WEBVTT 00:00:00.000 --> 00:00:01.924 align:middle line:90% [SQUEAKING] 00:00:01.924 --> 00:00:04.810 align:middle line:90% [RUSTLING] 00:00:04.810 --> 00:00:07.215 align:middle line:90% [CLICKING] 00:00:07.215 --> 00:00:10.120 align:middle line:90% 00:00:10.120 --> 00:00:12.610 align:middle line:84% JACK HARE: Today, we are going to be discussing 00:00:12.610 --> 00:00:14.510 align:middle line:90% neutral particle diagnostics. 00:00:14.510 --> 00:00:25.600 align:middle line:90% 00:00:25.600 --> 00:00:29.510 align:middle line:84% So the fact of the matter is, we have some plasma, 00:00:29.510 --> 00:00:33.610 align:middle line:84% like a tokamak, and it has some block surfaces. 00:00:33.610 --> 00:00:37.920 align:middle line:84% And we want to know what's going on inside the core, 00:00:37.920 --> 00:00:39.990 align:middle line:84% because this is where the fusion is happening. 00:00:39.990 --> 00:00:43.470 align:middle line:84% In particular, we want to know what the distribution 00:00:43.470 --> 00:00:45.540 align:middle line:90% function of the ions is. 00:00:45.540 --> 00:00:48.780 align:middle line:84% It's probably Maxwellian-ish, but the "ish" 00:00:48.780 --> 00:00:49.750 align:middle line:90% is the interesting bit. 00:00:49.750 --> 00:00:52.110 align:middle line:84% There may be some lovely tails of particles here, 00:00:52.110 --> 00:00:53.400 align:middle line:84% and those are the ones that might be doing 00:00:53.400 --> 00:00:54.730 align:middle line:90% most of our fusion reactions. 00:00:54.730 --> 00:00:56.147 align:middle line:84% So we'd like to be able to measure 00:00:56.147 --> 00:00:58.530 align:middle line:84% this distribution function f of i. 00:00:58.530 --> 00:01:00.660 align:middle line:84% The trouble is, the particles in the core 00:01:00.660 --> 00:01:04.225 align:middle line:84% are hopefully very well-confined. 00:01:04.225 --> 00:01:06.600 align:middle line:84% If they're not confined, we haven't done a very good job. 00:01:06.600 --> 00:01:09.200 align:middle line:84% So we can't exactly wait for them to wander out and see 00:01:09.200 --> 00:01:10.380 align:middle line:90% what they're up to. 00:01:10.380 --> 00:01:14.060 align:middle line:84% And so we need some technique of measuring this core distribution 00:01:14.060 --> 00:01:16.220 align:middle line:90% function f of i Vi. 00:01:16.220 --> 00:01:20.810 align:middle line:84% Now, we have some ideas based on some of the other diagnostics 00:01:20.810 --> 00:01:22.640 align:middle line:90% we've looked at already. 00:01:22.640 --> 00:01:26.302 align:middle line:84% For example, we could use electron cyclotron emission. 00:01:26.302 --> 00:01:28.760 align:middle line:84% That gave us information about what's going on in the core. 00:01:28.760 --> 00:01:31.550 align:middle line:84% But this gives us a measurement of Te. 00:01:31.550 --> 00:01:35.240 align:middle line:84% And Te does not necessarily have to be the same as Ti. 00:01:35.240 --> 00:01:37.610 align:middle line:84% So that's not a very good diagnostic. 00:01:37.610 --> 00:01:42.440 align:middle line:84% We could do something using laser-induced fluorescence, 00:01:42.440 --> 00:01:46.100 align:middle line:84% or two-photon absorption laser-induced fluorescence 00:01:46.100 --> 00:01:46.940 align:middle line:90% like this. 00:01:46.940 --> 00:01:50.570 align:middle line:84% If you remember, that's where we had an upper level and a lower 00:01:50.570 --> 00:01:55.970 align:middle line:84% level and we scanned our laser wavelength in frequency space 00:01:55.970 --> 00:01:58.118 align:middle line:84% here so that we could address particles which 00:01:58.118 --> 00:02:00.410 align:middle line:84% are Doppler shifted towards us and Doppler shifted away 00:02:00.410 --> 00:02:01.040 align:middle line:90% from us. 00:02:01.040 --> 00:02:03.710 align:middle line:84% And by looking at the intensity of light coming out, 00:02:03.710 --> 00:02:06.420 align:middle line:84% we could measure this distribution function here. 00:02:06.420 --> 00:02:09.139 align:middle line:84% So this looks like a pretty good technique 00:02:09.139 --> 00:02:10.520 align:middle line:90% for measuring the core. 00:02:10.520 --> 00:02:12.770 align:middle line:84% The trouble is that in the core, all of our particles 00:02:12.770 --> 00:02:13.890 align:middle line:90% are fully ionized. 00:02:13.890 --> 00:02:16.140 align:middle line:84% And so there are no electrons here. 00:02:16.140 --> 00:02:19.010 align:middle line:84% So we can't use these techniques because there 00:02:19.010 --> 00:02:24.050 align:middle line:84% are no ions with an electron in them in order 00:02:24.050 --> 00:02:26.510 align:middle line:84% for us to be able to address it using our laser. 00:02:26.510 --> 00:02:29.370 align:middle line:84% And thirdly, we could also use Thomson scattering, 00:02:29.370 --> 00:02:30.810 align:middle line:84% which we haven't talked about yet, 00:02:30.810 --> 00:02:32.930 align:middle line:90% but we will do in detail soon. 00:02:32.930 --> 00:02:34.400 align:middle line:84% The trouble with Thomson scattering 00:02:34.400 --> 00:02:37.490 align:middle line:84% is that it tends to give us information-- 00:02:37.490 --> 00:02:44.120 align:middle line:84% scattering-- about the electron distribution function, fe Ve, 00:02:44.120 --> 00:02:45.050 align:middle line:90% like that. 00:02:45.050 --> 00:02:47.030 align:middle line:84% And again, that doesn't have to necessarily 00:02:47.030 --> 00:02:51.550 align:middle line:84% be the same as the ion distribution function. 00:02:51.550 --> 00:02:53.580 align:middle line:84% So we're going to need a new technique in order 00:02:53.580 --> 00:02:56.650 align:middle line:84% to measure the distribution of these core particles. 00:02:56.650 --> 00:03:01.700 align:middle line:84% So the idea is, well, what if, spontaneously, 00:03:01.700 --> 00:03:03.935 align:middle line:84% some of these core ions turned into neutrals? 00:03:03.935 --> 00:03:11.210 align:middle line:90% 00:03:11.210 --> 00:03:16.540 align:middle line:84% Well, if some of these core ions turned into neutrals, then 00:03:16.540 --> 00:03:18.970 align:middle line:84% they would no longer be confined. 