WEBVTT 00:00:00.000 --> 00:00:01.940 align:middle line:90% [SQUEAKING] 00:00:01.940 --> 00:00:03.395 align:middle line:90% [RUSTLING] 00:00:03.395 --> 00:00:05.335 align:middle line:90% [CLICKING] 00:00:05.335 --> 00:00:10.200 align:middle line:90% 00:00:10.200 --> 00:00:12.270 align:middle line:84% JACK HARE: Well, welcome we few, we happy few. 00:00:12.270 --> 00:00:15.300 align:middle line:84% Let's do a little recap on electron cyclotron emission, 00:00:15.300 --> 00:00:17.800 align:middle line:84% and then we will go on to a few other things. 00:00:17.800 --> 00:00:23.610 align:middle line:84% So we had a look at the physics of electron cyclotron emission. 00:00:23.610 --> 00:00:27.660 align:middle line:84% We didn't actually derive the emissivity of it, 00:00:27.660 --> 00:00:31.350 align:middle line:84% but we gave ourselves a hand-wavy reason why there 00:00:31.350 --> 00:00:34.000 align:middle line:90% may be multiple peaks here. 00:00:34.000 --> 00:00:37.350 align:middle line:84% So if we have our emissivity as a function of frequency, 00:00:37.350 --> 00:00:41.130 align:middle line:84% we expect to have multiple different peaks, even 00:00:41.130 --> 00:00:42.390 align:middle line:90% from a single particle. 00:00:42.390 --> 00:00:47.070 align:middle line:84% And these peaks are going to be occurring at frequencies-- 00:00:47.070 --> 00:00:52.290 align:middle line:84% I'm going to switch into angular frequency units, omega m, which 00:00:52.290 --> 00:00:56.280 align:middle line:84% were equal to this cyclotron frequency, which was just 00:00:56.280 --> 00:00:58.140 align:middle line:84% our normal gyro frequency modified 00:00:58.140 --> 00:01:00.750 align:middle line:84% by a relativistic parameter here, 00:01:00.750 --> 00:01:05.190 align:middle line:84% and times by this relativistic rest mass 00:01:05.190 --> 00:01:08.550 align:middle line:84% term, which always makes the frequency smaller, 00:01:08.550 --> 00:01:12.970 align:middle line:84% divided by a relativistic Doppler term, which 00:01:12.970 --> 00:01:14.530 align:middle line:84% might make the frequency smaller, 00:01:14.530 --> 00:01:17.500 align:middle line:84% might make it larger, and, most importantly, all this 00:01:17.500 --> 00:01:24.910 align:middle line:84% multiplied by some integer m for some natural number N. 00:01:24.910 --> 00:01:26.950 align:middle line:84% And so, we have these peaks here. 00:01:26.950 --> 00:01:32.740 align:middle line:84% And we can say this is m equals 1, m equals 2, m equals 3. 00:01:32.740 --> 00:01:33.970 align:middle line:90% And they're evenly spaced. 00:01:33.970 --> 00:01:36.590 align:middle line:84% And this is just for a single particle. 00:01:36.590 --> 00:01:38.840 align:middle line:84% And then, when we put this all together, first of all, 00:01:38.840 --> 00:01:42.280 align:middle line:84% we looked at what a distribution of particles would do, 00:01:42.280 --> 00:01:45.580 align:middle line:84% and we agreed that these peaks would, in general, be broadened 00:01:45.580 --> 00:01:47.800 align:middle line:90% in some asymmetric fashion. 00:01:47.800 --> 00:01:50.410 align:middle line:84% But the exact shape will depend on exactly how 00:01:50.410 --> 00:01:53.628 align:middle line:84% big these two terms are with respect to each other. 00:01:53.628 --> 00:01:55.170 align:middle line:84% And we said the neat thing about this 00:01:55.170 --> 00:01:58.450 align:middle line:84% is that these frequencies depend only on the magnetic field. 00:01:58.450 --> 00:02:04.640 align:middle line:84% So this frequency here, eB over m e-- 00:02:04.640 --> 00:02:06.640 align:middle line:84% admittedly, there's a gamma factor inside there. 00:02:06.640 --> 00:02:08.669 align:middle line:84% But if we neglect that, the frequency 00:02:08.669 --> 00:02:10.930 align:middle line:84% depends only on the magnetic field. 00:02:10.930 --> 00:02:14.040 align:middle line:84% And so, if you see some emission at some certain frequency, 00:02:14.040 --> 00:02:17.490 align:middle line:84% then you know that it's been emitted by a region of plasma 00:02:17.490 --> 00:02:19.080 align:middle line:90% which has this magnetic field. 00:02:19.080 --> 00:02:20.730 align:middle line:84% And that was particularly useful when 00:02:20.730 --> 00:02:23.580 align:middle line:84% we considered a tokamak because, if we 00:02:23.580 --> 00:02:25.020 align:middle line:90% have something like a tokamak-- 00:02:25.020 --> 00:02:25.530 align:middle line:90% 00:02:25.530 --> 00:02:28.845 align:middle line:90% --or a stellarator-- hello? 00:02:28.845 --> 00:02:30.430 align:middle line:90% STUDENT: Oh, sorry, my bad. 00:02:30.430 --> 00:02:32.340 align:middle line:90% JACK HARE: No worries-- 00:02:32.340 --> 00:02:39.900 align:middle line:84% which has some magnetic field that goes 1 upon R, 00:02:39.900 --> 00:02:44.130 align:middle line:84% then different regions of our toroidal device 00:02:44.130 --> 00:02:48.295 align:middle line:84% are going to be emitting electron cyclotron emission 00:02:48.295 --> 00:02:49.420 align:middle line:90% with different frequencies. 00:02:49.420 --> 00:02:50.970 align:middle line:84% And those frequencies are different 00:02:50.970 --> 00:02:52.860 align:middle line:84% because the magnetic field is dropping 00:02:52.860 --> 00:02:56.800 align:middle line:84% off nice and monotonically throughout our device here. 00:02:56.800 --> 00:02:58.980 align:middle line:84% So we said that, for example, we might 00:02:58.980 --> 00:03:07.100 align:middle line:84% have three different regions, which we could 00:03:07.100 --> 00:03:15.700 align:middle line:90% label positions R1, R2, and R3. 00:03:15.700 --> 00:03:21.170 align:middle line:84% And each of these then have different magnetic fields, B1, 00:03:21.170 --> 00:03:25.815 align:middle line:90% B2, and B3. 00:03:25.815 --> 00:03:27.190 align:middle line:84% And each of these magnetic fields 00:03:27.190 --> 00:03:29.620 align:middle line:84% will then produce a spectra of lines 00:03:29.620 --> 00:03:32.170 align:middle line:84% at these different harmonics here. 00:03:32.170 --> 00:03:35.650 align:middle line:84% Now, the neat thing was, if we consider just the lowest 00:03:35.650 --> 00:03:42.100 align:middle line:84% harmonics, so the m equals 1 and often the m equals 2 harmonics, 00:03:42.100 --> 00:03:46.610 align:middle line:84% we said that these tend to be in an optically thick regime. 00:03:46.610 --> 00:03:48.490 align:middle line:84% So that is the region of plasma that's 00:03:48.490 --> 00:03:51.110 align:middle line:84% emitting is emitting as a black body. 00:03:51.110 --> 00:03:55.390 align:middle line:84% And that means the black body spectrum I of nu, 00:03:55.390 --> 00:04:00.802 align:middle line:84% is equal to T nu squared upon c squared. 00:04:00.802 --> 00:04:02.260 align:middle line:84% And what we would expect to get out 00:04:02.260 --> 00:04:05.020 align:middle line:84% if we put our little microwave horn 00:04:05.020 --> 00:04:09.400 align:middle line:84% and collected the different frequencies coming out 00:04:09.400 --> 00:04:20.279 align:middle line:84% from this plasma, is we'd expect some sort of spectrum 00:04:20.279 --> 00:04:23.280 align:middle line:84% where different parts of the spectrum 00:04:23.280 --> 00:04:25.780 align:middle line:84% correspond to different regions of this plasma. 00:04:25.780 --> 00:04:27.780 align:middle line:84% So, for example, we might have a region 00:04:27.780 --> 00:04:30.960 align:middle line:84% down here corresponding to lowish frequencies 00:04:30.960 --> 00:04:33.520 align:middle line:90% at low magnetic fields. 00:04:33.520 --> 00:04:35.340 align:middle line:84% So I've got this the wrong way around. 00:04:35.340 --> 00:04:36.780 align:middle line:90% R3 is the lowest magnetic field. 00:04:36.780 --> 00:04:39.460 align:middle line:90% 00:04:39.460 --> 00:04:43.000 align:middle line:84% We might have another region where the frequencies correspond 00:04:43.000 --> 00:04:46.210 align:middle line:84% to the center of the plasma and a higher frequency 00:04:46.210 --> 00:04:49.210 align:middle line:84% part of our spectrum which corresponds to the high field 00:04:49.210 --> 00:04:50.290 align:middle line:90% part of the plasma. 00:04:50.290 --> 00:04:53.650 align:middle line:84% And at each of these points, if we measure the intensity, 00:04:53.650 --> 00:04:55.840 align:middle line:84% we then know straight away what the temperature 00:04:55.840 --> 00:04:57.700 align:middle line:84% is corresponding to the black body 00:04:57.700 --> 00:04:59.590 align:middle line:90% spectrum for that frequency. 00:04:59.590 --> 00:05:02.500 align:middle line:84% And, therefore, we know what the temperature is inside 00:05:02.500 --> 00:05:03.250 align:middle line:90% our plasma. 00:05:03.250 --> 00:05:07.180 align:middle line:84% So we can go back and we can say, OK, 00:05:07.180 --> 00:05:12.860 align:middle line:84% using these measurements, maybe we have a temperature profile 00:05:12.860 --> 00:05:21.770 align:middle line:84% that looks like this where, again, we 00:05:21.770 --> 00:05:24.620 align:middle line:84% can identify three specific points 00:05:24.620 --> 00:05:27.680 align:middle line:84% inside here that we've been using as part of this example. 00:05:27.680 --> 00:05:30.605 align:middle line:84% But, in general, you can get it all the way through the plasma. 00:05:30.605 --> 00:05:33.987 align:middle line:90% 00:05:33.987 --> 00:05:35.570 align:middle line:84% And so, what we're doing here is we're 00:05:35.570 --> 00:05:39.810 align:middle line:84% saying that we've got some mapping from radius, 00:05:39.810 --> 00:05:45.450 align:middle line:84% the magnetic field, to frequency of maybe the first harmonic 00:05:45.450 --> 00:05:46.230 align:middle line:90% here. 00:05:46.230 --> 00:05:50.890 align:middle line:84% We have some intensity as a function of frequency, which 00:05:50.890 --> 00:05:52.870 align:middle line:84% is proportional just to temperature 00:05:52.870 --> 00:05:54.400 align:middle line:90% because of our black body case. 00:05:54.400 --> 00:05:56.800 align:middle line:84% And then we can back this temperature out. 00:05:56.800 --> 00:05:59.138 align:middle line:84% First it's temperature as a function of frequency. 00:05:59.138 --> 00:06:01.180 align:middle line:84% Then we can say, well, that frequency corresponds 00:06:01.180 --> 00:06:02.525 align:middle line:90% to a certain magnetic field. 00:06:02.525 --> 00:06:04.150 align:middle line:84% And then we can say that magnetic field 00:06:04.150 --> 00:06:07.870 align:middle line:84% corresponds to a certain spatial coordinate. 00:06:07.870 --> 00:06:09.880 align:middle line:84% And so, this is a technique which 00:06:09.880 --> 00:06:14.020 align:middle line:84% will give us, by looking at the spectrum for lowish frequencies, 00:06:14.020 --> 00:06:17.410 align:middle line:84% the first or maybe the second harmonics of this cyclotron 00:06:17.410 --> 00:06:19.570 align:middle line:84% emission, we can work out what the temperature 00:06:19.570 --> 00:06:21.200 align:middle line:90% is as a function of space. 00:06:21.200 --> 00:06:23.980 align:middle line:84% So this is why this is a powerful and popular diagnostic 00:06:23.980 --> 00:06:25.020 align:middle line:90% in MTF. 00:06:25.020 --> 00:06:29.380 align:middle line:84% And we also discussed a little bit about accessibility. 00:06:29.380 --> 00:06:30.880 align:middle line:84% If you remember, this is when we got 00:06:30.880 --> 00:06:34.180 align:middle line:84% into talking about the O mode and the X mode. 00:06:34.180 --> 00:06:38.220 align:middle line:90% 00:06:38.220 --> 00:06:40.230 align:middle line:84% And I'm not going to recap that now. 00:06:40.230 --> 00:06:42.180 align:middle line:84% And Sean posted an interesting way 00:06:42.180 --> 00:06:45.330 align:middle line:84% of looking at using something called a CMA diagram on Piazza 00:06:45.330 --> 00:06:47.920 align:middle line:84% if you want an alternative view on how this works. 00:06:47.920 --> 00:06:49.710 align:middle line:90% So that was just a quick recap. 00:06:49.710 --> 00:06:55.460 align:middle line:84% Any questions on ECE before we go into correlation ECE? 00:06:55.460 --> 00:07:22.865 align:middle line:90% 00:07:22.865 --> 00:07:23.365 align:middle line:90% OK. 00:07:23.365 --> 00:07:28.520 align:middle line:90% 00:07:28.520 --> 00:07:29.840 align:middle line:90% Ugh, a bad chalk. 00:07:29.840 --> 00:07:49.320 align:middle line:90% 00:07:49.320 --> 00:07:53.580 align:middle line:84% This is correlation ECE, often called CECE. 00:07:53.580 --> 00:07:55.260 align:middle line:84% So what is the problem we're trying 00:07:55.260 --> 00:07:56.940 align:middle line:90% to solve with correlation ECE? 00:07:56.940 --> 00:08:00.180 align:middle line:84% Why isn't this technique sufficient as it is? 00:08:00.180 --> 00:08:02.850 align:middle line:84% Well, what we want to do, we want 00:08:02.850 --> 00:08:06.360 align:middle line:84% to measure very small temperature fluctuations. 00:08:06.360 --> 00:08:09.330 align:middle line:84% We want to measure temperature fluctuations 00:08:09.330 --> 00:08:12.660 align:middle line:84% within the plasma that are maybe on the order 00:08:12.660 --> 00:08:16.060 align:middle line:84% of 1% of the baseline temperature, 00:08:16.060 --> 00:08:20.620 align:middle line:90% delta T upon T about 0.01. 00:08:20.620 --> 00:08:23.640 align:middle line:84% So if you have a small temperature fluctuation 00:08:23.640 --> 00:08:25.770 align:middle line:84% at some part in the plasma, that means 00:08:25.770 --> 00:08:27.870 align:middle line:84% you'll have a small intensity fluctuation. 00:08:27.870 --> 00:08:29.880 align:middle line:84% If the mean temperature is just Te, 00:08:29.880 --> 00:08:33.000 align:middle line:84% and we have some fluctuation around 1%, 00:08:33.000 --> 00:08:37.210 align:middle line:84% this intensity will also fluctuate by about 1%. 00:08:37.210 --> 00:08:41.370 align:middle line:84% And that 1% is actually extremely hard to measure. 00:08:41.370 --> 00:08:44.319 align:middle line:84% And this is because the noise is just too high on these systems. 00:08:44.319 --> 00:08:46.968 align:middle line:90% 00:08:46.968 --> 00:08:49.260 align:middle line:84% There are lots of different contributions to the noise. 00:08:49.260 --> 00:08:52.830 align:middle line:84% But, in general, they all add up to make it very hard to measure 00:08:52.830 --> 00:08:54.400 align:middle line:90% these very small fluctuations. 00:08:54.400 --> 00:08:56.850 align:middle line:84% So ECE, as it stands, is very good for measuring 00:08:56.850 --> 00:08:59.973 align:middle line:84% the broad average temperature profile with some error bars. 00:08:59.973 --> 00:09:02.640 align:middle line:84% But if you want to measure small fluctuations within those error 00:09:02.640 --> 00:09:05.490 align:middle line:84% bars, you don't stand a chance with this system. 00:09:05.490 --> 00:09:07.470 align:middle line:84% And you want to measure these fluctuations 00:09:07.470 --> 00:09:11.370 align:middle line:84% because these fluctuations are related to turbulence. 00:09:11.370 --> 00:09:13.140 align:middle line:84% And, as we've discussed before, turbulence 00:09:13.140 --> 00:09:14.880 align:middle line:84% is one of these key properties that we 00:09:14.880 --> 00:09:17.040 align:middle line:84% want to understand in plasmas so that we 00:09:17.040 --> 00:09:20.250 align:middle line:84% can build an economically viable fusion reactor. 00:09:20.250 --> 00:09:23.000 align:middle line:84% So it'd be very nice to be able to know. 00:09:23.000 --> 00:09:24.890 align:middle line:84% Now, the fact that the noise is too high 00:09:24.890 --> 00:09:26.660 align:middle line:90% does seem like a big limitation. 00:09:26.660 --> 00:09:28.610 align:middle line:84% But there are some clever tricks that we 00:09:28.610 --> 00:09:31.220 align:middle line:90% play where we use correlations. 00:09:31.220 --> 00:09:34.640 align:middle line:84% And I'll talk now about what exactly these correlations are 00:09:34.640 --> 00:09:36.620 align:middle line:84% and how they provide us with information 00:09:36.620 --> 00:09:38.270 align:middle line:84% that allows us to get a signal out 00:09:38.270 --> 00:09:40.950 align:middle line:84% despite the overwhelming [INAUDIBLE]. 00:09:40.950 --> 00:09:45.950 align:middle line:84% So our setup here is borrowed from ASDEX Upgrade. 00:09:45.950 --> 00:09:51.830 align:middle line:84% And, in effect, I referred to Alex Creely's PhD thesis, 00:09:51.830 --> 00:09:54.470 align:middle line:84% which you can find online if you want more information, 00:09:54.470 --> 00:09:57.850 align:middle line:84% from 2019, which is a pretty good summary of this. 00:09:57.850 --> 00:10:00.320 align:middle line:84% A top tip, if you're ever looking for an accessible 00:10:00.320 --> 00:10:02.450 align:middle line:84% description of some of the physics or a diagnostic, 00:10:02.450 --> 00:10:04.117 align:middle line:84% you should go find someone's PhD thesis. 00:10:04.117 --> 00:10:06.410 align:middle line:84% Usually much better than any of the papers that 00:10:06.410 --> 00:10:08.660 align:middle line:84% have been written about it, because there's not really 00:10:08.660 --> 00:10:09.785 align:middle line:90% any base restraint. 