WEBVTT 00:00:00.000 --> 00:00:02.395 align:middle line:90% [SQUEAKING] 00:00:02.395 --> 00:00:04.311 align:middle line:90% [RUSTLING] 00:00:04.311 --> 00:00:11.690 align:middle line:90% [CLICKING] 00:00:11.690 --> 00:00:13.910 align:middle line:84% JACK HARE: So just briefly, there 00:00:13.910 --> 00:00:19.910 align:middle line:84% was some discussion last time about Lyman sequence 00:00:19.910 --> 00:00:22.520 align:middle line:84% and the Balmer sequence and how these correspond 00:00:22.520 --> 00:00:23.958 align:middle line:90% to the K shell and the L shell. 00:00:23.958 --> 00:00:25.625 align:middle line:84% And I just looked this up, and I thought 00:00:25.625 --> 00:00:27.590 align:middle line:84% for your amusement and entertainment 00:00:27.590 --> 00:00:29.010 align:middle line:90% I would explain it. 00:00:29.010 --> 00:00:32.420 align:middle line:84% So the idea here is that we are looking 00:00:32.420 --> 00:00:35.480 align:middle line:84% at hydrogen. So the Lyman, the Balmer series only 00:00:35.480 --> 00:00:39.080 align:middle line:84% apply to hydrogen. And we have levels 00:00:39.080 --> 00:00:44.850 align:middle line:84% of principal quantum numbers, 1, 2, 3, 4, and things like that. 00:00:44.850 --> 00:00:47.960 align:middle line:84% And there were two series which are historically seen. 00:00:47.960 --> 00:00:50.060 align:middle line:84% There, first of all, was a set of lines 00:00:50.060 --> 00:00:54.170 align:middle line:84% which turned out to correspond to transitions down to-- 00:00:54.170 --> 00:00:59.137 align:middle line:90% sorry-- n equals 2. 00:00:59.137 --> 00:01:00.470 align:middle line:90% And these are the Balmer series. 00:01:00.470 --> 00:01:04.480 align:middle line:90% 00:01:04.480 --> 00:01:08.890 align:middle line:84% These are transitions to n equals 2 00:01:08.890 --> 00:01:11.290 align:middle line:90% from some other level like this. 00:01:11.290 --> 00:01:16.240 align:middle line:84% Confusingly, the symbol that we use to describe these is h. 00:01:16.240 --> 00:01:19.130 align:middle line:84% So we have, for example, h alpha, 00:01:19.130 --> 00:01:22.712 align:middle line:90% which is n goes from 3 to 2. 00:01:22.712 --> 00:01:28.090 align:middle line:84% h beta is n goes from 4 to 2, and so on. 00:01:28.090 --> 00:01:30.190 align:middle line:84% And the reason that these were discovered first 00:01:30.190 --> 00:01:33.152 align:middle line:84% is that h alpha is actually in the red. 00:01:33.152 --> 00:01:33.985 align:middle line:90% It's in the visible. 00:01:33.985 --> 00:01:36.910 align:middle line:90% 00:01:36.910 --> 00:01:40.075 align:middle line:84% And the other lines are increasingly high energy, 00:01:40.075 --> 00:01:42.700 align:middle line:84% as you can tell, because we're doing a transition from a higher 00:01:42.700 --> 00:01:43.640 align:middle line:90% and higher energy. 00:01:43.640 --> 00:01:47.000 align:middle line:84% And in fact, after h beta, these go off into the ultraviolet. 00:01:47.000 --> 00:01:49.330 align:middle line:84% So they're very hard to see in early experiments. 00:01:49.330 --> 00:01:52.090 align:middle line:84% The other sequence of lines which seem more fundamental, 00:01:52.090 --> 00:01:55.270 align:middle line:84% but were discovered later are the transitions down to n 00:01:55.270 --> 00:01:56.470 align:middle line:90% equals 1. 00:01:56.470 --> 00:01:57.790 align:middle line:90% These are the Lyman series. 00:01:57.790 --> 00:02:00.560 align:middle line:90% 00:02:00.560 --> 00:02:02.770 align:middle line:90% So this is n goes towards 1. 00:02:02.770 --> 00:02:08.370 align:middle line:84% And these are usually called Lyman alpha, Lyman beta, and so 00:02:08.370 --> 00:02:08.870 align:middle line:90% on. 00:02:08.870 --> 00:02:15.550 align:middle line:84% So that's transitions from n equals 2 to 1, and 3 to 1, 00:02:15.550 --> 00:02:16.390 align:middle line:90% and so on. 00:02:16.390 --> 00:02:19.960 align:middle line:84% And even the lowest energy of the Lyman alpha series 00:02:19.960 --> 00:02:22.220 align:middle line:90% is deep in the ultraviolet. 00:02:22.220 --> 00:02:24.937 align:middle line:84% So it took much longer for people to spot this. 00:02:24.937 --> 00:02:26.770 align:middle line:84% And so this is the Balmer series came first, 00:02:26.770 --> 00:02:28.103 align:middle line:90% and the Lyman series came later. 00:02:28.103 --> 00:02:29.937 align:middle line:84% So you're looking at this and you're saying, 00:02:29.937 --> 00:02:31.450 align:middle line:84% OK, this does look at an awful lot 00:02:31.450 --> 00:02:34.850 align:middle line:84% like what you told us was the K shell 00:02:34.850 --> 00:02:38.010 align:middle line:84% and what you told us was the L shell here. 00:02:38.010 --> 00:02:40.110 align:middle line:84% And apparently, the pedant's answer 00:02:40.110 --> 00:02:42.690 align:middle line:84% is when we defined the K shell, the way 00:02:42.690 --> 00:02:44.130 align:middle line:84% we were thinking about it involved 00:02:44.130 --> 00:02:45.700 align:middle line:90% some other electrons here. 00:02:45.700 --> 00:02:50.460 align:middle line:84% And so you need to have greater than three electrons left 00:02:50.460 --> 00:02:53.005 align:middle line:90% for both of these definitions. 00:02:53.005 --> 00:02:54.630 align:middle line:84% And so that means that you have to have 00:02:54.630 --> 00:02:58.700 align:middle line:90% at least lithium-like atoms. 00:02:58.700 --> 00:03:00.440 align:middle line:84% But I would say, frankly, these look 00:03:00.440 --> 00:03:02.870 align:middle line:84% almost a pretty obvious continuation of the L 00:03:02.870 --> 00:03:04.530 align:middle line:90% shell and the K shell stuff. 00:03:04.530 --> 00:03:06.560 align:middle line:84% There's also a series of lines for helium lines 00:03:06.560 --> 00:03:08.390 align:middle line:84% as well, which are for two electron atoms. 00:03:08.390 --> 00:03:10.580 align:middle line:90% These are for one electron. 00:03:10.580 --> 00:03:13.750 align:middle line:90% 00:03:13.750 --> 00:03:16.110 align:middle line:84% So my short answer would be, yes, the Lyman series 00:03:16.110 --> 00:03:19.470 align:middle line:84% corresponds to the K-shell emission 00:03:19.470 --> 00:03:21.910 align:middle line:84% and the Balmer series corresponds to the L-shell. 00:03:21.910 --> 00:03:24.870 align:middle line:84% And then, of course, you have all the fun things like L shell, 00:03:24.870 --> 00:03:29.440 align:middle line:84% Lyman, H K. Spectroscopy is awful for that sort of stuff. 00:03:29.440 --> 00:03:31.290 align:middle line:90% So it's just nomenclature. 00:03:31.290 --> 00:03:32.790 align:middle line:84% Any questions on that before we move 00:03:32.790 --> 00:03:35.010 align:middle line:84% on to line broadening, the reason we're here? 00:03:35.010 --> 00:03:45.260 align:middle line:90% 00:03:45.260 --> 00:03:50.790 align:middle line:84% So we're going to be talking about line broadening. 00:03:50.790 --> 00:03:54.800 align:middle line:84% So far we've mostly been considering line emission, which 00:03:54.800 --> 00:03:57.350 align:middle line:90% is at a specific frequency. 00:03:57.350 --> 00:04:00.410 align:middle line:84% We've said that we have some lower energy level 00:04:00.410 --> 00:04:02.520 align:middle line:90% and some upper energy level. 00:04:02.520 --> 00:04:04.880 align:middle line:84% And we have some transition of electron 00:04:04.880 --> 00:04:06.860 align:middle line:90% from an upper to a lower. 00:04:06.860 --> 00:04:09.650 align:middle line:84% It could be stimulated, or it could be spontaneous emission, 00:04:09.650 --> 00:04:14.870 align:middle line:84% and emit a photon with energy H bar omega upper lower. 00:04:14.870 --> 00:04:17.420 align:middle line:84% So what we'd expect to see in our spectrum, 00:04:17.420 --> 00:04:21.980 align:middle line:84% because we have lots of different levels available, 00:04:21.980 --> 00:04:26.720 align:middle line:84% is a spectrum that has a series of very sharp lines. 00:04:26.720 --> 00:04:32.140 align:middle line:84% Their spacing is determined by these energies. 00:04:32.140 --> 00:04:35.930 align:middle line:84% And the height of them is determined by the probability 00:04:35.930 --> 00:04:37.220 align:middle line:90% of transition. 00:04:37.220 --> 00:04:42.490 align:middle line:84% And in our plasma also, the occupation of the upper energy 00:04:42.490 --> 00:04:42.990 align:middle line:90% level. 00:04:42.990 --> 00:04:45.470 align:middle line:84% So how many atoms are in that excited state. 00:04:45.470 --> 00:04:49.830 align:middle line:84% And you with an electron up here have a chance to decay down. 00:04:49.830 --> 00:04:51.910 align:middle line:84% Now, in reality, when we look at it, 00:04:51.910 --> 00:04:55.700 align:middle line:84% our spectra does not consist of these delta functions. 00:04:55.700 --> 00:04:58.770 align:middle line:84% It has lines, some of which may be very broad, some of which 00:04:58.770 --> 00:05:00.563 align:middle line:90% may be very narrow. 00:05:00.563 --> 00:05:02.480 align:middle line:84% And so there are several different mechanisms, 00:05:02.480 --> 00:05:04.772 align:middle line:84% which we'll go through one after the other today, which 00:05:04.772 --> 00:05:08.710 align:middle line:84% broaden out these very narrow, single energy peaks 00:05:08.710 --> 00:05:11.600 align:middle line:84% into a range of different energies here. 00:05:11.600 --> 00:05:15.220 align:middle line:84% So the first of these is the one that we absolutely 00:05:15.220 --> 00:05:16.270 align:middle line:90% can never escape. 00:05:16.270 --> 00:05:18.190 align:middle line:84% It's always going to be present in our plasma. 00:05:18.190 --> 00:05:20.178 align:middle line:84% And this is called natural broadening. 00:05:20.178 --> 00:05:30.830 align:middle line:90% 00:05:30.830 --> 00:05:32.750 align:middle line:84% The idea of natural broadening is 00:05:32.750 --> 00:05:37.310 align:middle line:84% that our electron does not immediately transition down 00:05:37.310 --> 00:05:38.540 align:middle line:90% into a lower energy level. 00:05:38.540 --> 00:05:42.750 align:middle line:84% It has some finite dwell time that it will stay up here. 00:05:42.750 --> 00:05:45.330 align:middle line:84% So the transition is not instantaneous here. 00:05:45.330 --> 00:05:52.376 align:middle line:84% So we have what we call a finite excited state lifetime. 00:05:52.376 --> 00:06:03.177 align:middle line:90% 00:06:03.177 --> 00:06:05.760 align:middle line:84% And we assume this is going to be some sort of random process. 00:06:05.760 --> 00:06:08.000 align:middle line:84% It's not like all of the excited energy levels 00:06:08.000 --> 00:06:11.077 align:middle line:84% decay simultaneously after 1 millisecond. 00:06:11.077 --> 00:06:13.160 align:middle line:84% They're going to decay at various different times. 00:06:13.160 --> 00:06:16.730 align:middle line:84% So it looks a little bit like, for example, radioactive decay, 00:06:16.730 --> 00:06:19.850 align:middle line:84% where as a function of time, the probability 00:06:19.850 --> 00:06:24.920 align:middle line:84% of being in the upper state is going to decay away. 00:06:24.920 --> 00:06:27.140 align:middle line:84% And that probability is going to be 00:06:27.140 --> 00:06:33.500 align:middle line:84% proportional to exponential of minus time over some time scale 00:06:33.500 --> 00:06:34.490 align:middle line:90% tau. 00:06:34.490 --> 00:06:40.370 align:middle line:84% And that tau here is what we refer to as the finite excited 00:06:40.370 --> 00:06:41.520 align:middle line:90% state lifetime. 00:06:41.520 --> 00:06:44.120 align:middle line:84% So different states, some may have a short tau. 00:06:44.120 --> 00:06:45.440 align:middle line:90% They may decay very quickly. 00:06:45.440 --> 00:06:46.790 align:middle line:90% Some may have a long tau. 00:06:46.790 --> 00:06:49.580 align:middle line:90% They may decay very slowly. 00:06:49.580 --> 00:06:54.155 align:middle line:84% So we want to have some handle on what this tau parameter is. 00:06:54.155 --> 00:06:56.780 align:middle line:90% 00:06:56.780 --> 00:07:00.220 align:middle line:84% And so we make a very hand-wavy appeal 00:07:00.220 --> 00:07:01.930 align:middle line:84% to a sort of uncertainty principle 00:07:01.930 --> 00:07:08.290 align:middle line:84% here, where we say the energy of our line is h nu upper lower. 00:07:08.290 --> 00:07:11.050 align:middle line:84% Again, I'm switching between this in hertz 00:07:11.050 --> 00:07:12.580 align:middle line:90% and this in radians per second. 00:07:12.580 --> 00:07:14.180 align:middle line:90% But the same thing here. 00:07:14.180 --> 00:07:17.780 align:middle line:84% And we say there's going to be some uncertainty in energy, 00:07:17.780 --> 00:07:22.460 align:middle line:84% which is going to go like h over 2 pi 00:07:22.460 --> 00:07:24.560 align:middle line:90% this excited state lifetime. 00:07:24.560 --> 00:07:28.990 align:middle line:84% So this is effectively a bit like having delta e delta 00:07:28.990 --> 00:07:36.540 align:middle line:84% t is greater than h upon 2 pi, so greater than h bar like that. 00:07:36.540 --> 00:07:38.930 align:middle line:84% So this is an extension-- this sort of is an uncertainty 00:07:38.930 --> 00:07:40.040 align:middle line:90% principle type argument. 00:07:40.040 --> 00:07:43.665 align:middle line:84% You actually don't need to invoke the uncertainty principle 00:07:43.665 --> 00:07:44.540 align:middle line:90% in order to get this. 00:07:44.540 --> 00:07:46.920 align:middle line:84% But some people this way of looking at it. 00:07:46.920 --> 00:07:48.590 align:middle line:84% So this means there's some uncertainty 00:07:48.590 --> 00:07:50.840 align:middle line:84% in the energy of the line related to the excited state 00:07:50.840 --> 00:07:51.390 align:middle line:90% lifetime. 00:07:51.390 --> 00:07:52.730 align:middle line:84% And so some of the photons will just 00:07:52.730 --> 00:07:54.480 align:middle line:84% come out with a slightly different energy. 00:07:54.480 --> 00:07:57.170 align:middle line:84% So that should be enough to explain the broadening. 00:07:57.170 --> 00:08:01.620 align:middle line:84% But we'll do it a little bit more rigorously in a moment. 00:08:01.620 --> 00:08:07.050 align:middle line:84% The other thing I want to say is, yes, 00:08:07.050 --> 00:08:09.510 align:middle line:84% how to actually calculate this tau here. 00:08:09.510 --> 00:08:12.240 align:middle line:90% 00:08:12.240 --> 00:08:13.110 align:middle line:90% This is one way. 00:08:13.110 --> 00:08:15.980 align:middle line:90% 00:08:15.980 --> 00:08:18.820 align:middle line:84% Another way to do it is to say that the intensity 00:08:18.820 --> 00:08:22.960 align:middle line:84% of the emission i is going to go like the probability 00:08:22.960 --> 00:08:25.062 align:middle line:90% of the decay squared. 00:08:25.062 --> 00:08:26.770 align:middle line:84% And that's going to give us a factor of 2 00:08:26.770 --> 00:08:31.870 align:middle line:84% upon tau, which is equal to the sum over all 00:08:31.870 --> 00:08:33.580 align:middle line:84% of the spontaneous emission processes 00:08:33.580 --> 00:08:35.860 align:middle line:84% that take us from the upper level to the lower level, 00:08:35.860 --> 00:08:38.380 align:middle line:84% because, of course, what we're interested in 00:08:38.380 --> 00:08:41.740 align:middle line:84% is not just decay from this upper level to a specific lower 00:08:41.740 --> 00:08:43.780 align:middle line:90% level. 00:08:43.780 --> 00:08:44.800 align:middle line:90% What do I mean by that? 00:08:44.800 --> 00:08:58.190 align:middle line:90% 00:08:58.190 --> 00:09:00.440 align:middle line:84% Because I cannot work out what this means in my notes, 00:09:00.440 --> 00:09:03.990 align:middle line:90% I'm going to delete this here. 00:09:03.990 --> 00:09:05.568 align:middle line:84% Possibly, there's a decay chain that 00:09:05.568 --> 00:09:08.110 align:middle line:84% includes some other processes, and we want to sum over those. 00:09:08.110 --> 00:09:10.735 align:middle line:84% But in general, we're just going to be looking at, for example, 00:09:10.735 --> 00:09:12.690 align:middle line:84% in this case, spontaneous emission here. 00:09:12.690 --> 00:09:14.800 align:middle line:84% And this has units of 1 over seconds. 00:09:14.800 --> 00:09:19.650 align:middle line:84% So we can quickly identify the excited state lifetime with 1 00:09:19.650 --> 00:09:20.743 align:middle line:90% over this. 00:09:20.743 --> 00:09:22.410 align:middle line:84% The factor of 2 just comes from the fact 00:09:22.410 --> 00:09:24.118 align:middle line:84% that when we're dealing with intensities, 00:09:24.118 --> 00:09:25.330 align:middle line:90% we square the probability. 00:09:25.330 --> 00:09:27.480 align:middle line:84% So that goes into the exponential here. 00:09:27.480 --> 00:09:34.660 align:middle line:90% 00:09:34.660 --> 00:09:36.400 align:middle line:84% And that's what this comes out here. 00:09:36.400 --> 00:09:41.897 align:middle line:84% Now, we know that this Aul has some relationship-- 00:09:41.897 --> 00:09:43.480 align:middle line:84% could someone close the doors, please? 00:09:43.480 --> 00:09:48.470 align:middle line:90% Thank you-- to the black body. 00:09:48.470 --> 00:09:50.950 align:middle line:84% This is how we were able to calculate this before. 