00:03:18.970 --> 00:03:23.550 align:middle line:84% They would be able to wander freely out. 00:03:23.550 --> 00:03:25.470 align:middle line:84% And perhaps we could stick a detector 00:03:25.470 --> 00:03:28.890 align:middle line:84% on the outside of the plasma and measure these neutrals, which 00:03:28.890 --> 00:03:31.410 align:middle line:84% will carry with them some information about the ion 00:03:31.410 --> 00:03:32.640 align:middle line:90% distribution they came from. 00:03:32.640 --> 00:03:35.370 align:middle line:84% And that will allow us to indirectly measure 00:03:35.370 --> 00:03:37.420 align:middle line:90% the ion distribution. 00:03:37.420 --> 00:03:42.245 align:middle line:84% So what's a good way to summarize this? 00:03:42.245 --> 00:03:43.620 align:middle line:84% They're going to-- these neutrals 00:03:43.620 --> 00:03:49.610 align:middle line:84% would give us information on the distribution function. 00:03:49.610 --> 00:03:51.385 align:middle line:84% So there's two problems that's coming 00:03:51.385 --> 00:03:52.510 align:middle line:90% to your mind straight away. 00:03:52.510 --> 00:03:55.090 align:middle line:84% Why exactly would an iron suddenly turn itself 00:03:55.090 --> 00:03:56.470 align:middle line:90% into a neutral in the core? 00:03:56.470 --> 00:04:00.400 align:middle line:84% And does it stand a chance of actually escaping from the core 00:04:00.400 --> 00:04:03.140 align:middle line:84% to the outside, where we can detect it? 00:04:03.140 --> 00:04:06.740 align:middle line:84% And so we'll talk about those two issues one after the other. 00:04:06.740 --> 00:04:11.620 align:middle line:84% So first of all is the neutral production. 00:04:11.620 --> 00:04:17.730 align:middle line:90% 00:04:17.730 --> 00:04:19.620 align:middle line:84% And I guess we could call the second problem 00:04:19.620 --> 00:04:20.940 align:middle line:90% neutral transport. 00:04:20.940 --> 00:04:29.960 align:middle line:90% 00:04:29.960 --> 00:04:32.450 align:middle line:84% So in terms of neutral production, 00:04:32.450 --> 00:04:35.120 align:middle line:84% there are two major processes that we could have. 00:04:35.120 --> 00:04:37.050 align:middle line:90% We could have a charge exchange. 00:04:37.050 --> 00:04:39.560 align:middle line:84% So I'm just going to write that as CX. 00:04:39.560 --> 00:04:41.330 align:middle line:84% We talked about charge exchange before. 00:04:41.330 --> 00:04:45.530 align:middle line:84% This is where a neutral collides with an ion, and the neutral 00:04:45.530 --> 00:04:48.150 align:middle line:84% loses an electron and the ion gains an electron. 00:04:48.150 --> 00:04:52.685 align:middle line:84% So we could have charge exchange with edge neutrals. 00:04:52.685 --> 00:04:54.060 align:middle line:84% And they could be neutrals coming 00:04:54.060 --> 00:04:55.875 align:middle line:90% in from the edge of the plasma. 00:04:55.875 --> 00:04:58.990 align:middle line:90% 00:04:58.990 --> 00:05:02.380 align:middle line:84% And that would look like some neutrals coming in like this, 00:05:02.380 --> 00:05:07.000 align:middle line:84% and I'll use n sub a to be some density of neutral atoms. 00:05:07.000 --> 00:05:10.120 align:middle line:84% These are going to be wandering in from the edge all the time. 00:05:10.120 --> 00:05:14.610 align:middle line:84% Maybe a few of them make it to the center, 00:05:14.610 --> 00:05:16.710 align:middle line:84% and then they charge exchange of our core. 00:05:16.710 --> 00:05:17.625 align:middle line:90% And then those core-- 00:05:17.625 --> 00:05:20.420 align:middle line:90% 00:05:20.420 --> 00:05:22.280 align:middle line:90% [INAUDIBLE] 00:05:22.280 --> 00:05:26.000 align:middle line:84% Hence, the ions make it back out again and we can detect them. 00:05:26.000 --> 00:05:29.120 align:middle line:90% That's one possible mechanism. 00:05:29.120 --> 00:05:32.900 align:middle line:84% A more sort of active mechanism would be taking a neutral beam 00:05:32.900 --> 00:05:35.600 align:middle line:84% and putting a neutral beam into the center of the core here. 00:05:35.600 --> 00:05:37.350 align:middle line:90% This is neutral beam injection. 00:05:37.350 --> 00:05:39.620 align:middle line:84% We use neutral beam injection for all sorts of things, 00:05:39.620 --> 00:05:42.030 align:middle line:84% like current drive and heating of the plasma. 00:05:42.030 --> 00:05:45.212 align:middle line:84% And so we often have this process happening automatically. 00:05:45.212 --> 00:05:46.670 align:middle line:84% The whole point of the neutral beam 00:05:46.670 --> 00:05:50.420 align:middle line:84% here is that as these neutral particles come into the center, 00:05:50.420 --> 00:05:53.450 align:middle line:84% they'll charge exchange with the ions and become ions. 00:05:53.450 --> 00:05:55.700 align:middle line:84% But that means that the ions they charge exchange with 00:05:55.700 --> 00:05:56.640 align:middle line:90% become neutrals. 00:05:56.640 --> 00:05:59.968 align:middle line:84% And so those neutrals may come out of the plasma 00:05:59.968 --> 00:06:01.260 align:middle line:90% here, where we can detect them. 00:06:01.260 --> 00:06:03.950 align:middle line:84% So we have charge exchange with edge neutrals 00:06:03.950 --> 00:06:08.810 align:middle line:84% and charge exchange with neutral beam injection. 00:06:08.810 --> 00:06:11.900 align:middle line:90% 00:06:11.900 --> 00:06:15.042 align:middle line:84% Neutral transport is asking, can the neutral make it 00:06:15.042 --> 00:06:16.250 align:middle line:90% from the center of the core-- 00:06:16.250 --> 00:06:20.800 align:middle line:90% 00:06:20.800 --> 00:06:21.760 align:middle line:90% yeah. 00:06:21.760 --> 00:06:26.820 align:middle line:84% Can that neutral make it out along some path? 00:06:26.820 --> 00:06:29.070 align:middle line:84% And so there's going to be a series of processes which 00:06:29.070 --> 00:06:31.770 align:middle line:84% are trying to re-ionize this neutral as it 00:06:31.770 --> 00:06:33.340 align:middle line:90% tries to leave the plasma. 00:06:33.340 --> 00:06:36.860 align:middle line:84% So these processes are going to be things like-- 00:06:36.860 --> 00:06:40.730 align:middle line:84% I'm going to give them their cross-sections, sigma sub e. 00:06:40.730 --> 00:06:44.570 align:middle line:84% This is electron impact ionization, 00:06:44.570 --> 00:06:46.025 align:middle line:90% which we talked about before. 