.500 --> 01:14:19.810 align:middle line:90% Film is really high resolution. 01:14:19.810 --> 01:14:21.430 align:middle line:90% Film grains are very small. 01:14:21.430 --> 01:14:24.970 align:middle line:84% So it can be much higher resolution than a detector, 01:14:24.970 --> 01:14:26.680 align:middle line:90% like something that has pixels. 01:14:26.680 --> 01:14:29.180 align:middle line:84% You obviously don't have to scan it at very high resolution. 01:14:29.180 --> 01:14:30.040 align:middle line:90% But we can do that. 01:14:30.040 --> 01:14:31.790 align:middle line:84% It's also very well characterized. 01:14:31.790 --> 01:14:34.030 align:middle line:84% So although it may not be linear, 01:14:34.030 --> 01:14:36.790 align:middle line:84% we know like this amount of darkness corresponds 01:14:36.790 --> 01:14:38.230 align:middle line:90% to this much energy deposited. 01:14:38.230 --> 01:14:40.060 align:middle line:84% So film is actually really precious. 01:14:40.060 --> 01:14:42.910 align:middle line:84% And unfortunately, a lot of the film manufacturers, like Kodak, 01:14:42.910 --> 01:14:44.830 align:middle line:84% have stopped making X-ray film because there 01:14:44.830 --> 01:14:45.880 align:middle line:90% isn't a market anymore. 01:14:45.880 --> 01:14:48.553 align:middle line:84% I believe Omega has one of-- the Omega facility at Rochester 01:14:48.553 --> 01:14:50.470 align:middle line:84% has one of the largest stockpiles of remaining 01:14:50.470 --> 01:14:53.380 align:middle line:84% medical film in a fridge because they can't buy it anymore. 01:14:53.380 --> 01:14:55.705 align:middle line:90% And no one else has any left. 01:14:55.705 --> 01:14:57.830 align:middle line:84% So people keep begging Omega for some of their film 01:14:57.830 --> 01:14:58.640 align:middle line:90% from time to time. 01:14:58.640 --> 01:14:59.972 align:middle line:90% So it's good stuff. 01:14:59.972 --> 01:15:01.930 align:middle line:84% But a lot of people have now moved to something 01:15:01.930 --> 01:15:02.920 align:middle line:90% called image plates. 01:15:02.920 --> 01:15:08.690 align:middle line:90% 01:15:08.690 --> 01:15:11.990 align:middle line:84% Image plates, at first glance, looks an awful lot like film. 01:15:11.990 --> 01:15:15.230 align:middle line:84% It's a bit of plastic, plastic-looking stuff. 01:15:15.230 --> 01:15:16.490 align:middle line:90% It's time integrating. 01:15:16.490 --> 01:15:19.110 align:middle line:84% Again, there's no electronics to it. 01:15:19.110 --> 01:15:21.830 align:middle line:84% What happens with image plates, which is neat, is the X-rays 01:15:21.830 --> 01:15:24.440 align:middle line:84% excite it up to a metastable state. 01:15:24.440 --> 01:15:30.890 align:middle line:84% So you have the X-rays excited up to this metastable state 01:15:30.890 --> 01:15:31.580 align:middle line:90% up here. 01:15:31.580 --> 01:15:35.280 align:middle line:84% And because it's metastable, it doesn't actually 01:15:35.280 --> 01:15:37.476 align:middle line:90% decay straight away. 01:15:37.476 --> 01:15:40.538 align:middle line:84% This may be-- ah, sorry, yeah it doesn't make sense 01:15:40.538 --> 01:15:41.580 align:middle line:90% unless I do it like this. 01:15:41.580 --> 01:15:44.150 align:middle line:90% 01:15:44.150 --> 01:15:48.620 align:middle line:84% The X-rays excite the atoms in the plastic 01:15:48.620 --> 01:15:50.690 align:middle line:90% up to some upper state. 01:15:50.690 --> 01:15:54.050 align:middle line:84% And then via some non-radiative decays, 01:15:54.050 --> 01:15:55.970 align:middle line:84% because of the peculiarity of the plastic, 01:15:55.970 --> 01:15:58.490 align:middle line:84% the system decays down to a metastable state. 01:15:58.490 --> 01:16:00.290 align:middle line:84% And metastable, in this case, means 01:16:00.290 --> 01:16:04.180 align:middle line:84% that there is no permitted transition down 01:16:04.180 --> 01:16:05.880 align:middle line:90% to this lower state here. 01:16:05.880 --> 01:16:08.550 align:middle line:90% 01:16:08.550 --> 01:16:10.600 align:middle line:90% This doesn't happen. 01:16:10.600 --> 01:16:12.510 align:middle line:84% So this is a forbidden transition. 