00:10:09.785 --> 00:10:11.660 align:middle line:84% And, of course, the person writing the thesis 00:10:11.660 --> 00:10:14.240 align:middle line:84% is desperate to tell everyone about all the cool stuff they 00:10:14.240 --> 00:10:16.532 align:middle line:84% just spent the last six years of their life working on. 00:10:16.532 --> 00:10:18.860 align:middle line:90% So it can get very detailed. 00:10:18.860 --> 00:10:21.488 align:middle line:84% So in ASDEX Upgrade, we don't really 00:10:21.488 --> 00:10:23.030 align:middle line:84% have a circular cross-section plasma, 00:10:23.030 --> 00:10:26.690 align:middle line:84% but I'm just drawing it like that, be a nice D-shaped plasma, 00:10:26.690 --> 00:10:30.220 align:middle line:90% got our plasma inside here. 00:10:30.220 --> 00:10:32.650 align:middle line:84% And our system, at first glance, looks an awful lot 00:10:32.650 --> 00:10:34.990 align:middle line:84% like the system that we sketched out up here. 00:10:34.990 --> 00:10:37.583 align:middle line:84% We're going to have some sort of special lens. 00:10:37.583 --> 00:10:39.625 align:middle line:84% It turns out, you can make lenses for microwaves. 00:10:39.625 --> 00:10:41.030 align:middle line:90% I didn't know this-- 00:10:41.030 --> 00:10:43.720 align:middle line:84% but some sort of plastic HDPE lens that then 00:10:43.720 --> 00:10:47.130 align:middle line:90% couples into a waveguide here. 00:10:47.130 --> 00:10:49.650 align:middle line:84% And that lens is going to collect light 00:10:49.650 --> 00:10:52.420 align:middle line:90% from a region like this. 00:10:52.420 --> 00:10:55.260 align:middle line:84% So I exaggerated it slightly, but there'll 00:10:55.260 --> 00:10:58.500 align:middle line:84% be some region over which we can collect light from relatively 00:10:58.500 --> 00:11:00.400 align:middle line:90% small volumes inside here. 00:11:00.400 --> 00:11:10.000 align:middle line:84% So we can have a series of volumes inside here. 00:11:10.000 --> 00:11:14.070 align:middle line:84% And, once again, our magnetic field is going as 1 00:11:14.070 --> 00:11:18.770 align:middle line:84% upon R, all the standard stuff that we had previously. 00:11:18.770 --> 00:11:21.400 align:middle line:84% Now, specifically for this ASDEX Upgrade system, 00:11:21.400 --> 00:11:23.560 align:middle line:84% but generically for C-mod and other devices 00:11:23.560 --> 00:11:25.810 align:middle line:84% where you might have this, the first thing that's done 00:11:25.810 --> 00:11:27.830 align:middle line:90% is a band pass filter. 00:11:27.830 --> 00:11:31.720 align:middle line:84% So this is applying some filter to it that in frequency space 00:11:31.720 --> 00:11:35.770 align:middle line:84% looks a little bit like this, some sort of top hat. 00:11:35.770 --> 00:11:38.980 align:middle line:84% It's centered around the frequency 00:11:38.980 --> 00:11:41.290 align:middle line:84% where most of the electron cyclotron emission is. 00:11:41.290 --> 00:11:44.800 align:middle line:84% It's around about 110 gigahertz in ASDEX Upgrade. 00:11:44.800 --> 00:11:47.990 align:middle line:84% And this has got a bandwidth of 10 gigahertz. 00:11:47.990 --> 00:11:51.580 align:middle line:84% So we've cut out an awful lot of the radiation in bands 00:11:51.580 --> 00:11:52.820 align:middle line:90% that we're not interested in. 00:11:52.820 --> 00:11:55.237 align:middle line:84% We are no longer going to study those, any bremsstrahlung, 00:11:55.237 --> 00:11:57.010 align:middle line:90% any higher order things. 00:11:57.010 --> 00:12:00.430 align:middle line:84% This is going to capture all of the information 00:12:00.430 --> 00:12:03.790 align:middle line:84% in, say, the first harmonic within some relatively 00:12:03.790 --> 00:12:04.940 align:middle line:90% small window. 00:12:04.940 --> 00:12:07.210 align:middle line:84% And that's the important thing about correlation ECE. 00:12:07.210 --> 00:12:08.830 align:middle line:84% We're not trying to measure the temperature profile 00:12:08.830 --> 00:12:10.210 align:middle line:90% throughout the entire plasma. 00:12:10.210 --> 00:12:11.300 align:middle line:90% That's very challenging. 00:12:11.300 --> 00:12:14.600 align:middle line:84% We want to measure it inside some very small region. 00:12:14.600 --> 00:12:17.210 align:middle line:84% And the reason is that our turbulent eddies, 00:12:17.210 --> 00:12:19.580 align:middle line:84% our little fluctuations inside here, these 00:12:19.580 --> 00:12:21.060 align:middle line:90% are very small as well. 00:12:21.060 --> 00:12:26.420 align:middle line:84% So the size of our turbulence of R turb, 00:12:26.420 --> 00:12:30.020 align:middle line:90% is on the order of 100 microns. 00:12:30.020 --> 00:12:31.667 align:middle line:84% That's the width of a human hair. 00:12:31.667 --> 00:12:33.500 align:middle line:84% So we are trying to measure turbulent eddies 00:12:33.500 --> 00:12:36.890 align:middle line:84% inside a tokamak on this scale of a human hair here. 00:12:36.890 --> 00:12:38.390 align:middle line:84% And so, that means, we're not trying 00:12:38.390 --> 00:12:40.130 align:middle line:84% to cover this entire frequency range. 00:12:40.130 --> 00:12:44.570 align:middle line:84% We're zoomed in on only quite a small frequency range. 00:12:44.570 --> 00:12:47.270 align:middle line:84% Once we've got our bandpass filtered signal here, 00:12:47.270 --> 00:12:51.050 align:middle line:84% 110 kilohertz is still too fast for us to digitize. 00:12:51.050 --> 00:12:53.900 align:middle line:84% This would be an extremely expensive digitizer. 00:12:53.900 --> 00:12:59.980 align:middle line:84% And so, what we actually do is we downmix it 00:12:59.980 --> 00:13:03.650 align:middle line:84% with the signal at 100 gigahertz. 00:13:03.650 --> 00:13:07.520 align:middle line:84% And so, then we get out our beat signal, which we can digitize, 00:13:07.520 --> 00:13:10.850 align:middle line:90% which is at 10 gigahertz here. 00:13:10.850 --> 00:13:12.890 align:middle line:84% So 100 gigahertz mixing was this. 00:13:12.890 --> 00:13:15.297 align:middle line:84% Our beat frequency is about 10 gigahertz plus or minus 00:13:15.297 --> 00:13:16.500 align:middle line:90% 5 gigahertz. 00:13:16.500 --> 00:13:22.350 align:middle line:84% So this is-- actually, I will write this as 0 to 10 gigahertz. 00:13:22.350 --> 00:13:25.920 align:middle line:84% This is the sort of signal that we can actually digitize now. 00:13:25.920 --> 00:13:28.650 align:middle line:84% And what we do is we then amplify it. 00:13:28.650 --> 00:13:35.240 align:middle line:84% And when we split it off, as we did with our standard electron 00:13:35.240 --> 00:13:37.580 align:middle line:84% cyclotron diagnostic, and we split it 00:13:37.580 --> 00:13:40.680 align:middle line:84% through a series of different bandpass filters-- 00:13:40.680 --> 00:13:47.410 align:middle line:84% so there might be another low, a lower filter, medium filter, 00:13:47.410 --> 00:13:48.115 align:middle line:90% the high filter. 00:13:48.115 --> 00:13:50.740 align:middle line:90% 00:13:50.740 --> 00:13:53.380 align:middle line:84% And then we put these through to a set of detectors. 00:13:53.380 --> 00:13:58.580 align:middle line:90% 00:13:58.580 --> 00:14:01.100 align:middle line:84% And so, each of these channels, now that we've split off, 00:14:01.100 --> 00:14:05.810 align:middle line:84% is looking at frequencies in a very narrow range here. 00:14:05.810 --> 00:14:13.410 align:middle line:84% These are about 100 megahertz in width now. 00:14:13.410 --> 00:14:20.550 align:middle line:84% And the spacing between these different bins is 125 megahertz. 00:14:20.550 --> 00:14:23.090 align:middle line:90% 00:14:23.090 --> 00:14:24.890 align:middle line:84% It's important that these bins do not 00:14:24.890 --> 00:14:26.900 align:middle line:84% overlap in frequency space, which 00:14:26.900 --> 00:14:30.530 align:middle line:84% means that these volumes do not overlap in real space. 00:14:30.530 --> 00:14:33.530 align:middle line:84% They are each sampling a separate discrete part 00:14:33.530 --> 00:14:35.640 align:middle line:90% of the plasma inside here. 00:14:35.640 --> 00:14:39.390 align:middle line:90% So let me just write that down. 00:14:39.390 --> 00:15:00.380 align:middle line:84% So each channel samples a non-overlapping region 00:15:00.380 --> 00:15:03.880 align:middle line:90% in frequency. 00:15:03.880 --> 00:15:08.660 align:middle line:84% And, therefore, in real space, because, again, we've 00:15:08.660 --> 00:15:11.930 align:middle line:84% got this very strong link between our magnetic field 00:15:11.930 --> 00:15:13.940 align:middle line:84% and our spatial position and the frequency 00:15:13.940 --> 00:15:14.970 align:middle line:90% at which we're sampling. 00:15:14.970 --> 00:15:17.240 align:middle line:84% So each of these represents a measure 00:15:17.240 --> 00:15:20.450 align:middle line:84% of the power that's being emitted by a very small region. 00:15:20.450 --> 00:15:22.400 align:middle line:84% And these regions are clearly distinguished. 00:15:22.400 --> 00:15:23.858 align:middle line:84% And you can tell that these regions 00:15:23.858 --> 00:15:26.840 align:middle line:84% are very small because we're dealing with 100 megahertz 00:15:26.840 --> 00:15:27.590 align:middle line:90% bandwidth. 00:15:27.590 --> 00:15:32.250 align:middle line:84% And we originally started with 110 gigahertz here. 00:15:32.250 --> 00:15:34.460 align:middle line:84% And so, you see we've gone down by a factor of 1,000. 00:15:34.460 --> 00:15:38.540 align:middle line:84% If 110 gigahertz was roughly enough to cover this entire 00:15:38.540 --> 00:15:41.150 align:middle line:84% region here, then we're now dealing with regions which are 00:15:41.150 --> 00:15:43.550 align:middle line:84% 1,000 times smaller than the radius of our tokamak. 00:15:43.550 --> 00:15:47.830 align:middle line:84% And that's how we're able to get down to this 100 microns or so. 00:15:47.830 --> 00:15:49.330 align:middle line:90% And we digitize these signals. 00:15:49.330 --> 00:15:51.100 align:middle line:84% And, just for reference, the reason 00:15:51.100 --> 00:15:52.900 align:middle line:84% why we downsampled these is that digitized 00:15:52.900 --> 00:15:54.310 align:middle line:90% is now much less expensive. 00:15:54.310 --> 00:15:57.940 align:middle line:84% We're doing it something like 4 mega samples a second. 00:15:57.940 --> 00:16:01.420 align:middle line:84% And that is quite an affordable digitizer compared to the ones 00:16:01.420 --> 00:16:04.090 align:middle line:84% you would need to digitize this signal up 00:16:04.090 --> 00:16:05.932 align:middle line:84% at hundreds of gigasamples a second. 00:16:05.932 --> 00:16:07.390 align:middle line:84% So I have not yet told you anything 00:16:07.390 --> 00:16:09.350 align:middle line:90% about how correlation ECE works. 00:16:09.350 --> 00:16:11.800 align:middle line:84% I'm just giving you an outline of exactly how 00:16:11.800 --> 00:16:16.170 align:middle line:84% these measurements are made with an example from ASDEX Upgrade. 00:16:16.170 --> 00:16:21.130 align:middle line:84% But there are other similar devices on other tokamaks. 00:16:21.130 --> 00:16:23.590 align:middle line:84% Any questions on this before we get to the meat of what 00:16:23.590 --> 00:16:25.205 align:middle line:90% we're trying to achieve here? 00:16:25.205 --> 00:16:25.705 align:middle line:90% Yeah. 00:16:25.705 --> 00:16:33.655 align:middle line:90% 00:16:33.655 --> 00:16:35.440 align:middle line:90% This wave is too damn fast. 00:16:35.440 --> 00:16:37.180 align:middle line:90% We can't digitize it. 00:16:37.180 --> 00:16:39.717 align:middle line:90% We mix it with 100 gigahertz. 00:16:39.717 --> 00:16:41.550 align:middle line:84% We did this before when we were heterodyning 00:16:41.550 --> 00:16:43.560 align:middle line:90% our signals for interferometry. 00:16:43.560 --> 00:16:45.970 align:middle line:90% We get out two frequencies. 00:16:45.970 --> 00:16:49.410 align:middle line:84% We get out a frequency at omega 1 minus omega 2, 00:16:49.410 --> 00:16:53.310 align:middle line:84% and we get out a frequency at omega 1 plus omega 2. 00:16:53.310 --> 00:16:57.190 align:middle line:84% Omega 1 minus omega 2, that signal 00:16:57.190 --> 00:16:58.900 align:middle line:90% is about 0 to 10 gigahertz. 00:16:58.900 --> 00:17:00.220 align:middle line:90% We can digitize that. 00:17:00.220 --> 00:17:03.430 align:middle line:84% This one, whatever, 200 gigahertz, we still can't. 00:17:03.430 --> 00:17:07.030 align:middle line:84% On the integration time of our detector, the sampling 00:17:07.030 --> 00:17:10.480 align:middle line:84% time here, that will have many, many oscillations. 00:17:10.480 --> 00:17:12.579 align:middle line:90% And so, it will average out to-- 00:17:12.579 --> 00:17:14.530 align:middle line:84% well, because it's power, it will average out 00:17:14.530 --> 00:17:16.250 align:middle line:90% to 1 or something like that. 00:17:16.250 --> 00:17:19.060 align:middle line:84% So it's some DC offset that we can subtract off after. 00:17:19.060 --> 00:17:22.359 align:middle line:84% So all this is doing here is mixing the signal down 00:17:22.359 --> 00:17:27.440 align:middle line:84% so it gets to a regime that we can effectively digitize. 00:17:27.440 --> 00:17:29.098 align:middle line:90% Yeah, another question. 00:17:29.098 --> 00:17:31.538 align:middle line:90% STUDENT: [INAUDIBLE] 00:17:31.538 --> 00:17:52.000 align:middle line:90% 00:17:52.000 --> 00:17:54.850 align:middle line:84% JACK HARE: So if we were doing geometric optics, which 00:17:54.850 --> 00:17:59.500 align:middle line:84% we're not, then you would have a lens like this. 00:17:59.500 --> 00:18:02.350 align:middle line:84% That lens could collimate your beam, 00:18:02.350 --> 00:18:05.540 align:middle line:84% as in we'd have a load of rays coming out into our horn. 00:18:05.540 --> 00:18:07.510 align:middle line:84% And if it collimated that beam, that 00:18:07.510 --> 00:18:10.600 align:middle line:84% would mean there'd be a focus point at some distance 00:18:10.600 --> 00:18:13.310 align:middle line:84% f away-- if this lens has a focal length f, 00:18:13.310 --> 00:18:16.370 align:middle line:90% then it will diverge afterwards. 00:18:16.370 --> 00:18:19.918 align:middle line:84% So, because of reciprocity, that means that, as opposed 00:18:19.918 --> 00:18:22.210 align:middle line:84% to launching rays this way and seeing where they focus, 00:18:22.210 --> 00:18:23.650 align:middle line:84% we have rays coming from this way. 00:18:23.650 --> 00:18:27.760 align:middle line:84% Now, we don't ever actually get to infinitesimal point 00:18:27.760 --> 00:18:29.920 align:middle line:84% like we predict in geometric optics 00:18:29.920 --> 00:18:32.500 align:middle line:84% or Gaussian optics tells us that there's a beam waist. 00:18:32.500 --> 00:18:35.995 align:middle line:84% And our beam looks like this instead. 00:18:35.995 --> 00:18:37.870 align:middle line:84% And that was what was trying to draw up here. 00:18:37.870 --> 00:18:39.862 align:middle line:90% STUDENT: [INAUDIBLE] 00:18:39.862 --> 00:18:43.055 align:middle line:90% 00:18:43.055 --> 00:18:43.680 align:middle line:90% JACK HARE: Yes. 00:18:43.680 --> 00:18:45.330 align:middle line:90% STUDENT: [INAUDIBLE] very long. 00:18:45.330 --> 00:18:46.680 align:middle line:90% JACK HARE: Yes, exactly. 00:18:46.680 --> 00:18:50.670 align:middle line:84% Exactly, and you can choose properties of your lens 00:18:50.670 --> 00:18:52.650 align:middle line:84% that will give you a narrower waist or not. 00:18:52.650 --> 00:18:54.422 align:middle line:84% It depends on your size of your lens 00:18:54.422 --> 00:18:56.130 align:middle line:84% and the wavelength of light and all sorts 00:18:56.130 --> 00:18:57.840 align:middle line:90% of other [? goods ?] like that. 00:18:57.840 --> 00:19:00.990 align:middle line:84% So this is not exactly a picture-perfect sketch of it. 00:19:00.990 --> 00:19:04.710 align:middle line:84% But the idea here is that there was some region over which, 00:19:04.710 --> 00:19:08.070 align:middle line:84% in the transverse direction perpendicular to your collection 00:19:08.070 --> 00:19:11.130 align:middle line:84% volume, you have a very narrow scale, which 00:19:11.130 --> 00:19:14.550 align:middle line:84% means that you can actually collect from a very small region 00:19:14.550 --> 00:19:18.110 align:middle line:90% on the order of 100 microns. 00:19:18.110 --> 00:19:18.990 align:middle line:90% Any other questions? 00:19:18.990 --> 00:19:19.657 align:middle line:90% Anything online? 00:19:19.657 --> 00:19:27.100 align:middle line:90% 00:19:27.100 --> 00:19:27.600 align:middle line:90% OK. 00:19:27.600 --> 00:19:28.410 align:middle line:90% STUDENT: Professor? 00:19:28.410 --> 00:19:30.060 align:middle line:90% JACK HARE: Yes. 00:19:30.060 --> 00:19:34.880 align:middle line:84% STUDENT: I have a question about how you split the signal to each 00:19:34.880 --> 00:19:37.740 align:middle line:90% of the harmonics. 