00:06:46.025 --> 00:06:53.150 align:middle line:90% 00:06:53.150 --> 00:06:55.110 align:middle line:90% This is going to be-- 00:06:55.110 --> 00:06:56.970 align:middle line:90% we can use sigma subscript p. 00:06:56.970 --> 00:07:02.160 align:middle line:84% This is ion impact ionization, because we can also 00:07:02.160 --> 00:07:04.960 align:middle line:84% have collisions of ions causing ionization here. 00:07:04.960 --> 00:07:10.770 align:middle line:84% And finally, we can have the probability of charge exchange 00:07:10.770 --> 00:07:11.800 align:middle line:90% with ions. 00:07:11.800 --> 00:07:13.997 align:middle line:84% So if we've charge exchanged once in order 00:07:13.997 --> 00:07:15.580 align:middle line:84% to get our neutral in the first place, 00:07:15.580 --> 00:07:17.997 align:middle line:84% it's not at all impossible for us to charge exchange again 00:07:17.997 --> 00:07:20.137 align:middle line:84% as we head out, and then our core neutral that 00:07:20.137 --> 00:07:22.470 align:middle line:84% was heading out and giving us information about the core 00:07:22.470 --> 00:07:24.450 align:middle line:84% will become an ion and it'll be trapped again, 00:07:24.450 --> 00:07:27.420 align:middle line:84% and now, we'll have an ion and further out become a neutral, 00:07:27.420 --> 00:07:28.630 align:middle line:90% and that will try and leak. 00:07:28.630 --> 00:07:31.350 align:middle line:84% So this charge exchange process is particularly 00:07:31.350 --> 00:07:34.230 align:middle line:84% problematic because what we're ending up 00:07:34.230 --> 00:07:36.570 align:middle line:84% with is something that looks like a hydrogen 00:07:36.570 --> 00:07:42.090 align:middle line:84% neutral plus a hydrogen ion going to a hydrogen ion 00:07:42.090 --> 00:07:44.220 align:middle line:90% but a hydrogen neutral. 00:07:44.220 --> 00:07:46.590 align:middle line:84% Now, the beautiful symmetry in this equation 00:07:46.590 --> 00:07:49.700 align:middle line:84% here means that this is resonant. 00:07:49.700 --> 00:07:52.840 align:middle line:84% And so it's quite likely to happen. 00:07:52.840 --> 00:07:55.170 align:middle line:90% So this sigma C is large. 00:07:55.170 --> 00:07:59.960 align:middle line:90% 00:07:59.960 --> 00:08:02.840 align:middle line:84% So that's an overview of what we're going to try and do. 00:08:02.840 --> 00:08:05.150 align:middle line:84% I'm going to talk a little bit about the transport, 00:08:05.150 --> 00:08:07.340 align:middle line:84% estimate the size of these different coefficients, 00:08:07.340 --> 00:08:10.460 align:middle line:84% and work out how likely it is we can actually get any neutrals 00:08:10.460 --> 00:08:11.990 align:middle line:90% from the core back out again. 00:08:11.990 --> 00:08:14.073 align:middle line:84% And then we'll talk about the neutral productions. 00:08:14.073 --> 00:08:15.410 align:middle line:90% I'm going to go 2 and then 1. 00:08:15.410 --> 00:08:16.430 align:middle line:90% But that's an overview. 00:08:16.430 --> 00:08:18.347 align:middle line:84% If you have any questions before we get going, 00:08:18.347 --> 00:08:19.972 align:middle line:90% this is a good time to ask. 00:08:19.972 --> 00:08:20.936 align:middle line:90% AUDIENCE: [INAUDIBLE]. 00:08:20.936 --> 00:08:31.540 align:middle line:90% 00:08:31.540 --> 00:08:33.025 align:middle line:90% JACK HARE: OK, yes. 00:08:33.025 --> 00:08:36.640 align:middle line:90% 00:08:36.640 --> 00:08:40.150 align:middle line:84% You should take a closer look at Hutchinson's book for a more 00:08:40.150 --> 00:08:41.409 align:middle line:90% formal definition. 00:08:41.409 --> 00:08:43.055 align:middle line:84% But quantum mechanically, this is 00:08:43.055 --> 00:08:44.680 align:middle line:84% nice and likely to happen because we're 00:08:44.680 --> 00:08:46.780 align:middle line:84% starting-- or ending up with something very 00:08:46.780 --> 00:08:48.470 align:middle line:90% similar to what we've started. 00:08:48.470 --> 00:08:50.610 align:middle line:84% And so this process is likely to occur. 00:08:50.610 --> 00:08:52.620 align:middle line:90% Yeah. 00:08:52.620 --> 00:08:53.120 align:middle line:90% OK. 00:08:53.120 --> 00:08:58.140 align:middle line:90% 00:08:58.140 --> 00:09:01.920 align:middle line:84% So again, we've got some blob of plasma here. 00:09:01.920 --> 00:09:06.165 align:middle line:84% We've got some particle, which is born at a point A. 00:09:06.165 --> 00:09:10.540 align:middle line:84% And we want to know if we can get to a point B, like this. 00:09:10.540 --> 00:09:14.545 align:middle line:84% So this is the core, and B is where we have our detector. 00:09:14.545 --> 00:09:17.630 align:middle line:90% 00:09:17.630 --> 00:09:19.100 align:middle line:84% If you look at this, you say, this 00:09:19.100 --> 00:09:22.530 align:middle line:84% looks an awful lot like our radiation transport problem. 00:09:22.530 --> 00:09:26.150 align:middle line:84% And so we could say that there's a probability of the particle 00:09:26.150 --> 00:09:29.240 align:middle line:84% getting from A to B. Or this could be a power of particles 00:09:29.240 --> 00:09:32.090 align:middle line:84% as well if I multiply it by the particle energy per unit time. 00:09:32.090 --> 00:09:36.440 align:middle line:84% And that's going to look like the exponential of the line 00:09:36.440 --> 00:09:42.140 align:middle line:84% integral from A to B of some opacity, in this case, 00:09:42.140 --> 00:09:43.760 align:middle line:84% more to do with scattering than it 00:09:43.760 --> 00:09:46.360 align:middle line:84% is to do with absorption, which varies 00:09:46.360 --> 00:09:48.362 align:middle line:90% along the path integrated-- 00:09:48.362 --> 00:09:50.320 align:middle line:84% along the path, the L, and then the minus sign. 00:09:50.320 --> 00:09:53.010 align:middle line:90% 00:09:53.010 --> 00:09:55.667 align:middle line:84% So again, this looks like radiation transport. 00:09:55.667 --> 00:10:07.110 align:middle line:90% 00:10:07.110 --> 00:10:10.990 align:middle line:84% So we talked about three different processes over there 00:10:10.990 --> 00:10:14.050 align:middle line:90% which might be important. 00:10:14.050 --> 00:10:17.130 align:middle line:84% And the importance of those different processes 00:10:17.130 --> 00:10:20.130 align:middle line:84% will depend a lot on the distribution functions 00:10:20.130 --> 00:10:21.220 align:middle line:90% that we have here. 00:10:21.220 --> 00:10:25.830 align:middle line:84% So if this is V And this is f of V here, 00:10:25.830 --> 00:10:27.690 align:middle line:84% we'll have an ion distribution function. 