01:16:12.510 --> 01:16:15.940 align:middle line:90% 01:16:15.940 --> 01:16:18.340 align:middle line:84% Now, even though the transition is forbidden, 01:16:18.340 --> 01:16:20.320 align:middle line:84% there will be some other mechanism, 01:16:20.320 --> 01:16:23.330 align:middle line:84% mostly to do with collisions, which will eventually 01:16:23.330 --> 01:16:25.940 align:middle line:84% de-excite the atoms in your detector again. 01:16:25.940 --> 01:16:29.590 align:middle line:84% So you've got like a few hours to get this bit of image plate 01:16:29.590 --> 01:16:31.550 align:middle line:90% out and put it into a scanner. 01:16:31.550 --> 01:16:33.220 align:middle line:84% What the scanner does, very cleverly, 01:16:33.220 --> 01:16:36.250 align:middle line:84% is that it uses a laser to excite the image plate back 01:16:36.250 --> 01:16:37.217 align:middle line:90% up to some upper level. 01:16:37.217 --> 01:16:38.800 align:middle line:84% And then it looks for the fluorescence 01:16:38.800 --> 01:16:40.400 align:middle line:90% as it decays back down again. 01:16:40.400 --> 01:16:43.810 align:middle line:84% So you can read off the number of stored photons 01:16:43.810 --> 01:16:46.210 align:middle line:84% in each little bit of the plastic using this little laser 01:16:46.210 --> 01:16:47.050 align:middle line:90% and do this scan. 01:16:47.050 --> 01:16:48.692 align:middle line:84% And then you can reuse the image plate, 01:16:48.692 --> 01:16:49.900 align:middle line:90% which you can't do with film. 01:16:49.900 --> 01:16:53.260 align:middle line:90% So image plate is pretty nice. 01:16:53.260 --> 01:16:55.930 align:middle line:84% But you need an expensive scanner. 01:16:55.930 --> 01:16:57.895 align:middle line:90% So it has a laser readout. 01:16:57.895 --> 01:17:02.470 align:middle line:90% 01:17:02.470 --> 01:17:05.350 align:middle line:84% So both of these are time integrated. 01:17:05.350 --> 01:17:08.150 align:middle line:90% You can get time gated cameras. 01:17:08.150 --> 01:17:11.160 align:middle line:90% 01:17:11.160 --> 01:17:15.730 align:middle line:84% So these are cameras, for example, which have 01:17:15.730 --> 01:17:17.500 align:middle line:90% some gate on them, like this. 01:17:17.500 --> 01:17:20.772 align:middle line:84% And maybe that gate is 5 nanoseconds 01:17:20.772 --> 01:17:23.230 align:middle line:84% or something like that, where you're really getting a very, 01:17:23.230 --> 01:17:24.330 align:middle line:90% very fast burst of X-rays. 01:17:24.330 --> 01:17:25.497 align:middle line:90% So that avoids this problem. 01:17:25.497 --> 01:17:28.300 align:middle line:84% You know exactly when the X-rays were coming out. 01:17:28.300 --> 01:17:29.850 align:middle line:84% But of course, a time gated camera 01:17:29.850 --> 01:17:33.000 align:middle line:84% is very expensive because now it's got lots of electronics. 01:17:33.000 --> 01:17:38.760 align:middle line:90% 01:17:38.760 --> 01:17:42.375 align:middle line:84% These are often things with names like Hybrid-CMOS. 01:17:42.375 --> 01:17:46.710 align:middle line:90% 01:17:46.710 --> 01:17:48.640 align:middle line:84% These cameras can be very, very expensive. 01:17:48.640 --> 01:17:54.210 align:middle line:84% And they also may have relatively low resolution 01:17:54.210 --> 01:17:58.550 align:middle line:84% because each pixel costs a lot of money. 01:17:58.550 --> 01:18:00.800 align:middle line:84% So if you can get away with using film or image plate, 01:18:00.800 --> 01:18:03.617 align:middle line:90% you might be tempted to do that. 01:18:03.617 --> 01:18:05.700 align:middle line:84% Finally, there's something called a streak camera. 01:18:05.700 --> 01:18:14.676 align:middle line:90% 01:18:14.676 --> 01:18:17.110 align:middle line:84% A streak camera is a slightly odd device. 