00:09:50.950 --> 00:09:55.310 align:middle line:84% And this black body has a relationship like nu cubed. 00:09:55.310 --> 00:09:58.360 align:middle line:84% So what we're saying is for the higher energy lines here, 00:09:58.360 --> 00:10:01.420 align:middle line:84% we're going to have a shorter excited state lifetime. 00:10:01.420 --> 00:10:04.280 align:middle line:84% And we're going to have a larger energy uncertainty. 00:10:04.280 --> 00:10:11.410 align:middle line:90% So ie equals h nu. 00:10:11.410 --> 00:10:16.280 align:middle line:84% It gives a short excited state lifetime, 00:10:16.280 --> 00:10:21.570 align:middle line:84% and that gives a large range of energies. 00:10:21.570 --> 00:10:23.390 align:middle line:84% So in general, if you have i energy lines, 00:10:23.390 --> 00:10:26.112 align:middle line:84% they're going to have larger natural broadening. 00:10:26.112 --> 00:10:29.210 align:middle line:90% 00:10:29.210 --> 00:10:31.720 align:middle line:84% So as I said, this is a slightly unsatisfactory way 00:10:31.720 --> 00:10:34.660 align:middle line:84% of getting relationship between energy and time. 00:10:34.660 --> 00:10:37.060 align:middle line:84% And we can do it more precisely by looking 00:10:37.060 --> 00:10:40.300 align:middle line:84% at Fourier transformations of this time series here. 00:10:40.300 --> 00:10:49.000 align:middle line:90% 00:10:49.000 --> 00:10:53.448 align:middle line:84% So if we have a system, which is decaying in time-- 00:10:53.448 --> 00:10:54.865 align:middle line:84% no, I guess I've drawn it already. 00:10:54.865 --> 00:11:08.100 align:middle line:90% 00:11:08.100 --> 00:11:11.910 align:middle line:84% We have an intensity of time that has a proportionality 00:11:11.910 --> 00:11:16.020 align:middle line:90% exponential minus 2t upon tau. 00:11:16.020 --> 00:11:22.110 align:middle line:84% And we can Fourier transform this time-varying signal. 00:11:22.110 --> 00:11:26.260 align:middle line:84% And we will get out the spectrum that corresponds to that. 00:11:26.260 --> 00:11:28.170 align:middle line:84% And that spectrum, does anyone know 00:11:28.170 --> 00:11:32.950 align:middle line:84% what the Fourier transform of an exponential decay is? 00:11:32.950 --> 00:11:33.805 align:middle line:90% It's got a name. 00:11:33.805 --> 00:11:37.011 align:middle line:90% 00:11:37.011 --> 00:11:39.060 align:middle line:84% It looks like whatever the intensity 00:11:39.060 --> 00:11:48.200 align:middle line:84% is of the unshifted line here divided by 1 plus nu minus nu 00:11:48.200 --> 00:11:50.890 align:middle line:90% 0 2 pi tau. 00:11:50.890 --> 00:11:53.400 align:middle line:90% 00:11:53.400 --> 00:11:54.420 align:middle line:90% Where's the squared go? 00:11:54.420 --> 00:11:54.920 align:middle line:90% Here. 00:11:54.920 --> 00:12:02.550 align:middle line:90% 00:12:02.550 --> 00:12:07.940 align:middle line:84% This has a shape which is symmetric in frequency, 00:12:07.940 --> 00:12:09.690 align:middle line:84% because we're just squaring the difference 00:12:09.690 --> 00:12:11.110 align:middle line:90% between the frequencies here. 00:12:11.110 --> 00:12:14.232 align:middle line:90% And it looks like this. 00:12:14.232 --> 00:12:16.065 align:middle line:84% Does anyone know the name for this function? 00:12:16.065 --> 00:12:20.630 align:middle line:90% 00:12:20.630 --> 00:12:21.470 align:middle line:90% This is Lorentzian. 00:12:21.470 --> 00:12:22.460 align:middle line:90% Sorry? 00:12:22.460 --> 00:12:24.249 align:middle line:90% Yeah, this is Lorentzian. 00:12:24.249 --> 00:12:31.740 align:middle line:90% 00:12:31.740 --> 00:12:35.960 align:middle line:84% What this is saying is that there is some width 00:12:35.960 --> 00:12:38.660 align:middle line:84% through the distribution of frequencies and the width 00:12:38.660 --> 00:12:42.200 align:middle line:84% in the frequency space, which is obviously also the energy space. 00:12:42.200 --> 00:12:46.030 align:middle line:84% The full width at half maximum is equal to 1 00:12:46.030 --> 00:12:53.320 align:middle line:84% over pi tau, which you can get by just setting what is nu 00:12:53.320 --> 00:12:55.460 align:middle line:84% when i is half of its peak value here, 00:12:55.460 --> 00:13:00.610 align:middle line:84% so making this denominator equal to a half. 00:13:00.610 --> 00:13:03.860 align:middle line:84% And so what we find is that this full width at half maximum, 00:13:03.860 --> 00:13:07.960 align:middle line:84% which is proportional to 1 upon tau, which is proportional to nu 00:13:07.960 --> 00:13:10.150 align:middle line:84% cubed from our argument over here, 00:13:10.150 --> 00:13:15.430 align:middle line:84% means that as we said before, if we have higher energy photons, 00:13:15.430 --> 00:13:19.483 align:middle line:84% they're going to have more and more natural broadening here. 00:13:19.483 --> 00:13:20.650 align:middle line:90% So this we can't get rid of. 00:13:20.650 --> 00:13:22.240 align:middle line:84% This is just due to the uncertainty 00:13:22.240 --> 00:13:25.510 align:middle line:84% in when the electron is going to decay from the excited 00:13:25.510 --> 00:13:26.680 align:middle line:90% state to the ground state. 00:13:26.680 --> 00:13:30.890 align:middle line:84% And that naturally just leads to some broadening here. 00:13:30.890 --> 00:13:33.670 align:middle line:84% And so you're always going to have some Lorentzian broadening 00:13:33.670 --> 00:13:34.450 align:middle line:90% to your system. 00:13:34.450 --> 00:13:36.850 align:middle line:84% And then you'll also have other broadening mechanisms 00:13:36.850 --> 00:13:37.427 align:middle line:90% on top of it. 00:13:37.427 --> 00:13:39.010 align:middle line:84% But this means that when you're trying 00:13:39.010 --> 00:13:41.978 align:middle line:84% to fit, for example, like trying to fit these lines of something 00:13:41.978 --> 00:13:44.020 align:middle line:84% like a Gaussian function, because you look at it, 00:13:44.020 --> 00:13:45.860 align:middle line:84% and you go, ah, that looks like a Gaussian. 00:13:45.860 --> 00:13:48.220 align:middle line:84% Well, Lorentzians are slightly different from Gaussians. 00:13:48.220 --> 00:13:49.940 align:middle line:84% And you're fitting procedure won't work properly. 00:13:49.940 --> 00:13:51.482 align:middle line:84% So you need to be careful when you're 00:13:51.482 --> 00:13:54.820 align:middle line:84% fitting spectral lines not to just assume that the spread is 00:13:54.820 --> 00:13:55.700 align:middle line:90% Gaussian distributed. 00:13:55.700 --> 00:13:57.700 align:middle line:84% There are some other functions, like Lorentzian, 00:13:57.700 --> 00:14:00.390 align:middle line:90% which are more fundamental. 00:14:00.390 --> 00:14:03.710 align:middle line:84% Questions on that first natural broadening mechanism? 00:14:03.710 --> 00:14:05.681 align:middle line:90% Yeah. 00:14:05.681 --> 00:14:25.652 align:middle line:90% AUDIENCE: [INAUDIBLE] 00:14:25.652 --> 00:14:27.610 align:middle line:84% JACK HARE: Do you want me to give you intuition 00:14:27.610 --> 00:14:29.087 align:middle line:90% for quantum mechanics? 00:14:29.087 --> 00:14:32.035 align:middle line:90% [LAUGHTER] 00:14:32.035 --> 00:14:33.910 align:middle line:84% I don't think I've got a better answer to you 00:14:33.910 --> 00:14:35.720 align:middle line:84% than this mathematical derivation. 00:14:35.720 --> 00:14:37.697 align:middle line:84% I think the energy levels are not as exact. 00:14:37.697 --> 00:14:39.280 align:middle line:84% Because of this uncertainty principle, 00:14:39.280 --> 00:14:40.905 align:middle line:84% we can never be quite sure exactly what 00:14:40.905 --> 00:14:42.700 align:middle line:84% the momentum, and therefore the energy 00:14:42.700 --> 00:14:46.133 align:middle line:84% of the electron wave function is. 00:14:46.133 --> 00:14:47.800 align:middle line:84% There's some uncertainty in exactly what 00:14:47.800 --> 00:14:49.300 align:middle line:90% the energy of the function is. 00:14:49.300 --> 00:14:52.870 align:middle line:84% And that translates to this uncertainty in the frequency. 00:14:52.870 --> 00:14:57.760 align:middle line:90% AUDIENCE: [INAUDIBLE] 00:14:57.760 --> 00:14:59.945 align:middle line:84% JACK HARE: I feel like that's above my pay grade. 00:14:59.945 --> 00:15:02.500 align:middle line:90% 00:15:02.500 --> 00:15:04.810 align:middle line:90% AUDIENCE: How much [INAUDIBLE]? 00:15:04.810 --> 00:15:07.150 align:middle line:90% JACK HARE: Thank you. 00:15:07.150 --> 00:15:11.914 align:middle line:84% But if I can't answer this, then that's very embarrassing. 00:15:11.914 --> 00:15:16.260 align:middle line:84% AUDIENCE: [INAUDIBLE] the probability of [INAUDIBLE]? 00:15:16.260 --> 00:15:18.010 align:middle line:84% What's the state we're talking about here? 00:15:18.010 --> 00:15:19.520 align:middle line:90% Is that the end state? 00:15:19.520 --> 00:15:20.770 align:middle line:90% JACK HARE: No, the up-- sorry. 00:15:20.770 --> 00:15:26.800 align:middle line:84% So let's say this is 1 here at time t equals 0. 00:15:26.800 --> 00:15:31.300 align:middle line:84% We have whatever process has just promoted the electron up 00:15:31.300 --> 00:15:31.840 align:middle line:90% to here. 00:15:31.840 --> 00:15:34.240 align:middle line:84% This took place at time t equals 0. 00:15:34.240 --> 00:15:38.200 align:middle line:84% And then the down process takes place at time t greater than 0. 00:15:38.200 --> 00:15:41.442 align:middle line:90% AUDIENCE: Or up [INAUDIBLE] 00:15:41.442 --> 00:15:42.150 align:middle line:90% JACK HARE: Sorry. 00:15:42.150 --> 00:15:44.608 align:middle line:84% Yeah, so the probability that is still in that upper state. 00:15:44.608 --> 00:15:47.640 align:middle line:90% Yes, exactly. 00:15:47.640 --> 00:15:48.930 align:middle line:90% Yeah, I mean, in this-- 00:15:48.930 --> 00:15:51.990 align:middle line:84% if you're like, but it could decay to a different state, 00:15:51.990 --> 00:15:54.510 align:middle line:84% or it could go up again, then that wouldn't affect 00:15:54.510 --> 00:15:56.010 align:middle line:84% the shape of the line, because we're 00:15:56.010 --> 00:15:57.593 align:middle line:84% looking at a very specific line, which 00:15:57.593 --> 00:16:01.590 align:middle line:84% is the line with the energy h nu ul. 00:16:01.590 --> 00:16:03.270 align:middle line:90% And if you want to-- 00:16:03.270 --> 00:16:07.150 align:middle line:84% u and l-- you want to know the broadening for some other state, 00:16:07.150 --> 00:16:09.270 align:middle line:84% then you have to do this calculation with whatever 00:16:09.270 --> 00:16:10.478 align:middle line:90% other state you're going for. 00:16:10.478 --> 00:16:14.790 align:middle line:90% 00:16:14.790 --> 00:16:17.310 align:middle line:84% Any questions online or other questions in the room? 00:16:17.310 --> 00:16:21.630 align:middle line:90% 00:16:21.630 --> 00:16:22.230 align:middle line:90% Yeah. 00:16:22.230 --> 00:16:26.780 align:middle line:90% AUDIENCE: [INAUDIBLE] 00:16:26.780 --> 00:16:27.868 align:middle line:90% JACK HARE: OK. 00:16:27.868 --> 00:16:29.332 align:middle line:90% AUDIENCE: [INAUDIBLE]. 00:16:29.332 --> 00:16:35.410 align:middle line:90% 00:16:35.410 --> 00:16:39.482 align:middle line:84% That doesn't get [INAUDIBLE], does it? 00:16:39.482 --> 00:16:40.190 align:middle line:90% JACK HARE: Right. 00:16:40.190 --> 00:16:40.880 align:middle line:90% Yes, I agree. 00:16:40.880 --> 00:16:42.988 align:middle line:84% So we are dealing with an ensemble 00:16:42.988 --> 00:16:44.030 align:middle line:90% of different [INAUDIBLE]. 00:16:44.030 --> 00:16:44.923 align:middle line:90% Yes, thank you. 00:16:44.923 --> 00:16:46.340 align:middle line:84% That's actually a very good point. 00:16:46.340 --> 00:16:49.850 align:middle line:90% 00:16:49.850 --> 00:16:51.800 align:middle line:84% So the point that's being made here 00:16:51.800 --> 00:16:55.770 align:middle line:84% is that, in fact, in reality, any given photon decay, 00:16:55.770 --> 00:16:59.730 align:middle line:90% the intensity looks like this. 00:16:59.730 --> 00:17:01.662 align:middle line:84% It's a delta function at a particular time. 00:17:01.662 --> 00:17:03.120 align:middle line:84% That's when the photon was emitted. 00:17:03.120 --> 00:17:05.760 align:middle line:84% This treatment here is talking about an ensemble of particles 00:17:05.760 --> 00:17:07.650 align:middle line:84% that we've prepared into the upper state. 00:17:07.650 --> 00:17:10.266 align:middle line:84% And then we're watching the intensity as one 00:17:10.266 --> 00:17:11.849 align:middle line:84% after the other, different ones decay. 00:17:11.849 --> 00:17:13.650 align:middle line:84% More of them will decay early in time. 00:17:13.650 --> 00:17:15.430 align:middle line:84% A few of them will decay later in time. 00:17:15.430 --> 00:17:18.238 align:middle line:84% And so when we take the Fourier transform of that, we get this. 00:17:18.238 --> 00:17:18.780 align:middle line:90% You're right. 00:17:18.780 --> 00:17:21.089 align:middle line:84% Each individual photon has a specific energy. 00:17:21.089 --> 00:17:24.420 align:middle line:84% And this is made up of lots of different photons coming 00:17:24.420 --> 00:17:25.500 align:middle line:90% from particles. 00:17:25.500 --> 00:17:29.010 align:middle line:84% The ones here decay at t around 0. 00:17:29.010 --> 00:17:34.270 align:middle line:84% And the ones out here decayed at t a great deal larger than 0. 00:17:34.270 --> 00:17:34.770 align:middle line:90% Thank you. 00:17:34.770 --> 00:17:37.500 align:middle line:90% That's a better interpretation. 00:17:37.500 --> 00:17:39.378 align:middle line:90% OK, Doppler broadening. 00:17:39.378 --> 00:18:01.420 align:middle line:90% 00:18:01.420 --> 00:18:04.420 align:middle line:84% Doppler broadening, we have some intuitive understanding of it. 00:18:04.420 --> 00:18:06.545 align:middle line:84% It's to do with whether the particle is moving away 00:18:06.545 --> 00:18:07.570 align:middle line:90% from us or towards us. 00:18:07.570 --> 00:18:11.080 align:middle line:84% And we get a shift in the frequency of the light 00:18:11.080 --> 00:18:14.090 align:middle line:90% that we receive. 00:18:14.090 --> 00:18:16.220 align:middle line:84% To keep things simple here, I'm going to just stick 00:18:16.220 --> 00:18:17.660 align:middle line:90% in a non-relativistic limit. 00:18:17.660 --> 00:18:22.280 align:middle line:90% 00:18:22.280 --> 00:18:27.170 align:middle line:84% And then this limit, the shift in frequency of our light, which 00:18:27.170 --> 00:18:29.600 align:middle line:84% is defined as whatever frequency we 00:18:29.600 --> 00:18:33.500 align:middle line:84% see minus the initial frequency, the sort of, if I 00:18:33.500 --> 00:18:35.760 align:middle line:84% was in the same frame as the emitter frequency. 00:18:35.760 --> 00:18:38.150 align:middle line:84% And this is just a sign convention here. 00:18:38.150 --> 00:18:41.840 align:middle line:84% So I'm choosing it so that delta nu is greater than 1 00:18:41.840 --> 00:18:44.900 align:middle line:84% when the light has been upshifted in frequency. 00:18:44.900 --> 00:18:47.700 align:middle line:84% And for a non-relativistic system, 00:18:47.700 --> 00:18:52.370 align:middle line:84% this is just the velocity over the speed of light times 00:18:52.370 --> 00:18:56.600 align:middle line:84% whatever the initial frequency of the light was. 00:18:56.600 --> 00:19:00.050 align:middle line:84% So I can rewrite this in terms of velocity 00:19:00.050 --> 00:19:08.410 align:middle line:84% and I get nu over nu 0 minus 1 times the speed of light. 00:19:08.410 --> 00:19:17.150 align:middle line:84% So the intensity of light which I see at frequency nu 00:19:17.150 --> 00:19:21.510 align:middle line:84% is going to be proportional to the number of particles 00:19:21.510 --> 00:19:25.470 align:middle line:84% traveling at speed v, which cause a Doppler shift, which 00:19:25.470 --> 00:19:27.430 align:middle line:90% gives a frequency nu here. 00:19:27.430 --> 00:19:32.900 align:middle line:84% So this is the distribution of particles frequency 00:19:32.900 --> 00:19:37.622 align:middle line:90% nu over nu 0 minus 1 mc-- 00:19:37.622 --> 00:19:38.455 align:middle line:90% not enough brackets. 00:19:38.455 --> 00:19:47.582 align:middle line:90% 00:19:47.582 --> 00:19:49.790 align:middle line:84% So if we're dealing with something like a Maxwellian, 00:19:49.790 --> 00:19:59.400 align:middle line:84% where F of v is proportional to the exponential of minus 1/2 mv 00:19:59.400 --> 00:20:05.190 align:middle line:84% squared upon the temperature like this, 00:20:05.190 --> 00:20:11.690 align:middle line:84% then we will end up with an intensity, 00:20:11.690 --> 00:20:22.910 align:middle line:84% which is proportional to exponential nu over nu 0 minus 1 00:20:22.910 --> 00:20:27.405 align:middle line:90% squared mc squared over 2t. 00:20:27.405 --> 00:20:31.350 align:middle line:90% 00:20:31.350 --> 00:20:34.410 align:middle line:90% Have I missed the minus sign? 00:20:34.410 --> 00:20:35.095 align:middle line:90% It seems likely. 00:20:35.095 --> 00:20:41.400 align:middle line:90% 00:20:41.400 --> 00:20:43.410 align:middle line:84% So this is the broadening for Maxwellian. 