00:10:27.690 --> 00:10:30.690 align:middle line:84% And that's just the ions making up the plasma. 00:10:30.690 --> 00:10:35.080 align:middle line:84% And that will be relatively small in velocity space here. 00:10:35.080 --> 00:10:36.540 align:middle line:90% So this is f of i. 00:10:36.540 --> 00:10:40.650 align:middle line:84% And we'll also have an electron distribution function, which 00:10:40.650 --> 00:10:43.242 align:middle line:84% is much broader, and that's because the electrons 00:10:43.242 --> 00:10:43.950 align:middle line:90% are less massive. 00:10:43.950 --> 00:10:47.700 align:middle line:84% So for a similar temperature, they have higher velocities. 00:10:47.700 --> 00:10:52.710 align:middle line:84% And we'll also assume that our neutrals coming out here 00:10:52.710 --> 00:10:58.530 align:middle line:84% have some distribution that is relatively narrow and shifted 00:10:58.530 --> 00:10:59.470 align:middle line:90% like this. 00:10:59.470 --> 00:11:05.420 align:middle line:84% So this is at a loss T, the A like this for the neutrals. 00:11:05.420 --> 00:11:08.470 align:middle line:84% And so we're assuming here, to make our calculations, 00:11:08.470 --> 00:11:11.200 align:middle line:84% that the ion velocities are all much 00:11:11.200 --> 00:11:14.200 align:middle line:84% less than these core neutral velocities. 00:11:14.200 --> 00:11:22.070 align:middle line:84% And this means that the i minus the A is about VA. 00:11:22.070 --> 00:11:24.570 align:middle line:84% It's useful when we're working out these cross-sections that 00:11:24.570 --> 00:11:27.900 align:middle line:84% have the difference between the two velocity populations. 00:11:27.900 --> 00:11:30.660 align:middle line:84% And then we can write down, that our attenuation 00:11:30.660 --> 00:11:38.346 align:middle line:84% coefficient alpha here is going to look like one upon VA, 00:11:38.346 --> 00:11:41.410 align:middle line:84% the electron impact cross-section 00:11:41.410 --> 00:11:52.310 align:middle line:84% sigma e Ve evaluated at VA and e plus the ion impact ionization 00:11:52.310 --> 00:11:57.590 align:middle line:90% sigma p, Vi evaluated at VA. 00:11:57.590 --> 00:12:04.470 align:middle line:84% And that's times ni plus the charge exchange cross-section, 00:12:04.470 --> 00:12:11.180 align:middle line:84% sigma C Vi evaluated at VA times my ni, like that. 00:12:11.180 --> 00:12:14.970 align:middle line:90% 00:12:14.970 --> 00:12:18.780 align:middle line:84% And we'll also now assume that our beam 00:12:18.780 --> 00:12:21.750 align:middle line:90% velocity is much less than-- 00:12:21.750 --> 00:12:23.700 align:middle line:84% or, sorry, the neutral atom velocity-- 00:12:23.700 --> 00:12:25.920 align:middle line:84% the neutral is trying to get out of the plasma-- 00:12:25.920 --> 00:12:28.410 align:middle line:84% is much less than the sort of average thermal velocity 00:12:28.410 --> 00:12:30.930 align:middle line:84% of the electrons so that we can have this nice 00:12:30.930 --> 00:12:36.960 align:middle line:84% ordering where Vi is much less than VA much less than Ve. 00:12:36.960 --> 00:12:40.560 align:middle line:84% And that allows us to further simplify this. 00:12:40.560 --> 00:12:41.980 align:middle line:90% We'll simplify it in two ways. 00:12:41.980 --> 00:12:43.830 align:middle line:84% The first one is that from the point of view 00:12:43.830 --> 00:12:47.050 align:middle line:84% of the electrons, the ion-- sorry, 00:12:47.050 --> 00:12:48.790 align:middle line:84% the neutrals are basically not moving. 00:12:48.790 --> 00:12:52.200 align:middle line:90% So we can set this to 0. 00:12:52.200 --> 00:12:56.520 align:middle line:84% And from the point of view of the neutrals, 00:12:56.520 --> 00:12:58.443 align:middle line:84% this Vi is approximately constant. 00:12:58.443 --> 00:13:00.610 align:middle line:84% It's a small value, and it's approximately constant. 00:13:00.610 --> 00:13:02.880 align:middle line:84% And so we can just take this Vi out. 00:13:02.880 --> 00:13:03.390 align:middle line:90% Sorry. 00:13:03.390 --> 00:13:07.710 align:middle line:84% We can evaluate this Vi as just being VA 00:13:07.710 --> 00:13:16.460 align:middle line:84% and we can take it outside, where it will nicely 00:13:16.460 --> 00:13:18.620 align:middle line:90% cancel with this VA. 00:13:18.620 --> 00:13:20.780 align:middle line:84% So this gives us an expression that 00:13:20.780 --> 00:13:31.450 align:middle line:84% looks like 1 upon VA sigma e Ve evaluated for effectively 0 00:13:31.450 --> 00:13:38.040 align:middle line:84% neutral velocity ne plus just these two cross-sections, 00:13:38.040 --> 00:13:44.130 align:middle line:90% sigma p and sigma C, times ni. 00:13:44.130 --> 00:13:48.120 align:middle line:84% And we see that this term goes as 1 upon VA and this term 00:13:48.120 --> 00:13:48.750 align:middle line:90% doesn't. 00:13:48.750 --> 00:13:52.230 align:middle line:84% So if we're dealing with energetic enough neutrals 00:13:52.230 --> 00:13:54.208 align:middle line:84% coming out of the core, then we can 00:13:54.208 --> 00:13:56.250 align:middle line:84% imagine that this term could be relatively small. 00:13:56.250 --> 00:13:58.530 align:middle line:84% It will depend exactly on what sigma e, sigma p, 00:13:58.530 --> 00:14:01.950 align:middle line:84% and sigma C are, but we can imagine, for reasonable values, 00:14:01.950 --> 00:14:03.970 align:middle line:90% this term will cancel. 00:14:03.970 --> 00:14:07.620 align:middle line:84% So we end up with an expression that just has this. 00:14:07.620 --> 00:14:12.165 align:middle line:84% So this again, is, just roughly alpha. 00:14:12.165 --> 00:14:14.750 align:middle line:90% 00:14:14.750 --> 00:14:16.670 align:middle line:90% Neglecting this for large-- 00:14:16.670 --> 00:14:22.830 align:middle line:90% 00:14:22.830 --> 00:14:23.330 align:middle line:90% OK. 00:14:23.330 --> 00:14:26.370 align:middle line:90% 00:14:26.370 --> 00:14:28.800 align:middle line:84% So then, you can put this back up 00:14:28.800 --> 00:14:31.710 align:middle line:84% into our probability of the particle getting through, 00:14:31.710 --> 00:14:41.660 align:middle line:84% and we just get exponential of minus sigma p plus sigma C 00:14:41.660 --> 00:14:47.790 align:middle line:90% integral of ni dl, like this. 00:14:47.790 --> 00:14:49.610 align:middle line:84% And you can go into Hutchinson's book 00:14:49.610 --> 00:14:51.920 align:middle line:84% and see graphs of sigma p and sigma C, 00:14:51.920 --> 00:14:57.050 align:middle line:84% and sigma e, as well, for different plasma conditions. 