00:19:37.740 --> 00:19:42.610 align:middle line:84% JACK HARE: You mean this splitter here physically or-- 00:19:42.610 --> 00:19:46.462 align:middle line:84% STUDENT: Yeah, what's the physical method of splitting it? 00:19:46.462 --> 00:19:48.670 align:middle line:84% JACK HARE: I don't know how microwave splitters work. 00:19:48.670 --> 00:19:50.290 align:middle line:84% But there is something that you can 00:19:50.290 --> 00:19:52.020 align:middle line:84% buy from DigiKey or something like that 00:19:52.020 --> 00:19:53.020 align:middle line:90% that will do it for you. 00:19:53.020 --> 00:19:54.790 align:middle line:84% Anyone know how micro splitters work? 00:19:54.790 --> 00:19:56.660 align:middle line:90% Looking at you? 00:19:56.660 --> 00:19:57.898 align:middle line:90% STUDENT: RF. 00:19:57.898 --> 00:20:00.190 align:middle line:84% JACK HARE: The answer I got was RF, which I don't think 00:20:00.190 --> 00:20:02.590 align:middle line:84% is much more satisfying than my answer. 00:20:02.590 --> 00:20:05.800 align:middle line:84% So, yeah, there are circuits which will split microwaves. 00:20:05.800 --> 00:20:06.942 align:middle line:90% STUDENT: OK. 00:20:06.942 --> 00:20:08.400 align:middle line:84% JACK HARE: Thing called a rat race, 00:20:08.400 --> 00:20:09.780 align:middle line:84% but I don't think that's for gigahertz. 00:20:09.780 --> 00:20:11.322 align:middle line:84% Have you ever come across a rat race? 00:20:11.322 --> 00:20:13.820 align:middle line:84% If you're doing lower things, it has 00:20:13.820 --> 00:20:16.363 align:middle line:84% ports which are spaced by wavelengths of your microwave 00:20:16.363 --> 00:20:18.780 align:middle line:84% and then there's constructive and destructive interference 00:20:18.780 --> 00:20:19.620 align:middle line:90% in different places? 00:20:19.620 --> 00:20:20.160 align:middle line:90% Yeah. 00:20:20.160 --> 00:20:22.490 align:middle line:90% STUDENT: [INAUDIBLE] 00:20:22.490 --> 00:20:25.118 align:middle line:90% 00:20:25.118 --> 00:20:26.660 align:middle line:84% JACK HARE: I don't think that's how-- 00:20:26.660 --> 00:20:28.430 align:middle line:84% I think they are literally splitting it and then having 00:20:28.430 --> 00:20:29.270 align:middle line:90% separate band passes. 00:20:29.270 --> 00:20:30.230 align:middle line:84% But, you're right, you could come up 00:20:30.230 --> 00:20:32.573 align:middle line:84% with some clever analog way of doing the splitting. 00:20:32.573 --> 00:20:34.490 align:middle line:84% What they were actually doing with this system 00:20:34.490 --> 00:20:36.140 align:middle line:84% is all of these were very tunable. 00:20:36.140 --> 00:20:38.840 align:middle line:84% And so, if they wanted to look at turbulence in the edge 00:20:38.840 --> 00:20:39.860 align:middle line:84% or turbulence near the center, they 00:20:39.860 --> 00:20:42.277 align:middle line:84% could actually tune all their bandpass filters to do that. 00:20:42.277 --> 00:20:44.482 align:middle line:84% But this is getting way beyond what I was 00:20:44.482 --> 00:20:45.690 align:middle line:90% hoping to talk about on this. 00:20:45.690 --> 00:20:49.070 align:middle line:84% So let's get on to correlation ECE see what that does. 00:20:49.070 --> 00:21:28.990 align:middle line:90% 00:21:28.990 --> 00:21:32.235 align:middle line:84% So now you've got these n different channels up here. 00:21:32.235 --> 00:21:37.260 align:middle line:90% 00:21:37.260 --> 00:21:40.280 align:middle line:84% And each of those channels is measuring some signal. 00:21:40.280 --> 00:21:42.582 align:middle line:90% 00:21:42.582 --> 00:21:44.540 align:middle line:84% And we're going to write this little tilde here 00:21:44.540 --> 00:21:46.957 align:middle line:84% to remind us that this signal is some oscillating quantity 00:21:46.957 --> 00:21:48.200 align:middle line:90% or time varying quantity. 00:21:48.200 --> 00:21:50.460 align:middle line:84% And that signal has two components to it. 00:21:50.460 --> 00:21:53.360 align:middle line:84% It's got some fluctuation, which is 00:21:53.360 --> 00:21:55.160 align:middle line:90% due to temperature fluctuation. 00:21:55.160 --> 00:21:57.470 align:middle line:84% This is the thing that we want to measure. 00:21:57.470 --> 00:22:02.080 align:middle line:84% And then, it's also got some noise. 00:22:02.080 --> 00:22:04.510 align:middle line:84% This is the thing that we don't want to measure here. 00:22:04.510 --> 00:22:06.760 align:middle line:84% And so, we are making the assumption 00:22:06.760 --> 00:22:12.460 align:middle line:84% here that our noise is much, much bigger than our temperature 00:22:12.460 --> 00:22:13.395 align:middle line:90% fluctuation signal. 00:22:13.395 --> 00:22:15.520 align:middle line:84% If it's not the case, then you don't have a problem 00:22:15.520 --> 00:22:17.187 align:middle line:84% and you don't need to do this technique. 00:22:17.187 --> 00:22:19.600 align:middle line:84% But it is the case in most of the applications 00:22:19.600 --> 00:22:21.960 align:middle line:84% that we're going to see it's used for. 00:22:21.960 --> 00:22:26.060 align:middle line:84% And so, the signal, as a function of time, 00:22:26.060 --> 00:22:29.192 align:middle line:84% is going to-- what we want it to do is look like, again, 00:22:29.192 --> 00:22:30.650 align:middle line:84% our temperature signal, which might 00:22:30.650 --> 00:22:35.210 align:middle line:84% be some nice and smooth function like this corresponding 00:22:35.210 --> 00:22:36.440 align:middle line:90% to some turbulent eddy. 00:22:36.440 --> 00:22:41.000 align:middle line:84% But what it actually looks like is some messy noisy thing 00:22:41.000 --> 00:22:44.090 align:middle line:84% which, even with some very aggressive filtering, 00:22:44.090 --> 00:22:46.857 align:middle line:84% is still going to be extremely noisy instead. 00:22:46.857 --> 00:22:48.440 align:middle line:84% So what we want to do is find some way 00:22:48.440 --> 00:22:51.770 align:middle line:84% of extracting this temperature from the noise here. 00:22:51.770 --> 00:22:55.440 align:middle line:84% And what we do is we pick two adjacent channels. 00:22:55.440 --> 00:23:01.090 align:middle line:90% So we'll call them S1 and S2. 00:23:01.090 --> 00:23:05.560 align:middle line:84% These channels are adjacent in frequency space, which 00:23:05.560 --> 00:23:09.550 align:middle line:84% means that they are measuring from adjacent parcels of plasma 00:23:09.550 --> 00:23:13.030 align:middle line:84% in real space or inside the tokamak. 00:23:13.030 --> 00:23:15.940 align:middle line:84% So, again, if we have our tokamak cross-section here, 00:23:15.940 --> 00:23:21.965 align:middle line:84% we have the plasma, we zoom in right at the edge of the plasma 00:23:21.965 --> 00:23:22.465 align:middle line:90% here. 00:23:22.465 --> 00:23:27.662 align:middle line:90% 00:23:27.662 --> 00:23:28.870 align:middle line:90% No, that's not going to work. 00:23:28.870 --> 00:23:33.100 align:middle line:90% 00:23:33.100 --> 00:23:38.900 align:middle line:84% We would have two volumes very close together but not 00:23:38.900 --> 00:23:39.980 align:middle line:90% quite touching. 00:23:39.980 --> 00:23:46.290 align:middle line:84% And these volumes we could call 1 and 2, like that. 00:23:46.290 --> 00:23:48.950 align:middle line:84% And what we do is we say, we arrange-- 00:23:48.950 --> 00:23:53.713 align:middle line:84% we have some simulation or some prior, which tells us 00:23:53.713 --> 00:23:55.130 align:middle line:84% that the size of a turbulent eddy, 00:23:55.130 --> 00:23:57.410 align:middle line:84% the size of one of these swirls, is 00:23:57.410 --> 00:24:01.850 align:middle line:84% larger than the separation between these two points. 00:24:01.850 --> 00:24:09.310 align:middle line:84% So we say, our term is greater than delta R. Which 00:24:09.310 --> 00:24:10.810 align:middle line:84% means that, if there's a temperature 00:24:10.810 --> 00:24:13.630 align:middle line:84% fluctuation associated with this little vortex, 00:24:13.630 --> 00:24:18.070 align:middle line:84% it is the same temperature fluctuation in S1 as in S2. 00:24:18.070 --> 00:24:21.910 align:middle line:84% And, again-- oh, I don't need this to be much greater than. 00:24:21.910 --> 00:24:25.375 align:middle line:84% I just need it to be greater than or on the order of. 00:24:25.375 --> 00:24:28.290 align:middle line:90% 00:24:28.290 --> 00:24:31.080 align:middle line:84% And, again, these are really, really closely spaced, 00:24:31.080 --> 00:24:32.700 align:middle line:90% 100 microns or so apart. 00:24:32.700 --> 00:24:34.110 align:middle line:90% This is really, really tiny. 00:24:34.110 --> 00:24:36.540 align:middle line:84% But, the nice thing is now that these two signals 00:24:36.540 --> 00:24:40.060 align:middle line:84% are carrying the same components that we're trying to measure. 00:24:40.060 --> 00:24:41.890 align:middle line:84% And this is where the correlation comes in. 00:24:41.890 --> 00:24:43.740 align:middle line:84% We are going to correlate these two signals. 00:24:43.740 --> 00:24:46.650 align:middle line:84% And we're going to find that the noise is uncorrelated at random, 00:24:46.650 --> 00:24:48.840 align:middle line:84% but these two signals will correlate together, 00:24:48.840 --> 00:24:51.150 align:middle line:90% and we'll be able to measure it. 00:24:51.150 --> 00:24:55.020 align:middle line:84% So we have-- just to be clear, we 00:24:55.020 --> 00:25:03.020 align:middle line:84% have chosen the frequencies omega 1 and omega 2 such 00:25:03.020 --> 00:25:14.430 align:middle line:84% that delta R 1 2 is less than the length scale associated 00:25:14.430 --> 00:25:16.710 align:middle line:90% with turbulence. 00:25:16.710 --> 00:25:18.570 align:middle line:84% And we can choose these frequencies 00:25:18.570 --> 00:25:21.660 align:middle line:84% because we have control over all of these bandpass filters 00:25:21.660 --> 00:25:22.840 align:middle line:90% and funky things like that. 00:25:22.840 --> 00:25:24.465 align:middle line:84% So you might need to do this experiment 00:25:24.465 --> 00:25:26.190 align:middle line:90% a few times to get it right. 00:25:26.190 --> 00:25:29.070 align:middle line:84% But once you get it right, your signal will leap out. 00:25:29.070 --> 00:25:32.500 align:middle line:84% Because what we find is that the temperature-- 00:25:32.500 --> 00:25:34.810 align:middle line:84% well, we find that the temperature is correlated. 00:25:34.810 --> 00:25:42.950 align:middle line:84% So if do S1, S2, and we do a correlation operation on these. 00:25:42.950 --> 00:25:45.200 align:middle line:84% And there are a few different ways to do correlations, 00:25:45.200 --> 00:25:46.640 align:middle line:84% and I'm not going to go into them, 00:25:46.640 --> 00:25:48.560 align:middle line:84% but I will give you a citation at the moment. 00:25:48.560 --> 00:25:50.690 align:middle line:84% We get out a term here that looks 00:25:50.690 --> 00:25:57.490 align:middle line:84% like the temperature term squared, the thing we want, 00:25:57.490 --> 00:26:02.000 align:middle line:84% the cross-correlation between the two noise terms, 00:26:02.000 --> 00:26:06.140 align:middle line:84% plus two cross-terms between the noise 00:26:06.140 --> 00:26:09.770 align:middle line:84% and the temperature signal from channel 1 and the noise 00:26:09.770 --> 00:26:14.210 align:middle line:84% and the temperature signal from channel 2. 00:26:14.210 --> 00:26:16.730 align:middle line:84% And because this noise is just random, 00:26:16.730 --> 00:26:18.740 align:middle line:84% when we do some sort of averaging, 00:26:18.740 --> 00:26:21.230 align:middle line:84% this could be in time or best to think 00:26:21.230 --> 00:26:24.650 align:middle line:84% of it is a short time integral, then these terms are all 00:26:24.650 --> 00:26:25.490 align:middle line:90% going to drop out. 00:26:25.490 --> 00:26:31.020 align:middle line:90% 00:26:31.020 --> 00:26:33.300 align:middle line:84% And we'll just be left with a correlation 00:26:33.300 --> 00:26:36.750 align:middle line:84% signal that is proportional to the temperature squared here. 00:26:36.750 --> 00:26:39.300 align:middle line:84% And, again, I've been a bit hazy about what these angle 00:26:39.300 --> 00:26:40.470 align:middle line:90% brackets are doing here. 00:26:40.470 --> 00:26:47.730 align:middle line:84% You could think of it as equal to some sort of short time 00:26:47.730 --> 00:26:56.055 align:middle line:84% integration of S1 and S2 from T to T plus delta T, like that. 00:26:56.055 --> 00:26:57.430 align:middle line:84% That would be a time correlation. 00:26:57.430 --> 00:27:00.170 align:middle line:84% But there are actually lots of different ways of doing this. 00:27:00.170 --> 00:27:08.283 align:middle line:84% And the citation here for you is a review paper by Watts, 2007. 00:27:08.283 --> 00:27:09.700 align:middle line:84% I don't know if this is an example 00:27:09.700 --> 00:27:11.052 align:middle line:90% of nominative determinism. 00:27:11.052 --> 00:27:13.510 align:middle line:84% Someone called Watts goes around making power measurements. 00:27:13.510 --> 00:27:14.920 align:middle line:90% [LAUGHTER] 00:27:14.920 --> 00:27:17.440 align:middle line:90% There we go. 00:27:17.440 --> 00:27:20.200 align:middle line:84% Yeah, and this technique is incredibly powerful 00:27:20.200 --> 00:27:26.330 align:middle line:84% because it's enabled people to measure, again, delta Te upon Te 00:27:26.330 --> 00:27:29.600 align:middle line:90% on the order of 1%. 00:27:29.600 --> 00:27:31.820 align:middle line:90% And they've done this at 13-- 00:27:31.820 --> 00:27:36.670 align:middle line:84% on ASDEX Upgrade-- 13 radial locations. 00:27:36.670 --> 00:27:39.480 align:middle line:84% So 13 positions they can measure these temperature fluctuations. 00:27:39.480 --> 00:27:44.280 align:middle line:90% 00:27:44.280 --> 00:27:49.640 align:middle line:84% And they've done this with a time step of 100 kilohertz. 00:27:49.640 --> 00:27:53.358 align:middle line:84% So 100,000 times a second they've been able to measure 00:27:53.358 --> 00:27:54.650 align:middle line:90% these temperature fluctuations. 00:27:54.650 --> 00:27:57.555 align:middle line:84% So on very small scales, very fast time scales, 00:27:57.555 --> 00:27:59.930 align:middle line:84% we can now measure temperature fluctuations in a tokamak. 00:27:59.930 --> 00:28:02.060 align:middle line:84% And this is something that has revolutionized 00:28:02.060 --> 00:28:05.810 align:middle line:84% our understanding of turbulence and its importance in tokamaks, 00:28:05.810 --> 00:28:09.790 align:middle line:84% because now we can finally characterize it. 00:28:09.790 --> 00:28:10.940 align:middle line:90% That was a lot. 00:28:10.940 --> 00:28:12.630 align:middle line:90% Any questions? 00:28:12.630 --> 00:28:16.350 align:middle line:84% We're going to move on from ECE [INAUDIBLE]. 00:28:16.350 --> 00:28:16.920 align:middle line:90% Yes. 00:28:16.920 --> 00:28:18.744 align:middle line:90% STUDENT: [INAUDIBLE] 00:28:18.744 --> 00:28:29.483 align:middle line:90% 00:28:29.483 --> 00:28:31.150 align:middle line:84% JACK HARE: I think the idea is that this 00:28:31.150 --> 00:28:34.000 align:middle line:84% is so noisy that if you try and just-- that's effectively 00:28:34.000 --> 00:28:37.390 align:middle line:90% a bandpass filter at that point. 00:28:37.390 --> 00:28:40.670 align:middle line:84% Yeah, I don't think you can get this out of an autocorrelation. 00:28:40.670 --> 00:28:42.290 align:middle line:84% So this is more sensitive than that. 00:28:42.290 --> 00:28:42.790 align:middle line:90% Yeah. 00:28:42.790 --> 00:28:46.206 align:middle line:90% 00:28:46.206 --> 00:28:47.840 align:middle line:90% STUDENT: [INAUDIBLE] 00:28:47.840 --> 00:28:50.390 align:middle line:90% 00:28:50.390 --> 00:28:53.060 align:middle line:84% JACK HARE: Yeah, so the idea is that we have positioned 00:28:53.060 --> 00:28:56.120 align:middle line:84% these two volumes, which are producing frequencies 00:28:56.120 --> 00:28:59.420 align:middle line:84% omega 1 and omega 2, we've chosen omega 1 and omega 2 00:28:59.420 --> 00:29:00.900 align:middle line:90% so they're very close together. 00:29:00.900 --> 00:29:02.720 align:middle line:84% And we think that that distance is 00:29:02.720 --> 00:29:04.932 align:middle line:84% smaller than the size of our turbulent eddy. 00:29:04.932 --> 00:29:06.890 align:middle line:84% And within that turbulent eddy, the temperature 00:29:06.890 --> 00:29:08.550 align:middle line:84% should be the same going up and down. 00:29:08.550 --> 00:29:10.997 align:middle line:84% And if you do this correlation and you get out nothing, 00:29:10.997 --> 00:29:12.830 align:middle line:84% that probably means your volumes are too far 00:29:12.830 --> 00:29:14.420 align:middle line:90% apart because there is-- 00:29:14.420 --> 00:29:17.261 align:middle line:84% this T correlation would just go T1 T2. 00:29:17.261 --> 00:29:24.738 align:middle line:90% 00:29:24.738 --> 00:29:27.030 align:middle line:84% And there's no good reason to believe those temperature 00:29:27.030 --> 00:29:29.700 align:middle line:84% fluctuations are correlated, because they'll be part 00:29:29.700 --> 00:29:31.500 align:middle line:90% of a different turbulent eddy. 00:29:31.500 --> 00:29:34.290 align:middle line:84% And so, that would just go to 0 as well. 00:29:34.290 --> 00:29:35.148 align:middle line:90% Yeah. 00:29:35.148 --> 00:29:52.768 align:middle line:84% STUDENT: [INAUDIBLE] 13 times [INAUDIBLE]. 00:29:52.768 --> 00:29:54.310 align:middle line:84% JACK HARE: Yeah, so the question was, 00:29:54.310 --> 00:29:56.800 align:middle line:84% what is the actual spatial range of this? 00:29:56.800 --> 00:29:58.797 align:middle line:84% Do you have pairs and then a gap and pairs? 