00:20:43.410 --> 00:20:46.450 align:middle line:84% Now we're looking in frequency space here. 00:20:46.450 --> 00:20:50.430 align:middle line:84% So if we initially had some line at nu 0, 00:20:50.430 --> 00:20:55.470 align:middle line:84% and I'm plotting i of nu against nu with my spectrometer, 00:20:55.470 --> 00:20:58.800 align:middle line:84% what can we say about this function, any facts about it? 00:20:58.800 --> 00:21:10.150 align:middle line:90% 00:21:10.150 --> 00:21:11.080 align:middle line:90% Is it symmetric? 00:21:11.080 --> 00:21:15.660 align:middle line:90% 00:21:15.660 --> 00:21:18.330 align:middle line:90% Close to symmetric, good answer. 00:21:18.330 --> 00:21:25.650 align:middle line:84% So for delta nu over nu 0 much less than 1, 00:21:25.650 --> 00:21:29.040 align:middle line:84% so for small shifts, this is a very symmetric function. 00:21:29.040 --> 00:21:33.380 align:middle line:90% And it's peaked at nu 0 here. 00:21:33.380 --> 00:21:36.050 align:middle line:84% And it does indeed look like a Gaussian. 00:21:36.050 --> 00:21:38.630 align:middle line:84% So your normal approach when you see 00:21:38.630 --> 00:21:41.420 align:middle line:84% some function that is symmetric and peaked 00:21:41.420 --> 00:21:42.830 align:middle line:90% is to fit it with a Gaussian. 00:21:42.830 --> 00:21:44.840 align:middle line:84% And that would be a reasonable approach here. 00:21:44.840 --> 00:21:47.863 align:middle line:84% It just turns out in the wings, where probably you 00:21:47.863 --> 00:21:50.030 align:middle line:84% can't measure it, because signal to noise is so bad, 00:21:50.030 --> 00:21:52.370 align:middle line:90% this may be slightly asymmetric. 00:21:52.370 --> 00:21:55.130 align:middle line:84% This is symmetric if you do the Taylor expansion around 0. 00:21:55.130 --> 00:21:59.430 align:middle line:90% 00:21:59.430 --> 00:22:05.250 align:middle line:84% And what we find here is that the full width at half maximum 00:22:05.250 --> 00:22:18.060 align:middle line:84% total delta nu at 1/2 is equal to 2 nu 0 2t over mc squared 2 00:22:18.060 --> 00:22:23.760 align:middle line:84% natural logarithm 2 to the 1/2, which the punchline of this is 00:22:23.760 --> 00:22:27.030 align:middle line:84% that the broadening is proportional to t for the 1/2 00:22:27.030 --> 00:22:31.495 align:middle line:84% here, which is the thermal velocity, as you might expect. 00:22:31.495 --> 00:22:36.030 align:middle line:90% 00:22:36.030 --> 00:22:39.780 align:middle line:84% So this means if you measure the width of a line, 00:22:39.780 --> 00:22:42.660 align:middle line:84% then you may be able to infer the temperature of it. 00:22:42.660 --> 00:22:45.238 align:middle line:84% Now, you noticed here I've used delta nu to the half. 00:22:45.238 --> 00:22:47.030 align:middle line:84% I like using the full width at half maximum 00:22:47.030 --> 00:22:49.460 align:middle line:84% for these, because this is a relatively unambiguous thing 00:22:49.460 --> 00:22:50.330 align:middle line:90% to define. 00:22:50.330 --> 00:22:53.030 align:middle line:84% If you start writing down sigma, then you're 00:22:53.030 --> 00:22:56.000 align:middle line:84% intrinsically thinking about Gaussians, really. 00:22:56.000 --> 00:23:00.680 align:middle line:84% And that means that when you use this full width at half maximum 00:23:00.680 --> 00:23:01.430 align:middle line:90% here-- 00:23:01.430 --> 00:23:04.370 align:middle line:84% again, this I could also write as delta nu to the 1/2-- 00:23:04.370 --> 00:23:07.170 align:middle line:90% 00:23:07.170 --> 00:23:08.420 align:middle line:90% it makes it harder to compare. 00:23:08.420 --> 00:23:10.700 align:middle line:84% This picks up loads of extra factors of log 2 00:23:10.700 --> 00:23:12.120 align:middle line:90% and stuff like that. 00:23:12.120 --> 00:23:14.270 align:middle line:84% So I like working with full width at half maximum. 00:23:14.270 --> 00:23:15.650 align:middle line:90% It's easy to find here. 00:23:15.650 --> 00:23:18.020 align:middle line:84% So this result is not really very surprising. 00:23:18.020 --> 00:23:22.460 align:middle line:84% Effectively, the line traces out the distribution function here. 00:23:22.460 --> 00:23:24.630 align:middle line:84% There are some particles which are moving-- 00:23:24.630 --> 00:23:27.530 align:middle line:84% so a few number of particles which are moving very fast 00:23:27.530 --> 00:23:29.690 align:middle line:84% away from you, redshifted, a few particles 00:23:29.690 --> 00:23:32.210 align:middle line:84% which are moving very far towards you, blueshifted. 00:23:32.210 --> 00:23:35.660 align:middle line:84% But most of the particles are not moving towards or away 00:23:35.660 --> 00:23:36.270 align:middle line:90% from you. 00:23:36.270 --> 00:23:38.960 align:middle line:84% So we have most of our mission at the initial line 00:23:38.960 --> 00:23:41.470 align:middle line:90% frequency here. 00:23:41.470 --> 00:23:43.026 align:middle line:84% Any questions on Doppler broadening? 00:23:43.026 --> 00:23:51.407 align:middle line:90% 00:23:51.407 --> 00:23:52.240 align:middle line:90% AUDIENCE: Professor. 00:23:52.240 --> 00:23:53.350 align:middle line:90% JACK HARE: Yeah. 00:23:53.350 --> 00:23:56.320 align:middle line:84% AUDIENCE: So I'm assuming all these happen 00:23:56.320 --> 00:23:59.350 align:middle line:90% in laboratory plasma settings. 00:23:59.350 --> 00:24:03.280 align:middle line:84% But which one plays more of a role? 00:24:03.280 --> 00:24:06.220 align:middle line:84% Do they have equal amounts or is it 00:24:06.220 --> 00:24:09.213 align:middle line:84% one or the other that has more of an effect? 00:24:09.213 --> 00:24:09.880 align:middle line:90% JACK HARE: Yeah. 00:24:09.880 --> 00:24:11.800 align:middle line:84% So we'll go through all of these and maybe discuss 00:24:11.800 --> 00:24:12.740 align:middle line:90% that in a bit more detail. 00:24:12.740 --> 00:24:14.073 align:middle line:90% But all of these have an effect. 00:24:14.073 --> 00:24:15.987 align:middle line:84% But some of them may be negligible. 00:24:15.987 --> 00:24:18.070 align:middle line:84% And so it will depend a great deal on your plasma, 00:24:18.070 --> 00:24:19.670 align:middle line:90% and you'll want to calculate it. 00:24:19.670 --> 00:24:22.000 align:middle line:84% So for example, we did an experiment recently 00:24:22.000 --> 00:24:23.530 align:middle line:84% where all of the broadening we saw 00:24:23.530 --> 00:24:25.510 align:middle line:84% was due to natural broadening and the response 00:24:25.510 --> 00:24:28.390 align:middle line:84% of our spectrometer, and not to do with Doppler broadening. 00:24:28.390 --> 00:24:29.890 align:middle line:84% Though we thought it was going to be 00:24:29.890 --> 00:24:31.060 align:middle line:90% Doppler broadening originally. 00:24:31.060 --> 00:24:31.900 align:middle line:90% But you can calculate it. 00:24:31.900 --> 00:24:33.430 align:middle line:84% If you think, I know what the temperature roughly 00:24:33.430 --> 00:24:35.770 align:middle line:84% is, I can calculate the amount of Doppler broadening. 00:24:35.770 --> 00:24:40.183 align:middle line:84% And then you can compare that to the natural broadening. 00:24:40.183 --> 00:24:42.600 align:middle line:84% And remember that you can calculate the natural broadening 00:24:42.600 --> 00:24:46.230 align:middle line:84% if you have access to a database with these spontaneous emission 00:24:46.230 --> 00:24:47.160 align:middle line:90% coefficients. 00:24:47.160 --> 00:24:50.940 align:middle line:84% You can quickly estimate what the lifetime of the state is. 00:24:50.940 --> 00:24:53.310 align:middle line:84% And so then you can estimate the natural broadening. 00:24:53.310 --> 00:24:57.270 align:middle line:84% And you can compare that to the Doppler broadening you expect. 00:24:57.270 --> 00:24:58.860 align:middle line:90% And depending on your plasma-- 00:24:58.860 --> 00:25:00.527 align:middle line:84% remember, the natural broadening doesn't 00:25:00.527 --> 00:25:01.750 align:middle line:90% care about the temperature. 00:25:01.750 --> 00:25:03.750 align:middle line:84% So for a colder plasma, the natural broadening 00:25:03.750 --> 00:25:04.770 align:middle line:90% will probably dominate. 00:25:04.770 --> 00:25:06.930 align:middle line:84% And for a hotter plasma, the Doppler broadening 00:25:06.930 --> 00:25:07.560 align:middle line:90% might dominate. 00:25:07.560 --> 00:25:09.120 align:middle line:84% Or there might be other mechanisms 00:25:09.120 --> 00:25:10.440 align:middle line:90% that dominate as well. 00:25:10.440 --> 00:25:12.985 align:middle line:84% I briefly mentioned it then, the response function 00:25:12.985 --> 00:25:14.610 align:middle line:84% of your spectrometer is also important, 00:25:14.610 --> 00:25:19.750 align:middle line:84% because your spectrometer has some finite size detector to it, 00:25:19.750 --> 00:25:22.350 align:middle line:84% which means that even if you give it a nice delta function 00:25:22.350 --> 00:25:27.360 align:middle line:84% here, it'll be broadened in some way. 00:25:27.360 --> 00:25:29.240 align:middle line:84% And if you're lucky, this will be Gaussian. 00:25:29.240 --> 00:25:30.320 align:middle line:90% And it'll be easy to understand. 00:25:30.320 --> 00:25:32.000 align:middle line:84% But of course, your spectrometer doesn't 00:25:32.000 --> 00:25:34.320 align:middle line:84% have to have a nice response function. 00:25:34.320 --> 00:25:36.770 align:middle line:84% It could have a response function like this due to some 00:25:36.770 --> 00:25:38.060 align:middle line:90% weird reflections inside it. 00:25:38.060 --> 00:25:40.430 align:middle line:84% So you also need to understand the response function 00:25:40.430 --> 00:25:43.430 align:middle line:84% of your spectrometer before you try and use, 00:25:43.430 --> 00:25:45.263 align:middle line:84% for example, the broadness of a line 00:25:45.263 --> 00:25:46.430 align:middle line:90% to estimate the temperature. 00:25:46.430 --> 00:25:48.463 align:middle line:90% It might just not be possible. 00:25:48.463 --> 00:25:49.130 align:middle line:90% AUDIENCE: I see. 00:25:49.130 --> 00:25:49.680 align:middle line:90% That makes sense. 00:25:49.680 --> 00:25:49.970 align:middle line:90% Thank you. 00:25:49.970 --> 00:25:50.270 align:middle line:90% JACK HARE: Yeah. 00:25:50.270 --> 00:25:52.970 align:middle line:84% I'll talk a bit more about that with the other three mechanisms 00:25:52.970 --> 00:25:54.710 align:middle line:90% as well. 00:25:54.710 --> 00:25:55.610 align:middle line:90% Other questions? 00:25:55.610 --> 00:26:01.340 align:middle line:90% 00:26:01.340 --> 00:26:03.500 align:middle line:90% AUDIENCE: [INAUDIBLE] 00:26:03.500 --> 00:26:14.733 align:middle line:90% 00:26:14.733 --> 00:26:15.400 align:middle line:90% JACK HARE: Yeah. 00:26:15.400 --> 00:26:18.370 align:middle line:84% We've taken a one-dimensional slice of the distribution 00:26:18.370 --> 00:26:19.242 align:middle line:90% function here. 00:26:19.242 --> 00:26:20.950 align:middle line:84% And because we're doing non-relativistic, 00:26:20.950 --> 00:26:23.075 align:middle line:84% we don't really care about the motion perpendicular 00:26:23.075 --> 00:26:25.550 align:middle line:84% to us, which in the relativistic case does happen. 00:26:25.550 --> 00:26:28.750 align:middle line:84% So yeah, this is sufficient for a three-dimensional system, 00:26:28.750 --> 00:26:33.250 align:middle line:84% because the three components of the velocity are-- 00:26:33.250 --> 00:26:36.490 align:middle line:90% 00:26:36.490 --> 00:26:37.810 align:middle line:90% no, this is OK. 00:26:37.810 --> 00:26:40.197 align:middle line:84% We can use this one-dimensional approximation 00:26:40.197 --> 00:26:42.280 align:middle line:84% as long as the distribution function is isotropic. 00:26:42.280 --> 00:26:43.738 align:middle line:84% If the distribution is anisotropic, 00:26:43.738 --> 00:26:45.363 align:middle line:84% then you would see different broadening 00:26:45.363 --> 00:26:46.525 align:middle line:90% in different directions. 00:26:46.525 --> 00:27:02.162 align:middle line:90% 00:27:02.162 --> 00:27:04.120 align:middle line:84% So the next mechanism we're going to talk about 00:27:04.120 --> 00:27:05.710 align:middle line:90% is called Stark broadening. 00:27:05.710 --> 00:27:21.970 align:middle line:90% 00:27:21.970 --> 00:27:26.310 align:middle line:84% Now, the only way to do this properly is with quantum. 00:27:26.310 --> 00:27:28.990 align:middle line:84% And you can go have a look at Professor Hutchinson's book. 00:27:28.990 --> 00:27:31.590 align:middle line:84% And you can see that there's a very long derivation for this. 00:27:31.590 --> 00:27:33.570 align:middle line:84% And even in his derivation, he admits 00:27:33.570 --> 00:27:36.250 align:middle line:84% that he doesn't cover all of the possible cases. 00:27:36.250 --> 00:27:40.090 align:middle line:84% So Stark broadening in general is extremely complicated. 00:27:40.090 --> 00:27:43.200 align:middle line:84% So what I'm going to give you is a very hand-wavy motivation 00:27:43.200 --> 00:27:45.760 align:middle line:84% for why Stark broadening might be happening. 00:27:45.760 --> 00:27:47.533 align:middle line:84% And then you can either accept that, 00:27:47.533 --> 00:27:49.950 align:middle line:84% or if you need to go and do spectroscopy Stark broadening, 00:27:49.950 --> 00:27:52.950 align:middle line:84% you can go do the calculations properly. 00:27:52.950 --> 00:27:57.662 align:middle line:84% So effectively, the idea of this is we have some ion, 00:27:57.662 --> 00:27:59.620 align:middle line:84% or some atom, I guess, we've been calling them. 00:27:59.620 --> 00:28:03.920 align:middle line:90% 00:28:03.920 --> 00:28:07.360 align:middle line:84% And if this atom is alone in the entire universe 00:28:07.360 --> 00:28:10.960 align:middle line:84% and it has few enough electrons, we can just about 00:28:10.960 --> 00:28:13.450 align:middle line:90% calculate the energy levels. 00:28:13.450 --> 00:28:15.910 align:middle line:84% And then we can do all of our nice quantum mechanics 00:28:15.910 --> 00:28:16.960 align:middle line:90% that we talked about. 00:28:16.960 --> 00:28:22.630 align:middle line:84% These have wave functions that possibly we can calculate. 00:28:22.630 --> 00:28:26.290 align:middle line:84% And so we can work out what the spontaneous emission coefficient 00:28:26.290 --> 00:28:35.740 align:middle line:84% is, because it goes lower upper upper, all that sort of stuff. 00:28:35.740 --> 00:28:36.670 align:middle line:90% But this is great. 00:28:36.670 --> 00:28:40.050 align:middle line:84% But as soon as we put anything else in the universe, 00:28:40.050 --> 00:28:42.820 align:middle line:84% this treatment will stop working very well. 00:28:42.820 --> 00:28:45.150 align:middle line:84% And the reason is, say, we've got some sort 00:28:45.150 --> 00:28:50.720 align:middle line:90% of electron here flying around. 00:28:50.720 --> 00:28:53.420 align:middle line:84% At some snapshot in time, this electron 00:28:53.420 --> 00:29:00.500 align:middle line:84% has a radial electric field like that. 00:29:00.500 --> 00:29:04.700 align:middle line:84% And that radial electric field will distort the potential 00:29:04.700 --> 00:29:05.630 align:middle line:90% around the atom. 00:29:05.630 --> 00:29:08.990 align:middle line:84% And it, for example, will distort these energy levels. 00:29:08.990 --> 00:29:11.840 align:middle line:84% And maybe we don't know exactly how they're being distorted, 00:29:11.840 --> 00:29:13.130 align:middle line:90% but maybe some of them go up. 00:29:13.130 --> 00:29:14.225 align:middle line:90% Some of them go down. 00:29:14.225 --> 00:29:16.980 align:middle line:84% It changes all of these energy levels. 00:29:16.980 --> 00:29:20.690 align:middle line:84% And that means now when we have transitions, their energy, 00:29:20.690 --> 00:29:23.570 align:middle line:90% h u prime l prime-- 00:29:23.570 --> 00:29:25.010 align:middle line:90% this is the lower state. 00:29:25.010 --> 00:29:26.300 align:middle line:90% This is the upper state-- 00:29:26.300 --> 00:29:34.280 align:middle line:84% does not have to be the same as the original energy level hul. 00:29:34.280 --> 00:29:36.510 align:middle line:84% So the photons will come out differently. 00:29:36.510 --> 00:29:38.375 align:middle line:84% So effectively, what Stark broadening is 00:29:38.375 --> 00:29:41.870 align:middle line:84% is the effect of the electric fields of other particles 00:29:41.870 --> 00:29:44.480 align:middle line:84% on the energy levels, shifting the energy levels, 00:29:44.480 --> 00:29:45.800 align:middle line:90% giving us different energies. 00:29:45.800 --> 00:29:49.100 align:middle line:84% And we can imagine as these electrons move around, they're 00:29:49.100 --> 00:29:50.750 align:middle line:84% going to create some sort net effect, 00:29:50.750 --> 00:29:52.080 align:middle line:90% because there's not just one. 00:29:52.080 --> 00:29:53.060 align:middle line:90% There's more of them. 00:29:53.060 --> 00:29:55.463 align:middle line:90% 00:29:55.463 --> 00:29:57.380 align:middle line:84% And all of these are going to shift the energy 00:29:57.380 --> 00:29:58.580 align:middle line:90% levels in different ways. 00:29:58.580 --> 00:30:01.190 align:middle line:84% And we might imagine there's some smearing out at this point, 00:30:01.190 --> 00:30:03.710 align:middle line:84% because some atoms are going to see some electric field, 00:30:03.710 --> 00:30:05.510 align:middle line:84% and some atoms are going to see different electric field 00:30:05.510 --> 00:30:08.030 align:middle line:84% configuration, which may move the lines apart or closer 00:30:08.030 --> 00:30:10.142 align:middle line:84% together and give us that broadening. 