00:14:57.050 --> 00:14:59.780 align:middle line:84% And so if we just use an example that maybe we 00:14:59.780 --> 00:15:04.028 align:middle line:84% have 10 keV neutrals streaming out of the core, 00:15:04.028 --> 00:15:05.820 align:middle line:84% because that's the sort of temperature we'd 00:15:05.820 --> 00:15:11.350 align:middle line:84% like in a fusion reactor, so 10 keV neutrals, 00:15:11.350 --> 00:15:19.040 align:middle line:84% we've got a density of around 10 to the 20 per meter cubed. 00:15:19.040 --> 00:15:21.365 align:middle line:84% So this is on the dense side for an MCF reactor, 00:15:21.365 --> 00:15:22.990 align:middle line:84% but that's the sort of density we might 00:15:22.990 --> 00:15:25.150 align:middle line:90% need for reactable conditions. 00:15:25.150 --> 00:15:30.060 align:middle line:84% Then, using this, we will get a length scale 00:15:30.060 --> 00:15:34.040 align:middle line:84% in this exponent, which is effectively 00:15:34.040 --> 00:15:36.380 align:middle line:84% the mean free path of the neutrals trying 00:15:36.380 --> 00:15:37.500 align:middle line:90% to leave the plasma. 00:15:37.500 --> 00:15:41.520 align:middle line:84% And that is going to be about 10 centimeters. 00:15:41.520 --> 00:15:44.410 align:middle line:84% So for this relatively hot, relatively dense plasma, 00:15:44.410 --> 00:15:46.660 align:middle line:84% we're not going to see very many neutrals more than 10 00:15:46.660 --> 00:15:48.150 align:middle line:90% centimeters away from the core. 00:15:48.150 --> 00:15:49.650 align:middle line:84% And probably, our reactor is going 00:15:49.650 --> 00:15:55.550 align:middle line:84% to have a diameter A of about 100 centimeters or so. 00:15:55.550 --> 00:15:58.610 align:middle line:84% So we're not going to see very many of these particles, which 00:15:58.610 --> 00:16:01.460 align:middle line:84% means that in order for these neutral diagnostics 00:16:01.460 --> 00:16:04.920 align:middle line:84% to work at all, we're going to require. 00:16:04.920 --> 00:16:05.900 align:middle line:90% But that require... 00:16:05.900 --> 00:16:07.620 align:middle line:90% AUDIENCE: And-- Yes. 00:16:07.620 --> 00:16:09.860 align:middle line:90% JACK HARE: Yeah. 00:16:09.860 --> 00:16:10.610 align:middle line:90% AUDIENCE: Have a-- 00:16:10.610 --> 00:16:17.280 align:middle line:90% 00:16:17.280 --> 00:16:19.600 align:middle line:90% JACK HARE: OK, thank you. 00:16:19.600 --> 00:16:23.880 align:middle line:84% So we're going to require that the line integrated density here 00:16:23.880 --> 00:16:29.260 align:middle line:84% is going to be less than about 10 to the 19 per meter 00:16:29.260 --> 00:16:29.990 align:middle line:90% squared here. 00:16:29.990 --> 00:16:34.960 align:middle line:84% And if you do that, then you get lambda A more like a meter 00:16:34.960 --> 00:16:37.180 align:middle line:90% or so. 00:16:37.180 --> 00:16:41.900 align:middle line:90% So we need "low" density. 00:16:41.900 --> 00:16:45.525 align:middle line:84% I put it in quote marks because low means different things 00:16:45.525 --> 00:16:46.400 align:middle line:90% for different people. 00:16:46.400 --> 00:16:49.250 align:middle line:84% But we need a relatively low density tokamak 00:16:49.250 --> 00:16:51.110 align:middle line:84% or magnetic confinement fusion device 00:16:51.110 --> 00:16:54.410 align:middle line:84% in order to get neutrals escaping from the core. 00:16:54.410 --> 00:17:01.970 align:middle line:90% 00:17:01.970 --> 00:17:03.365 align:middle line:90% OK, questions on this? 00:17:03.365 --> 00:17:09.849 align:middle line:90% 00:17:09.849 --> 00:17:10.569 align:middle line:90% Yes, Audrey? 00:17:10.569 --> 00:17:14.569 align:middle line:90% AUDIENCE: [INAUDIBLE] 00:17:14.569 --> 00:17:18.270 align:middle line:84% JACK HARE: This is just, like, a feed of the neutrals coming out 00:17:18.270 --> 00:17:18.770 align:middle line:90% here. 00:17:18.770 --> 00:17:20.089 align:middle line:84% I realize, actually, drawing this, 00:17:20.089 --> 00:17:21.547 align:middle line:84% I don't think this is right at all. 00:17:21.547 --> 00:17:24.542 align:middle line:84% I don't think this is a delta function, because we're 00:17:24.542 --> 00:17:25.750 align:middle line:90% talking about a distribution. 00:17:25.750 --> 00:17:27.917 align:middle line:84% That's the whole thing we're trying to measure here. 00:17:27.917 --> 00:17:30.790 align:middle line:84% So I think that, actually, I should be drawing it like this 00:17:30.790 --> 00:17:32.467 align:middle line:90% and call it f of A. 00:17:32.467 --> 00:17:34.300 align:middle line:84% So this is the distribution of the neutrals. 00:17:34.300 --> 00:17:36.220 align:middle line:90% It's something Maxwellian-ish. 00:17:36.220 --> 00:17:38.560 align:middle line:84% But the average velocity here, which 00:17:38.560 --> 00:17:47.260 align:middle line:84% I could call VTa, which is maybe here, is much larger than VTi, 00:17:47.260 --> 00:17:52.310 align:middle line:90% but much smaller than VTe. 00:17:52.310 --> 00:17:56.690 align:middle line:84% So this is just the idea that for these neutrals here, 00:17:56.690 --> 00:17:58.520 align:middle line:84% from the point of view of the neutrals, 00:17:58.520 --> 00:18:00.077 align:middle line:84% the ions are basically stationary, 00:18:00.077 --> 00:18:01.910 align:middle line:84% and from the point of view of the electrons, 00:18:01.910 --> 00:18:04.220 align:middle line:84% the neutrals are basically stationary as well. 00:18:04.220 --> 00:18:06.447 align:middle line:84% And that allows us to simplify all of these angle 00:18:06.447 --> 00:18:08.030 align:middle line:84% brackets, which are actually averaging 00:18:08.030 --> 00:18:11.420 align:middle line:84% over the difference between the two velocity distributions. 00:18:11.420 --> 00:18:15.135 align:middle line:84% We can even set it to 0, or just be the velocity of the neutrals. 