01:18:17.110 --> 01:18:18.985 align:middle line:84% And when you first see a streak camera image, 01:18:18.985 --> 01:18:21.820 align:middle line:84% it's very hard to understand what's going on. 01:18:21.820 --> 01:18:23.620 align:middle line:84% What you get out of your streak camera 01:18:23.620 --> 01:18:30.350 align:middle line:84% is actually something that has got a lot of intensity, 01:18:30.350 --> 01:18:33.930 align:middle line:84% position on one axis, and time on the other axis. 01:18:33.930 --> 01:18:36.830 align:middle line:84% So if you have something like an ICF capsule 01:18:36.830 --> 01:18:44.610 align:middle line:84% that is roughly circular and you put your streak slit here, 01:18:44.610 --> 01:18:47.700 align:middle line:84% initially, if this little circular blob 01:18:47.700 --> 01:18:49.890 align:middle line:84% is emitting nice and uniformly, you 01:18:49.890 --> 01:18:55.360 align:middle line:84% would see nice, uniform emission in all of x. 01:18:55.360 --> 01:19:00.660 align:middle line:84% And as this ICF capsule gets smaller, 01:19:00.660 --> 01:19:02.830 align:middle line:90% your slit stays the same. 01:19:02.830 --> 01:19:04.950 align:middle line:84% And so the region that's being lit up on the slit 01:19:04.950 --> 01:19:05.933 align:middle line:90% gets smaller as well. 01:19:05.933 --> 01:19:07.350 align:middle line:84% So you'd see a streaked image that 01:19:07.350 --> 01:19:12.740 align:middle line:84% looks like this, where this has got more light on it 01:19:12.740 --> 01:19:14.550 align:middle line:84% and this region has no light on it. 01:19:14.550 --> 01:19:17.180 align:middle line:84% So this is a very clever technique for monitoring like 01:19:17.180 --> 01:19:20.820 align:middle line:84% the evolution of a 1D profile of intensity in time. 01:19:20.820 --> 01:19:23.240 align:middle line:84% And the reason these streak cameras are so popular 01:19:23.240 --> 01:19:25.788 align:middle line:90% is that they're extremely fast. 01:19:25.788 --> 01:19:27.830 align:middle line:84% And they're actually based on the same technology 01:19:27.830 --> 01:19:33.230 align:middle line:84% that our CRT television uses with a beam of electrons 01:19:33.230 --> 01:19:36.930 align:middle line:90% being swept across here. 01:19:36.930 --> 01:19:38.160 align:middle line:90% They are very old, though. 01:19:38.160 --> 01:19:40.620 align:middle line:84% So everyone who has one, they keep breaking all the time. 01:19:40.620 --> 01:19:43.740 align:middle line:90% 01:19:43.740 --> 01:19:45.220 align:middle line:90% OK. 01:19:45.220 --> 01:19:47.476 align:middle line:90% Any questions on detectors? 01:19:47.476 --> 01:19:49.605 align:middle line:90% That's all I have for you today. 01:19:49.605 --> 01:19:50.105 align:middle line:90% Yes? 01:19:50.105 --> 01:19:52.750 align:middle line:90% 01:19:52.750 --> 01:19:54.317 align:middle line:90% STUDENT: [INAUDIBLE]? 01:19:54.317 --> 01:19:55.900 align:middle line:84% JACK HARE: Normally, what you actually 01:19:55.900 --> 01:20:00.290 align:middle line:84% have is a bit of film that sits behind the streak camera window. 01:20:00.290 --> 01:20:02.110 align:middle line:90% And so the film gets exposed. 01:20:02.110 --> 01:20:03.580 align:middle line:90% And it has this pattern on it. 01:20:03.580 --> 01:20:08.400 align:middle line:84% And you'll have some timing dots from a laser 01:20:08.400 --> 01:20:10.890 align:middle line:84% that will tell you how to calibrate your time axis. 01:20:10.890 --> 01:20:13.620 align:middle line:84% And you might have some fiducial that 01:20:13.620 --> 01:20:16.140 align:middle line:84% tells you how to calibrate the spatial axis here. 01:20:16.140 --> 01:20:18.300 align:middle line:84% But because it's something like film, 01:20:18.300 --> 01:20:20.320 align:middle line:84% it does have a dependence on the intensity. 01:20:20.320 --> 01:20:21.600 align:middle line:90% So it's not binary. 01:20:21.600 --> 01:20:23.795 align:middle line:84% But the intensity may be very non-linear 01:20:23.795 --> 01:20:25.170 align:middle line:84% because to get this image, you're 01:20:25.170 --> 01:20:27.003 align:middle line:84% generating an electron beam and sweeping it. 01:20:27.003 --> 01:20:29.793 align:middle line:84% And there's, like, magnets, and electron bunching, 01:20:29.793 --> 01:20:31.210 align:middle line:84% and all sorts of things like that. 01:20:31.210 --> 01:20:33.420 align:middle line:84% So interpreting these in a very quantitative way 01:20:33.420 --> 01:20:36.520 align:middle line:90% can be very, very hard. 01:20:36.520 --> 01:20:37.060 align:middle line:90% Yeah? 01:20:37.060 --> 01:20:38.056 align:middle line:90% STUDENT: [INAUDIBLE]? 