00:30:10.142 --> 00:30:13.230 align:middle line:90% 00:30:13.230 --> 00:30:16.760 align:middle line:84% So that's the first level of hand-wavy approximation. 00:30:16.760 --> 00:30:19.260 align:middle line:84% The next level is to try and put a little bit of math to it. 00:30:19.260 --> 00:30:21.840 align:middle line:84% And we say that the change in the frequency 00:30:21.840 --> 00:30:26.100 align:middle line:84% is going to be proportional to the electric field felt 00:30:26.100 --> 00:30:26.920 align:middle line:90% by the atom. 00:30:26.920 --> 00:30:30.300 align:middle line:84% Now, I've used this symbol to mean energy a lot. 00:30:30.300 --> 00:30:34.108 align:middle line:84% In my notes, I started writing the electric field like this, 00:30:34.108 --> 00:30:36.400 align:middle line:84% simply to make it clear that there's a difference here. 00:30:36.400 --> 00:30:41.080 align:middle line:90% So I'll do that. 00:30:41.080 --> 00:30:44.710 align:middle line:90% This big curly E is the E field. 00:30:44.710 --> 00:30:47.542 align:middle line:90% 00:30:47.542 --> 00:30:48.290 align:middle line:90% I want to know-- 00:30:48.290 --> 00:30:49.940 align:middle line:90% I kind of just stated this. 00:30:49.940 --> 00:30:52.640 align:middle line:84% You might be able to motivate it by thinking 00:30:52.640 --> 00:30:55.760 align:middle line:84% about the energy of an electron in an electric field 00:30:55.760 --> 00:30:56.960 align:middle line:90% and how that energy shifts. 00:30:56.960 --> 00:30:59.360 align:middle line:84% But it turns out that, quantum mechanically, 00:30:59.360 --> 00:31:04.580 align:middle line:84% sometimes you get delta nu goes as the electric field squared. 00:31:04.580 --> 00:31:06.080 align:middle line:84% This is called the quadratic Stark 00:31:06.080 --> 00:31:11.437 align:middle line:90% effect for obvious reasons. 00:31:11.437 --> 00:31:13.020 align:middle line:84% This is the linear Stark effect, which 00:31:13.020 --> 00:31:16.210 align:middle line:84% is the one I'm going to use as my toy model today. 00:31:16.210 --> 00:31:17.740 align:middle line:84% And the only way to really find out 00:31:17.740 --> 00:31:19.240 align:middle line:84% whether you have quadratic or linear 00:31:19.240 --> 00:31:21.370 align:middle line:84% is to go do the quantum theory properly for this. 00:31:21.370 --> 00:31:22.940 align:middle line:90% My apologies. 00:31:22.940 --> 00:31:28.210 align:middle line:84% So this electric field is going to be related 00:31:28.210 --> 00:31:30.223 align:middle line:90% through the distance between-- 00:31:30.223 --> 00:31:32.140 align:middle line:84% say there's one electron that's closest that's 00:31:32.140 --> 00:31:33.470 align:middle line:90% doing the most distortion. 00:31:33.470 --> 00:31:35.500 align:middle line:84% And so that is inducing electric field 00:31:35.500 --> 00:31:37.990 align:middle line:84% by Coulomb's law that goes as 1 over r squared. 00:31:37.990 --> 00:31:41.860 align:middle line:84% There's some distance r between these. 00:31:41.860 --> 00:31:43.890 align:middle line:84% And so we'll get some shift that's 00:31:43.890 --> 00:31:46.320 align:middle line:84% related to distance to the closest electron. 00:31:46.320 --> 00:31:48.730 align:middle line:84% Well, how close are these electrons? 00:31:48.730 --> 00:31:52.630 align:middle line:84% Well, we have a density n like this. 00:31:52.630 --> 00:31:57.090 align:middle line:84% And so that density is going to give us an average spacing of 1 00:31:57.090 --> 00:31:58.210 align:middle line:90% upon r cubed. 00:31:58.210 --> 00:32:02.280 align:middle line:84% So we can write that the other way around and say that r goes 00:32:02.280 --> 00:32:05.680 align:middle line:84% as density to the minus 1/3 like this. 00:32:05.680 --> 00:32:07.710 align:middle line:84% But this is asking for some density 00:32:07.710 --> 00:32:11.650 align:middle line:84% n, what is the average spacing between particles? 00:32:11.650 --> 00:32:14.760 align:middle line:84% So if I just plot them around in this volume, 00:32:14.760 --> 00:32:17.910 align:middle line:84% I can see as n goes up, r goes down. 00:32:17.910 --> 00:32:22.160 align:middle line:84% If I put more dots here, I get a smaller r. 00:32:22.160 --> 00:32:24.230 align:middle line:90% This is a very crude estimate. 00:32:24.230 --> 00:32:27.440 align:middle line:84% So that means that the electric field that the atoms are feeling 00:32:27.440 --> 00:32:31.620 align:middle line:84% is going to scale as n to the 2/3 like this. 00:32:31.620 --> 00:32:36.020 align:middle line:84% And so therefore, that's also our scaling with delta nu. 00:32:36.020 --> 00:32:38.900 align:middle line:90% 00:32:38.900 --> 00:32:42.060 align:middle line:84% Obviously, what I've not got is the coefficient out the front 00:32:42.060 --> 00:32:42.560 align:middle line:90% here. 00:32:42.560 --> 00:32:46.280 align:middle line:84% You need that coefficient to actually link the frequency 00:32:46.280 --> 00:32:47.990 align:middle line:90% shift back to the density. 00:32:47.990 --> 00:32:51.140 align:middle line:84% But in general, the idea is, as we had before, 00:32:51.140 --> 00:33:01.400 align:middle line:84% that we have some line at nu 0 and that line is broadened 00:33:01.400 --> 00:33:09.830 align:middle line:84% and the width of that broadening at full width at half maximum is 00:33:09.830 --> 00:33:13.210 align:middle line:84% proportional to 2/3 of the density. 00:33:13.210 --> 00:33:16.825 align:middle line:84% So potentially, by measuring this broadening, as long 00:33:16.825 --> 00:33:19.200 align:middle line:84% as you've got this coefficient from doing all the quantum 00:33:19.200 --> 00:33:22.170 align:middle line:84% mechanics right, you can infer the density here. 00:33:22.170 --> 00:33:24.300 align:middle line:84% Doppler broadening got us the temperature. 00:33:24.300 --> 00:33:27.180 align:middle line:84% Stark broadening might get us the density. 00:33:27.180 --> 00:33:33.290 align:middle line:90% 00:33:33.290 --> 00:33:36.710 align:middle line:84% Not very satisfactory, I appreciate it. 00:33:36.710 --> 00:33:40.783 align:middle line:90% AUDIENCE: [INAUDIBLE] 00:33:40.783 --> 00:33:41.450 align:middle line:90% JACK HARE: Yeah. 00:33:41.450 --> 00:33:44.800 align:middle line:84% These are the electrons which are inside your Debye cloud. 00:33:44.800 --> 00:33:46.550 align:middle line:84% So they are the Debye shielding electrons, 00:33:46.550 --> 00:33:49.220 align:middle line:84% but some of those electrons may still get very, very close 00:33:49.220 --> 00:33:52.090 align:middle line:90% to the ion. 00:33:52.090 --> 00:33:55.030 align:middle line:90% AUDIENCE: [INAUDIBLE] 00:33:55.030 --> 00:33:59.978 align:middle line:90% 00:33:59.978 --> 00:34:02.020 align:middle line:84% JACK HARE: I think that that's the electric field 00:34:02.020 --> 00:34:07.650 align:middle line:84% outside of the Debye cloud, but I might be wrong. 00:34:07.650 --> 00:34:10.213 align:middle line:90% 00:34:10.213 --> 00:34:11.880 align:middle line:84% I think that's the electric field, which 00:34:11.880 --> 00:34:14.500 align:middle line:84% drops off far away from the atom, and then goes to 0 very, 00:34:14.500 --> 00:34:15.159 align:middle line:90% very quickly. 00:34:15.159 --> 00:34:17.520 align:middle line:84% But I think if you imagine you have your ion 00:34:17.520 --> 00:34:19.614 align:middle line:84% and you have this cloud of electrons 00:34:19.614 --> 00:34:21.239 align:middle line:84% which are shielding the charge, there's 00:34:21.239 --> 00:34:24.280 align:middle line:84% still a possibility of one electron going very close. 00:34:24.280 --> 00:34:27.060 align:middle line:84% And that's sort of averaged closest approach thing 00:34:27.060 --> 00:34:28.770 align:middle line:90% is what we're estimating here. 00:34:28.770 --> 00:34:31.650 align:middle line:84% So you still will get some perturbation 00:34:31.650 --> 00:34:33.989 align:middle line:84% to the energy levels here and some broadening from it. 00:34:33.989 --> 00:34:36.570 align:middle line:90% 00:34:36.570 --> 00:34:39.630 align:middle line:84% Again, I think my picture with individual electrons 00:34:39.630 --> 00:34:41.310 align:middle line:84% here is not the right way to do this. 00:34:41.310 --> 00:34:43.727 align:middle line:84% To do it properly, you have to do it with a wave function. 00:34:43.727 --> 00:34:46.168 align:middle line:90% 00:34:46.168 --> 00:34:46.960 align:middle line:90% But people do this. 00:34:46.960 --> 00:34:49.968 align:middle line:84% People use Stark broadening to measure density. 00:34:49.968 --> 00:34:52.510 align:middle line:84% And so what you'd want in order for this broadening mechanism 00:34:52.510 --> 00:34:54.190 align:middle line:84% to dominate is to have a dense plasma 00:34:54.190 --> 00:34:58.870 align:middle line:84% at relatively low temperature so that you don't get the Doppler 00:34:58.870 --> 00:35:00.970 align:middle line:84% broadening, which is proportional 00:35:00.970 --> 00:35:04.500 align:middle line:90% to temperature to the half. 00:35:04.500 --> 00:35:05.976 align:middle line:90% Yeah. 00:35:05.976 --> 00:35:07.970 align:middle line:90% AUDIENCE: [INAUDIBLE] 00:35:07.970 --> 00:35:11.587 align:middle line:90% 00:35:11.587 --> 00:35:12.170 align:middle line:90% JACK HARE: OK. 00:35:12.170 --> 00:35:14.266 align:middle line:90% Maybe that's a better answer. 00:35:14.266 --> 00:35:16.500 align:middle line:90% [LAUGHTER] 00:35:16.500 --> 00:35:18.360 align:middle line:84% Any other questions on Stark broadening? 00:35:18.360 --> 00:35:21.191 align:middle line:84% Sometimes called collisional broadening as well. 00:35:21.191 --> 00:35:30.100 align:middle line:90% [INAUDIBLE] Yeah. 00:35:30.100 --> 00:35:32.925 align:middle line:90% AUDIENCE: [INAUDIBLE] 00:35:32.925 --> 00:35:35.652 align:middle line:90% 00:35:35.652 --> 00:35:37.860 align:middle line:84% JACK HARE: I never worked out what the motional Stark 00:35:37.860 --> 00:35:38.460 align:middle line:90% effect is. 00:35:38.460 --> 00:35:42.640 align:middle line:84% It's like it's the electric field that the particle feels 00:35:42.640 --> 00:35:43.870 align:middle line:90% in its lab frame. 00:35:43.870 --> 00:35:46.400 align:middle line:84% So it's actually related to the magnetic field. 00:35:46.400 --> 00:35:48.880 align:middle line:84% So you use the motional Stark effect 00:35:48.880 --> 00:35:50.980 align:middle line:84% to make local measurements of the magnetic field. 00:35:50.980 --> 00:35:53.368 align:middle line:84% But they call it Stark because it's effectively 00:35:53.368 --> 00:35:54.160 align:middle line:90% the electric field. 00:35:54.160 --> 00:35:56.380 align:middle line:84% But I don't think it's Stark in terms of density. 00:35:56.380 --> 00:35:58.180 align:middle line:84% I think it's to do with that lab, 00:35:58.180 --> 00:36:00.248 align:middle line:84% like you transform into the co-moving frame 00:36:00.248 --> 00:36:02.290 align:middle line:84% with the particle, and it fills an electric field 00:36:02.290 --> 00:36:03.550 align:middle line:90% instead of a magnetic field. 00:36:03.550 --> 00:36:04.510 align:middle line:90% Never quite got it. 00:36:04.510 --> 00:36:08.375 align:middle line:90% 00:36:08.375 --> 00:36:12.740 align:middle line:90% AUDIENCE: [INAUDIBLE] 00:36:12.740 --> 00:36:20.013 align:middle line:90% 00:36:20.013 --> 00:36:20.680 align:middle line:90% JACK HARE: Yeah. 00:36:20.680 --> 00:36:23.830 align:middle line:84% So the question is, if you have both Docker and Spark, 00:36:23.830 --> 00:36:25.673 align:middle line:84% are the line shapes different in such a way 00:36:25.673 --> 00:36:27.340 align:middle line:84% that you might be able to pluck out both 00:36:27.340 --> 00:36:28.900 align:middle line:90% the density and temperature? 00:36:28.900 --> 00:36:30.910 align:middle line:84% I think, in general, because all of the line 00:36:30.910 --> 00:36:34.750 align:middle line:84% shapes that we get are Gaussian-like functions-- they 00:36:34.750 --> 00:36:36.220 align:middle line:90% look pretty Gaussian. 00:36:36.220 --> 00:36:38.950 align:middle line:84% They are symmetric, and their peak's in the middle. 00:36:38.950 --> 00:36:41.740 align:middle line:84% It's quite hard to deconvolve both of those. 00:36:41.740 --> 00:36:46.640 align:middle line:84% For the natural broadening, Though we have a Lorentzian, 00:36:46.640 --> 00:36:48.368 align:middle line:84% you end up-- if you have a Lorentzian, 00:36:48.368 --> 00:36:49.910 align:middle line:84% or if you have the natural broadening 00:36:49.910 --> 00:36:51.830 align:middle line:84% and the thermal broadening, the Doppler broadening, 00:36:51.830 --> 00:36:54.193 align:middle line:84% you end up with something called a Voigt profile, which 00:36:54.193 --> 00:36:55.235 align:middle line:90% is a well known function. 00:36:55.235 --> 00:36:57.920 align:middle line:90% 00:36:57.920 --> 00:37:01.280 align:middle line:84% And then you can fit a Voigt profile to your line. 00:37:01.280 --> 00:37:04.260 align:middle line:84% And then you can get out the thermal broadening component, 00:37:04.260 --> 00:37:05.990 align:middle line:84% which is what you actually want to do. 00:37:05.990 --> 00:37:09.760 align:middle line:84% Presumably, there is some function 00:37:09.760 --> 00:37:12.520 align:middle line:84% that we can come up with, which is a convolution of whatever 00:37:12.520 --> 00:37:14.020 align:middle line:84% the Stark broadening is and whatever 00:37:14.020 --> 00:37:14.860 align:middle line:90% the thermal broadening is. 00:37:14.860 --> 00:37:16.120 align:middle line:90% And maybe you could fit that. 00:37:16.120 --> 00:37:18.407 align:middle line:84% But as always, you're really at the mercy of noise. 00:37:18.407 --> 00:37:20.740 align:middle line:84% And so if you're not measuring this line very precisely, 00:37:20.740 --> 00:37:22.960 align:middle line:84% it's going to be really hard to determine the difference. 00:37:22.960 --> 00:37:24.835 align:middle line:84% By the way, if you look in Hutchinson's book, 00:37:24.835 --> 00:37:27.233 align:middle line:84% there's some really weird Stark broadening features, 00:37:27.233 --> 00:37:28.900 align:middle line:84% some of which actually have a little dip 00:37:28.900 --> 00:37:30.290 align:middle line:90% in the middle like that. 00:37:30.290 --> 00:37:33.570 align:middle line:84% So Stark broadening, depending on the quantum mechanics 00:37:33.570 --> 00:37:36.240 align:middle line:84% of the quadratic and the linear can give you really funky line 00:37:36.240 --> 00:37:37.223 align:middle line:90% shapes as well. 00:37:37.223 --> 00:37:39.390 align:middle line:84% So that could be a good way of trying to deconvolve, 00:37:39.390 --> 00:37:40.932 align:middle line:84% because then this function here looks 00:37:40.932 --> 00:37:42.645 align:middle line:84% quite different from a peaked function. 00:37:42.645 --> 00:37:46.600 align:middle line:90% 00:37:46.600 --> 00:37:49.150 align:middle line:90% Any other questions? 00:37:49.150 --> 00:37:50.584 align:middle line:90% Yeah. 00:37:50.584 --> 00:37:54.028 align:middle line:90% AUDIENCE: [INAUDIBLE] 00:37:54.028 --> 00:38:00.430 align:middle line:90% 00:38:00.430 --> 00:38:02.250 align:middle line:90% JACK HARE: Yeah. 00:38:02.250 --> 00:38:03.820 align:middle line:90% I think you're right. 00:38:03.820 --> 00:38:07.270 align:middle line:84% I think any particle coming near will distort the electric field. 00:38:07.270 --> 00:38:09.030 align:middle line:84% And it could be another ion as well. 00:38:09.030 --> 00:38:10.950 align:middle line:84% I was just using electrons [INAUDIBLE]. 00:38:10.950 --> 00:38:14.165 align:middle line:90% 00:38:14.165 --> 00:38:19.190 align:middle line:84% The next mechanism is Zeeman splitting. 00:38:19.190 --> 00:38:38.827 align:middle line:90% 00:38:38.827 --> 00:38:39.910 align:middle line:90% I'm going to explain this. 00:38:39.910 --> 00:38:42.520 align:middle line:84% And you're going to say, this isn't broadening. 00:38:42.520 --> 00:38:43.420 align:middle line:90% But it is. 00:38:43.420 --> 00:38:44.890 align:middle line:90% I promise you. 00:38:44.890 --> 00:38:48.100 align:middle line:84% So Zeeman splitting is what happens in the presence 00:38:48.100 --> 00:38:50.060 align:middle line:90% of a magnetic field. 00:38:50.060 --> 00:39:00.015 align:middle line:84% So this is effectively the B field splits energy levels. 00:39:00.015 --> 00:39:07.780 align:middle line:90% 00:39:07.780 --> 00:39:14.332 align:middle line:84% So if we think of a system that has, for example, a shell with p 00:39:14.332 --> 00:39:16.040 align:middle line:84% angular momentum and s angular momentum-- 00:39:16.040 --> 00:39:17.545 align:middle line:84% if you haven't seen this in quantum. 00:39:17.545 --> 00:39:18.420 align:middle line:90% Don't worry about it. 00:39:18.420 --> 00:39:21.920 align:middle line:84% But these are letters which refer to specific amounts 00:39:21.920 --> 00:39:24.660 align:middle line:90% of orbital angular momentum. 