00:18:15.135 --> 00:18:15.635 align:middle line:90% Yeah? 00:18:15.635 --> 00:18:18.290 align:middle line:90% AUDIENCE: [INAUDIBLE] 00:18:18.290 --> 00:18:21.705 align:middle line:90% 00:18:21.705 --> 00:18:23.080 align:middle line:84% JACK HARE: Yeah, well, we imagine 00:18:23.080 --> 00:18:25.430 align:middle line:84% there's some temperature distribution inside this. 00:18:25.430 --> 00:18:27.760 align:middle line:84% So we're talking about, these neutrals here 00:18:27.760 --> 00:18:30.430 align:middle line:84% are neutrals that are in the core of the plasma, 00:18:30.430 --> 00:18:32.920 align:middle line:84% so we hope they're hotter than the ions 00:18:32.920 --> 00:18:34.498 align:middle line:90% in the rest of the plasma. 00:18:34.498 --> 00:18:35.040 align:middle line:90% AUDIENCE: OK. 00:18:35.040 --> 00:18:37.530 align:middle line:90% So that [INAUDIBLE]. 00:18:37.530 --> 00:18:39.600 align:middle line:84% JACK HARE: No, these are the ions out here 00:18:39.600 --> 00:18:41.130 align:middle line:84% or something like that, further out. 00:18:41.130 --> 00:18:42.338 align:middle line:90% Yeah, that's a good question. 00:18:42.338 --> 00:18:46.890 align:middle line:84% So if we have a sort of radius and temperature-type thing, 00:18:46.890 --> 00:18:51.580 align:middle line:84% we assume, for a good reactor, that it's peaked in some way. 00:18:51.580 --> 00:18:57.990 align:middle line:84% And so we're asking you about this, the f of i Vi at r 00:18:57.990 --> 00:19:07.000 align:middle line:84% equals 0 becomes rf of neutrals V neutral at r equals 0. 00:19:07.000 --> 00:19:12.310 align:middle line:84% But they're streaming through some f of i Vi 00:19:12.310 --> 00:19:15.767 align:middle line:84% at r greater than 0, which in general is going 00:19:15.767 --> 00:19:16.850 align:middle line:90% to be a lower temperature. 00:19:16.850 --> 00:19:18.250 align:middle line:90% So the distribution is smaller. 00:19:18.250 --> 00:19:19.062 align:middle line:90% Yeah. 00:19:19.062 --> 00:19:20.770 align:middle line:84% All of this is very hand-wavy, of course. 00:19:20.770 --> 00:19:21.970 align:middle line:84% If you want to do this properly, you 00:19:21.970 --> 00:19:24.303 align:middle line:84% have to keep track and do all these integrals correctly. 00:19:24.303 --> 00:19:28.270 align:middle line:84% But just to give an idea of the most important effect, 00:19:28.270 --> 00:19:31.300 align:middle line:84% it turns out r-- the [? ion-ion ?] impact ionization 00:19:31.300 --> 00:19:32.590 align:middle line:90% and the charge exchange. 00:19:32.590 --> 00:19:35.030 align:middle line:84% And the charge exchange dominates this pretty strongly, 00:19:35.030 --> 00:19:35.530 align:middle line:90% actually. 00:19:35.530 --> 00:19:37.393 align:middle line:84% So it's mostly just charge exchange 00:19:37.393 --> 00:19:38.560 align:middle line:90% with some of the other ions. 00:19:38.560 --> 00:19:40.420 align:middle line:90% Yeah. 00:19:40.420 --> 00:19:43.050 align:middle line:90% AUDIENCE: [INAUDIBLE] 00:19:43.050 --> 00:19:44.323 align:middle line:90% 00:19:44.323 --> 00:19:45.990 align:middle line:84% JACK HARE: We haven't talked about that. 00:19:45.990 --> 00:19:46.710 align:middle line:90% No. 00:19:46.710 --> 00:19:49.380 align:middle line:84% So what I'm saying is, imagine somehow you have 00:19:49.380 --> 00:19:51.205 align:middle line:90% created neutrals in the core. 00:19:51.205 --> 00:19:52.830 align:middle line:84% Would they actually be able to get out? 00:19:52.830 --> 00:19:54.210 align:middle line:84% Because if they can't get out, there's 00:19:54.210 --> 00:19:56.440 align:middle line:84% no point even trying to create them in the first place. 00:19:56.440 --> 00:19:59.065 align:middle line:84% So we're sort of working our way backwards through the problem. 00:19:59.065 --> 00:20:01.140 align:middle line:84% The next step is, OK, now that we know, 00:20:01.140 --> 00:20:03.240 align:middle line:84% if we create some neutrals, they can escape, 00:20:03.240 --> 00:20:05.040 align:middle line:84% we can probably measure them in some way 00:20:05.040 --> 00:20:07.620 align:middle line:84% and learn about the core ion distribution. 00:20:07.620 --> 00:20:09.450 align:middle line:84% Now that we know that that's the case, 00:20:09.450 --> 00:20:11.713 align:middle line:84% can we now work out how to create the neutrals? 00:20:11.713 --> 00:20:13.630 align:middle line:84% And we'll talk about some techniques for that. 00:20:13.630 --> 00:20:15.022 align:middle line:90% Yeah. 00:20:15.022 --> 00:20:16.926 align:middle line:90% Yeah. 00:20:16.926 --> 00:20:18.768 align:middle line:84% AUDIENCE: Why would we [INAUDIBLE]? 00:20:18.768 --> 00:20:23.393 align:middle line:90% 00:20:23.393 --> 00:20:24.060 align:middle line:90% JACK HARE: Yeah. 00:20:24.060 --> 00:20:24.990 align:middle line:90% I mean, this is very crude. 00:20:24.990 --> 00:20:25.782 align:middle line:90% You're quite right. 00:20:25.782 --> 00:20:27.725 align:middle line:84% I mean, this should be inside here. 00:20:27.725 --> 00:20:29.100 align:middle line:84% But if we assume that these don't 00:20:29.100 --> 00:20:31.620 align:middle line:84% vary too much as the particle travels from the core 00:20:31.620 --> 00:20:33.377 align:middle line:84% to the edge, then it allows us just 00:20:33.377 --> 00:20:35.460 align:middle line:84% to pull out this factor of ni dl and make it clear 00:20:35.460 --> 00:20:37.390 align:middle line:84% that it's like the line-integrated density that's 00:20:37.390 --> 00:20:38.070 align:middle line:90% important thing. 00:20:38.070 --> 00:20:41.220 align:middle line:84% In reality, it would have to stay inside. 00:20:41.220 --> 00:20:43.810 align:middle line:90% Yeah. 00:20:43.810 --> 00:20:44.820 align:middle line:90% Cool. 00:20:44.820 --> 00:20:45.700 align:middle line:90% Any questions online? 00:20:45.700 --> 00:20:50.840 align:middle line:90% 00:20:50.840 --> 00:20:51.350 align:middle line:90% All right. 00:20:51.350 --> 00:20:53.840 align:middle line:84% Let's go find out how to put some neutrals in the core. 00:20:53.840 --> 00:21:04.315 align:middle line:90% 00:21:04.315 --> 00:21:06.190 align:middle line:84% I'm trying to spell neutrals with an A there. 00:21:06.190 --> 00:21:13.990 align:middle line:90% 00:21:13.990 --> 00:21:14.920 align:middle line:90% OK. 00:21:14.920 --> 00:21:21.570 align:middle line:84% So again, Let's have some flux surfaces, some plasma like this. 00:21:21.570 --> 00:21:24.680 align:middle line:84% So one of the ways the neutrals could get there, 00:21:24.680 --> 00:21:27.350 align:middle line:84% as we discussed before, is from the edge. 00:21:27.350 --> 00:21:29.210 align:middle line:84% So around the edge of the plasma, 00:21:29.210 --> 00:21:31.888 align:middle line:84% there's, for example, the scrape-off layer. 