00:29:58.797 --> 00:30:00.880 align:middle line:84% I believe that, for this, if I remember correctly, 00:30:00.880 --> 00:30:05.020 align:middle line:84% they literally just had 14 channels side by side, 00:30:05.020 --> 00:30:07.960 align:middle line:84% and that gave them 13 points of correlation 00:30:07.960 --> 00:30:09.680 align:middle line:90% between each adjacent pair. 00:30:09.680 --> 00:30:12.760 align:middle line:84% And so, they were interested in measuring transport in the edge. 00:30:12.760 --> 00:30:14.200 align:middle line:84% But I believe, in a separate shot, 00:30:14.200 --> 00:30:17.230 align:middle line:84% you can then tune all of this slightly differently 00:30:17.230 --> 00:30:19.450 align:middle line:84% and move slightly further in depending on where you 00:30:19.450 --> 00:30:20.793 align:middle line:90% think transport is important. 00:30:20.793 --> 00:30:22.210 align:middle line:84% But if you're looking at transport 00:30:22.210 --> 00:30:25.040 align:middle line:84% in the pedestal region, you have some idea where that is. 00:30:25.040 --> 00:30:27.430 align:middle line:84% And so you focus your measurements in the pedestal. 00:30:27.430 --> 00:30:29.470 align:middle line:84% But, yeah, you're right, this does not 00:30:29.470 --> 00:30:32.108 align:middle line:90% get you a huge spatial range. 00:30:32.108 --> 00:30:33.400 align:middle line:90% It gets you about a millimeter. 00:30:33.400 --> 00:30:38.300 align:middle line:84% But that might be enough for your measurements. 00:30:38.300 --> 00:30:41.230 align:middle line:84% STUDENT: [INAUDIBLE] would you have [INAUDIBLE] 00:30:41.230 --> 00:30:43.840 align:middle line:90% in this localized [INAUDIBLE]? 00:30:43.840 --> 00:30:45.280 align:middle line:84% JACK HARE: Yeah, so the idea here 00:30:45.280 --> 00:30:47.980 align:middle line:84% is that your eddies are sort of like-- 00:30:47.980 --> 00:30:52.210 align:middle line:84% there are eddies like this, or maybe, at some other point, 00:30:52.210 --> 00:30:54.022 align:middle line:90% there is an eddy like this. 00:30:54.022 --> 00:30:55.480 align:middle line:84% And so, it will depend a little bit 00:30:55.480 --> 00:30:59.555 align:middle line:84% on how you do your time integration step here. 00:30:59.555 --> 00:31:01.180 align:middle line:84% So this is part of the art of it as far 00:31:01.180 --> 00:31:04.848 align:middle line:84% as I understand, is that you need to pick pairs 00:31:04.848 --> 00:31:06.890 align:middle line:84% because they're the only ones that could possibly 00:31:06.890 --> 00:31:08.098 align:middle line:90% be close enough to correlate. 00:31:08.098 --> 00:31:12.500 align:middle line:84% If you try and pick this one and this one, it will go to 0. 00:31:12.500 --> 00:31:15.057 align:middle line:84% But, as well, the eddies are going to be moving in time. 00:31:15.057 --> 00:31:17.390 align:middle line:84% So you may end up with a situation where, at some point, 00:31:17.390 --> 00:31:19.520 align:middle line:84% your eddy has moved across, and these two are 00:31:19.520 --> 00:31:22.950 align:middle line:84% no longer correlated because the next two are correlated. 00:31:22.950 --> 00:31:26.890 align:middle line:90% So it-- yeah. 00:31:26.890 --> 00:31:29.110 align:middle line:84% I think we're reaching the limits of my knowledge. 00:31:29.110 --> 00:31:29.410 align:middle line:90% Yeah. 00:31:29.410 --> 00:31:29.910 align:middle line:90% [LAUGHS] 00:31:29.910 --> 00:31:33.112 align:middle line:84% STUDENT: [INAUDIBLE] correlated, [INAUDIBLE] 00:31:33.112 --> 00:31:35.850 align:middle line:84% second and the third one are [INAUDIBLE]. 00:31:35.850 --> 00:31:36.680 align:middle line:90% 00:31:36.680 --> 00:31:38.180 align:middle line:84% JACK HARE: I mean, there's no reason 00:31:38.180 --> 00:31:40.400 align:middle line:84% to believe that each of the fluctuations is the same size. 00:31:40.400 --> 00:31:42.067 align:middle line:84% And there's no reason to believe they're 00:31:42.067 --> 00:31:44.100 align:middle line:90% stationary in space with time. 00:31:44.100 --> 00:31:47.210 align:middle line:84% So this is going to be a time-evolving system here. 00:31:47.210 --> 00:31:48.800 align:middle line:90% Yeah, exactly. 00:31:48.800 --> 00:31:49.507 align:middle line:90% Cool. 00:31:49.507 --> 00:31:50.340 align:middle line:90% Any other questions? 00:31:50.340 --> 00:31:51.007 align:middle line:90% Anything online? 00:31:51.007 --> 00:32:03.760 align:middle line:90% 00:32:03.760 --> 00:32:06.479 align:middle line:84% Now we're going to go to bremsstrahlung. 00:32:06.479 --> 00:32:31.960 align:middle line:90% 00:32:31.960 --> 00:32:35.720 align:middle line:84% Some people these days just call this breaking radiation, 00:32:35.720 --> 00:32:38.380 align:middle line:84% which is just the translation from the German, 00:32:38.380 --> 00:32:41.720 align:middle line:84% and that's a perfectly reasonable term to use. 00:32:41.720 --> 00:32:44.770 align:middle line:84% But if you haven't come across bremsstrahlung as a word before, 00:32:44.770 --> 00:32:46.010 align:middle line:90% that's what it means. 00:32:46.010 --> 00:32:50.820 align:middle line:84% And so, what we're dealing with is heavy ions, 00:32:50.820 --> 00:32:53.910 align:middle line:84% and all ions are heavy compared to electrons. 00:32:53.910 --> 00:32:56.775 align:middle line:84% And we've got some electron whizzing by. 00:32:56.775 --> 00:32:59.450 align:middle line:90% 00:32:59.450 --> 00:33:05.300 align:middle line:84% As the electron whizzes by, it feels a force of attraction 00:33:05.300 --> 00:33:05.990 align:middle line:90% to the ion. 00:33:05.990 --> 00:33:09.150 align:middle line:84% And so, it is briefly an accelerating charge. 00:33:09.150 --> 00:33:15.320 align:middle line:84% And so, it is going to emit photons as it's 00:33:15.320 --> 00:33:16.820 align:middle line:90% deflected from its trajectory. 00:33:16.820 --> 00:33:19.350 align:middle line:90% 00:33:19.350 --> 00:33:23.760 align:middle line:84% Now, this electron isn't then just going to sail off and never 00:33:23.760 --> 00:33:24.610 align:middle line:90% see an ion again. 00:33:24.610 --> 00:33:27.370 align:middle line:84% In fact, it's going to see one very, very soon. 00:33:27.370 --> 00:33:29.310 align:middle line:84% And so, effectively, our entire plasma 00:33:29.310 --> 00:33:31.650 align:middle line:84% is full of electrons which are gently 00:33:31.650 --> 00:33:36.152 align:middle line:84% being deflected and breaking and emitting these photons. 00:33:36.152 --> 00:33:38.360 align:middle line:84% So the main thing we can say in a classical treatment 00:33:38.360 --> 00:33:41.160 align:middle line:84% is that the bremsstrahlung is going to be isotropic. 00:33:41.160 --> 00:33:43.910 align:middle line:84% It's going to be the same in every direction. 00:33:43.910 --> 00:33:46.250 align:middle line:84% That's actually quite different from electron cyclotron 00:33:46.250 --> 00:33:47.960 align:middle line:84% emission, even though we didn't really 00:33:47.960 --> 00:33:52.130 align:middle line:84% look at the anisotropy of that in any detail. 00:33:52.130 --> 00:33:54.860 align:middle line:84% There are lots of different ways to deal with bremsstrahlung 00:33:54.860 --> 00:33:56.960 align:middle line:90% to do the actual calculation. 00:33:56.960 --> 00:34:00.560 align:middle line:84% Remember, we said we wanted to have v and v 00:34:00.560 --> 00:34:04.420 align:middle line:84% dot, that was our first thing, by solving 00:34:04.420 --> 00:34:05.980 align:middle line:90% the equation of motion. 00:34:05.980 --> 00:34:11.380 align:middle line:84% And then we want to integrate over the distribution function f 00:34:11.380 --> 00:34:16.510 align:middle line:84% of v e 3v That would give us the emissivity that is the input 00:34:16.510 --> 00:34:18.380 align:middle line:90% that we're looking for here. 00:34:18.380 --> 00:34:20.380 align:middle line:84% So there's lots of different ways of doing this, 00:34:20.380 --> 00:34:22.449 align:middle line:84% and Hutchinson lists a few of them. 00:34:22.449 --> 00:34:24.270 align:middle line:84% There's a purely classical picture. 00:34:24.270 --> 00:34:27.150 align:middle line:84% That classical picture looks an awful lot 00:34:27.150 --> 00:34:30.420 align:middle line:84% like what I've drawn here with the ions and electrons as point 00:34:30.420 --> 00:34:31.230 align:middle line:90% particles. 00:34:31.230 --> 00:34:33.520 align:middle line:84% There's a semi-classical approach 00:34:33.520 --> 00:34:35.520 align:middle line:84% where you start bringing in some quantum physics 00:34:35.520 --> 00:34:39.150 align:middle line:84% and treat, I think, the electron as a wave. 00:34:39.150 --> 00:34:41.190 align:middle line:84% And then there's a full quantum approach. 00:34:41.190 --> 00:34:43.719 align:middle line:90% 00:34:43.719 --> 00:34:46.630 align:middle line:84% What's remarkable about all of these approaches 00:34:46.630 --> 00:34:50.050 align:middle line:84% is they all give the same answer with just a very slightly 00:34:50.050 --> 00:34:51.350 align:middle line:90% different coefficient. 00:34:51.350 --> 00:34:54.310 align:middle line:84% So we get a small change in coefficient. 00:34:54.310 --> 00:34:58.810 align:middle line:90% 00:34:58.810 --> 00:35:01.000 align:middle line:90% The scalings are the same. 00:35:01.000 --> 00:35:03.600 align:middle line:84% So, in some sense, although it's important to get 00:35:03.600 --> 00:35:07.360 align:middle line:84% the exact coefficient, it doesn't matter exactly 00:35:07.360 --> 00:35:09.043 align:middle line:84% which one of these techniques you use. 00:35:09.043 --> 00:35:11.710 align:middle line:84% And that's why I'm not going to go through any of them in class. 00:35:11.710 --> 00:35:14.870 align:middle line:84% They're also, I think, quite complicated derivations. 00:35:14.870 --> 00:35:19.290 align:middle line:84% So we'll talk about it in a moment, 00:35:19.290 --> 00:35:23.880 align:middle line:84% but this j has some scaling, which is n squared T to the 1/2 00:35:23.880 --> 00:35:29.100 align:middle line:84% E to the minus h nu upon T. And then there's a load of stuff out 00:35:29.100 --> 00:35:30.000 align:middle line:90% the front here. 00:35:30.000 --> 00:35:33.690 align:middle line:84% And these coefficients change from 1 to 2. 00:35:33.690 --> 00:35:35.783 align:middle line:84% So it's not really a big difference. 00:35:35.783 --> 00:35:37.200 align:middle line:84% I mean, it makes a huge difference 00:35:37.200 --> 00:35:38.325 align:middle line:90% if you design your reactor. 00:35:38.325 --> 00:35:40.700 align:middle line:84% Because [? if it's ?] 2, you could be a very long way off 00:35:40.700 --> 00:35:41.340 align:middle line:90% from breakeven. 00:35:41.340 --> 00:35:42.690 align:middle line:84% But, from the point of view of this course, 00:35:42.690 --> 00:35:43.648 align:middle line:90% it makes no difference. 00:35:43.648 --> 00:35:45.780 align:middle line:84% Yeah, I think it's kind of remarkable that it 00:35:45.780 --> 00:35:47.020 align:middle line:90% doesn't make any difference. 00:35:47.020 --> 00:35:49.890 align:middle line:84% So, again, if you want the full treatment, 00:35:49.890 --> 00:35:51.840 align:middle line:90% go have a look in Hutchinson. 00:35:51.840 --> 00:35:54.660 align:middle line:84% And there's also a long treatment 00:35:54.660 --> 00:35:56.140 align:middle line:90% in Jackson of this same problem. 00:35:56.140 --> 00:35:58.778 align:middle line:90% 00:35:58.778 --> 00:36:00.320 align:middle line:84% I'm just going to quote some results. 00:36:00.320 --> 00:36:04.133 align:middle line:90% 00:36:04.133 --> 00:36:05.550 align:middle line:84% I'm going to quote results at you. 00:36:05.550 --> 00:36:07.200 align:middle line:84% I kind of already spoiled it now. 00:36:07.200 --> 00:36:07.740 align:middle line:90% It's here. 00:36:07.740 --> 00:36:11.590 align:middle line:90% 00:36:11.590 --> 00:36:15.252 align:middle line:84% For the Maxwellian average, because, again, 00:36:15.252 --> 00:36:17.210 align:middle line:84% we can have all sorts of different distribution 00:36:17.210 --> 00:36:21.440 align:middle line:84% functions, but our plasma tends towards a Maxwellian. 00:36:21.440 --> 00:36:26.630 align:middle line:84% So a Maxwellian averaged bremsstrahlung emissivity, 00:36:26.630 --> 00:36:32.880 align:middle line:84% this is equation 5.3.40 in Hutchinson. 00:36:32.880 --> 00:36:38.290 align:middle line:84% This looks like 4 pi j nu the emissivity. 00:36:38.290 --> 00:36:40.960 align:middle line:84% I'm just putting 4 pi here because it's isotropic. 00:36:40.960 --> 00:36:43.780 align:middle line:84% So j is normally in terms of per steradian. 00:36:43.780 --> 00:36:46.000 align:middle line:84% But, because it's isotropic, I can just multiply. 00:36:46.000 --> 00:36:47.840 align:middle line:84% I can integrate over the solid angle, 00:36:47.840 --> 00:36:50.080 align:middle line:84% and I'll just get a 4 pi here, and it 00:36:50.080 --> 00:36:51.970 align:middle line:90% won't change the j at all. 00:36:51.970 --> 00:37:05.090 align:middle line:84% This is ne, ni, z squared, T to the minus 1/2 e to minus h nu 00:37:05.090 --> 00:37:10.190 align:middle line:84% upon T. And then, there's a factor called G bar, 00:37:10.190 --> 00:37:12.990 align:middle line:84% the Gaunt factor, which we'll talk about in a moment, 00:37:12.990 --> 00:37:14.930 align:middle line:90% and lots of other constants. 00:37:14.930 --> 00:37:17.830 align:middle line:90% 00:37:17.830 --> 00:37:20.950 align:middle line:84% And these constants are things like e, 00:37:20.950 --> 00:37:24.040 align:middle line:84% the electron charge, and the electron mass, and epsilon 0, 00:37:24.040 --> 00:37:27.040 align:middle line:84% and h bar, and c, all arranged in some way 00:37:27.040 --> 00:37:28.790 align:middle line:90% to make all the dimensions work. 00:37:28.790 --> 00:37:32.730 align:middle line:84% So we're not going to go in too much detail. 00:37:32.730 --> 00:37:44.140 align:middle line:84% This, therefore, has units of watts per hertz per meter cubed. 00:37:44.140 --> 00:37:44.710 align:middle line:90% Yeah. 00:37:44.710 --> 00:37:46.460 align:middle line:90% STUDENT: [INAUDIBLE] 00:37:46.460 --> 00:37:46.960 align:middle line:90% 00:37:46.960 --> 00:37:49.175 align:middle line:84% JACK HARE: Yeah, it should be minus 1/2 of my notes. 00:37:49.175 --> 00:37:49.800 align:middle line:90% That should be. 00:37:49.800 --> 00:37:54.970 align:middle line:90% 00:37:54.970 --> 00:38:04.200 align:middle line:84% So this Gaunt factor here, this is 00:38:04.200 --> 00:38:07.980 align:middle line:84% the bit where you can spend a lot of time 00:38:07.980 --> 00:38:09.690 align:middle line:84% refining your treatment, and you'll 00:38:09.690 --> 00:38:11.790 align:middle line:84% get different values of the Gaunt factor. 00:38:11.790 --> 00:38:13.380 align:middle line:84% And you'll also find this Gaunt factor 00:38:13.380 --> 00:38:17.530 align:middle line:84% varies very weakly with the temperature of the plasma here. 00:38:17.530 --> 00:38:23.120 align:middle line:84% So the Gaunt factor G bar goes from about 0.3 to-- 00:38:23.120 --> 00:38:26.210 align:middle line:90% 00:38:26.210 --> 00:38:29.750 align:middle line:84% in a range where the photon energy compared to the plasma 00:38:29.750 --> 00:38:33.187 align:middle line:90% temperature goes from 0.1 to-- 00:38:33.187 --> 00:38:34.520 align:middle line:90% I'm not writing this very well-- 00:38:34.520 --> 00:38:38.890 align:middle line:90% 00:38:38.890 --> 00:38:41.710 align:middle line:84% where the photon energy compared to the plasma temperature 00:38:41.710 --> 00:38:44.200 align:middle line:90% goes from 0.1 to 10. 00:38:44.200 --> 00:38:46.270 align:middle line:84% So this is a pretty weakly varying function. 00:38:46.270 --> 00:38:49.210 align:middle line:84% We can change it by two orders of magnitude in this parameter 00:38:49.210 --> 00:38:53.120 align:middle line:84% here, but this only changes by one order of magnitude. 00:38:53.120 --> 00:38:56.110 align:middle line:84% And so, in general, it's reasonable to just treat 00:38:56.110 --> 00:38:59.917 align:middle line:84% G as being a constant and then, for this calculations 00:38:59.917 --> 00:39:02.500 align:middle line:84% we're doing, where we're going to drop the absolute intensity, 00:39:02.500 --> 00:39:05.540 align:middle line:84% we can just drop G with all the other constants as well. 00:39:05.540 --> 00:39:09.792 align:middle line:90% So we can drop [INAUDIBLE]. 00:39:09.792 --> 00:39:11.750 align:middle line:84% But if you want to go back and do this properly 00:39:11.750 --> 00:39:13.375 align:middle line:84% for some measurement that you're doing, 00:39:13.375 --> 00:39:15.030 align:middle line:90% then you'd have to include this. 00:39:15.030 --> 00:39:22.970 align:middle line:84% And so, this emissivity, as a function of photon energy, 00:39:22.970 --> 00:39:25.580 align:middle line:84% is a very simple function because it just 00:39:25.580 --> 00:39:28.910 align:middle line:84% decays exponentially with photon energy. 00:39:28.910 --> 00:39:31.090 align:middle line:84% So that is the spectrum coming out 00:39:31.090 --> 00:39:36.250 align:middle line:84% of a plasma that's emitting bremsstrahlung radiation here. 00:39:36.250 --> 00:39:42.390 align:middle line:84% And that is all you need to do Problem Set 3. 