00:39:24.660 --> 00:39:28.380 align:middle line:84% Then we can have a transition from the p level 00:39:28.380 --> 00:39:29.790 align:middle line:90% down to the s level. 00:39:29.790 --> 00:39:33.090 align:middle line:84% And this is allowed because we have 00:39:33.090 --> 00:39:35.820 align:middle line:84% a change in angular momentum of plus or minus 1, 00:39:35.820 --> 00:39:37.380 align:middle line:84% which is the selection rule that's 00:39:37.380 --> 00:39:41.160 align:middle line:84% enforced by our dipole operator here 00:39:41.160 --> 00:39:45.600 align:middle line:84% that converts from the s energy level or the p energy level 00:39:45.600 --> 00:39:48.020 align:middle line:90% down here. 00:39:48.020 --> 00:39:49.970 align:middle line:84% When we have a magnetic field, we 00:39:49.970 --> 00:39:53.220 align:middle line:84% see that this line actually splits. 00:39:53.220 --> 00:39:54.870 align:middle line:90% So the s does not split. 00:39:54.870 --> 00:39:59.290 align:middle line:84% But the p, for example, will split into three energy levels 00:39:59.290 --> 00:39:59.790 align:middle line:90% here. 00:39:59.790 --> 00:40:06.590 align:middle line:84% And these energy levels will now have different angular momentums 00:40:06.590 --> 00:40:08.330 align:middle line:90% and they will also-- 00:40:08.330 --> 00:40:13.980 align:middle line:84% we're going to give them a label of sigma minus, sigma 00:40:13.980 --> 00:40:16.470 align:middle line:90% plus, and pi. 00:40:16.470 --> 00:40:19.270 align:middle line:84% The reason for these are just obscure spectroscopy notation. 00:40:19.270 --> 00:40:22.880 align:middle line:84% But this is what they've been called. 00:40:22.880 --> 00:40:30.470 align:middle line:84% The energy is different because the magnetic field 00:40:30.470 --> 00:40:34.946 align:middle line:84% is coupled to the magnetic dipole of the electrons. 00:40:34.946 --> 00:40:38.350 align:middle line:90% 00:40:38.350 --> 00:40:39.720 align:middle line:90% So we have a change in energy-- 00:40:39.720 --> 00:40:42.543 align:middle line:90% 00:40:42.543 --> 00:40:43.960 align:middle line:84% do I want to draw that as delta e? 00:40:43.960 --> 00:40:52.490 align:middle line:90% No-- of delta e. 00:40:52.490 --> 00:40:55.660 align:middle line:84% And this change in energy, delta e, 00:40:55.660 --> 00:41:00.460 align:middle line:84% is equal to minus mu, the magnetic moment of the electron, 00:41:00.460 --> 00:41:03.040 align:middle line:90% dotted with e like this. 00:41:03.040 --> 00:41:10.850 align:middle line:84% And this mu is a combination of the orbital angular 00:41:10.850 --> 00:41:13.833 align:middle line:84% momentum of the electron and the spin of the electron. 00:41:13.833 --> 00:41:15.750 align:middle line:84% If you've ever seen this in quantum mechanics, 00:41:15.750 --> 00:41:17.417 align:middle line:84% I apologize for butchering it like this. 00:41:17.417 --> 00:41:20.210 align:middle line:84% I'm just trying very quickly to get to the result. 00:41:20.210 --> 00:41:23.450 align:middle line:84% But effectively, you can have electrons which are spin up 00:41:23.450 --> 00:41:24.990 align:middle line:84% and electrons which are spin down. 00:41:24.990 --> 00:41:27.532 align:middle line:84% And so some of them are going to have their energy shifted up 00:41:27.532 --> 00:41:30.588 align:middle line:84% and some of them are going to have their energy shifted down. 00:41:30.588 --> 00:41:32.630 align:middle line:84% And that means that we're going to be looking out 00:41:32.630 --> 00:41:33.650 align:middle line:90% for transitions. 00:41:33.650 --> 00:41:38.240 align:middle line:84% Now, as opposed to just having a single transition down, 00:41:38.240 --> 00:41:41.630 align:middle line:84% we're going to have three different transitions, 00:41:41.630 --> 00:41:44.720 align:middle line:84% all of which are allowed, and all of which 00:41:44.720 --> 00:41:48.270 align:middle line:84% have slightly different energies here. 00:41:48.270 --> 00:41:57.660 align:middle line:84% So if I now look at my initial frequency on an intensity plot 00:41:57.660 --> 00:42:05.560 align:middle line:84% here, as opposed to initially having a single line, 00:42:05.560 --> 00:42:07.260 align:middle line:90% I may now have three lines. 00:42:07.260 --> 00:42:15.330 align:middle line:90% 00:42:15.330 --> 00:42:17.160 align:middle line:84% I've labeled them with their labels. 00:42:17.160 --> 00:42:19.015 align:middle line:84% And see the sigma minus has lower energy. 00:42:19.015 --> 00:42:19.890 align:middle line:90% AUDIENCE: [INAUDIBLE] 00:42:19.890 --> 00:42:20.400 align:middle line:90% JACK HARE: Yeah. 00:42:20.400 --> 00:42:22.240 align:middle line:84% AUDIENCE: Is there anything like [INAUDIBLE]? 00:42:22.240 --> 00:42:22.823 align:middle line:90% JACK HARE: No. 00:42:22.823 --> 00:42:23.871 align:middle line:90% So this is this s. 00:42:23.871 --> 00:42:24.793 align:middle line:90% AUDIENCE: Ah, no, no. 00:42:24.793 --> 00:42:26.640 align:middle line:90% [INAUDIBLE] 00:42:26.640 --> 00:42:29.930 align:middle line:90% 00:42:29.930 --> 00:42:32.510 align:middle line:84% JACK HARE: This doesn't, because it's a singlet state. 00:42:32.510 --> 00:42:34.982 align:middle line:90% But that's quantum mechanics. 00:42:34.982 --> 00:42:36.440 align:middle line:84% And if you haven't seen it, I'm not 00:42:36.440 --> 00:42:37.732 align:middle line:90% going to explain it to you now. 00:42:37.732 --> 00:42:40.310 align:middle line:84% You can, in general, have a splitting of the other state, 00:42:40.310 --> 00:42:42.770 align:middle line:84% but then often transitions in those states is forbidden 00:42:42.770 --> 00:42:43.728 align:middle line:90% by the selection rules. 00:42:43.728 --> 00:42:45.110 align:middle line:90% So you won't see those lines. 00:42:45.110 --> 00:42:47.613 align:middle line:84% And also, this can split into two, or five, 00:42:47.613 --> 00:42:49.280 align:middle line:84% or all sorts of other numbers like that. 00:42:49.280 --> 00:42:51.470 align:middle line:84% I'm just doing a case where it split into three. 00:42:51.470 --> 00:42:52.378 align:middle line:90% Yeah. 00:42:52.378 --> 00:42:55.465 align:middle line:90% AUDIENCE: [INAUDIBLE] 00:42:55.465 --> 00:42:57.840 align:middle line:84% JACK HARE: It's to do with a number of different ways you 00:42:57.840 --> 00:43:00.790 align:middle line:84% can add up the angular momentum vector and the s vector. 00:43:00.790 --> 00:43:01.560 align:middle line:90% So it is finite. 00:43:01.560 --> 00:43:03.120 align:middle line:84% There's only a finite number of them. 00:43:03.120 --> 00:43:05.790 align:middle line:84% But oh god, you've really taken me back now here. 00:43:05.790 --> 00:43:11.320 align:middle line:90% But we have some vector B here. 00:43:11.320 --> 00:43:15.718 align:middle line:84% It depends on how we can add up i and s. 00:43:15.718 --> 00:43:18.560 align:middle line:84% And because s is the spin of the electron, 00:43:18.560 --> 00:43:20.820 align:middle line:84% this can only take finite values. 00:43:20.820 --> 00:43:28.340 align:middle line:84% And so this is 1l plus s projected onto b. 00:43:28.340 --> 00:43:30.450 align:middle line:84% But we can also have s like this. 00:43:30.450 --> 00:43:35.540 align:middle line:84% And so this would be another l plus s projected onto b. 00:43:35.540 --> 00:43:37.450 align:middle line:84% So it does take discrete energy levels, 00:43:37.450 --> 00:43:39.950 align:middle line:84% and it depends on the angular momentum. 00:43:39.950 --> 00:43:42.280 align:middle line:84% And this s is actually the total spin 00:43:42.280 --> 00:43:44.210 align:middle line:84% of the electrons in this energy level. 00:43:44.210 --> 00:43:46.390 align:middle line:84% So these electrons, it doesn't have to just be one. 00:43:46.390 --> 00:43:47.570 align:middle line:90% There can be three here. 00:43:47.570 --> 00:43:49.195 align:middle line:84% And then there's lots of different ways 00:43:49.195 --> 00:43:50.560 align:middle line:90% you can get s out of that. 00:43:50.560 --> 00:43:53.060 align:middle line:84% We're really not going to go into quantum mechanics in this. 00:43:53.060 --> 00:43:54.910 align:middle line:84% You should look it up if you're interested. 00:43:54.910 --> 00:43:58.460 align:middle line:84% I realize as I try to explain it we're getting deeper and deeper. 00:43:58.460 --> 00:44:03.850 align:middle line:84% The fact is magnetic fields, I think the heuristic motivation 00:44:03.850 --> 00:44:06.670 align:middle line:84% here is that the magnetic field will shift these energy levels, 00:44:06.670 --> 00:44:10.180 align:middle line:84% and it will create new energy levels, which are-- either have 00:44:10.180 --> 00:44:12.200 align:middle line:84% their spin aligned with the magnetic field 00:44:12.200 --> 00:44:13.450 align:middle line:90% or against the magnetic field. 00:44:13.450 --> 00:44:15.658 align:middle line:84% And those energy levels will have different energies. 00:44:15.658 --> 00:44:17.920 align:middle line:84% It's like a little bar magnet rotating to align itself 00:44:17.920 --> 00:44:19.167 align:middle line:90% with the magnet. 00:44:19.167 --> 00:44:21.500 align:middle line:84% And because those energy levels have different energies, 00:44:21.500 --> 00:44:24.490 align:middle line:84% the lines will have different energies. 00:44:24.490 --> 00:44:27.060 align:middle line:84% The light that we get has different energies. 00:44:27.060 --> 00:44:31.190 align:middle line:84% And so if you're in a state where your broadening is 00:44:31.190 --> 00:44:31.920 align:middle line:90% very narrow-- 00:44:31.920 --> 00:44:33.410 align:middle line:84% so there's not very much natural broadening, 00:44:33.410 --> 00:44:34.952 align:middle line:84% or not very much thermal broadening-- 00:44:34.952 --> 00:44:39.035 align:middle line:84% you will get out these maybe three very distinct lines. 00:44:39.035 --> 00:44:40.910 align:middle line:84% And then the cool thing that you can do there 00:44:40.910 --> 00:44:43.040 align:middle line:90% is you can measure delta nu. 00:44:43.040 --> 00:44:49.310 align:middle line:84% And you can get out the magnetic field magnitude. 00:44:49.310 --> 00:44:51.900 align:middle line:90% So that's pretty neat. 00:44:51.900 --> 00:44:54.130 align:middle line:84% In many plasmas, we don't know the magnetic fields. 00:44:54.130 --> 00:44:55.980 align:middle line:84% And so Zeeman splitting is a good technique. 00:44:55.980 --> 00:44:58.320 align:middle line:84% In something like a tokamak, we tend to know the magnetic field 00:44:58.320 --> 00:44:58.820 align:middle line:90% very well. 00:44:58.820 --> 00:45:02.330 align:middle line:84% So Zeeman splitting is not that useful a technique. 00:45:02.330 --> 00:45:05.360 align:middle line:84% The trouble comes that actually a lot of the time, these lines 00:45:05.360 --> 00:45:08.220 align:middle line:90% are relatively small splitting. 00:45:08.220 --> 00:45:10.980 align:middle line:84% So the magnetic field may not be very large. 00:45:10.980 --> 00:45:13.040 align:middle line:84% And so these lines may be very close together, 00:45:13.040 --> 00:45:14.790 align:middle line:84% or they may have large thermal broadening. 00:45:14.790 --> 00:45:17.600 align:middle line:84% So if I draw this now with each of these lines having 00:45:17.600 --> 00:45:20.390 align:middle line:84% significant thermal broadening, we 00:45:20.390 --> 00:45:24.660 align:middle line:84% can see that we won't see this well resolved triplet anymore. 00:45:24.660 --> 00:45:28.340 align:middle line:84% We will instead see some big blob of lines. 00:45:28.340 --> 00:45:31.550 align:middle line:84% And so this is effectively another broadening mechanism, 00:45:31.550 --> 00:45:33.960 align:middle line:84% because we split these lines, but we don't resolve them. 00:45:33.960 --> 00:45:45.840 align:middle line:84% So the total overall shape here, delta nu 1/2 is greater than 00:45:45.840 --> 00:45:47.460 align:middle line:90% delta nu 1/2 of the Doppler. 00:45:47.460 --> 00:45:50.550 align:middle line:90% 00:45:50.550 --> 00:45:54.000 align:middle line:84% So if you interpret this line as just being Doppler broadened, 00:45:54.000 --> 00:45:56.490 align:middle line:84% you'll infer like some ridiculously high temperature. 00:45:56.490 --> 00:45:58.650 align:middle line:84% But in fact, that only looks so high 00:45:58.650 --> 00:46:01.150 align:middle line:84% because you've got some of this Doppler-- 00:46:01.150 --> 00:46:03.240 align:middle line:84% this Zeeman splitting broadening built in. 00:46:03.240 --> 00:46:06.950 align:middle line:90% 00:46:06.950 --> 00:46:07.970 align:middle line:90% Questions on this? 00:46:07.970 --> 00:46:10.610 align:middle line:84% I have another point, but I just want to pause here. 00:46:10.610 --> 00:46:11.160 align:middle line:90% Yeah. 00:46:11.160 --> 00:46:11.660 align:middle line:90% [INAUDIBLE] 00:46:11.660 --> 00:46:12.110 align:middle line:90% AUDIENCE: [INAUDIBLE] 00:46:12.110 --> 00:46:13.100 align:middle line:90% JACK HARE: Oh, sorry. 00:46:13.100 --> 00:46:20.660 align:middle line:90% 00:46:20.660 --> 00:46:22.610 align:middle line:90% Yes. 00:46:22.610 --> 00:46:25.100 align:middle line:84% That's from-- so you know mu because it's actually 00:46:25.100 --> 00:46:26.930 align:middle line:84% very constrained by quantum mechanics. 00:46:26.930 --> 00:46:28.850 align:middle line:84% And so if you're seeing this line, 00:46:28.850 --> 00:46:30.740 align:middle line:90% you know what the energy is. 00:46:30.740 --> 00:46:33.470 align:middle line:84% And so you know what transition that corresponds to. 00:46:33.470 --> 00:46:35.600 align:middle line:84% So you know the electronic configuration 00:46:35.600 --> 00:46:36.650 align:middle line:90% of the upper state. 00:46:36.650 --> 00:46:38.780 align:middle line:84% And then you can go do your quantum mechanics and be like, 00:46:38.780 --> 00:46:40.655 align:middle line:84% there's three levels, or there's five levels, 00:46:40.655 --> 00:46:44.300 align:middle line:84% and the spacing of those levels is this or that. 00:46:44.300 --> 00:46:46.960 align:middle line:90% So that's OK. 00:46:46.960 --> 00:46:51.420 align:middle line:90% AUDIENCE: [INAUDIBLE] 00:46:51.420 --> 00:46:52.045 align:middle line:90% JACK HARE: Yes. 00:46:52.045 --> 00:46:52.920 align:middle line:90% AUDIENCE: [INAUDIBLE] 00:46:52.920 --> 00:46:53.795 align:middle line:90% JACK HARE: Oh, yeah. 00:46:53.795 --> 00:46:55.177 align:middle line:90% Yeah, yeah. 00:46:55.177 --> 00:46:58.446 align:middle line:84% AUDIENCE: [INAUDIBLE] the bottom [INAUDIBLE]. 00:46:58.446 --> 00:47:01.250 align:middle line:90% 00:47:01.250 --> 00:47:02.480 align:middle line:90% JACK HARE: Yes. 00:47:02.480 --> 00:47:03.680 align:middle line:90% That will smear things out. 00:47:03.680 --> 00:47:05.030 align:middle line:84% As always with spectroscopy, if you're 00:47:05.030 --> 00:47:06.410 align:middle line:84% line integrating through a region that 00:47:06.410 --> 00:47:07.910 align:middle line:84% has different parameters, then there 00:47:07.910 --> 00:47:10.211 align:middle line:90% will be some smearing there. 00:47:10.211 --> 00:47:12.770 align:middle line:90% AUDIENCE: [INAUDIBLE] 00:47:12.770 --> 00:47:15.340 align:middle line:90% JACK HARE: Oh, we've got time. 00:47:15.340 --> 00:47:18.850 align:middle line:84% It's a rather famous work by the group at the Weizmann Institute 00:47:18.850 --> 00:47:22.660 align:middle line:84% in Israel, where what they do is they do Zeeman splitting 00:47:22.660 --> 00:47:25.300 align:middle line:84% spectroscopy, but they do Zeeman splitting on a range 00:47:25.300 --> 00:47:26.440 align:middle line:90% of different lines. 00:47:26.440 --> 00:47:28.263 align:middle line:84% And what they have in their Z-pinch 00:47:28.263 --> 00:47:29.305 align:middle line:90% is a temperature profile. 00:47:29.305 --> 00:47:35.418 align:middle line:90% 00:47:35.418 --> 00:47:36.960 align:middle line:84% Maybe something that looks like this, 00:47:36.960 --> 00:47:40.090 align:middle line:84% the temperature of the Z-pinch is hottest in the center. 00:47:40.090 --> 00:47:42.930 align:middle line:84% And so they make the Z-pinch out of oxygen. 00:47:42.930 --> 00:47:46.750 align:middle line:84% And the reason they do that is that as you look 00:47:46.750 --> 00:47:49.540 align:middle line:84% at different shells of the Z-pinch, different radial 00:47:49.540 --> 00:47:51.490 align:middle line:84% bins like this, for example, in this bin, 00:47:51.490 --> 00:47:53.830 align:middle line:90% it's dominated by oxygen 2. 00:47:53.830 --> 00:47:56.290 align:middle line:84% And then this bin is dominated by oxygen 3. 00:47:56.290 --> 00:47:59.740 align:middle line:84% Maybe the center is dominated by oxygen 4. 00:47:59.740 --> 00:48:02.420 align:middle line:84% And so these different ions of oxygen-- 00:48:02.420 --> 00:48:05.890 align:middle line:84% so this is oxygen that's once ionized, twice ionized, 00:48:05.890 --> 00:48:07.060 align:middle line:90% three times ionized-- 00:48:07.060 --> 00:48:10.880 align:middle line:84% has different energy levels available to it. 00:48:10.880 --> 00:48:13.760 align:middle line:84% So it has different excited states available to it. 00:48:13.760 --> 00:48:16.430 align:middle line:84% And so it has different lines available to it. 00:48:16.430 --> 00:48:19.120 align:middle line:84% And so here, for example, there's 00:48:19.120 --> 00:48:22.180 align:middle line:84% a well-defined line at this frequency. 