00:21:31.888 --> 00:21:33.680 align:middle line:84% And then there's going to be a region which 00:21:33.680 --> 00:21:36.650 align:middle line:84% is in contact with the wall, which is relatively cold. 00:21:36.650 --> 00:21:39.530 align:middle line:84% And so we can have neutrals being produced here. 00:21:39.530 --> 00:21:42.017 align:middle line:84% And these neutrals will wander in 00:21:42.017 --> 00:21:43.850 align:middle line:84% and they won't see the magnetic field lines, 00:21:43.850 --> 00:21:46.820 align:middle line:84% and so maybe one of them will only get so far here 00:21:46.820 --> 00:21:48.268 align:middle line:90% before the charge exchanges. 00:21:48.268 --> 00:21:50.060 align:middle line:84% And this one will get a little bit further. 00:21:50.060 --> 00:21:53.420 align:middle line:84% But you could imagine that maybe a couple of these neutrals 00:21:53.420 --> 00:21:56.600 align:middle line:84% wander into the center, they charge exchange, 00:21:56.600 --> 00:22:01.520 align:middle line:84% and then we can start getting the new neutrals, the ones that 00:22:01.520 --> 00:22:04.880 align:middle line:84% represent the core ions, start moving back out again. 00:22:04.880 --> 00:22:08.230 align:middle line:90% 00:22:08.230 --> 00:22:10.345 align:middle line:90% So one possibility is-- 00:22:10.345 --> 00:22:11.470 align:middle line:90% we'll call it edge fueling. 00:22:11.470 --> 00:22:17.830 align:middle line:90% 00:22:17.830 --> 00:22:20.470 align:middle line:84% And we know how to calculate the probability of that, 00:22:20.470 --> 00:22:22.240 align:middle line:84% because we just spent a long time trying 00:22:22.240 --> 00:22:25.280 align:middle line:84% to calculate the probability of the opposite process. 00:22:25.280 --> 00:22:27.550 align:middle line:84% So now, we know that it's basically 00:22:27.550 --> 00:22:32.020 align:middle line:84% PBA, which is the probability of going from the outside, B, 00:22:32.020 --> 00:22:35.720 align:middle line:84% into the core, which we called A in our previous diagram. 00:22:35.720 --> 00:22:39.040 align:middle line:84% So we can estimate how likely it is that any of these particles 00:22:39.040 --> 00:22:39.610 align:middle line:90% get through. 00:22:39.610 --> 00:22:41.110 align:middle line:84% And the answer is that this actually 00:22:41.110 --> 00:22:43.623 align:middle line:84% does create a fair amount of neutrals in the core. 00:22:43.623 --> 00:22:45.790 align:middle line:84% Just because there are so many neutrals in the edge, 00:22:45.790 --> 00:22:47.040 align:middle line:90% some of them will get through. 00:22:47.040 --> 00:22:49.180 align:middle line:84% So this technique by itself will create 00:22:49.180 --> 00:22:53.080 align:middle line:84% a detectable flux of core neutrals coming back out again. 00:22:53.080 --> 00:22:55.620 align:middle line:90% 00:22:55.620 --> 00:22:57.480 align:middle line:90% So PBA, which is edge to core. 00:22:57.480 --> 00:23:02.673 align:middle line:90% 00:23:02.673 --> 00:23:03.840 align:middle line:90% Another thing you might say. 00:23:03.840 --> 00:23:07.080 align:middle line:84% Well, perhaps, just by some atomic processes in the core 00:23:07.080 --> 00:23:09.960 align:middle line:84% here, we could get neutrals developing here. 00:23:09.960 --> 00:23:21.522 align:middle line:84% So we could have radiative recombination, 00:23:21.522 --> 00:23:24.105 align:middle line:84% because, after all, there's a load of electrons flying around. 00:23:24.105 --> 00:23:29.250 align:middle line:90% 00:23:29.250 --> 00:23:31.598 align:middle line:84% These electrons are up above the ionization energy, 00:23:31.598 --> 00:23:32.265 align:middle line:90% so they're free. 00:23:32.265 --> 00:23:35.160 align:middle line:90% 00:23:35.160 --> 00:23:38.460 align:middle line:84% This electron could be caught by the electric potential 00:23:38.460 --> 00:23:41.050 align:middle line:84% of the ion and become a bound electron. 00:23:41.050 --> 00:23:46.350 align:middle line:84% And then we would get out our recombination photon. 00:23:46.350 --> 00:23:47.610 align:middle line:90% That process could happen. 00:23:47.610 --> 00:23:52.800 align:middle line:84% But of course, the other process we've already discussed 00:23:52.800 --> 00:23:56.570 align:middle line:84% is when we have an electron come in and collide 00:23:56.570 --> 00:23:58.160 align:middle line:84% with one of the inner shell electrons, 00:23:58.160 --> 00:24:01.400 align:middle line:84% and we end up with two electrons coming back out again. 00:24:01.400 --> 00:24:07.840 align:middle line:84% And this is electron impact ionization. 00:24:07.840 --> 00:24:13.200 align:middle line:84% And there'll be a balance in the steady state between these two 00:24:13.200 --> 00:24:15.270 align:middle line:84% processes and that balance will look 00:24:15.270 --> 00:24:18.990 align:middle line:84% like the density of electrons, the density of ions, 00:24:18.990 --> 00:24:21.120 align:middle line:84% the reactivity or the cross-section 00:24:21.120 --> 00:24:25.110 align:middle line:84% for the radiative recombination, timesed by the electron 00:24:25.110 --> 00:24:26.490 align:middle line:90% velocity. 00:24:26.490 --> 00:24:30.960 align:middle line:84% And that will be balanced by the electron density, the density 00:24:30.960 --> 00:24:37.980 align:middle line:84% of neutrals here, sigma e for electron impact ionization, Ve, 00:24:37.980 --> 00:24:38.950 align:middle line:90% like that. 00:24:38.950 --> 00:24:40.620 align:middle line:84% So that means that we can look at this 00:24:40.620 --> 00:24:45.210 align:middle line:84% and go, OK, what is the steady state density of neutrals? 00:24:45.210 --> 00:24:49.080 align:middle line:90% That's going to be nA over ni. 00:24:49.080 --> 00:24:51.660 align:middle line:84% These cancel, so it's just going to be 00:24:51.660 --> 00:25:00.180 align:middle line:84% the ratio of these reactivities, sigma r Ve over sigma e Ve, 00:25:00.180 --> 00:25:02.020 align:middle line:90% like that. 00:25:02.020 --> 00:25:06.730 align:middle line:84% And at 1 keV, which is a reasonable temperature for you 00:25:06.730 --> 00:25:12.750 align:middle line:84% to have in your core, this is about 10 to the minus 8. 