00:39:42.390 --> 00:39:43.455 align:middle line:90% Any questions about this? 00:39:43.455 --> 00:40:11.290 align:middle line:90% 00:40:11.290 --> 00:40:11.790 align:middle line:90% Yeah. 00:40:11.790 --> 00:40:13.710 align:middle line:90% STUDENT: [INAUDIBLE] 00:40:13.710 --> 00:40:21.108 align:middle line:90% 00:40:21.108 --> 00:40:23.650 align:middle line:84% JACK HARE: You mean you take the bremsstrahlung into account? 00:40:23.650 --> 00:40:25.300 align:middle line:84% Well, so the thing about bremsstrahlung 00:40:25.300 --> 00:40:27.620 align:middle line:90% is, it's always there. 00:40:27.620 --> 00:40:30.040 align:middle line:84% It is the irreducible minimum amount 00:40:30.040 --> 00:40:32.400 align:middle line:90% of emission from your plasma. 00:40:32.400 --> 00:40:36.207 align:middle line:84% Cyclotron emission is a very specific frequency. 00:40:36.207 --> 00:40:38.040 align:middle line:84% So although, when we were drawing it before, 00:40:38.040 --> 00:40:39.720 align:middle line:90% we drew it over long range. 00:40:39.720 --> 00:40:42.360 align:middle line:84% Inside your plasma, the cyclotron emission 00:40:42.360 --> 00:40:46.410 align:middle line:84% might be just at some very narrow window here. 00:40:46.410 --> 00:40:50.820 align:middle line:84% But this is everywhere inside your plasma at all frequencies, 00:40:50.820 --> 00:40:52.590 align:middle line:84% like a black body kind of spectrum here. 00:40:52.590 --> 00:40:54.173 align:middle line:84% That goes down to very low frequencies 00:40:54.173 --> 00:40:56.512 align:middle line:84% and goes up to very high frequencies. 00:40:56.512 --> 00:40:58.470 align:middle line:84% We're going to talk about lots of other effects 00:40:58.470 --> 00:41:00.660 align:middle line:84% which produce emissivity which is 00:41:00.660 --> 00:41:02.190 align:middle line:90% higher than the bremsstrahlung. 00:41:02.190 --> 00:41:05.280 align:middle line:84% But, often, when we're doing power balance calculations 00:41:05.280 --> 00:41:08.220 align:middle line:84% for a tokamak, we will just use this, 00:41:08.220 --> 00:41:10.620 align:middle line:84% and that represents our most optimistic take. 00:41:10.620 --> 00:41:12.870 align:middle line:84% So, I guess, you always need to worry about this, 00:41:12.870 --> 00:41:14.760 align:middle line:84% even if you managed to clear out all the impurities, 00:41:14.760 --> 00:41:16.218 align:middle line:84% you don't have any lines, you don't 00:41:16.218 --> 00:41:17.820 align:middle line:84% have any electron cyclotron emission, 00:41:17.820 --> 00:41:19.110 align:middle line:84% you don't have any recombination, 00:41:19.110 --> 00:41:19.920 align:middle line:90% which we'll talk about next. 00:41:19.920 --> 00:41:21.480 align:middle line:90% This is still going to be there. 00:41:21.480 --> 00:41:23.838 align:middle line:90% STUDENT: So [INAUDIBLE]? 00:41:23.838 --> 00:41:25.630 align:middle line:84% JACK HARE: It's going to be on top of this. 00:41:25.630 --> 00:41:27.190 align:middle line:84% You're going to have this on top of. 00:41:27.190 --> 00:41:30.680 align:middle line:84% Now, the nice thing is, over a short frequency range, 00:41:30.680 --> 00:41:32.630 align:middle line:90% this does not change very much. 00:41:32.630 --> 00:41:37.750 align:middle line:84% So if I'm doing my ECE and I zoom in on this region here, 00:41:37.750 --> 00:41:43.350 align:middle line:84% I'm going to have i frequency here, 00:41:43.350 --> 00:41:47.310 align:middle line:84% this bremsstrahlung is going to be basically constant. 00:41:47.310 --> 00:41:51.480 align:middle line:84% And, on top of that, I'd have my ECE lines or, in reality, 00:41:51.480 --> 00:41:54.730 align:middle line:84% my black body ECE spectrum or something like that. 00:41:54.730 --> 00:41:57.810 align:middle line:84% But this bremsstrahlung may be quite small. 00:41:57.810 --> 00:41:59.310 align:middle line:84% But even if it's not quite small, 00:41:59.310 --> 00:42:01.950 align:middle line:84% it is constant because it varies only slowly 00:42:01.950 --> 00:42:04.120 align:middle line:90% as a function of a frequency. 00:42:04.120 --> 00:42:06.340 align:middle line:84% So for a small frequency window, it looks constant. 00:42:06.340 --> 00:42:09.380 align:middle line:84% And then you can just subtract off some background intensity 00:42:09.380 --> 00:42:11.880 align:middle line:84% and look at the actual signal you're interested in, like you 00:42:11.880 --> 00:42:12.990 align:middle line:90% see there. 00:42:12.990 --> 00:42:14.140 align:middle line:90% Yeah. 00:42:14.140 --> 00:42:21.980 align:middle line:90% STUDENT: [INAUDIBLE] 00:42:21.980 --> 00:42:23.850 align:middle line:90% JACK HARE: Ooh, ha, yeah. 00:42:23.850 --> 00:42:25.635 align:middle line:90% I mean, it should couple into-- 00:42:25.635 --> 00:42:27.552 align:middle line:84% So I mean, so the important thing to realize 00:42:27.552 --> 00:42:29.010 align:middle line:84% is what mode it couples in actually 00:42:29.010 --> 00:42:32.340 align:middle line:84% depends on where you're looking from in some sense. 00:42:32.340 --> 00:42:34.920 align:middle line:84% So if this is being emitted isotropically, some of it's 00:42:34.920 --> 00:42:36.753 align:middle line:84% going along the magnetic field, some of it's 00:42:36.753 --> 00:42:38.340 align:middle line:84% going perpendicular to magnetic field. 00:42:38.340 --> 00:42:41.130 align:middle line:84% If I'm observing perpendicular to magnetic field, 00:42:41.130 --> 00:42:44.030 align:middle line:84% I must be observing it coming out as O mode or X mode. 00:42:44.030 --> 00:42:45.780 align:middle line:84% I'm observing it along the magnetic field, 00:42:45.780 --> 00:42:48.120 align:middle line:84% I see it coming out as R mode or L mode, right 00:42:48.120 --> 00:42:50.170 align:middle line:84% or left-handed circularly polarized light. 00:42:50.170 --> 00:42:52.290 align:middle line:84% So, actually, in a way, as the observer, 00:42:52.290 --> 00:42:54.360 align:middle line:84% we choose what mode it goes into. 00:42:54.360 --> 00:42:55.950 align:middle line:90% But this emission is isotropic. 00:42:55.950 --> 00:42:58.440 align:middle line:84% So you can imagine you have a blob of plasma that emits. 00:42:58.440 --> 00:43:01.260 align:middle line:84% And then the wave has to ask itself, well, what sort of wave 00:43:01.260 --> 00:43:01.792 align:middle line:90% am I? 00:43:01.792 --> 00:43:03.750 align:middle line:84% At this point, well, if I'm going perpendicular 00:43:03.750 --> 00:43:06.630 align:middle line:84% to the magnetic field, I'm going to be O mode or X mode. 00:43:06.630 --> 00:43:08.550 align:middle line:84% And, in reality, there'll be some emission 00:43:08.550 --> 00:43:10.890 align:middle line:84% in O mode, some emission in X mode. 00:43:10.890 --> 00:43:13.600 align:middle line:84% And the exact coupling between those 00:43:13.600 --> 00:43:15.550 align:middle line:84% will be related to the polarization 00:43:15.550 --> 00:43:16.510 align:middle line:90% of the bremsstrahlung. 00:43:16.510 --> 00:43:18.980 align:middle line:84% And the polarization should be pretty random as well. 00:43:18.980 --> 00:43:20.772 align:middle line:84% So I would guess, without thinking about it 00:43:20.772 --> 00:43:23.330 align:middle line:84% very much, you get roughly equal into both of those. 00:43:23.330 --> 00:43:25.115 align:middle line:84% And if you're then-- if your wave that's 00:43:25.115 --> 00:43:26.740 align:middle line:84% being emitted along the magnetic field, 00:43:26.740 --> 00:43:29.070 align:middle line:84% you'll be roughly equal into the R and the L. 00:43:29.070 --> 00:43:30.820 align:middle line:84% But I haven't thought about that too much. 00:43:30.820 --> 00:43:33.805 align:middle line:84% Yeah, and then there will be differences 00:43:33.805 --> 00:43:35.680 align:middle line:84% in speed of propagation and things like that. 00:43:35.680 --> 00:43:37.510 align:middle line:84% But the bremsstrahlung is being constantly produced, 00:43:37.510 --> 00:43:40.110 align:middle line:84% so you probably won't be able to notice that very [INAUDIBLE]. 00:43:40.110 --> 00:43:42.730 align:middle line:90% Yeah, good question. 00:43:42.730 --> 00:43:43.965 align:middle line:90% Other questions? 00:43:43.965 --> 00:43:46.790 align:middle line:90% 00:43:46.790 --> 00:43:47.290 align:middle line:90% Sorry? 00:43:47.290 --> 00:43:48.660 align:middle line:90% STUDENT: [INAUDIBLE] 00:43:48.660 --> 00:43:51.370 align:middle line:84% JACK HARE: If it's optically thick. 00:43:51.370 --> 00:43:53.420 align:middle line:84% So, yeah, we haven't really talked about that. 00:43:53.420 --> 00:43:56.560 align:middle line:84% So from this j, you can now calculate alpha, 00:43:56.560 --> 00:44:03.840 align:middle line:84% the opacity, because we had j upon alpha 00:44:03.840 --> 00:44:09.680 align:middle line:84% is equal to nu squared upon c squared T. 00:44:09.680 --> 00:44:11.450 align:middle line:90% That was Kirchhoff's law here-- 00:44:11.450 --> 00:44:12.680 align:middle line:90% that's a terrible j. 00:44:12.680 --> 00:44:14.750 align:middle line:90% So I can now calculate alpha. 00:44:14.750 --> 00:44:17.870 align:middle line:84% And might look at this and I might go, ooh, interesting alpha 00:44:17.870 --> 00:44:20.490 align:middle line:84% is actually quite high for low frequencies. 00:44:20.490 --> 00:44:23.240 align:middle line:84% And so, that means for any reasonable distance of plasma 00:44:23.240 --> 00:44:26.180 align:middle line:84% that I'm looking through, that will be absorbed, 00:44:26.180 --> 00:44:27.530 align:middle line:90% and it will become black body. 00:44:27.530 --> 00:44:30.530 align:middle line:84% And so, in reality, for some plasma, 00:44:30.530 --> 00:44:32.150 align:middle line:84% we might have a spectrum that looks 00:44:32.150 --> 00:44:38.480 align:middle line:84% like this, where in this region here tau is greater than 1, 00:44:38.480 --> 00:44:43.217 align:middle line:84% and in this region here, tau is less than 1 or much less than 1. 00:44:43.217 --> 00:44:45.050 align:middle line:84% So it goes back to being optically thin here 00:44:45.050 --> 00:44:46.280 align:middle line:90% for the high energy photons. 00:44:46.280 --> 00:44:49.287 align:middle line:84% But the low energy photons will get absorbed as well. 00:44:49.287 --> 00:44:50.870 align:middle line:84% There's actually another effect, which 00:44:50.870 --> 00:44:53.537 align:middle line:84% is in Hutchinson's book, which I haven't covered here, which is, 00:44:53.537 --> 00:44:56.420 align:middle line:84% of course, there is no mode in a plasma which propagates 00:44:56.420 --> 00:44:59.580 align:middle line:90% below the plasma frequency. 00:44:59.580 --> 00:45:02.120 align:middle line:84% And so, the spectrum will be even further modified 00:45:02.120 --> 00:45:03.800 align:middle line:84% because that wave will be evanescent. 00:45:03.800 --> 00:45:06.505 align:middle line:84% But we're skipping over that this year. 00:45:06.505 --> 00:45:08.130 align:middle line:84% But it's in there if you're interested. 00:45:08.130 --> 00:45:09.512 align:middle line:90% Yeah. 00:45:09.512 --> 00:45:11.528 align:middle line:90% STUDENT: [INAUDIBLE] 00:45:11.528 --> 00:45:13.820 align:middle line:84% JACK HARE: We're not going to look at synchrotron, yes. 00:45:13.820 --> 00:45:14.800 align:middle line:90% STUDENT: [INAUDIBLE] 00:45:14.800 --> 00:45:16.247 align:middle line:90% JACK HARE: I think we had-- 00:45:16.247 --> 00:45:17.330 align:middle line:90% Sean's not here this time. 00:45:17.330 --> 00:45:18.913 align:middle line:84% Sean asked me that a couple of classes 00:45:18.913 --> 00:45:20.070 align:middle line:90% ago, I said I didn't know. 00:45:20.070 --> 00:45:21.240 align:middle line:84% And then he came and told me the next class. 00:45:21.240 --> 00:45:23.570 align:middle line:84% So cyclotron is when the particles are spiraling 00:45:23.570 --> 00:45:24.672 align:middle line:90% around the magnetic field. 00:45:24.672 --> 00:45:26.630 align:middle line:84% Synchrotron is when the particles are following 00:45:26.630 --> 00:45:29.090 align:middle line:90% the magnetic field in a curve. 00:45:29.090 --> 00:45:31.990 align:middle line:84% So there's two types of magnetic field doing acceleration, 00:45:31.990 --> 00:45:34.720 align:middle line:84% but they are distinct ways of producing light. 00:45:34.720 --> 00:45:37.660 align:middle line:84% Yeah, I think someone told me that maybe for a high field 00:45:37.660 --> 00:45:41.620 align:middle line:84% tokamaks synchrotron could start being significant. 00:45:41.620 --> 00:45:45.787 align:middle line:84% But I actually have no idea how big a deal it is. 00:45:45.787 --> 00:45:48.120 align:middle line:84% And I don't know if people are using it as a diagnostic. 00:45:48.120 --> 00:45:49.578 align:middle line:84% I've not heard of someone using it. 00:45:49.578 --> 00:45:52.035 align:middle line:84% But synchrotron light is used as a source of X-rays 00:45:52.035 --> 00:45:53.410 align:middle line:84% for diagnosing many other things. 00:45:53.410 --> 00:45:54.952 align:middle line:84% So it's interesting in its own right. 00:45:54.952 --> 00:45:57.510 align:middle line:84% But I don't know whether people use the synchrotron radiation 00:45:57.510 --> 00:45:59.220 align:middle line:84% from a high field tokamak if we've ever 00:45:59.220 --> 00:46:00.637 align:middle line:84% built one high enough for it to be 00:46:00.637 --> 00:46:03.325 align:middle line:84% a problem as a diagnostic of something. 00:46:03.325 --> 00:46:04.950 align:middle line:84% And I don't want to be a diagnostic of, 00:46:04.950 --> 00:46:06.210 align:middle line:84% because I think it depends mostly 00:46:06.210 --> 00:46:07.800 align:middle line:84% on the magnetic field and the radius. 00:46:07.800 --> 00:46:10.242 align:middle line:84% And those are two things in a tokamak you already know. 00:46:10.242 --> 00:46:11.700 align:middle line:84% So you probably-- but maybe there's 00:46:11.700 --> 00:46:14.340 align:middle line:84% a really clever diagnostic you can do, like fast particles 00:46:14.340 --> 00:46:16.150 align:middle line:90% or something like that. 00:46:16.150 --> 00:46:17.514 align:middle line:90% So worth thinking about. 00:46:17.514 --> 00:46:18.547 align:middle line:90% STUDENT: [INAUDIBLE] 00:46:18.547 --> 00:46:20.880 align:middle line:84% JACK HARE: Right, but I'm not interested in [INAUDIBLE]. 00:46:20.880 --> 00:46:22.368 align:middle line:90% This is a diagnostics course. 00:46:22.368 --> 00:46:26.078 align:middle line:90% [LAUGHS] 00:46:26.078 --> 00:46:29.190 align:middle line:90% 00:46:29.190 --> 00:46:30.735 align:middle line:84% Any questions online while we pause? 00:46:30.735 --> 00:46:35.720 align:middle line:90% 00:46:35.720 --> 00:46:38.750 align:middle line:84% So this is bremsstrahlung radiation, 00:46:38.750 --> 00:46:41.435 align:middle line:84% and often people call this free-free. 00:46:41.435 --> 00:46:44.270 align:middle line:90% 00:46:44.270 --> 00:46:48.140 align:middle line:84% And the idea here with free-free is that your particle starts 00:46:48.140 --> 00:46:53.810 align:middle line:90% off free, and it ends up free. 00:46:53.810 --> 00:46:55.133 align:middle line:90% So it hasn't changed. 00:46:55.133 --> 00:46:57.050 align:middle line:84% This is in contrast to some of the other types 00:46:57.050 --> 00:47:00.050 align:middle line:84% we'll be dealing with, like bound-free, free-bound, 00:47:00.050 --> 00:47:02.210 align:middle line:84% and bound-bound, you get the idea. 00:47:02.210 --> 00:47:05.190 align:middle line:84% Electron cyclotron is, of course, also free-free. 00:47:05.190 --> 00:47:07.910 align:middle line:84% So there are multiple types that people often just 00:47:07.910 --> 00:47:09.890 align:middle line:84% call bremsstrahlung free-free radiation. 00:47:09.890 --> 00:47:12.530 align:middle line:84% Now we're going to do free-bound radiation or recombination 00:47:12.530 --> 00:47:13.250 align:middle line:90% radiation. 00:47:13.250 --> 00:47:50.630 align:middle line:90% 00:47:50.630 --> 00:48:02.454 align:middle line:84% So recombination, otherwise known as free-bound. 00:48:02.454 --> 00:48:12.350 align:middle line:90% 00:48:12.350 --> 00:48:16.070 align:middle line:84% So our particle is going along, our electron, 00:48:16.070 --> 00:48:19.480 align:middle line:90% [? past ?] this ion here. 00:48:19.480 --> 00:48:21.420 align:middle line:84% And this particle is going along. 00:48:21.420 --> 00:48:24.220 align:middle line:84% And it's got some velocity to start with. 00:48:24.220 --> 00:48:30.270 align:middle line:84% And it's emitting, let's say, a single photon of energy h nu, 00:48:30.270 --> 00:48:31.280 align:middle line:90% like that. 00:48:31.280 --> 00:48:35.560 align:middle line:84% That entire acceleration yields one photon, one energy. 00:48:35.560 --> 00:48:37.950 align:middle line:84% And so, initially, we have a kinetic energy, 00:48:37.950 --> 00:48:42.270 align:middle line:90% a 1/2 mv squared. 00:48:42.270 --> 00:48:47.610 align:middle line:84% Then, afterwards, we're going to have an energy 1/2 mv prime 00:48:47.610 --> 00:48:50.830 align:middle line:90% squared minus h nu. 00:48:50.830 --> 00:48:55.760 align:middle line:84% So I have e, that, e prime, that. 00:48:55.760 --> 00:49:00.805 align:middle line:84% This is the energy here, and this is the energy here, 00:49:00.805 --> 00:49:01.951 align:middle line:90% [INAUDIBLE]. 