00:48:22.180 --> 00:48:24.310 align:middle line:84% For this one, there's a well-defined line here. 00:48:24.310 --> 00:48:27.880 align:middle line:84% And for four, there's a well-defined line 00:48:27.880 --> 00:48:28.975 align:middle line:90% here going up in energy. 00:48:28.975 --> 00:48:32.810 align:middle line:90% 00:48:32.810 --> 00:48:35.500 align:middle line:84% And so they know when they see this line 00:48:35.500 --> 00:48:39.400 align:middle line:84% that it must correspond to the outside of the plasma. 00:48:39.400 --> 00:48:41.612 align:middle line:84% And they know when they see this higher energy line, 00:48:41.612 --> 00:48:43.570 align:middle line:84% it must correspond to the inside of the plasma. 00:48:43.570 --> 00:48:47.870 align:middle line:90% 00:48:47.870 --> 00:48:50.470 align:middle line:84% And so when they look at the Zeeman splitting of these lines, 00:48:50.470 --> 00:48:53.625 align:middle line:84% they can effectively localize where the magnetic field 00:48:53.625 --> 00:48:55.750 align:middle line:84% is in space, because they're able to localize where 00:48:55.750 --> 00:48:57.820 align:middle line:90% those lines come from in space. 00:48:57.820 --> 00:49:00.430 align:middle line:84% This looks a little bit like with the electron cyclotron 00:49:00.430 --> 00:49:02.810 align:middle line:90% emission all over again. 00:49:02.810 --> 00:49:05.990 align:middle line:84% So you need to have some idea of what the temperature is inside 00:49:05.990 --> 00:49:06.490 align:middle line:90% here. 00:49:06.490 --> 00:49:09.130 align:middle line:84% And this, effectively, then looks like an [INAUDIBLE] 00:49:09.130 --> 00:49:10.070 align:middle line:90% inversion problem. 00:49:10.070 --> 00:49:14.110 align:middle line:84% So if we look at the Z-pinch down from above, 00:49:14.110 --> 00:49:18.490 align:middle line:84% there are these different rings with oxygen 4, oxygen 3, 00:49:18.490 --> 00:49:20.470 align:middle line:90% and oxygen 2. 00:49:20.470 --> 00:49:24.220 align:middle line:84% And you can do spectroscopy on a series of parallel lines 00:49:24.220 --> 00:49:27.490 align:middle line:84% of sight like that, and do an [INAUDIBLE] inversion on it, 00:49:27.490 --> 00:49:30.520 align:middle line:84% and work out what regions emit oxygen four lines, three 00:49:30.520 --> 00:49:32.450 align:middle line:90% lines, two lines, and so on. 00:49:32.450 --> 00:49:37.720 align:middle line:84% So a rather nice technique that you can use. 00:49:37.720 --> 00:49:39.453 align:middle line:90% But in general, you're right. 00:49:39.453 --> 00:49:41.370 align:middle line:84% If you're looking at some astrophysical plasma 00:49:41.370 --> 00:49:43.530 align:middle line:84% where you can't do an [INAUDIBLE] inversion easily, 00:49:43.530 --> 00:49:46.340 align:middle line:84% then this may not be the best technique. 00:49:46.340 --> 00:49:48.930 align:middle line:90% 00:49:48.930 --> 00:49:52.563 align:middle line:84% A couple more things on Zeeman splitting-- 00:49:52.563 --> 00:49:56.910 align:middle line:90% 00:49:56.910 --> 00:49:59.610 align:middle line:84% interestingly, these transitions here 00:49:59.610 --> 00:50:02.250 align:middle line:84% from the sigma plus and minus and the pi levels 00:50:02.250 --> 00:50:03.870 align:middle line:90% have different polarizations. 00:50:03.870 --> 00:50:06.090 align:middle line:84% And that can be used to actually do 00:50:06.090 --> 00:50:08.320 align:middle line:84% things like measuring the field direction. 00:50:08.320 --> 00:50:10.818 align:middle line:84% So trying to find somewhere where I've got enough space 00:50:10.818 --> 00:50:11.360 align:middle line:90% to draw this. 00:50:11.360 --> 00:50:23.860 align:middle line:90% 00:50:23.860 --> 00:50:30.610 align:middle line:84% If we've got some magnetic field B like this and a plasma, which 00:50:30.610 --> 00:50:33.910 align:middle line:84% is emitting Zeeman split lines, then 00:50:33.910 --> 00:50:44.350 align:middle line:84% if we observe at 90 degrees, then the light 00:50:44.350 --> 00:50:47.020 align:middle line:84% has two polarizations, depending on whether it 00:50:47.020 --> 00:50:50.000 align:middle line:84% comes from the sigma plus or minus levels, or the pi levels. 00:50:50.000 --> 00:50:53.440 align:middle line:84% And so in this polarization here, 00:50:53.440 --> 00:50:56.200 align:middle line:90% we get the sigma plus or minus. 00:50:56.200 --> 00:51:02.070 align:middle line:84% And in this polarization, we get the pi. 00:51:02.070 --> 00:51:04.910 align:middle line:84% And so by using a spectrometer with a polarizer in front of it 00:51:04.910 --> 00:51:07.250 align:middle line:84% and measuring the ratio of these two lines 00:51:07.250 --> 00:51:09.980 align:middle line:84% at different polarizations, we can back out the angle 00:51:09.980 --> 00:51:11.930 align:middle line:90% of the magnetic field here. 00:51:11.930 --> 00:51:14.630 align:middle line:84% And this can actually be very useful in a tokamak, where 00:51:14.630 --> 00:51:15.897 align:middle line:90% we know what the size of B is. 00:51:15.897 --> 00:51:17.480 align:middle line:84% So we don't need the Zeeman splitting. 00:51:17.480 --> 00:51:19.880 align:middle line:84% But we do want to know what the twist of the field lines 00:51:19.880 --> 00:51:22.190 align:middle line:84% is because that tells us about how 00:51:22.190 --> 00:51:25.340 align:middle line:84% big the poloidal field, particularly a useful diagnostic 00:51:25.340 --> 00:51:27.200 align:middle line:84% on devices with large poloidal fields, 00:51:27.200 --> 00:51:29.500 align:middle line:90% like reversed field pinches. 00:51:29.500 --> 00:51:34.200 align:middle line:84% It turns out if you look along the magnetic field, by the way, 00:51:34.200 --> 00:51:37.800 align:middle line:84% then you just see the sigma plus and minus lines. 00:51:37.800 --> 00:51:39.330 align:middle line:90% But you don't see the pi line. 00:51:39.330 --> 00:51:42.910 align:middle line:90% 00:51:42.910 --> 00:51:45.220 align:middle line:84% And I did at one point understand 00:51:45.220 --> 00:51:46.240 align:middle line:90% why that was the case. 00:51:46.240 --> 00:51:48.700 align:middle line:84% And it probably comes into quantum here as well. 00:51:48.700 --> 00:51:55.763 align:middle line:90% 00:51:55.763 --> 00:51:57.680 align:middle line:84% I don't think that was a chat noise from Zoom. 00:51:57.680 --> 00:51:59.270 align:middle line:90% I think it was something else. 00:51:59.270 --> 00:52:00.660 align:middle line:90% All right, any questions? 00:52:00.660 --> 00:52:01.160 align:middle line:90% Yes. 00:52:01.160 --> 00:52:12.050 align:middle line:90% 00:52:12.050 --> 00:52:13.670 align:middle line:90% No, not for quantum mechanics. 00:52:13.670 --> 00:52:18.095 align:middle line:90% 00:52:18.095 --> 00:52:19.220 align:middle line:90% What are you talking about? 00:52:19.220 --> 00:52:21.281 align:middle line:84% Are you talking about this gyration? 00:52:21.281 --> 00:52:21.948 align:middle line:90% AUDIENCE: Right. 00:52:21.948 --> 00:52:22.904 align:middle line:90% [INAUDIBLE] 00:52:22.904 --> 00:52:26.730 align:middle line:90% 00:52:26.730 --> 00:52:29.120 align:middle line:90% JACK HARE: Is it? 00:52:29.120 --> 00:52:31.530 align:middle line:90% AUDIENCE: [INAUDIBLE] 00:52:31.530 --> 00:52:33.280 align:middle line:84% JACK HARE: The electrons are not gyrating. 00:52:33.280 --> 00:52:34.113 align:middle line:90% The ion is gyrating. 00:52:34.113 --> 00:52:36.405 align:middle line:84% It has electrons which are bound to it, which have wave 00:52:36.405 --> 00:52:37.630 align:middle line:90% functions moving around it. 00:52:37.630 --> 00:52:39.700 align:middle line:84% All the electrons are gyrating with the ions. 00:52:39.700 --> 00:52:41.410 align:middle line:84% I don't think that's going to be a big perturbation 00:52:41.410 --> 00:52:42.130 align:middle line:90% to their energy. 00:52:42.130 --> 00:52:46.808 align:middle line:90% 00:52:46.808 --> 00:52:49.100 align:middle line:84% So when we talk about hyperfine, we talk about coupling 00:52:49.100 --> 00:52:51.790 align:middle line:90% with the nucleus. 00:52:51.790 --> 00:52:55.570 align:middle line:84% And we're-- I am not talking about the hyperfine coupling 00:52:55.570 --> 00:52:58.390 align:middle line:84% here, because that's very hard to measure. 00:52:58.390 --> 00:53:00.580 align:middle line:84% So here, this is the spin angular momentum. 00:53:00.580 --> 00:53:07.870 align:middle line:90% 00:53:07.870 --> 00:53:10.340 align:middle line:90% And this is the orbital. 00:53:10.340 --> 00:53:13.528 align:middle line:90% 00:53:13.528 --> 00:53:15.570 align:middle line:84% I don't know whether someone has done the quantum 00:53:15.570 --> 00:53:18.420 align:middle line:84% mechanics on how the gyrating particle affects the energy 00:53:18.420 --> 00:53:19.080 align:middle line:90% levels. 00:53:19.080 --> 00:53:20.300 align:middle line:90% I imagine it would be small. 00:53:20.300 --> 00:53:22.800 align:middle line:84% Can we come up with an argument that shows that it is small? 00:53:22.800 --> 00:53:26.810 align:middle line:90% 00:53:26.810 --> 00:53:28.508 align:middle line:90% Or is it the case that because-- 00:53:28.508 --> 00:53:30.050 align:middle line:84% does it not change the energy levels? 00:53:30.050 --> 00:53:35.140 align:middle line:84% Because if you move into the frame of the particle, the ion-- 00:53:35.140 --> 00:53:36.700 align:middle line:84% all the energy levels are going to be 00:53:36.700 --> 00:53:37.825 align:middle line:90% shifted by the same amount. 00:53:37.825 --> 00:53:40.455 align:middle line:90% 00:53:40.455 --> 00:53:41.955 align:middle line:84% I don't know-- interesting question. 00:53:41.955 --> 00:53:44.820 align:middle line:90% 00:53:44.820 --> 00:53:46.500 align:middle line:90% Any other questions on-- 00:53:46.500 --> 00:53:47.000 align:middle line:90% sorry. 00:53:47.000 --> 00:53:48.793 align:middle line:90% I don't know the answer to that. 00:53:48.793 --> 00:53:50.210 align:middle line:84% As I said, it's been like a decade 00:53:50.210 --> 00:53:52.420 align:middle line:84% since I had to really do this math. 00:53:52.420 --> 00:53:54.110 align:middle line:90% So any other questions? 00:53:54.110 --> 00:53:55.750 align:middle line:90% Yeah. 00:53:55.750 --> 00:53:57.940 align:middle line:90% AUDIENCE: [INAUDIBLE] 00:53:57.940 --> 00:54:02.325 align:middle line:90% 00:54:02.325 --> 00:54:04.450 align:middle line:84% JACK HARE: Yeah, I guess it depends on the exposure 00:54:04.450 --> 00:54:05.830 align:middle line:90% time of your spectrometer. 00:54:05.830 --> 00:54:08.230 align:middle line:84% You're capturing this spectrum on a camera. 00:54:08.230 --> 00:54:11.300 align:middle line:84% And that camera has a shutter, which is open for some time. 00:54:11.300 --> 00:54:14.710 align:middle line:84% So if the shutter time is shorter than the time 00:54:14.710 --> 00:54:16.780 align:middle line:84% over which parameters change, you effectively 00:54:16.780 --> 00:54:18.010 align:middle line:90% got a snapshot of the plasma. 00:54:18.010 --> 00:54:19.070 align:middle line:90% So that doesn't matter. 00:54:19.070 --> 00:54:20.528 align:middle line:84% But if the plasma is changing a lot 00:54:20.528 --> 00:54:23.540 align:middle line:84% and you just have a spectrum that is collecting for all time, 00:54:23.540 --> 00:54:24.710 align:middle line:90% then it will be a problem. 00:54:24.710 --> 00:54:26.752 align:middle line:84% So for example, if you have a spectrometer that's 00:54:26.752 --> 00:54:28.335 align:middle line:84% using a bit of film without a shutter, 00:54:28.335 --> 00:54:31.044 align:middle line:84% and you're just like give me all the light over the entire course 00:54:31.044 --> 00:54:33.507 align:middle line:84% of the plasma experiment, then the time changing properties 00:54:33.507 --> 00:54:34.090 align:middle line:90% are important. 00:54:34.090 --> 00:54:35.710 align:middle line:84% And you would be better off using 00:54:35.710 --> 00:54:38.569 align:middle line:90% a camera that had a shutter. 00:54:38.569 --> 00:54:39.555 align:middle line:90% Yeah. 00:54:39.555 --> 00:54:42.020 align:middle line:90% AUDIENCE: [INAUDIBLE] 00:54:42.020 --> 00:54:49.162 align:middle line:90% 00:54:49.162 --> 00:54:51.620 align:middle line:84% JACK HARE: So I don't know where your statement comes from. 00:54:51.620 --> 00:54:54.060 align:middle line:84% You might be right, but I can't verify that. 00:54:54.060 --> 00:54:56.665 align:middle line:90% [LAUGHTER] 00:54:56.665 --> 00:54:59.010 align:middle line:90% 00:54:59.010 --> 00:55:00.220 align:middle line:90% Is it really smaller? 00:55:00.220 --> 00:55:04.070 align:middle line:90% I mean, it feels [INAUDIBLE]. 00:55:04.070 --> 00:55:05.842 align:middle line:84% So the field strength here, we're 00:55:05.842 --> 00:55:07.800 align:middle line:84% talking about relatively large magnetic fields. 00:55:07.800 --> 00:55:09.660 align:middle line:90% You see Zeeman splitting. 00:55:09.660 --> 00:55:12.832 align:middle line:84% And the nice thing about Zeeman splitting 00:55:12.832 --> 00:55:15.040 align:middle line:84% is it does just keep increasing with magnetic fields. 00:55:15.040 --> 00:55:16.450 align:middle line:84% So you can get very large splittings. 00:55:16.450 --> 00:55:18.408 align:middle line:84% I think it is a pretty large effect in general. 00:55:18.408 --> 00:55:21.290 align:middle line:90% 00:55:21.290 --> 00:55:27.890 align:middle line:84% The final mechanism we're going to talk about 00:55:27.890 --> 00:55:30.650 align:middle line:90% is blackbody absorption. 00:55:30.650 --> 00:55:47.400 align:middle line:90% 00:55:47.400 --> 00:55:50.000 align:middle line:84% So we talked a little bit about this before. 00:55:50.000 --> 00:55:55.280 align:middle line:84% We had this idea that if we are an optically thick plasma, where 00:55:55.280 --> 00:55:57.230 align:middle line:84% tau is much greater than 1, then we 00:55:57.230 --> 00:56:01.550 align:middle line:84% end up having an emission profile that looks like i of nu 00:56:01.550 --> 00:56:05.940 align:middle line:84% is equal to nu squared t upon c squared. 00:56:05.940 --> 00:56:07.400 align:middle line:90% This is the blackbody spectrum. 00:56:07.400 --> 00:56:19.190 align:middle line:90% 00:56:19.190 --> 00:56:21.890 align:middle line:84% Now, it turns out from thermodynamics, 00:56:21.890 --> 00:56:25.280 align:middle line:84% you can also show that for whatever plasma you have-- 00:56:25.280 --> 00:56:27.200 align:middle line:84% optically thin or optically thick-- 00:56:27.200 --> 00:56:33.420 align:middle line:84% the emission i of nu is strictly going to be less than 00:56:33.420 --> 00:56:36.680 align:middle line:84% or equal to this blackbody spectrum. 00:56:36.680 --> 00:56:39.050 align:middle line:90% You can never exceed that. 00:56:39.050 --> 00:56:42.800 align:middle line:84% And so that means if you've got a system with a very bright 00:56:42.800 --> 00:56:53.720 align:middle line:84% line, like this line here, and it's 00:56:53.720 --> 00:56:55.610 align:middle line:84% got some width to it because of all 00:56:55.610 --> 00:56:58.520 align:middle line:84% the other broadening mechanisms that we've discussed, 00:56:58.520 --> 00:57:00.950 align:middle line:84% then the intensity of this line is 00:57:00.950 --> 00:57:03.960 align:middle line:84% going to be capped by the blackbody emission spectrum. 00:57:03.960 --> 00:57:08.840 align:middle line:84% And so for example, if the blackbody emission, 00:57:08.840 --> 00:57:10.830 align:middle line:84% we're dealing with a small range of nu here. 00:57:10.830 --> 00:57:12.710 align:middle line:84% So this is roughly flat, even though it's got 00:57:12.710 --> 00:57:15.390 align:middle line:90% a nu squared dependence on it. 00:57:15.390 --> 00:57:17.860 align:middle line:84% Then our line would end up actually 00:57:17.860 --> 00:57:21.040 align:middle line:90% having a flat top to it. 00:57:21.040 --> 00:57:25.040 align:middle line:84% And if the temperature was even lower, 00:57:25.040 --> 00:57:28.450 align:middle line:84% then our line would have a broader flat top like this. 00:57:28.450 --> 00:57:37.870 align:middle line:84% So this T1, T2, but T2 is greater than T1 here. 00:57:37.870 --> 00:57:39.745 align:middle line:90% And again, because I'm-- 00:57:39.745 --> 00:57:41.620 align:middle line:84% although there's a nu square dependence here, 00:57:41.620 --> 00:57:43.700 align:middle line:84% I'm only looking at a very small range of nu. 00:57:43.700 --> 00:57:46.280 align:middle line:84% So the nu is roughly constant over this. 00:57:46.280 --> 00:57:49.780 align:middle line:84% And so we get these little flat tops for the lines. 