01:20:38.056 --> 01:20:44.540 align:middle line:90% 01:20:44.540 --> 01:20:46.897 align:middle line:84% JACK HARE: Yeah, so there's something called a-- 01:20:46.897 --> 01:20:48.980 align:middle line:84% often something called a microchannel plate, which 01:20:48.980 --> 01:20:50.105 align:middle line:90% has some voltage across it. 01:20:50.105 --> 01:20:54.757 align:middle line:84% When the photons come in, they ionize. 01:20:54.757 --> 01:20:56.840 align:middle line:84% The photoelectric effect, they release an electron 01:20:56.840 --> 01:20:57.680 align:middle line:90% from the surface. 01:20:57.680 --> 01:21:01.970 align:middle line:84% That voltage sweeps the electron and accelerates it up. 01:21:01.970 --> 01:21:05.420 align:middle line:84% There'll be magnets, which bend the electron for a certain part 01:21:05.420 --> 01:21:06.680 align:middle line:90% of the time axis. 01:21:06.680 --> 01:21:09.260 align:middle line:84% The electron will collide with the phosphor screen. 01:21:09.260 --> 01:21:10.930 align:middle line:84% The electron excites the phosphor. 01:21:10.930 --> 01:21:12.680 align:middle line:84% The phosphor decays and emits green light. 01:21:12.680 --> 01:21:16.150 align:middle line:84% The green light is recorded by [INAUDIBLE]. 01:21:16.150 --> 01:21:18.550 align:middle line:90% Yeah, so they're very fun. 01:21:18.550 --> 01:21:20.710 align:middle line:84% But they are very complicated, which is why you 01:21:20.710 --> 01:21:23.890 align:middle line:84% shouldn't-- if you see a region that is twice as bright here 01:21:23.890 --> 01:21:26.290 align:middle line:84% than it is here, that doesn't necessarily mean that 01:21:26.290 --> 01:21:28.520 align:middle line:84% it's emitting twice as many X-rays because it's very, 01:21:28.520 --> 01:21:29.717 align:middle line:90% very non-linear. 01:21:29.717 --> 01:21:31.300 align:middle line:84% And they're very sensitive to voltage. 01:21:31.300 --> 01:21:34.730 align:middle line:90% 01:21:34.730 --> 01:21:35.720 align:middle line:90% STUDENT: [INAUDIBLE]? 01:21:35.720 --> 01:21:47.085 align:middle line:90% 01:21:47.085 --> 01:21:48.960 align:middle line:84% JACK HARE: Yeah, it's a pulsed magnetic field 01:21:48.960 --> 01:21:50.800 align:middle line:90% that's ramping up in time. 01:21:50.800 --> 01:21:52.350 align:middle line:84% So as the magnetic field ramps up, 01:21:52.350 --> 01:21:54.183 align:middle line:84% it sweeps the electrons to different places. 01:21:54.183 --> 01:21:55.910 align:middle line:84% That's exactly how a cathode ray works. 01:21:55.910 --> 01:21:58.410 align:middle line:84% And we were able to do cathode ray TVs to make moving images 01:21:58.410 --> 01:22:01.334 align:middle line:90% at 30 frames a second, so yeah. 01:22:01.334 --> 01:22:03.827 align:middle line:90% STUDENT: [INAUDIBLE]? 01:22:03.827 --> 01:22:05.410 align:middle line:84% JACK HARE: Yeah, but all the electrons 01:22:05.410 --> 01:22:06.820 align:middle line:84% from the photoelectric effect are be coming out 01:22:06.820 --> 01:22:07.990 align:middle line:90% with very similar energies. 01:22:07.990 --> 01:22:08.800 align:middle line:90% And then they're accelerating. 01:22:08.800 --> 01:22:11.020 align:middle line:84% So maybe they've got an energy range of a few EV. 01:22:11.020 --> 01:22:13.562 align:middle line:84% But they're being accelerated over a kiloelectron volt, which 01:22:13.562 --> 01:22:15.610 align:middle line:84% is also why you should not mess around with a CRT 01:22:15.610 --> 01:22:17.830 align:middle line:84% because inside it there is an electron beam that 01:22:17.830 --> 01:22:21.030 align:middle line:90% has kiloelectronvolts, yeah. 01:22:21.030 --> 01:22:22.910 align:middle line:90% Any other questions? 01:22:22.910 --> 01:22:23.525 align:middle line:90% Anyone online? 01:22:23.525 --> 01:22:27.000 align:middle line:90% 01:22:27.000 --> 01:22:27.500 align:middle line:90% OK. 01:22:27.500 --> 01:22:30.058 align:middle line:84% Next lecture, we are going to talk about line broadening. 01:22:30.058 --> 01:22:31.850 align:middle line:84% And we're going to finish off spectroscopy. 01:22:31.850 --> 01:22:35.260 align:middle line:90% So see you on Tuesday. 01:22:35.260 --> 01:22:38.000 align:middle line:90%