00:49:01.951 --> 00:49:04.160 align:middle line:90% 00:49:04.160 --> 00:49:06.140 align:middle line:90% --b prime. 00:49:06.140 --> 00:49:13.290 align:middle line:84% Now, if h nu is less than the initial kinetic energy here, 00:49:13.290 --> 00:49:16.600 align:middle line:84% then we still have some kinetic energy left. 00:49:16.600 --> 00:49:22.110 align:middle line:84% So v prime is greater than 0, our particle is still free, 00:49:22.110 --> 00:49:23.070 align:middle line:90% and it can continue. 00:49:23.070 --> 00:49:27.180 align:middle line:90% 00:49:27.180 --> 00:49:29.490 align:middle line:84% That's the case we've just considered, bremsstrahlung. 00:49:29.490 --> 00:49:30.990 align:middle line:84% But, of course, there's another case 00:49:30.990 --> 00:49:40.841 align:middle line:84% where this photon takes away so much energy that this starts, 00:49:40.841 --> 00:49:42.093 align:middle line:90% I guess it becomes imaginary. 00:49:42.093 --> 00:49:44.260 align:middle line:84% So it's sort of pointless to continue at this point. 00:49:44.260 --> 00:49:46.600 align:middle line:84% But it's clear that the electron no longer 00:49:46.600 --> 00:49:47.770 align:middle line:90% has any kinetic energy. 00:49:47.770 --> 00:49:50.260 align:middle line:84% And, indeed, it's going to have to pay back any debt it 00:49:50.260 --> 00:49:51.770 align:middle line:90% has in some other way. 00:49:51.770 --> 00:49:53.620 align:middle line:84% And it's going to do that by becoming bound. 00:49:53.620 --> 00:49:56.410 align:middle line:90% 00:49:56.410 --> 00:49:58.350 align:middle line:84% And you can do that because we're 00:49:58.350 --> 00:50:00.810 align:middle line:84% going to switch to a slightly quantum model of the atom 00:50:00.810 --> 00:50:02.730 align:middle line:84% though, to be honest, the Bohr model 00:50:02.730 --> 00:50:05.310 align:middle line:84% works for this as well, where we have 00:50:05.310 --> 00:50:09.360 align:middle line:84% a range of different discrete energy levels 00:50:09.360 --> 00:50:12.360 align:middle line:90% that the electrons can occupy. 00:50:12.360 --> 00:50:16.410 align:middle line:84% So these energy levels are labeled by the principal quantum 00:50:16.410 --> 00:50:17.820 align:middle line:90% number n. 00:50:17.820 --> 00:50:23.520 align:middle line:90% n equals 1, 2, 3, 4, and so on. 00:50:23.520 --> 00:50:29.200 align:middle line:84% And, up here, infinity, this is ionization. 00:50:29.200 --> 00:50:32.620 align:middle line:84% If your electron gets this much energy, it becomes free again. 00:50:32.620 --> 00:50:38.340 align:middle line:84% And the energies of these levels are 00:50:38.340 --> 00:50:46.450 align:middle line:84% given by this unit, Ry, which is the Rydberg z squared 00:50:46.450 --> 00:50:49.600 align:middle line:90% of our ion over n squared. 00:50:49.600 --> 00:50:53.080 align:middle line:84% Just to be clear here, n is this principal quantum number. 00:50:53.080 --> 00:50:54.640 align:middle line:90% It is not the density anymore. 00:50:54.640 --> 00:50:58.240 align:middle line:84% We're dealing still with the single-atom picture, 00:50:58.240 --> 00:51:00.190 align:middle line:90% one electron, one ion. 00:51:00.190 --> 00:51:03.790 align:middle line:90% The ion has a charge z here. 00:51:03.790 --> 00:51:08.070 align:middle line:84% Anyone remind me what a Rydberg is? 00:51:08.070 --> 00:51:09.390 align:middle line:90% What its value is? 00:51:09.390 --> 00:51:18.620 align:middle line:90% 00:51:18.620 --> 00:51:23.354 align:middle line:84% 13.6 electron volts-- good number to know. 00:51:23.354 --> 00:51:30.430 align:middle line:84% So that's the ionization potential of hydrogen. 00:51:30.430 --> 00:51:35.580 align:middle line:84% So that means that when we have an electron coming in, 00:51:35.580 --> 00:51:40.950 align:middle line:84% that's initially up here, if it wants to become a bound 00:51:40.950 --> 00:51:45.015 align:middle line:84% electron, it has to drop down to one of these energy levels. 00:51:45.015 --> 00:51:48.100 align:middle line:90% 00:51:48.100 --> 00:51:50.570 align:middle line:84% And these energy levels only have discrete values. 00:51:50.570 --> 00:51:52.570 align:middle line:84% And so, what we're going to see in our spectrum 00:51:52.570 --> 00:51:57.100 align:middle line:84% is that this is only allowed if the electron energy fulfills 00:51:57.100 --> 00:52:00.820 align:middle line:84% this equation, which involves these discrete energy levels. 00:52:00.820 --> 00:52:03.700 align:middle line:84% And that equation is going to be the photon that is emitted. 00:52:03.700 --> 00:52:05.742 align:middle line:84% And that's the thing that we're going to see with 00:52:05.742 --> 00:52:12.250 align:middle line:84% our spectrometer is going to be equal to 1/2 mv squared plus z 00:52:12.250 --> 00:52:17.570 align:middle line:84% squared upon n squared times the Rydberg. 00:52:17.570 --> 00:52:23.200 align:middle line:84% We're going to get out different photons. 00:52:23.200 --> 00:52:25.970 align:middle line:84% Now, of course, these are not going 00:52:25.970 --> 00:52:28.670 align:middle line:84% to be at completely discrete lines 00:52:28.670 --> 00:52:30.990 align:middle line:84% because it's going to be broadened by our distribution 00:52:30.990 --> 00:52:31.490 align:middle line:90% function. 00:52:31.490 --> 00:52:33.948 align:middle line:84% There's a range of different electron velocities available. 00:52:33.948 --> 00:52:38.150 align:middle line:84% So each of these photons has some sort of variance around it. 00:52:38.150 --> 00:52:41.240 align:middle line:84% It's going to be some value, which is strictly greater 00:52:41.240 --> 00:52:43.565 align:middle line:90% than the Rydberg energy. 00:52:43.565 --> 00:52:47.458 align:middle line:90% 00:52:47.458 --> 00:52:48.625 align:middle line:90% So what does this look like? 00:52:48.625 --> 00:52:54.280 align:middle line:90% 00:52:54.280 --> 00:52:57.720 align:middle line:84% If we integrate over a Maxwellian-- 00:52:57.720 --> 00:52:59.640 align:middle line:84% so, again, this is Maxwellian averaged-- 00:52:59.640 --> 00:53:07.480 align:middle line:90% 00:53:07.480 --> 00:53:10.160 align:middle line:90% we get out two terms here. 00:53:10.160 --> 00:53:14.095 align:middle line:84% So we have-- do I want to say two terms? 00:53:14.095 --> 00:53:16.680 align:middle line:90% 00:53:16.680 --> 00:53:19.200 align:middle line:84% Well, I'm going to write it as the emissivity 00:53:19.200 --> 00:53:25.928 align:middle line:84% per principal quantum number n, so the emissivity per each 00:53:25.928 --> 00:53:26.970 align:middle line:90% of these discrete levels. 00:53:26.970 --> 00:53:28.637 align:middle line:84% And then we can sum them all up in order 00:53:28.637 --> 00:53:29.770 align:middle line:90% to get the total spectrum. 00:53:29.770 --> 00:53:33.300 align:middle line:84% So that just has our familiar bremsstrahlung type 00:53:33.300 --> 00:53:37.350 align:middle line:84% coefficients, electron density times the ion density times z 00:53:37.350 --> 00:53:46.260 align:middle line:84% squared e to the 1/2, e to the minus h nu upon T times 00:53:46.260 --> 00:53:48.890 align:middle line:90% a constant. 00:53:48.890 --> 00:53:53.210 align:middle line:84% But now we have an additional term, which is a new Gaunt 00:53:53.210 --> 00:53:54.752 align:middle line:90% factor for level n. 00:53:54.752 --> 00:53:56.960 align:middle line:84% But, don't worry, these Gaunt factors are all about 1 00:53:56.960 --> 00:53:58.835 align:middle line:84% again, so it doesn't really matter that much. 00:53:58.835 --> 00:54:07.020 align:middle line:84% And then we have a term z squared upon T Rydberg energy 2 00:54:07.020 --> 00:54:09.220 align:middle line:90% upon n cubed. 00:54:09.220 --> 00:54:12.960 align:middle line:84% So the strength of this emission drops very fast with n. 00:54:12.960 --> 00:54:14.730 align:middle line:84% So it's going to be strongest for n equals 00:54:14.730 --> 00:54:19.680 align:middle line:84% 1 and less strong for the higher principal quantum numbers here. 00:54:19.680 --> 00:54:24.780 align:middle line:84% And then, there's going to be a factor of exponential z squared 00:54:24.780 --> 00:54:34.327 align:middle line:84% upon n squared Rydberg energy upon T, like that. 00:54:34.327 --> 00:54:36.910 align:middle line:84% If you're wondering where the energies are canceling out here, 00:54:36.910 --> 00:54:38.620 align:middle line:84% the Rydberg is in electron volts, 00:54:38.620 --> 00:54:40.700 align:middle line:84% and we're putting T in energy units. 00:54:40.700 --> 00:54:42.560 align:middle line:84% So that can be in electron volts as well. 00:54:42.560 --> 00:54:44.493 align:middle line:84% These will cancel out quite nicely here. 00:54:44.493 --> 00:54:45.910 align:middle line:84% So you end up something that looks 00:54:45.910 --> 00:54:47.680 align:middle line:84% a lot like the bremsstrahlung but 00:54:47.680 --> 00:54:50.800 align:middle line:84% with an additional emissivity for each of these principal 00:54:50.800 --> 00:54:51.760 align:middle line:90% quantum numbers. 00:54:51.760 --> 00:54:55.000 align:middle line:84% And then, to get the total j, you 00:54:55.000 --> 00:55:04.750 align:middle line:84% have j brems plus the sum over n of jn here. 00:55:04.750 --> 00:55:06.280 align:middle line:84% And the spectrum, therefore, looks 00:55:06.280 --> 00:55:15.680 align:middle line:84% like we had something like this for bremsstrahlung before, 00:55:15.680 --> 00:55:23.290 align:middle line:84% and now we have a spectrum that contains a series of edges, 00:55:23.290 --> 00:55:24.280 align:middle line:90% like this. 00:55:24.280 --> 00:55:25.790 align:middle line:90% And this lowest edge here-- 00:55:25.790 --> 00:55:27.415 align:middle line:84% I should draw this as a straight line-- 00:55:27.415 --> 00:55:30.820 align:middle line:90% 00:55:30.820 --> 00:55:36.100 align:middle line:84% this is n equals 1, 2, 3, 4, and all the way 00:55:36.100 --> 00:55:46.670 align:middle line:84% back up here, where, again, this is our brems result, 00:55:46.670 --> 00:55:49.100 align:middle line:90% and this is our recombination. 00:55:49.100 --> 00:55:57.798 align:middle line:90% 00:55:57.798 --> 00:55:58.590 align:middle line:90% STUDENT: Professor? 00:55:58.590 --> 00:55:59.910 align:middle line:90% JACK HARE: Yeah. 00:55:59.910 --> 00:56:02.910 align:middle line:84% STUDENT: So if the photons released 00:56:02.910 --> 00:56:05.400 align:middle line:84% are greater than the kinetic energy, 00:56:05.400 --> 00:56:11.670 align:middle line:84% but it's not equivalent to one of the discrete energy 00:56:11.670 --> 00:56:14.560 align:middle line:90% levels, what happens then? 00:56:14.560 --> 00:56:16.180 align:middle line:90% Does it just not get bound? 00:56:16.180 --> 00:56:20.690 align:middle line:90% 00:56:20.690 --> 00:56:23.050 align:middle line:84% JACK HARE: Sorry, could you rephrase that? 00:56:23.050 --> 00:56:25.210 align:middle line:84% STUDENT: Yeah, so earlier you mentioned 00:56:25.210 --> 00:56:28.930 align:middle line:84% that it needed to be equivalent to one of the discrete energy 00:56:28.930 --> 00:56:30.280 align:middle line:90% levels. 00:56:30.280 --> 00:56:32.860 align:middle line:84% JACK HARE: It has to fulfill this equation here, 00:56:32.860 --> 00:56:34.870 align:middle line:84% where the photon that's emitted is 00:56:34.870 --> 00:56:37.520 align:middle line:84% going to have an energy equal to the initial kinetic energy 00:56:37.520 --> 00:56:41.098 align:middle line:84% and plus the energy that the photon gains 00:56:41.098 --> 00:56:43.390 align:middle line:84% by virtue of the electron occupying one of these energy 00:56:43.390 --> 00:56:44.120 align:middle line:90% levels. 00:56:44.120 --> 00:56:47.600 align:middle line:84% So if you're asking, what happens if you can't fulfill 00:56:47.600 --> 00:56:49.040 align:middle line:90% that, it just doesn't happen. 00:56:49.040 --> 00:56:51.578 align:middle line:84% Quantum mechanically, that would be a forbidden transition. 00:56:51.578 --> 00:56:52.370 align:middle line:90% STUDENT: Oh, I see. 00:56:52.370 --> 00:56:54.260 align:middle line:90% So it either becomes-- 00:56:54.260 --> 00:56:57.570 align:middle line:84% it either doesn't recombine if it doesn't have that 00:56:57.570 --> 00:56:59.220 align:middle line:84% and it's still free, and then that's 00:56:59.220 --> 00:57:00.720 align:middle line:84% just bremsstrahlung radiation, or it 00:57:00.720 --> 00:57:03.190 align:middle line:84% does recombine at these certain locations? 00:57:03.190 --> 00:57:05.190 align:middle line:84% JACK HARE: Yeah, so you could imagine that you-- 00:57:05.190 --> 00:57:13.110 align:middle line:90% 00:57:13.110 --> 00:57:15.720 align:middle line:84% I feel like for every electron there 00:57:15.720 --> 00:57:20.190 align:middle line:84% should be, at some velocity v, there should be some wavelength 00:57:20.190 --> 00:57:21.120 align:middle line:90% that it can emit at. 00:57:21.120 --> 00:57:27.580 align:middle line:90% 00:57:27.580 --> 00:57:29.900 align:middle line:84% I mean, this is a spectrum of solutions, 00:57:29.900 --> 00:57:33.130 align:middle line:84% it's not a discrete number of solutions. 00:57:33.130 --> 00:57:37.270 align:middle line:84% If I put in some velocity v and I occupy some principle quantum 00:57:37.270 --> 00:57:40.240 align:middle line:84% number n, then I will get out a photon here. 00:57:40.240 --> 00:57:44.210 align:middle line:84% There's no forbidden solution to this. 00:57:44.210 --> 00:57:46.820 align:middle line:84% I think what's being reflected here with these sharp edges is, 00:57:46.820 --> 00:57:50.990 align:middle line:84% these correspond the sharp edge here, corresponds to v equals 0, 00:57:50.990 --> 00:57:54.140 align:middle line:84% and this corresponds to v greater than 0. 00:57:54.140 --> 00:57:56.540 align:middle line:84% And if you get up to a point where your energy is 00:57:56.540 --> 00:57:59.345 align:middle line:84% so high that you can then access the next level, 00:57:59.345 --> 00:58:01.970 align:middle line:84% then that becomes very favorable and, in fact, there are some-- 00:58:01.970 --> 00:58:06.512 align:middle line:84% these ones down here, it might continue from the 2 level 00:58:06.512 --> 00:58:08.470 align:middle line:84% or it might start occupying this level instead. 00:58:08.470 --> 00:58:11.350 align:middle line:90% 00:58:11.350 --> 00:58:12.860 align:middle line:84% STUDENT: Yeah, I think I understand. 00:58:12.860 --> 00:58:15.152 align:middle line:84% So I was just wondering, because it's not the condition 00:58:15.152 --> 00:58:21.070 align:middle line:84% that there are photons that are released with greater than 12 mv 00:58:21.070 --> 00:58:22.600 align:middle line:90% squared the kinetic energy. 00:58:22.600 --> 00:58:26.620 align:middle line:84% It has to be either it's not released with greater than, 00:58:26.620 --> 00:58:27.430 align:middle line:90% and it's not-- 00:58:27.430 --> 00:58:29.763 align:middle line:84% JACK HARE: So see, it's the photon energy that's-- yeah, 00:58:29.763 --> 00:58:31.750 align:middle line:84% maybe we're doing this backwards in some sense. 00:58:31.750 --> 00:58:32.375 align:middle line:90% STUDENT: I see. 00:58:32.375 --> 00:58:34.720 align:middle line:84% JACK HARE: So if you see a photon energy 00:58:34.720 --> 00:58:37.720 align:middle line:84% with less than the kinetic energy of an electron, 00:58:37.720 --> 00:58:39.850 align:middle line:84% then that photon will have been emitted 00:58:39.850 --> 00:58:42.020 align:middle line:84% and the electron will remain free. 00:58:42.020 --> 00:58:43.630 align:middle line:84% You see a photon energy, how you would 00:58:43.630 --> 00:58:46.150 align:middle line:84% know what the velocity of your electron is, I don't know. 00:58:46.150 --> 00:58:48.075 align:middle line:84% But if you're in this single particle picture, 00:58:48.075 --> 00:58:50.200 align:middle line:84% if you had all the information, if you see a photon 00:58:50.200 --> 00:58:52.240 align:middle line:84% that's released with less than 1/2 mv squared, 00:58:52.240 --> 00:58:56.090 align:middle line:84% then the electron still has some residual kinetic energy left. 00:58:56.090 --> 00:58:57.582 align:middle line:84% And so, therefore, it must be free. 00:58:57.582 --> 00:59:00.040 align:middle line:84% But if you see a photon being emitted with more than 1/2 mv 00:59:00.040 --> 00:59:02.902 align:middle line:84% squared, then the electron has over-emitted. 00:59:02.902 --> 00:59:04.360 align:middle line:84% And the only way it could have done 00:59:04.360 --> 00:59:06.940 align:middle line:84% that is if it fell down into one of these principles. 00:59:06.940 --> 00:59:07.060 align:middle line:90% STUDENT: Oh, I see. 00:59:07.060 --> 00:59:08.110 align:middle line:90% OK, we just did it in reverse. 00:59:08.110 --> 00:59:08.620 align:middle line:90% I understand. 00:59:08.620 --> 00:59:10.600 align:middle line:84% JACK HARE: Yeah, I think maybe I motivated this the wrong way 00:59:10.600 --> 00:59:11.100 align:middle line:90% around. 00:59:11.100 --> 00:59:12.983 align:middle line:90% Yeah. 00:59:12.983 --> 00:59:13.650 align:middle line:90% Other questions? 