00:57:49.780 --> 00:57:53.110 align:middle line:84% And this looks like another form of broadening, 00:57:53.110 --> 00:57:58.420 align:middle line:84% because, previously, we were defining delta nu to the 1/2, 00:57:58.420 --> 00:58:00.680 align:middle line:84% which is the full width at half maximum, 00:58:00.680 --> 00:58:04.690 align:middle line:84% which is where you take the peak value and go halfway down 00:58:04.690 --> 00:58:06.850 align:middle line:90% and define it like this. 00:58:06.850 --> 00:58:10.780 align:middle line:84% But now when you take-- if you just naively apply this formula, 00:58:10.780 --> 00:58:14.045 align:middle line:84% you're going to end up with a broader looking line. 00:58:14.045 --> 00:58:18.308 align:middle line:90% 00:58:18.308 --> 00:58:20.850 align:middle line:84% You may observe some broadening, but it's actually just using 00:58:20.850 --> 00:58:22.038 align:middle line:90% this blackbody effect. 00:58:22.038 --> 00:58:24.580 align:middle line:84% So this is only really a problem for very, very bright lines. 00:58:24.580 --> 00:58:27.050 align:middle line:84% This is usually a very large value for your plasma. 00:58:27.050 --> 00:58:28.922 align:middle line:84% But those lines will have a cut off to them 00:58:28.922 --> 00:58:31.630 align:middle line:84% where the intensity can't go any higher than the blackbody level. 00:58:31.630 --> 00:58:35.390 align:middle line:90% 00:58:35.390 --> 00:58:36.675 align:middle line:90% Any questions on that? 00:58:36.675 --> 00:58:37.175 align:middle line:90% Yeah. 00:58:37.175 --> 00:58:43.122 align:middle line:90% 00:58:43.122 --> 00:58:45.080 align:middle line:84% So I was saying, for an optically thick plasma, 00:58:45.080 --> 00:58:46.640 align:middle line:90% you get the blackbody spectrum. 00:58:46.640 --> 00:58:48.260 align:middle line:84% But from thermodynamic arguments, 00:58:48.260 --> 00:58:52.310 align:middle line:84% you also find that the spectrum from any plasma for a given 00:58:52.310 --> 00:58:54.410 align:middle line:84% frequency cannot exceed that blackbody value. 00:58:54.410 --> 00:58:55.868 align:middle line:84% If you did that, you could work out 00:58:55.868 --> 00:58:57.993 align:middle line:84% how to break the second law or something like that. 00:58:57.993 --> 00:58:58.670 align:middle line:90% So not allowed. 00:58:58.670 --> 00:59:02.190 align:middle line:90% 00:59:02.190 --> 00:59:03.060 align:middle line:90% Other questions? 00:59:03.060 --> 00:59:13.690 align:middle line:90% 00:59:13.690 --> 00:59:16.930 align:middle line:84% So maybe a couple of applications 00:59:16.930 --> 00:59:21.700 align:middle line:84% here for the spectroscopy, starting 00:59:21.700 --> 00:59:23.170 align:middle line:90% with this Doppler broadening. 00:59:23.170 --> 00:59:30.690 align:middle line:90% 00:59:30.690 --> 00:59:33.900 align:middle line:84% There's the obvious use of Doppler broadening to measure 00:59:33.900 --> 00:59:35.580 align:middle line:90% the thermal velocity. 00:59:35.580 --> 00:59:38.010 align:middle line:84% Less obviously is when the Doppler broadening actually 00:59:38.010 --> 00:59:41.250 align:middle line:84% stops you making a measurement of the overall Doppler shift. 00:59:41.250 --> 00:59:46.670 align:middle line:84% So if we have a plasma which has some bulk motion, 00:59:46.670 --> 00:59:50.420 align:middle line:84% all the particles have some bulk velocity towards you or away 00:59:50.420 --> 00:59:51.080 align:middle line:90% from you. 00:59:51.080 --> 00:59:54.270 align:middle line:84% Then you're going to have a shift 00:59:54.270 --> 00:59:56.890 align:middle line:84% of wavelength, delta lambda over lambda, 00:59:56.890 --> 01:00:01.470 align:middle line:84% which is approximately the same as delta omega over omega. 01:00:01.470 --> 01:00:09.760 align:middle line:84% And that delta omega is going to be whatever the k of your wave 01:00:09.760 --> 01:00:11.920 align:middle line:90% is dotted with v here. 01:00:11.920 --> 01:00:15.550 align:middle line:84% This is just the classical non-relativistic Doppler shift 01:00:15.550 --> 01:00:18.810 align:middle line:90% that we talked about back here. 01:00:18.810 --> 01:00:26.550 align:middle line:84% So this Doppler shift has a size delta omega a dot v upon omega, 01:00:26.550 --> 01:00:33.110 align:middle line:84% and the broadening, as we've already said, 01:00:33.110 --> 01:00:38.720 align:middle line:84% has a delta omega that is about the ion temperature square 01:00:38.720 --> 01:00:41.360 align:middle line:90% rooted. 01:00:41.360 --> 01:00:46.070 align:middle line:84% So if you have a system in which your Doppler broadening is 01:00:46.070 --> 01:00:52.700 align:middle line:84% very large, then you will not be able to measure your Doppler 01:00:52.700 --> 01:00:54.770 align:middle line:90% shift. 01:00:54.770 --> 01:01:06.270 align:middle line:84% So for example, if your Doppler shift is just a tiny bit over, 01:01:06.270 --> 01:01:08.020 align:middle line:84% it's going to be very hard to measure that 01:01:08.020 --> 01:01:10.400 align:middle line:90% on top of a very broad profile. 01:01:10.400 --> 01:01:13.100 align:middle line:84% On the other hand, if you have relatively narrow Doppler 01:01:13.100 --> 01:01:18.680 align:middle line:84% broadening, then you should be able to measure 01:01:18.680 --> 01:01:22.180 align:middle line:90% that Doppler shift very easily. 01:01:22.180 --> 01:01:26.460 align:middle line:84% So this kind of puts a limit, but the interesting thing 01:01:26.460 --> 01:01:31.080 align:middle line:84% is we can exploit the fact that this square root of temperature 01:01:31.080 --> 01:01:35.310 align:middle line:84% is really square root of temperature over the ion mass, 01:01:35.310 --> 01:01:40.660 align:middle line:84% because it's related to the ion thermal velocity here, which 01:01:40.660 --> 01:01:42.670 align:middle line:84% means that we can actually choose to look 01:01:42.670 --> 01:01:45.380 align:middle line:90% at ions with very heavy masses. 01:01:45.380 --> 01:01:47.570 align:middle line:84% So these would be impurities in a tokamak. 01:01:47.570 --> 01:01:51.788 align:middle line:84% So this would be, for example, your hydrogen, 01:01:51.788 --> 01:01:52.830 align:middle line:90% it's got a very low mass. 01:01:52.830 --> 01:01:55.620 align:middle line:84% So it has very large thermal Doppler broadening. 01:01:55.620 --> 01:01:58.510 align:middle line:84% And so we can't measure the Doppler shift very easily. 01:01:58.510 --> 01:02:01.530 align:middle line:84% But if you've injected some tungsten into your plasma 01:02:01.530 --> 01:02:04.080 align:middle line:84% from the walls, for example, then you're 01:02:04.080 --> 01:02:06.510 align:middle line:84% going to have very, very small Doppler broadening. 01:02:06.510 --> 01:02:08.635 align:middle line:84% And you're going to be able to measure that Doppler 01:02:08.635 --> 01:02:09.610 align:middle line:90% shift very accurately. 01:02:09.610 --> 01:02:14.450 align:middle line:84% So this is basically using an impurity 01:02:14.450 --> 01:02:15.860 align:middle line:90% as a tracer of the flow. 01:02:15.860 --> 01:02:18.920 align:middle line:90% 01:02:18.920 --> 01:02:22.600 align:middle line:84% And if you are APS this year, and you made it to the Tuesday 01:02:22.600 --> 01:02:26.480 align:middle line:84% morning plenary, where John Rice was talking about this, 01:02:26.480 --> 01:02:28.900 align:middle line:84% people have built their whole careers out of this idea 01:02:28.900 --> 01:02:31.540 align:middle line:84% that you can use the impurity ions, which 01:02:31.540 --> 01:02:33.220 align:middle line:84% are easy to measure Doppler shift for, 01:02:33.220 --> 01:02:36.430 align:middle line:84% as a proxy for the motion of the whole plasma. 01:02:36.430 --> 01:02:38.950 align:middle line:84% And it turns out it is more complicated than that, 01:02:38.950 --> 01:02:40.600 align:middle line:84% but this is, at least, the basic idea 01:02:40.600 --> 01:02:43.480 align:middle line:84% is it's much easier to measure Doppler shifts for heavy ions 01:02:43.480 --> 01:02:46.730 align:middle line:90% than for light ions. 01:02:46.730 --> 01:02:49.310 align:middle line:90% Questions on that? 01:02:49.310 --> 01:02:50.040 align:middle line:90% Yeah. 01:02:50.040 --> 01:02:52.732 align:middle line:84% AUDIENCE: [INAUDIBLE] Doppler broadening [INAUDIBLE]. 01:02:52.732 --> 01:02:57.050 align:middle line:90% 01:02:57.050 --> 01:02:58.067 align:middle line:90% JACK HARE: So sorry. 01:02:58.067 --> 01:02:59.150 align:middle line:90% Let me be very clear then. 01:02:59.150 --> 01:03:06.622 align:middle line:84% So Doppler broadening is when you-- 01:03:06.622 --> 01:03:09.080 align:middle line:84% the Doppler shift is to do with the entire plasma movement. 01:03:09.080 --> 01:03:10.250 align:middle line:90% So imagine a tokamak. 01:03:10.250 --> 01:03:13.703 align:middle line:84% This is a toroidal velocity of the plasma moving 01:03:13.703 --> 01:03:14.870 align:middle line:90% round and round in a circle. 01:03:14.870 --> 01:03:17.900 align:middle line:84% The broadening is due to within that moving plasma, 01:03:17.900 --> 01:03:20.390 align:middle line:84% some particles going slightly faster and slightly slower. 01:03:20.390 --> 01:03:22.970 align:middle line:84% So it's sort of like they're all going like this, 01:03:22.970 --> 01:03:28.894 align:middle line:84% and some of them are also going like this as well. 01:03:28.894 --> 01:03:30.322 align:middle line:84% AUDIENCE: Broadening [INAUDIBLE]. 01:03:30.322 --> 01:03:34.130 align:middle line:90% 01:03:34.130 --> 01:03:35.227 align:middle line:90% JACK HARE: Yeah, exactly. 01:03:35.227 --> 01:03:35.810 align:middle line:90% Yes, yes, yes. 01:03:35.810 --> 01:03:37.910 align:middle line:84% So in order to get the broadening, 01:03:37.910 --> 01:03:41.570 align:middle line:84% you need to know your distribution function, 01:03:41.570 --> 01:03:43.550 align:middle line:90% like a Maxwellian like this. 01:03:43.550 --> 01:03:45.380 align:middle line:84% In order to get the shift, you just 01:03:45.380 --> 01:03:47.540 align:middle line:84% need to know the velocity of the entire fluid. 01:03:47.540 --> 01:03:49.760 align:middle line:84% Yeah, that's a good way of looking at it. 01:03:49.760 --> 01:03:53.540 align:middle line:90% 01:03:53.540 --> 01:03:56.310 align:middle line:90% Any other questions? 01:03:56.310 --> 01:03:57.200 align:middle line:90% Yeah. 01:03:57.200 --> 01:03:59.588 align:middle line:84% AUDIENCE: [INAUDIBLE] broadening [INAUDIBLE]? 01:03:59.588 --> 01:04:03.900 align:middle line:90% 01:04:03.900 --> 01:04:04.610 align:middle line:90% JACK HARE: Yeah. 01:04:04.610 --> 01:04:06.360 align:middle line:84% In general, with all of those diagnostics, 01:04:06.360 --> 01:04:09.908 align:middle line:84% the answer is, in theory, yes, but the noise floor 01:04:09.908 --> 01:04:11.700 align:middle line:84% of your diagnostic will probably limit you, 01:04:11.700 --> 01:04:14.070 align:middle line:84% because there's very few of those fast particles, 01:04:14.070 --> 01:04:17.070 align:middle line:84% and so they're not making very much light. 01:04:17.070 --> 01:04:19.500 align:middle line:84% And so any noise is going to make things hard. 01:04:19.500 --> 01:04:21.720 align:middle line:84% So this is true with any diagnostic 01:04:21.720 --> 01:04:24.902 align:middle line:84% that promises to map out the distribution function. 01:04:24.902 --> 01:04:27.360 align:middle line:84% The problem is that it's usually proportional to the number 01:04:27.360 --> 01:04:29.010 align:middle line:84% of particles at that velocity, and there's not 01:04:29.010 --> 01:04:31.350 align:middle line:84% very many of those particles because our distributions 01:04:31.350 --> 01:04:33.760 align:middle line:90% are close to Maxwell. 01:04:33.760 --> 01:04:35.760 align:middle line:84% I'll talk about another one of these diagnostics 01:04:35.760 --> 01:04:40.070 align:middle line:84% that you might be able to use as well in a moment. 01:04:40.070 --> 01:04:44.690 align:middle line:84% I want to finish up with a couple of diagnostics which 01:04:44.690 --> 01:04:45.980 align:middle line:90% are spectroscopy adjacent. 01:04:45.980 --> 01:04:48.550 align:middle line:90% 01:04:48.550 --> 01:04:52.720 align:middle line:84% And these are often called active spectroscopy diagnostics. 01:04:52.720 --> 01:04:55.630 align:middle line:84% So all the other diagnostics we've been talking about, 01:04:55.630 --> 01:04:59.620 align:middle line:84% we just look at the light coming from the plasma. 01:04:59.620 --> 01:05:01.780 align:middle line:84% With these active diagnostics, we actually 01:05:01.780 --> 01:05:04.690 align:middle line:84% do something to the plasma, and then look at the light 01:05:04.690 --> 01:05:05.450 align:middle line:90% coming out of it. 01:05:05.450 --> 01:05:07.158 align:middle line:84% So it gives us a little bit more control. 01:05:07.158 --> 01:05:14.700 align:middle line:90% 01:05:14.700 --> 01:05:24.350 align:middle line:84% Active spectroscopy-- so the main one I want to talk about 01:05:24.350 --> 01:05:26.750 align:middle line:84% here is called laser-induced fluorescence-- 01:05:26.750 --> 01:05:39.970 align:middle line:90% 01:05:39.970 --> 01:05:40.720 align:middle line:90% LIF. 01:05:40.720 --> 01:05:44.090 align:middle line:90% 01:05:44.090 --> 01:05:46.040 align:middle line:84% The idea of laser-induced fluorescence 01:05:46.040 --> 01:05:48.830 align:middle line:84% is that we have a system with maybe 01:05:48.830 --> 01:05:53.180 align:middle line:84% three energy levels like this, lower, upper, and intermediate. 01:05:53.180 --> 01:06:00.260 align:middle line:84% We actively pump the atoms in our plasma up to this level u. 01:06:00.260 --> 01:06:08.480 align:middle line:84% And then we look for light emitted when the system drops 01:06:08.480 --> 01:06:14.460 align:middle line:84% from level u back down to some intermediate level i like this. 01:06:14.460 --> 01:06:16.520 align:middle line:84% So we're stimulating the absorption. 01:06:16.520 --> 01:06:19.040 align:middle line:90% 01:06:19.040 --> 01:06:21.960 align:middle line:84% And then we're looking for the fluorescence coming out. 01:06:21.960 --> 01:06:24.110 align:middle line:84% And the reason this is a powerful technique 01:06:24.110 --> 01:06:26.510 align:middle line:84% is if you have a plasma like this 01:06:26.510 --> 01:06:34.800 align:middle line:84% and you focus your laser beam through it, 01:06:34.800 --> 01:06:43.760 align:middle line:84% you can now have your viewing cord perpendicular to the laser 01:06:43.760 --> 01:06:47.610 align:middle line:84% and collect the lights like this on your spectrometer. 01:06:47.610 --> 01:06:51.070 align:middle line:90% 01:06:51.070 --> 01:06:53.740 align:middle line:84% And you have chosen this transition 01:06:53.740 --> 01:06:55.280 align:middle line:90% to be very unlikely to happen. 01:06:55.280 --> 01:06:57.190 align:middle line:84% So you're not going to randomly get 01:06:57.190 --> 01:06:58.870 align:middle line:84% that many atoms in the upper state. 01:06:58.870 --> 01:07:00.970 align:middle line:84% So you're not going to spontaneously get 01:07:00.970 --> 01:07:03.820 align:middle line:84% that many photons with this wavelength being emitted. 01:07:03.820 --> 01:07:05.860 align:middle line:84% So that means when you see any light there, 01:07:05.860 --> 01:07:08.560 align:middle line:84% you know it came from the region of the plasma, which 01:07:08.560 --> 01:07:11.410 align:middle line:84% is the intersection between where you are pumping 01:07:11.410 --> 01:07:14.350 align:middle line:84% the plasma with your laser, and where you are collecting 01:07:14.350 --> 01:07:15.760 align:middle line:90% with your spectrometer. 01:07:15.760 --> 01:07:18.460 align:middle line:84% And you remember previously the trouble with spectroscopy 01:07:18.460 --> 01:07:21.190 align:middle line:84% is you collected all the way along the line of sight. 01:07:21.190 --> 01:07:22.810 align:middle line:84% And you didn't have any localization. 01:07:22.810 --> 01:07:25.960 align:middle line:84% But this technique gives you that localization. 01:07:25.960 --> 01:07:33.400 align:middle line:90% 01:07:33.400 --> 01:07:35.650 align:middle line:90% That's very powerful. 01:07:35.650 --> 01:07:37.800 align:middle line:84% You can also-- because of this, if you 01:07:37.800 --> 01:07:40.170 align:middle line:84% have your spectrometer absolutely calibrated 01:07:40.170 --> 01:07:42.780 align:middle line:84% and you know exactly how many photons you've counted, 01:07:42.780 --> 01:07:45.210 align:middle line:84% and how many photons you've put in with the laser, 01:07:45.210 --> 01:07:48.930 align:middle line:84% you may be able to get out a measurement of the density here, 01:07:48.930 --> 01:07:49.920 align:middle line:90% of the atom density. 01:07:49.920 --> 01:07:53.180 align:middle line:90% 01:07:53.180 --> 01:07:56.835 align:middle line:84% So this can be a way of directly measuring the number of atoms 01:07:56.835 --> 01:07:57.460 align:middle line:90% in this volume. 01:07:57.460 --> 01:07:59.293 align:middle line:84% And indeed, people use this even for neutral 01:07:59.293 --> 01:08:02.200 align:middle line:84% gas, or measuring neutral gas density. 01:08:02.200 --> 01:08:05.470 align:middle line:84% An extremely clever thing you can do on top of this 01:08:05.470 --> 01:08:13.850 align:middle line:90% is to scan this frequency here. 01:08:13.850 --> 01:08:15.460 align:middle line:84% So the laser frequency, you can get 01:08:15.460 --> 01:08:18.609 align:middle line:84% a laser, which you can gently tune up and down 01:08:18.609 --> 01:08:19.960 align:middle line:90% by a very small amount. 01:08:19.960 --> 01:08:22.779 align:middle line:84% And the neat thing about that is that you can then 01:08:22.779 --> 01:08:27.939 align:middle line:84% choose which atoms are absorbing the light inside here, 01:08:27.939 --> 01:08:29.740 align:middle line:84% whether the atoms are moving towards you 01:08:29.740 --> 01:08:32.960 align:middle line:84% or away from you due to their blue shift here. 01:08:32.960 --> 01:08:38.652 align:middle line:84% So if we-- this is a little bit exciting to draw. 01:08:38.652 --> 01:08:39.694 align:middle line:90% So we'll see how it goes. 01:08:39.694 --> 01:08:42.850 align:middle line:90% 01:08:42.850 --> 01:08:54.399 align:middle line:84% If I scan my laser over a range of frequencies around omega 0, 01:08:54.399 --> 01:08:58.750 align:middle line:84% which will correspond to this transition in a stationary atom, 01:08:58.750 --> 01:09:03.420 align:middle line:84% then for these frequencies down here, the red-- 01:09:03.420 --> 01:09:06.760 align:middle line:84% the lower frequencies here, they will be resonant with 01:09:06.760 --> 01:09:08.890 align:middle line:90% the redshifted or with the-- 01:09:08.890 --> 01:09:15.663 align:middle line:90% 01:09:15.663 --> 01:09:17.580 align:middle line:84% they will be resonant with the particles which 01:09:17.580 --> 01:09:20.100 align:middle line:90% are moving away from them. 01:09:20.100 --> 01:09:22.229 align:middle line:84% They'll be resonant with these particles here. 01:09:22.229 --> 01:09:27.270 align:middle line:84% If instead I'm using a laser light, which is upshifted, 01:09:27.270 --> 01:09:29.790 align:middle line:84% then it will be resonant with the particles which 01:09:29.790 --> 01:09:32.080 align:middle line:90% are moving towards me here. 01:09:32.080 --> 01:09:35.880 align:middle line:84% So as I scan my laser, I'm exciting particles, 01:09:35.880 --> 01:09:37.380 align:middle line:84% some of which are moving towards me. 01:09:37.380 --> 01:09:38.963 align:middle line:84% Some of which are moving away from me. 01:09:38.963 --> 01:09:45.069 align:middle line:84% And then I'm going to get out a spectrum at the upper 01:09:45.069 --> 01:09:46.990 align:middle line:90% to intermediate transition. 01:09:46.990 --> 01:09:49.149 align:middle line:84% Here is the upper, the lower transition here. 01:09:49.149 --> 01:09:53.689 align:middle line:90% 01:09:53.689 --> 01:09:55.130 align:middle line:84% And the amount of light I get out 01:09:55.130 --> 01:09:57.350 align:middle line:84% is going to tell me how many particles there 01:09:57.350 --> 01:09:59.943 align:middle line:84% were that were resonant with this frequency 01:09:59.943 --> 01:10:01.610 align:middle line:84% here, how many particles there were that 01:10:01.610 --> 01:10:03.030 align:middle line:90% resonanted with this frequency. 01:10:03.030 --> 01:10:06.110 align:middle line:84% And so I can actually map out the entire distribution function 01:10:06.110 --> 01:10:09.180 align:middle line:84% using this, because I'm very carefully tuning the light. 01:10:09.180 --> 01:10:11.900 align:middle line:84% And so I know when I meet the resonance condition 01:10:11.900 --> 01:10:14.570 align:middle line:84% how fast these particles are going with respect to me. 01:10:14.570 --> 01:10:16.670 align:middle line:84% You need to have a steady plasma to do this, 01:10:16.670 --> 01:10:18.200 align:middle line:84% because what you're actually doing 01:10:18.200 --> 01:10:26.180 align:middle line:84% is ramping the laser frequency in time from some initial value. 01:10:26.180 --> 01:10:28.400 align:middle line:84% You will ramp it around that, and then you'll 01:10:28.400 --> 01:10:30.960 align:middle line:90% probably sawtooth it like this. 01:10:30.960 --> 01:10:34.365 align:middle line:84% So your plasma has to be nice and steady during this time 01:10:34.365 --> 01:10:35.490 align:middle line:90% now that you're ramping it. 01:10:35.490 --> 01:10:37.820 align:middle line:84% So this doesn't work on very short lived plasmas, 01:10:37.820 --> 01:10:40.340 align:middle line:84% but it does work very nicely on like low temperature plasmas 01:10:40.340 --> 01:10:43.250 align:middle line:84% that people use for various chemical processes. 01:10:43.250 --> 01:10:47.733 align:middle line:90% 01:10:47.733 --> 01:10:48.650 align:middle line:90% Any questions on that? 01:10:48.650 --> 01:10:52.038 align:middle line:90% 01:10:52.038 --> 01:10:53.006 align:middle line:90% Yeah. 01:10:53.006 --> 01:10:56.394 align:middle line:90% AUDIENCE: [INAUDIBLE] 01:10:56.394 --> 01:11:01.720 align:middle line:90% 01:11:01.720 --> 01:11:03.520 align:middle line:84% JACK HARE: So it can perform arbitrarily 01:11:03.520 --> 01:11:05.243 align:middle line:84% well if your plasma is very, very stable, 01:11:05.243 --> 01:11:06.910 align:middle line:84% because you can just do this many times, 01:11:06.910 --> 01:11:09.310 align:middle line:84% or you can have a very long integration time. 01:11:09.310 --> 01:11:10.960 align:middle line:84% So if you run it for twice as long, 01:11:10.960 --> 01:11:12.847 align:middle line:84% you're going to get twice as many photons, 01:11:12.847 --> 01:11:15.430 align:middle line:84% and then the error goes to the square root of n kind of thing. 01:11:15.430 --> 01:11:16.750 align:middle line:90% So you can make this very good. 01:11:16.750 --> 01:11:18.520 align:middle line:84% The trouble is if your plasma is only short lived, 01:11:18.520 --> 01:11:20.187 align:middle line:84% then you can't do this many, many times. 01:11:20.187 --> 01:11:22.960 align:middle line:84% But if you've got like a glow discharge that 01:11:22.960 --> 01:11:25.120 align:middle line:84% just sits in the chamber for 24 hours, 01:11:25.120 --> 01:11:26.612 align:middle line:84% then you can just do this 24 hours, 01:11:26.612 --> 01:11:27.820 align:middle line:90% and get very good statistics. 01:11:27.820 --> 01:11:33.110 align:middle line:84% And you really can measure the tail very, very carefully. 01:11:33.110 --> 01:11:36.440 align:middle line:90% Any other questions? 01:11:36.440 --> 01:11:42.430 align:middle line:84% There's a variant on this, which is 01:11:42.430 --> 01:11:58.770 align:middle line:84% called two-photon absorption LIF, Laser-Induced Fluorescence. 01:11:58.770 --> 01:12:04.910 align:middle line:84% And so this has the very compounded acronym TALIF. 01:12:04.910 --> 01:12:09.890 align:middle line:84% TALIF is used because in many of the interesting transitions 01:12:09.890 --> 01:12:10.910 align:middle line:90% we've talked about-- 01:12:10.910 --> 01:12:15.910 align:middle line:84% and you'll remember I talked about the Balmer series 01:12:15.910 --> 01:12:18.040 align:middle line:90% and the Lyman series earlier. 01:12:18.040 --> 01:12:21.040 align:middle line:84% And I said for the Lyman series, even 01:12:21.040 --> 01:12:22.540 align:middle line:84% the lowest one of these transitions 01:12:22.540 --> 01:12:26.370 align:middle line:84% here requires an ultraviolet photon, maybe 01:12:26.370 --> 01:12:32.010 align:middle line:84% something the Lyman series at 121 nanometers or higher-- 01:12:32.010 --> 01:12:34.730 align:middle line:90% lower, shorter wavelength. 01:12:34.730 --> 01:12:37.220 align:middle line:84% So if you're trying to do this LIF technique with hydrogen, 01:12:37.220 --> 01:12:39.030 align:middle line:84% which you might very well want to do, 01:12:39.030 --> 01:12:40.780 align:middle line:84% then you're not going to be able to do it, 01:12:40.780 --> 01:12:44.165 align:middle line:84% because these photons don't propagate through free space. 01:12:44.165 --> 01:12:45.790 align:middle line:84% And so you can't just set up your laser 01:12:45.790 --> 01:12:47.080 align:middle line:90% outside the vacuum chamber. 01:12:47.080 --> 01:12:49.460 align:middle line:84% The air will absorb it very strongly. 01:12:49.460 --> 01:12:55.750 align:middle line:84% So tau is much, much greater than 1 for air. 01:12:55.750 --> 01:12:59.060 align:middle line:84% That's your big problem with all sorts of vacuum spectroscopy 01:12:59.060 --> 01:13:01.060 align:middle line:84% is that a lot of the wavelengths of vacuum light 01:13:01.060 --> 01:13:02.200 align:middle line:90% gets absorbed in air. 01:13:02.200 --> 01:13:04.957 align:middle line:84% So you either have to put your spectrometer inside the vacuum 01:13:04.957 --> 01:13:06.040 align:middle line:90% chamber or something else. 01:13:06.040 --> 01:13:08.350 align:middle line:84% You can't put a laser inside the vacuum chamber. 01:13:08.350 --> 01:13:10.070 align:middle line:90% That just simply doesn't work. 01:13:10.070 --> 01:13:12.910 align:middle line:84% So what you do instead is you take advantage 01:13:12.910 --> 01:13:16.080 align:middle line:84% of a very, very strong laser, because if you have 01:13:16.080 --> 01:13:20.820 align:middle line:84% a very strong laser, there can be a virtual energy level here, 01:13:20.820 --> 01:13:27.090 align:middle line:84% where we have a photon coming in with h lower upper divided 01:13:27.090 --> 01:13:30.140 align:middle line:90% by 2, half the energy. 01:13:30.140 --> 01:13:32.960 align:middle line:84% This will excite the electron into this virtual energy 01:13:32.960 --> 01:13:35.360 align:middle line:84% level, which absolutely does not exist. 01:13:35.360 --> 01:13:40.430 align:middle line:84% But if quickly enough another photon comes along, also 01:13:40.430 --> 01:13:45.010 align:middle line:84% with the right energy level, then we 01:13:45.010 --> 01:13:47.360 align:middle line:84% can successfully promote that electron all the way up 01:13:47.360 --> 01:13:49.120 align:middle line:90% into the other energy level. 01:13:49.120 --> 01:13:53.140 align:middle line:84% Because this frequency only has to be half of this transition 01:13:53.140 --> 01:13:55.690 align:middle line:84% frequency, we can go from having something 01:13:55.690 --> 01:13:59.200 align:middle line:84% at 121 nanometers, which is in the vacuum ultraviolet, 01:13:59.200 --> 01:14:06.780 align:middle line:84% or maybe 240 nanometers, which is just in the near ultraviolet. 01:14:06.780 --> 01:14:10.600 align:middle line:84% And we can propagate through a vacuum here. 01:14:10.600 --> 01:14:12.510 align:middle line:84% So this means you can still do TALIF, 01:14:12.510 --> 01:14:16.260 align:middle line:84% even if the energy levels of the atoms you want to work with 01:14:16.260 --> 01:14:18.010 align:middle line:90% aren't really playing ball. 01:14:18.010 --> 01:14:22.110 align:middle line:84% But what you do need is a very intense laser, because 01:14:22.110 --> 01:14:25.500 align:middle line:84% at this point, if you don't have another photon come along, 01:14:25.500 --> 01:14:28.570 align:middle line:84% then the electron will realize that this is not a real energy 01:14:28.570 --> 01:14:29.070 align:middle line:90% state. 01:14:29.070 --> 01:14:31.620 align:middle line:84% And it will just return back down to here. 01:14:31.620 --> 01:14:33.150 align:middle line:84% And the original photon will just 01:14:33.150 --> 01:14:35.170 align:middle line:84% go on as if nothing has ever happened. 01:14:35.170 --> 01:14:37.080 align:middle line:84% So you need to have a very high probability 01:14:37.080 --> 01:14:40.360 align:middle line:84% of two photons coming in a very short period of time. 01:14:40.360 --> 01:14:42.182 align:middle line:84% So we need a very intense [INAUDIBLE]. 01:14:42.182 --> 01:14:47.087 align:middle line:90% 01:14:47.087 --> 01:14:48.920 align:middle line:84% And you can still do exactly the same tricks 01:14:48.920 --> 01:14:52.490 align:middle line:84% we talked about here with scanning your laser in order 01:14:52.490 --> 01:14:54.487 align:middle line:84% to slowly map out the distribution 01:14:54.487 --> 01:14:56.195 align:middle line:84% function of the particles in your plasma. 01:14:56.195 --> 01:15:00.820 align:middle line:90% 01:15:00.820 --> 01:15:01.870 align:middle line:90% Any questions on that? 01:15:01.870 --> 01:15:04.708 align:middle line:90% 01:15:04.708 --> 01:15:06.600 align:middle line:90% Yes. 01:15:06.600 --> 01:15:08.860 align:middle line:90% AUDIENCE: [INAUDIBLE] 01:15:08.860 --> 01:15:11.683 align:middle line:90% 01:15:11.683 --> 01:15:12.600 align:middle line:90% JACK HARE: Not really. 01:15:12.600 --> 01:15:15.504 align:middle line:90% 01:15:15.504 --> 01:15:19.210 align:middle line:84% I mean, almost going back to what 01:15:19.210 --> 01:15:21.250 align:middle line:84% I'd erased with the natural broadening, 01:15:21.250 --> 01:15:24.100 align:middle line:84% any energy state in a particle does 01:15:24.100 --> 01:15:26.670 align:middle line:84% exist for a very, very short amount of time. 01:15:26.670 --> 01:15:28.420 align:middle line:84% The stable energy states are the solutions 01:15:28.420 --> 01:15:29.530 align:middle line:90% to Schrodinger's equation. 01:15:29.530 --> 01:15:31.630 align:middle line:84% But we can have unstable states, which have 01:15:31.630 --> 01:15:33.140 align:middle line:90% very, very short lifetimes. 01:15:33.140 --> 01:15:36.460 align:middle line:84% And so we can make an electron into this state here. 01:15:36.460 --> 01:15:39.160 align:middle line:84% It's just that this is extremely short lived. 01:15:39.160 --> 01:15:41.270 align:middle line:84% So it may be picoseconds, or something like that, 01:15:41.270 --> 01:15:44.620 align:middle line:84% before we need another photon to come along. 01:15:44.620 --> 01:15:45.636 align:middle line:90% Yeah. 01:15:45.636 --> 01:15:48.020 align:middle line:90% AUDIENCE: [INAUDIBLE] 01:15:48.020 --> 01:15:51.703 align:middle line:90% 01:15:51.703 --> 01:15:53.620 align:middle line:84% JACK HARE: No, these are not measurable light. 01:15:53.620 --> 01:15:55.370 align:middle line:84% This is why you need a very intense laser. 01:15:55.370 --> 01:15:57.290 align:middle line:84% This is not something that you can-- 01:15:57.290 --> 01:15:59.620 align:middle line:84% I don't believe that you can measure the virtual state 01:15:59.620 --> 01:16:00.400 align:middle line:90% lifetime. 01:16:00.400 --> 01:16:05.720 align:middle line:90% 01:16:05.720 --> 01:16:06.323 align:middle line:90% Oh, sorry. 01:16:06.323 --> 01:16:07.490 align:middle line:90% [INAUDIBLE] first, and then. 01:16:07.490 --> 01:16:10.969 align:middle line:90% 01:16:10.969 --> 01:16:13.951 align:middle line:90% AUDIENCE: [INAUDIBLE] 01:16:13.951 --> 01:16:18.380 align:middle line:90% 01:16:18.380 --> 01:16:20.930 align:middle line:84% JACK HARE: This is better if you have the same energy, 01:16:20.930 --> 01:16:23.097 align:middle line:84% because then it's more likely the second photon that 01:16:23.097 --> 01:16:26.240 align:middle line:84% comes along will have the right energy, and also 01:16:26.240 --> 01:16:29.810 align:middle line:84% half as many lasers, which is always good. 01:16:29.810 --> 01:16:31.670 align:middle line:90% Yes, I believe you're right. 01:16:31.670 --> 01:16:34.310 align:middle line:84% This scheme could work with various other things. 01:16:34.310 --> 01:16:37.440 align:middle line:90% 01:16:37.440 --> 01:16:39.570 align:middle line:84% I'm sure you'll get $10 million in venture capital 01:16:39.570 --> 01:16:41.810 align:middle line:90% with no problem. 01:16:41.810 --> 01:16:43.154 align:middle line:90% Good. 01:16:43.154 --> 01:16:45.464 align:middle line:90% AUDIENCE: [INAUDIBLE] 01:16:45.464 --> 01:16:47.852 align:middle line:90% 01:16:47.852 --> 01:16:49.310 align:middle line:84% JACK HARE: And I think there's even 01:16:49.310 --> 01:16:51.643 align:middle line:84% a way of looking at this where you're like, ooh, there's 01:16:51.643 --> 01:16:54.320 align:middle line:84% a nonlinearity in the system, and the medium itself 01:16:54.320 --> 01:16:56.420 align:middle line:84% does the second harmonic generation, 01:16:56.420 --> 01:16:58.010 align:middle line:90% and then absorbs that photon. 01:16:58.010 --> 01:16:59.960 align:middle line:84% So if you prefer to think of it in terms 01:16:59.960 --> 01:17:02.550 align:middle line:84% of second harmonic generation within a medium, 01:17:02.550 --> 01:17:04.880 align:middle line:84% any medium is nonlinear if you drive it hard enough. 01:17:04.880 --> 01:17:07.010 align:middle line:90% So again, a very intense laser-- 01:17:07.010 --> 01:17:09.980 align:middle line:84% you can get out the second harmonic generation 01:17:09.980 --> 01:17:10.925 align:middle line:90% from anything. 01:17:10.925 --> 01:17:13.050 align:middle line:84% So you can think about it like that, if you prefer. 01:17:13.050 --> 01:17:16.010 align:middle line:84% And then all it is is the medium converts these two 01:17:16.010 --> 01:17:19.490 align:middle line:84% photons into one photon, and then it immediately 01:17:19.490 --> 01:17:20.840 align:middle line:90% absorbs that photon. 01:17:20.840 --> 01:17:23.690 align:middle line:84% So maybe that's a nicer way to think about it. 01:17:23.690 --> 01:17:24.190 align:middle line:90% Yeah. 01:17:24.190 --> 01:17:25.023 align:middle line:90% AUDIENCE: Thank you. 01:17:25.023 --> 01:17:26.560 align:middle line:90% JACK HARE: Oh, OK, cool, great. 01:17:26.560 --> 01:17:30.230 align:middle line:90% Any other questions? 01:17:30.230 --> 01:17:31.040 align:middle line:90% Okie doke. 01:17:31.040 --> 01:17:33.010 align:middle line:90% See you on Thursday. 01:17:33.010 --> 01:17:37.000 align:middle line:90%