00:59:13.650 --> 00:59:14.150 align:middle line:90% Yeah. 00:59:14.150 --> 00:59:15.724 align:middle line:90% STUDENT: [INAUDIBLE] 00:59:15.724 --> 00:59:24.000 align:middle line:90% 00:59:24.000 --> 00:59:25.000 align:middle line:90% JACK HARE: Yes, exactly. 00:59:25.000 --> 00:59:26.710 align:middle line:84% So this long tail here is due to the fact 00:59:26.710 --> 00:59:28.900 align:middle line:84% that we have electrons not just with v 00:59:28.900 --> 00:59:32.880 align:middle line:84% equal 0 but much more than that, yeah. 00:59:32.880 --> 00:59:34.572 align:middle line:90% STUDENT: [INAUDIBLE] 00:59:34.572 --> 00:59:36.982 align:middle line:90% 00:59:36.982 --> 00:59:39.530 align:middle line:84% JACK HARE: Hmm, it's a good question. 00:59:39.530 --> 00:59:43.960 align:middle line:90% 00:59:43.960 --> 00:59:46.180 align:middle line:84% Now, are they actually sharp or is it 00:59:46.180 --> 00:59:53.210 align:middle line:84% that we want f of distribution of v squared, 00:59:53.210 --> 00:59:59.370 align:middle line:84% the distribution of v squared, like that? 00:59:59.370 --> 01:00:03.510 align:middle line:84% So perhaps these are actually like this. 01:00:03.510 --> 01:00:05.040 align:middle line:84% I have to admit, in the book, it's 01:00:05.040 --> 01:00:06.207 align:middle line:90% drawn with very sharp lines. 01:00:06.207 --> 01:00:07.950 align:middle line:84% But maybe my eyesight is failing me 01:00:07.950 --> 01:00:09.435 align:middle line:90% and I should look more closely. 01:00:09.435 --> 01:00:10.560 align:middle line:90% I'll have a look into that. 01:00:10.560 --> 01:00:11.143 align:middle line:90% Good question. 01:00:11.143 --> 01:00:14.957 align:middle line:90% 01:00:14.957 --> 01:00:15.790 align:middle line:90% Any other questions? 01:00:15.790 --> 01:00:16.290 align:middle line:90% Yeah. 01:00:16.290 --> 01:00:17.709 align:middle line:90% STUDENT: So [INAUDIBLE]. 01:00:17.709 --> 01:00:22.499 align:middle line:90% 01:00:22.499 --> 01:00:25.060 align:middle line:84% JACK HARE: [LAUGHS] It's quantum, it's worse than that. 01:00:25.060 --> 01:00:25.560 align:middle line:90% [LAUGHTER] 01:00:25.560 --> 01:00:26.910 align:middle line:90% STUDENT: [INAUDIBLE] 01:00:26.910 --> 01:00:28.710 align:middle line:84% JACK HARE: Right, there was a probability 01:00:28.710 --> 01:00:30.690 align:middle line:84% that this process happens, and that is related 01:00:30.690 --> 01:00:33.750 align:middle line:84% to the overlap in the wave function between the wave 01:00:33.750 --> 01:00:36.040 align:middle line:84% function and the free electron, like a plane wave, 01:00:36.040 --> 01:00:38.130 align:middle line:84% and the wave function of a bound electron there. 01:00:38.130 --> 01:00:39.630 align:middle line:84% So the probability of that happening 01:00:39.630 --> 01:00:41.820 align:middle line:84% is related to the overlap integral between those 01:00:41.820 --> 01:00:44.630 align:middle line:84% with a dipole operator, the dipole operator being 01:00:44.630 --> 01:00:46.630 align:middle line:84% the thing that emits the photon in between them. 01:00:46.630 --> 01:00:55.470 align:middle line:84% So you could write it as Psi prime dipole operator, 01:00:55.470 --> 01:00:55.970 align:middle line:90% like that. 01:00:55.970 --> 01:00:57.928 align:middle line:84% That's the probability of this thing occurring. 01:00:57.928 --> 01:00:58.460 align:middle line:90% Yeah, but-- 01:00:58.460 --> 01:01:00.340 align:middle line:90% STUDENT: [INAUDIBLE] 01:01:00.340 --> 01:01:02.993 align:middle line:90% 01:01:02.993 --> 01:01:05.160 align:middle line:84% JACK HARE: I mean, this is where, again, our quantum 01:01:05.160 --> 01:01:07.260 align:middle line:84% picture and our classical picture are irreconcilable, 01:01:07.260 --> 01:01:08.843 align:middle line:84% because if we're treating the electron 01:01:08.843 --> 01:01:11.080 align:middle line:84% as a plane wave delocalized over the entire volume. 01:01:11.080 --> 01:01:13.305 align:middle line:84% So, yeah, this is-- you can't really-- 01:01:13.305 --> 01:01:15.780 align:middle line:84% [LAUGHS] even in a single particle picture, 01:01:15.780 --> 01:01:18.820 align:middle line:84% this drawing is not reconcilable with quantum [? theory. ?] 01:01:18.820 --> 01:01:20.574 align:middle line:90% So, yeah. 01:01:20.574 --> 01:01:22.914 align:middle line:90% STUDENT: [INAUDIBLE] 01:01:22.914 --> 01:01:25.260 align:middle line:90% 01:01:25.260 --> 01:01:29.050 align:middle line:84% JACK HARE: Yeah, it depends on the ion charge. 01:01:29.050 --> 01:01:32.220 align:middle line:84% So if you've got some helium with 2 times ionized helium, 01:01:32.220 --> 01:01:33.840 align:middle line:84% and you've got some hydrogen, then it 01:01:33.840 --> 01:01:36.353 align:middle line:84% will have different recombination lines here. 01:01:36.353 --> 01:01:38.520 align:middle line:84% And that's because, fundamentally, the energy levels 01:01:38.520 --> 01:01:40.740 align:middle line:84% are in different places inside here. 01:01:40.740 --> 01:01:43.780 align:middle line:84% And the energy levels shift by the ion charge here. 01:01:43.780 --> 01:01:44.280 align:middle line:90% Yeah. 01:01:44.280 --> 01:01:49.520 align:middle line:90% 01:01:49.520 --> 01:01:51.580 align:middle line:90% Any other questions? 01:01:51.580 --> 01:01:54.500 align:middle line:84% We'll go into some ways of actually making some use out 01:01:54.500 --> 01:01:55.750 align:middle line:90% of all this stuff in a moment. 01:01:55.750 --> 01:01:59.970 align:middle line:90% 01:01:59.970 --> 01:02:00.470 align:middle line:90% Yeah. 01:02:00.470 --> 01:02:03.420 align:middle line:90% 01:02:03.420 --> 01:02:07.990 align:middle line:84% STUDENT: So an electron gets bound by an ion, 01:02:07.990 --> 01:02:12.640 align:middle line:84% then, presumably, at a later time, [INAUDIBLE] that 01:02:12.640 --> 01:02:14.265 align:middle line:90% absorbs some [INAUDIBLE]. 01:02:14.265 --> 01:02:14.890 align:middle line:90% JACK HARE: Ooh. 01:02:14.890 --> 01:02:18.308 align:middle line:84% STUDENT: Wouldn't this balance out, electricity 01:02:18.308 --> 01:02:19.350 align:middle line:90% going in and out of ions? 01:02:19.350 --> 01:02:21.832 align:middle line:90% 01:02:21.832 --> 01:02:23.040 align:middle line:90% JACK HARE: We'll get to that. 01:02:23.040 --> 01:02:24.248 align:middle line:90% There's a very good question. 01:02:24.248 --> 01:02:27.030 align:middle line:84% We're going to get to that and the idea of detailed balance 01:02:27.030 --> 01:02:29.550 align:middle line:84% and thermodynamic equilibrium and things of that ilk. 01:02:29.550 --> 01:02:31.290 align:middle line:84% Yeah, I'm not going to skip ahead. 01:02:31.290 --> 01:02:32.820 align:middle line:84% But, yeah, we have a section where 01:02:32.820 --> 01:02:34.680 align:middle line:84% we talk about all these inverse processes. 01:02:34.680 --> 01:02:38.730 align:middle line:84% But these are the two simplest ones, free-free and free-bound, 01:02:38.730 --> 01:02:41.280 align:middle line:84% that I wanted to discuss before we did some diagnostics. 01:02:41.280 --> 01:02:43.447 align:middle line:84% But, yeah, you're right, there are inverse processes 01:02:43.447 --> 01:02:46.380 align:middle line:84% for all of these that will affect the spectra that you get. 01:02:46.380 --> 01:02:49.670 align:middle line:90% 01:02:49.670 --> 01:02:51.050 align:middle line:90% Any other questions? 01:02:51.050 --> 01:02:51.815 align:middle line:90% Let's keep going. 01:02:51.815 --> 01:02:57.750 align:middle line:90% 01:02:57.750 --> 01:03:04.800 align:middle line:84% So one use of this is a diagnostic called bolometry. 01:03:04.800 --> 01:03:08.540 align:middle line:84% In fact, bolometry is, in some sense, a very simple diagnostic. 01:03:08.540 --> 01:03:12.770 align:middle line:84% It cares not at all about the detailed spectrum 01:03:12.770 --> 01:03:14.780 align:middle line:90% of what the emission is. 01:03:14.780 --> 01:03:18.680 align:middle line:84% It just wants to know how much power is being radiated 01:03:18.680 --> 01:03:22.000 align:middle line:90% by the plasma, so bolometry. 01:03:22.000 --> 01:03:27.830 align:middle line:90% 01:03:27.830 --> 01:03:31.730 align:middle line:84% And to motivate this, let's go back to our 0D power balance 01:03:31.730 --> 01:03:35.750 align:middle line:84% from a fusion plasma, where we have alpha heating, 01:03:35.750 --> 01:03:40.130 align:middle line:84% we have some external heating, and in steady state this is 01:03:40.130 --> 01:03:45.607 align:middle line:84% balanced by conduction losses and what we, at the time, 01:03:45.607 --> 01:03:47.190 align:middle line:84% we assumed were bremsstrahlung losses, 01:03:47.190 --> 01:03:50.840 align:middle line:84% but in general could be any sort of radiative losses here. 01:03:50.840 --> 01:03:53.790 align:middle line:84% So I'll write this as S rad here. 01:03:53.790 --> 01:03:58.910 align:middle line:84% And so, bolometry is focused on measuring the total power that's 01:03:58.910 --> 01:04:00.030 align:middle line:90% being emitted. 01:04:00.030 --> 01:04:10.450 align:middle line:84% And so, that is going to be the integral d nu of j of nu. 01:04:10.450 --> 01:04:16.080 align:middle line:84% So we take our beautiful spectrum like this, 01:04:16.080 --> 01:04:17.580 align:middle line:84% and we integrate over all of this. 01:04:17.580 --> 01:04:19.320 align:middle line:90% We lose all of this detail. 01:04:19.320 --> 01:04:21.180 align:middle line:84% But, of course, the detail matters 01:04:21.180 --> 01:04:22.890 align:middle line:84% when we're doing the integral because you 01:04:22.890 --> 01:04:25.230 align:middle line:84% can see the recombination increases 01:04:25.230 --> 01:04:28.970 align:middle line:84% the amount of emission above that baseline bremsstrahlung 01:04:28.970 --> 01:04:29.470 align:middle line:90% value. 01:04:29.470 --> 01:04:31.873 align:middle line:84% So there'll be more emission here. 01:04:31.873 --> 01:04:33.290 align:middle line:84% And the reason, of course, we want 01:04:33.290 --> 01:04:36.440 align:middle line:84% to measure this is we want to know how much power our plasma 01:04:36.440 --> 01:04:38.630 align:middle line:90% is losing by radiation. 01:04:38.630 --> 01:04:41.240 align:middle line:84% That's a quantity that, in general, we want to minimize. 01:04:41.240 --> 01:04:44.072 align:middle line:84% Maybe we want to know where it's losing that power. 01:04:44.072 --> 01:04:46.280 align:middle line:84% And so, we can say, OK, well, that part of the plasma 01:04:46.280 --> 01:04:47.820 align:middle line:90% is clearly radiating too much. 01:04:47.820 --> 01:04:49.110 align:middle line:90% What can we do about it? 01:04:49.110 --> 01:04:51.330 align:middle line:84% So this is what bolometry is trying to measure. 01:04:51.330 --> 01:04:54.080 align:middle line:84% And a really simple way to do bolometry 01:04:54.080 --> 01:05:00.090 align:middle line:84% is we have some radiation coming out of the plasma. 01:05:00.090 --> 01:05:04.470 align:middle line:84% We'll call it P rad here because it's 01:05:04.470 --> 01:05:09.120 align:middle line:84% an integral over S rad over the distance of the plasma 01:05:09.120 --> 01:05:09.840 align:middle line:90% here, whatever. 01:05:09.840 --> 01:05:11.730 align:middle line:84% It's going to have different units. 01:05:11.730 --> 01:05:14.910 align:middle line:84% And we have a little sensor sitting 01:05:14.910 --> 01:05:16.560 align:middle line:84% at the wall of our vacuum vessel. 01:05:16.560 --> 01:05:21.140 align:middle line:84% And that sensor is just a resistor. 01:05:21.140 --> 01:05:25.790 align:middle line:84% And we'll call this resistor M. It has a resistance M. 01:05:25.790 --> 01:05:31.940 align:middle line:84% And that resistance M is a function of temperature here. 01:05:31.940 --> 01:05:41.410 align:middle line:84% And we apply some voltage, V0, over this resistor. 01:05:41.410 --> 01:05:46.340 align:middle line:84% And we also put another resistor that is shielded from the plasma 01:05:46.340 --> 01:05:55.240 align:middle line:84% that we call R, and we measured the voltage over this resistor 01:05:55.240 --> 01:05:57.070 align:middle line:84% R. Effectively, what we're trying to do 01:05:57.070 --> 01:06:02.080 align:middle line:84% is measure this volt-- this resistance M of T. 01:06:02.080 --> 01:06:05.950 align:middle line:84% We'll choose R to be less than or roughly equal 01:06:05.950 --> 01:06:08.500 align:middle line:84% to M so it doesn't dominate this measurement. 01:06:08.500 --> 01:06:12.660 align:middle line:84% And the voltage that we measure, VR, 01:06:12.660 --> 01:06:16.560 align:middle line:84% is equal to whatever voltage we used across all 01:06:16.560 --> 01:06:25.740 align:middle line:90% of this system R divided by M. 01:06:25.740 --> 01:06:30.180 align:middle line:84% So by measuring this voltage VR, by knowing the voltage V0, 01:06:30.180 --> 01:06:33.240 align:middle line:84% by knowing the reference resistor R, 01:06:33.240 --> 01:06:36.780 align:middle line:84% we can measure the voltage M. This is a very simple resistive 01:06:36.780 --> 01:06:39.100 align:middle line:84% divider just drawn in a complicated way. 01:06:39.100 --> 01:06:40.770 align:middle line:84% And the reason why this is interesting 01:06:40.770 --> 01:06:46.740 align:middle line:84% is that, in general, M is going to change with T. 01:06:46.740 --> 01:06:49.050 align:middle line:84% We're going to have some resistivity 01:06:49.050 --> 01:06:51.130 align:middle line:90% as a function of temperature. 01:06:51.130 --> 01:06:54.780 align:middle line:84% And so, as this resistor heats up from absorbing the radiation, 01:06:54.780 --> 01:06:56.470 align:middle line:84% its resistance is going to change. 01:06:56.470 --> 01:07:00.060 align:middle line:90% And so, we can have-- 01:07:00.060 --> 01:07:00.660 align:middle line:90% yeah. 01:07:00.660 --> 01:07:02.604 align:middle line:90% STUDENT: [INAUDIBLE] 01:07:02.604 --> 01:07:05.040 align:middle line:90% 01:07:05.040 --> 01:07:07.405 align:middle line:90% JACK HARE: Have I broken this? 01:07:07.405 --> 01:07:07.905 align:middle line:90% Yeah. 01:07:07.905 --> 01:07:10.910 align:middle line:90% 01:07:10.910 --> 01:07:11.570 align:middle line:90% Thank you. 01:07:11.570 --> 01:07:17.970 align:middle line:90% 01:07:17.970 --> 01:07:20.405 align:middle line:84% It was right in my notes and I decided to innovate-- 01:07:20.405 --> 01:07:22.320 align:middle line:90% it's a terrible mistake. 01:07:22.320 --> 01:07:23.130 align:middle line:90% Never do that. 01:07:23.130 --> 01:07:23.940 align:middle line:90% Thank you. 01:07:23.940 --> 01:07:26.290 align:middle line:90% Right, that looks better. 01:07:26.290 --> 01:07:26.790 align:middle line:90% Good. 01:07:26.790 --> 01:07:27.960 align:middle line:90% So it's a voltage divider. 01:07:27.960 --> 01:07:30.690 align:middle line:84% We're dividing V0 between M and R. 01:07:30.690 --> 01:07:34.300 align:middle line:84% And we're measuring the voltage across R, which then, of course, 01:07:34.300 --> 01:07:36.990 align:middle line:84% tells us the voltage across M, which then tells us 01:07:36.990 --> 01:07:39.570 align:middle line:90% what resistance M has here. 01:07:39.570 --> 01:07:42.810 align:middle line:84% So if we're measuring the resistance M, 01:07:42.810 --> 01:07:46.950 align:middle line:84% we can then use some table of rho of T 01:07:46.950 --> 01:07:48.610 align:middle line:90% to get out the temperature. 01:07:48.610 --> 01:07:51.000 align:middle line:84% And, from that temperature, we can 01:07:51.000 --> 01:07:54.960 align:middle line:84% make an estimate of the radiation power incident 01:07:54.960 --> 01:07:55.470 align:middle line:90% upon it. 01:07:55.470 --> 01:07:57.220 align:middle line:84% And we'll talk a little bit more about how 01:07:57.220 --> 01:07:59.490 align:middle line:90% to do that in the next step. 01:07:59.490 --> 01:08:02.560 align:middle line:84% But this, effectively, serves as a very, very simple system. 01:08:02.560 --> 01:08:04.980 align:middle line:84% And you can be digitizing this as a function of time. 01:08:04.980 --> 01:08:08.620 align:middle line:90% 01:08:08.620 --> 01:08:13.750 align:middle line:84% And so, this is also a function of time and temperature. 01:08:13.750 --> 01:08:19.120 align:middle line:84% And so, we could get out some graph of our fusion reactor's 01:08:19.120 --> 01:08:22.689 align:middle line:84% radiation power as a function of time like this 01:08:22.689 --> 01:08:24.503 align:middle line:84% just by looking at the resistance. 01:08:24.503 --> 01:08:33.377 align:middle line:90% 01:08:33.377 --> 01:08:36.870 align:middle line:84% Do I want to introduce this equation yet? 01:08:36.870 --> 01:08:39.819 align:middle line:84% OK, I'm going to do this, but I might regret it. 01:08:39.819 --> 01:08:42.450 align:middle line:84% So the way that you link these back to each other 01:08:42.450 --> 01:08:49.432 align:middle line:84% is you say, for some radiation power incident on my resistor-- 01:08:49.432 --> 01:08:52.569 align:middle line:84% and I'll make it explicitly a function of time-- 01:08:52.569 --> 01:09:00.330 align:middle line:84% that's going to cause some change in temperature with time. 01:09:00.330 --> 01:09:02.880 align:middle line:84% And all of this is time some heat capacity. 01:09:02.880 --> 01:09:16.200 align:middle line:90% 01:09:16.200 --> 01:09:21.279 align:middle line:84% And, in general, this resistor is going to be connected. 01:09:21.279 --> 01:09:23.790 align:middle line:84% It has its own heat capacity c, but it's also 01:09:23.790 --> 01:09:30.307 align:middle line:84% going to be connected to some heat sink, which is unavoidable. 01:09:30.307 --> 01:09:32.140 align:middle line:84% Even if you don't connect it to a heat sink, 01:09:32.140 --> 01:09:34.390 align:middle line:84% it'll be connected to a heat sink through these wires. 01:09:34.390 --> 01:09:39.069 align:middle line:84% And that heat sink will have some thermal transport time tau. 01:09:39.069 --> 01:09:41.540 align:middle line:84% There's actually a second term here, 01:09:41.540 --> 01:09:46.660 align:middle line:84% which is delta tau delta T upon tau, like that. 01:09:46.660 --> 01:09:49.279 align:middle line:90% 01:09:49.279 --> 01:09:51.310 align:middle line:84% So there's two different ways that the radiation 01:09:51.310 --> 01:09:51.979 align:middle line:90% can affect this. 01:09:51.979 --> 01:09:55.150 align:middle line:84% And so, by measuring delta T up here, 01:09:55.150 --> 01:09:58.510 align:middle line:84% the change in temperature in our resistance from the change 01:09:58.510 --> 01:10:01.060 align:middle line:84% in resistance, we can invert this equation 01:10:01.060 --> 01:10:03.350 align:middle line:84% and we can back out the radiation power. 01:10:03.350 --> 01:10:05.055 align:middle line:84% So this is just a really simple way 01:10:05.055 --> 01:10:07.180 align:middle line:84% of using a resistor to measure the power coming out 01:10:07.180 --> 01:10:08.050 align:middle line:90% of the plasma. 01:10:08.050 --> 01:10:09.967 align:middle line:84% And bolometry was one of the first diagnostics 01:10:09.967 --> 01:10:12.595 align:middle line:90% that we had on many MCF devices. 01:10:12.595 --> 01:10:15.580 align:middle line:90% 01:10:15.580 --> 01:10:18.675 align:middle line:90% Questions on this? 01:10:18.675 --> 01:10:20.591 align:middle line:90% STUDENT: [INAUDIBLE] 01:10:20.591 --> 01:10:21.550 align:middle line:90% 01:10:21.550 --> 01:10:24.440 align:middle line:84% JACK HARE: [INAUDIBLE], we'll talk about that in a moment. 01:10:24.440 --> 01:10:26.320 align:middle line:84% I worked on the bolometers for [INAUDIBLE], 01:10:26.320 --> 01:10:27.862 align:middle line:84% so neutrons were the bane of my life. 01:10:27.862 --> 01:10:31.650 align:middle line:90% 01:10:31.650 --> 01:10:34.080 align:middle line:84% Now, this itself is a very simplistic system, 01:10:34.080 --> 01:10:37.360 align:middle line:84% and it does not work because it is very susceptible to noise. 01:10:37.360 --> 01:10:39.300 align:middle line:84% So we have to, as always, come up 01:10:39.300 --> 01:10:42.210 align:middle line:84% with a clever system, which is noise resistant. 01:10:42.210 --> 01:10:44.356 align:middle line:90% And think I'm just going to-- 01:10:44.356 --> 01:10:49.480 align:middle line:90% ugh-- get myself another board. 01:10:49.480 --> 01:10:50.640 align:middle line:90% What time are we on? 01:10:50.640 --> 01:10:52.970 align:middle line:90% Oh. 01:10:52.970 --> 01:10:53.470 align:middle line:90% OK. 01:10:53.470 --> 01:11:09.010 align:middle line:90% 01:11:09.010 --> 01:11:10.600 align:middle line:90% So what we do in-- 01:11:10.600 --> 01:11:12.370 align:middle line:84% to make this measurement more precise 01:11:12.370 --> 01:11:14.180 align:middle line:90% is first we do two things. 01:11:14.180 --> 01:11:16.270 align:middle line:84% First of all, we do something called 01:11:16.270 --> 01:11:19.060 align:middle line:84% a Wheatstone bridge, which many of you have come across before. 01:11:19.060 --> 01:11:22.990 align:middle line:84% A Wheatstone bridge is an arrangement of four resistors. 01:11:22.990 --> 01:11:26.300 align:middle line:90% 01:11:26.300 --> 01:11:30.330 align:middle line:84% So there's a resistor here, another resistor here, 01:11:30.330 --> 01:11:36.400 align:middle line:84% a resistor here, and another resistor here. 01:11:36.400 --> 01:11:39.790 align:middle line:84% And we connect these resistors up. 01:11:39.790 --> 01:11:41.740 align:middle line:84% And the clever thing, in a bolometer, 01:11:41.740 --> 01:11:47.477 align:middle line:84% is we allow two of the resistors to see the plasma. 01:11:47.477 --> 01:11:49.810 align:middle line:84% And these are the ones we call the measurement resistors 01:11:49.810 --> 01:11:53.240 align:middle line:90% M1 and M2. 01:11:53.240 --> 01:11:55.930 align:middle line:84% So you can imagine these resistors just having a little 01:11:55.930 --> 01:11:58.120 align:middle line:84% window that allows them to see the plasma, 01:11:58.120 --> 01:12:00.970 align:middle line:84% and the other two resistors cannot see the plasma. 01:12:00.970 --> 01:12:04.900 align:middle line:84% They have a large lump of metal which gets in the way. 01:12:04.900 --> 01:12:08.000 align:middle line:90% 01:12:08.000 --> 01:12:11.810 align:middle line:84% And these are the reference resistors, R1 and R2. 01:12:11.810 --> 01:12:14.865 align:middle line:90% 01:12:14.865 --> 01:12:19.940 align:middle line:84% I think I'm just going to call these R2 and R1. 01:12:19.940 --> 01:12:22.760 align:middle line:84% And, in a Wheatstone bridge, what we now do is 01:12:22.760 --> 01:12:27.680 align:middle line:84% we still have a potential drop, V0, over the entire bridge. 01:12:27.680 --> 01:12:32.880 align:middle line:84% But we now measure the potential difference 01:12:32.880 --> 01:12:35.340 align:middle line:90% across these pairs here. 01:12:35.340 --> 01:12:37.335 align:middle line:90% And that is called V bridge. 01:12:37.335 --> 01:12:45.150 align:middle line:90% 01:12:45.150 --> 01:12:52.860 align:middle line:84% So these measurement resistors, they see the radiated power P 01:12:52.860 --> 01:12:57.840 align:middle line:84% rad, and their temperature is equal to the temperature 01:12:57.840 --> 01:13:01.920 align:middle line:84% of the reference resistors plus a change 01:13:01.920 --> 01:13:05.790 align:middle line:84% in temperature due to radiation, whereas the reference resistors 01:13:05.790 --> 01:13:08.520 align:middle line:84% just have a temperature which is equal to the reference 01:13:08.520 --> 01:13:10.490 align:middle line:90% resistors. 01:13:10.490 --> 01:13:12.950 align:middle line:84% The point of this setup is your entire bolometer 01:13:12.950 --> 01:13:15.050 align:middle line:84% is going to heat up because the entire vacuum 01:13:15.050 --> 01:13:16.370 align:middle line:90% vessel is going to get hot. 01:13:16.370 --> 01:13:18.830 align:middle line:84% And so, what you want to know is not just how hot they are, 01:13:18.830 --> 01:13:21.865 align:middle line:84% but how hot they are relative to the vacuum vessel. 01:13:21.865 --> 01:13:23.990 align:middle line:84% And so, this is why we have this system where we're 01:13:23.990 --> 01:13:27.170 align:middle line:84% trying to measure a very small change between R1 and R2, 01:13:27.170 --> 01:13:29.930 align:middle line:84% which would be identical, and M1 and M2. 01:13:29.930 --> 01:13:35.460 align:middle line:84% And it's this small quantity here, delta T, 01:13:35.460 --> 01:13:39.720 align:middle line:84% that's due to the radiated power that we're really 01:13:39.720 --> 01:13:41.680 align:middle line:90% trying to measure. 01:13:41.680 --> 01:13:43.240 align:middle line:84% And we do this because-- or the way 01:13:43.240 --> 01:13:48.847 align:middle line:84% that we do this is we notice that V bridge is 01:13:48.847 --> 01:13:50.930 align:middle line:84% the difference between two potential dividers, one 01:13:50.930 --> 01:13:53.390 align:middle line:84% potential divider that goes on M1 R1. 01:13:53.390 --> 01:13:57.020 align:middle line:84% And so, the potential that this floats at here, Va, 01:13:57.020 --> 01:13:59.630 align:middle line:84% is going to be different in general from the potential 01:13:59.630 --> 01:14:03.110 align:middle line:84% that this floats at, Vb, where the two resistors are arranged 01:14:03.110 --> 01:14:04.940 align:middle line:90% in the opposite way around. 01:14:04.940 --> 01:14:14.450 align:middle line:84% So V bridge is going to be equal to V0 R upon R plus M. That's 01:14:14.450 --> 01:14:20.020 align:middle line:90% just a potential at a here-- 01:14:20.020 --> 01:14:27.370 align:middle line:84% minus the potential at b, V0 M over R plus M. 01:14:27.370 --> 01:14:29.230 align:middle line:84% And if you look at this, quite simply, 01:14:29.230 --> 01:14:32.815 align:middle line:84% you can see that it's proportional to R plus-- 01:14:32.815 --> 01:14:35.800 align:middle line:84% or R minus M. So it's a differential measurement. 01:14:35.800 --> 01:14:37.720 align:middle line:84% We're just measuring a voltage which 01:14:37.720 --> 01:14:40.150 align:middle line:84% is proportional to this small quantity. 01:14:40.150 --> 01:14:46.600 align:middle line:84% And that is entirely due to the change in temperature. 01:14:46.600 --> 01:14:49.020 align:middle line:84% So we're now able to isolate the change in temperature 01:14:49.020 --> 01:14:50.370 align:middle line:90% very, very precisely. 01:14:50.370 --> 01:14:54.510 align:middle line:84% And, in general, we don't just use this Wheatstone bridge, 01:14:54.510 --> 01:14:57.210 align:middle line:84% we also use a phase locked loop measurement, which 01:14:57.210 --> 01:15:00.570 align:middle line:84% is a form of heterodyning again, my favorite technique. 01:15:00.570 --> 01:15:05.190 align:middle line:84% And so, we actually have V0 is oscillating 01:15:05.190 --> 01:15:07.485 align:middle line:90% at around 50 kilohertz or so. 01:15:07.485 --> 01:15:10.270 align:middle line:90% 01:15:10.270 --> 01:15:16.330 align:middle line:84% And so, we can see that our signal, delta T, or the change 01:15:16.330 --> 01:15:17.890 align:middle line:84% in temperature as a function of time, 01:15:17.890 --> 01:15:20.650 align:middle line:84% is a slowly varying signal which is embedded 01:15:20.650 --> 01:15:22.120 align:middle line:90% on top of this 50 kilohertz. 01:15:22.120 --> 01:15:23.950 align:middle line:84% And then, using heterodyning techniques, 01:15:23.950 --> 01:15:26.290 align:middle line:84% we can measure it very cleanly without noise. 01:15:26.290 --> 01:15:30.012 align:middle line:90% 01:15:30.012 --> 01:15:32.470 align:middle line:84% This may be an experimental technique you're familiar with. 01:15:32.470 --> 01:15:37.580 align:middle line:90% 01:15:37.580 --> 01:15:41.990 align:middle line:84% What the bolometer head actually looks like is we 01:15:41.990 --> 01:15:46.790 align:middle line:84% have some large lump of gold here. 01:15:46.790 --> 01:15:53.090 align:middle line:84% And by large, I mean it's about 100 microns thick 01:15:53.090 --> 01:15:57.240 align:middle line:90% and about 1 millimeter long. 01:15:57.240 --> 01:15:58.865 align:middle line:84% This is what faces the radiation. 01:15:58.865 --> 01:16:00.615 align:middle line:84% The radiation is coming in from this side. 01:16:00.615 --> 01:16:03.900 align:middle line:90% 01:16:03.900 --> 01:16:07.310 align:middle line:90% This is often made out of gold. 01:16:07.310 --> 01:16:10.990 align:middle line:84% Gold is chosen because it absorbs all wavelengths 01:16:10.990 --> 01:16:11.895 align:middle line:90% relatively evenly. 01:16:11.895 --> 01:16:14.520 align:middle line:84% So you don't need to worry too much about the spectral response 01:16:14.520 --> 01:16:15.775 align:middle line:90% of this. 01:16:15.775 --> 01:16:21.220 align:middle line:84% This thin layer of gold has been deposited on top of a substrate. 01:16:21.220 --> 01:16:28.450 align:middle line:90% 01:16:28.450 --> 01:16:30.250 align:middle line:84% And it's on the back of the substrate 01:16:30.250 --> 01:16:32.380 align:middle line:90% that you have your resistor. 01:16:32.380 --> 01:16:36.940 align:middle line:84% And your resistor is literally a little zig zag of gold deposited 01:16:36.940 --> 01:16:38.030 align:middle line:90% on the back side of this. 01:16:38.030 --> 01:16:43.280 align:middle line:84% So this is M or R. And depending on whether it is M or R, 01:16:43.280 --> 01:16:46.330 align:middle line:84% you either have this open to the plasma 01:16:46.330 --> 01:16:48.820 align:middle line:84% or you have a thick block some distance in front of it 01:16:48.820 --> 01:16:50.031 align:middle line:90% so it can't see the plasma. 01:16:50.031 --> 01:16:54.450 align:middle line:90% 01:16:54.450 --> 01:16:59.100 align:middle line:84% It's the heat capacity of the absorber, c, that goes 01:16:59.100 --> 01:17:00.480 align:middle line:90% into our previous equation. 01:17:00.480 --> 01:17:03.360 align:middle line:84% And it's the heat transport kappa 01:17:03.360 --> 01:17:09.440 align:middle line:84% grad T that gives us the time constant for thermal conduction 01:17:09.440 --> 01:17:13.160 align:middle line:84% through the substrate from the absorber to the resistor. 01:17:13.160 --> 01:17:14.960 align:middle line:84% And I'll just write that equation again 01:17:14.960 --> 01:17:16.970 align:middle line:90% because it's disappeared now-- 01:17:16.970 --> 01:17:20.630 align:middle line:84% that we can work out the radiated power 01:17:20.630 --> 01:17:25.100 align:middle line:84% by looking at how the temperature of the measurement 01:17:25.100 --> 01:17:27.530 align:middle line:90% resistor M changes in time. 01:17:27.530 --> 01:17:31.490 align:middle line:84% And that change in time is due to heating up and heating down 01:17:31.490 --> 01:17:34.130 align:middle line:84% from direct heating and then also a time 01:17:34.130 --> 01:17:40.790 align:middle line:90% lag phenomena delta T on tau. 01:17:40.790 --> 01:17:48.720 align:middle line:84% And, effectively, this tau here sets the timescale 01:17:48.720 --> 01:17:49.900 align:middle line:90% at which we can measure. 01:17:49.900 --> 01:17:53.580 align:middle line:84% So the larger tau is the slower our measurement 01:17:53.580 --> 01:17:55.320 align:middle line:84% of the radiated power is going to be. 01:17:55.320 --> 01:17:57.028 align:middle line:84% And if tau gets very large, because we've 01:17:57.028 --> 01:17:59.040 align:middle line:84% got a very thick substrate here, or it doesn't 01:17:59.040 --> 01:18:00.840 align:middle line:84% have very good heat transport, then we're 01:18:00.840 --> 01:18:05.020 align:middle line:84% going to have a very poor time resolution of our radiation 01:18:05.020 --> 01:18:05.520 align:middle line:90% power. 01:18:05.520 --> 01:18:07.395 align:middle line:84% And, of course, we'd like to have a nice time 01:18:07.395 --> 01:18:09.862 align:middle line:90% resolution of that. 01:18:09.862 --> 01:18:12.070 align:middle line:84% I'm just going to finish up with a couple of details. 01:18:12.070 --> 01:18:14.790 align:middle line:84% Then I'll take some questions and we'll leave it there. 01:18:14.790 --> 01:18:16.560 align:middle line:84% So the trouble with these, as someone 01:18:16.560 --> 01:18:24.190 align:middle line:84% asked, when it comes to radiation, first of all, 01:18:24.190 --> 01:18:26.730 align:middle line:84% they do actually sense, basically, 01:18:26.730 --> 01:18:29.040 align:middle line:84% all energy coming out of the plasma or all power 01:18:29.040 --> 01:18:30.082 align:middle line:90% coming out of the plasma. 01:18:30.082 --> 01:18:33.090 align:middle line:84% It's not just radiated power, but they will also 01:18:33.090 --> 01:18:37.983 align:middle line:90% sense neutrons and particles. 01:18:37.983 --> 01:18:39.400 align:middle line:84% So if you've got ions or electrons 01:18:39.400 --> 01:18:41.400 align:middle line:84% coming out and hitting these and being absorbed, 01:18:41.400 --> 01:18:42.937 align:middle line:84% that will also heat up the absorber. 01:18:42.937 --> 01:18:44.270 align:middle line:90% This will measure those as well. 01:18:44.270 --> 01:18:46.562 align:middle line:84% So it's very hard to tell the difference between those. 01:18:46.562 --> 01:18:53.490 align:middle line:84% But, also, the neutron damage leads 01:18:53.490 --> 01:19:07.720 align:middle line:84% us to use much thicker substrates, which gives us 01:19:07.720 --> 01:19:14.790 align:middle line:84% a longer time response and so, therefore, a worse bolometer. 01:19:14.790 --> 01:19:18.880 align:middle line:84% So, ironically, the bolometers that will be used on [INAUDIBLE] 01:19:18.880 --> 01:19:21.028 align:middle line:84% are significantly worse than the bolometers used 01:19:21.028 --> 01:19:23.320 align:middle line:84% on existing devices, not because they couldn't work out 01:19:23.320 --> 01:19:26.290 align:middle line:84% how to make better ones, but because the radiation forces you 01:19:26.290 --> 01:19:28.748 align:middle line:84% into a regime where you can't use a good bolometer anymore. 01:19:28.748 --> 01:19:30.165 align:middle line:84% And I'm sure that [? Spark ?] will 01:19:30.165 --> 01:19:31.540 align:middle line:90% have exactly the same problem. 01:19:31.540 --> 01:19:34.330 align:middle line:84% Almost everyone in the world uses this design of bolometer 01:19:34.330 --> 01:19:36.520 align:middle line:84% that they pioneered on ASDEX Upgrade in the '80s. 01:19:36.520 --> 01:19:39.420 align:middle line:84% No one has come up with a better system yet. 01:19:39.420 --> 01:19:43.000 align:middle line:90%