00:25:12.750 --> 00:25:14.250 align:middle line:84% So the point I'm trying to make here 00:25:14.250 --> 00:25:16.530 align:middle line:84% is although you might occasionally 00:25:16.530 --> 00:25:19.950 align:middle line:84% have some recombination process, because the other processes 00:25:19.950 --> 00:25:22.200 align:middle line:84% which lead to ionization, again, are so rapid, 00:25:22.200 --> 00:25:24.000 align:middle line:90% you quickly will re-ionize. 00:25:24.000 --> 00:25:27.430 align:middle line:84% And so if you have 10 to the 13 or 10 00:25:27.430 --> 00:25:30.270 align:middle line:84% to the 20 ions per cubic meter, they'll 00:25:30.270 --> 00:25:31.620 align:middle line:90% only have 10 to the 12 neutrals. 00:25:31.620 --> 00:25:33.245 align:middle line:84% And that's not really enough to detect. 00:25:33.245 --> 00:25:34.860 align:middle line:90% So this is negligible. 00:25:34.860 --> 00:25:41.840 align:middle line:90% 00:25:41.840 --> 00:25:43.690 align:middle line:90% So edge fueling. 00:25:43.690 --> 00:25:46.390 align:middle line:84% Yes, it could be a way of getting neutrals in the core. 00:25:46.390 --> 00:25:48.610 align:middle line:84% Radiative recombination is not a way. 00:25:48.610 --> 00:25:50.920 align:middle line:84% And you kind of know this because if this 00:25:50.920 --> 00:25:52.630 align:middle line:84% was an effective process, then you 00:25:52.630 --> 00:25:54.380 align:middle line:84% would end up with a large neutral fraction 00:25:54.380 --> 00:25:56.380 align:middle line:84% in the core of your tokamak, and that's 00:25:56.380 --> 00:25:58.300 align:middle line:84% not something that we generally think about 00:25:58.300 --> 00:26:02.000 align:middle line:90% and doesn't generally happen. 00:26:02.000 --> 00:26:05.330 align:middle line:84% And then finally, there are beams. 00:26:05.330 --> 00:26:08.000 align:middle line:84% And I'll talk a little bit more about beams in a second, 00:26:08.000 --> 00:26:09.860 align:middle line:84% as an active version of the diagnostic, 00:26:09.860 --> 00:26:12.320 align:middle line:84% but I just want to talk about how we actually 00:26:12.320 --> 00:26:17.500 align:middle line:84% measure these neutrals coming out in this passive version 00:26:17.500 --> 00:26:19.660 align:middle line:84% where we just let edge fueling do the work. 00:26:19.660 --> 00:26:23.270 align:middle line:90% 00:26:23.270 --> 00:26:32.935 align:middle line:84% So passive cx with edge neutrals. 00:26:32.935 --> 00:26:39.750 align:middle line:90% 00:26:39.750 --> 00:26:45.390 align:middle line:84% So we've got some tokamak vacuum chamber, some MCF vacuum 00:26:45.390 --> 00:26:48.550 align:middle line:84% chamber, with some plasma like this. 00:26:48.550 --> 00:26:55.030 align:middle line:84% We have all of the particles coming in from the edge, 00:26:55.030 --> 00:26:57.970 align:middle line:84% and then the charge exchanging with particles in the core. 00:26:57.970 --> 00:27:04.300 align:middle line:84% And they're producing, for example, 00:27:04.300 --> 00:27:07.290 align:middle line:84% a hydrogen neutral that's coming out from the core. 00:27:07.290 --> 00:27:10.440 align:middle line:84% And we put that hydrogen neutral into something 00:27:10.440 --> 00:27:12.285 align:middle line:90% called a stripping cell. 00:27:12.285 --> 00:27:20.770 align:middle line:90% 00:27:20.770 --> 00:27:24.190 align:middle line:84% And it comes out as a hydrogen ion again, but a hydrogen 00:27:24.190 --> 00:27:26.200 align:middle line:84% ion with the same velocity, or effectively, 00:27:26.200 --> 00:27:28.870 align:middle line:84% the same distribution function, as the neutral coming in. 00:27:28.870 --> 00:27:32.890 align:middle line:84% The stripping cell has a very electropositive gas, 00:27:32.890 --> 00:27:34.690 align:middle line:84% so it wants to take off the electrons, 00:27:34.690 --> 00:27:36.520 align:middle line:84% and it will charge exchange without really 00:27:36.520 --> 00:27:38.410 align:middle line:84% changing the trajectory of this very much. 00:27:38.410 --> 00:27:42.970 align:middle line:84% And then we have, for example, a large magnetic field 00:27:42.970 --> 00:27:47.920 align:middle line:84% in this region that bends the particles according 00:27:47.920 --> 00:27:50.140 align:middle line:90% to their velocity. 00:27:50.140 --> 00:27:55.750 align:middle line:84% And then we have a detector like this with bins in it, 00:27:55.750 --> 00:27:58.870 align:middle line:84% and the bins have different sensitivity 00:27:58.870 --> 00:28:00.320 align:middle line:90% to different velocities here. 00:28:00.320 --> 00:28:06.260 align:middle line:84% And so by counting out a number of particles in each bin, 00:28:06.260 --> 00:28:14.490 align:middle line:84% we get out that distribution function, like that. 00:28:14.490 --> 00:28:17.610 align:middle line:84% And we hope that, during their travels from the core 00:28:17.610 --> 00:28:19.530 align:middle line:84% through our stripping cell onto our detector, 00:28:19.530 --> 00:28:21.905 align:middle line:84% the distribution function has not been changed very much. 00:28:21.905 --> 00:28:24.090 align:middle line:84% So we really are measuring the distribution function 00:28:24.090 --> 00:28:26.530 align:middle line:84% of the particles in the center there. 00:28:26.530 --> 00:28:29.370 align:middle line:84% So if we look at that on our detector, 00:28:29.370 --> 00:28:33.150 align:middle line:84% I plot it on a logarithmic scale. 00:28:33.150 --> 00:28:39.750 align:middle line:84% The log of intensity, which is equal to log of particle number 00:28:39.750 --> 00:28:45.230 align:middle line:84% versus particle energy here, but not velocity but energy, 00:28:45.230 --> 00:28:53.550 align:middle line:84% which is 1/2 mv squared, we see that we have a region that is 00:28:53.550 --> 00:28:59.680 align:middle line:84% approximately straight, and that has a slope of 1 over Ti, 00:28:59.680 --> 00:29:02.500 align:middle line:84% because our distribution function for Maxwellian is 00:29:02.500 --> 00:29:07.580 align:middle line:84% exponential of minus e over Ti like that. 00:29:07.580 --> 00:29:10.660 align:middle line:84% And then we might have some interesting features 00:29:10.660 --> 00:29:14.440 align:middle line:84% down at the bottom here, where it looks non-Maxwellian. 00:29:14.440 --> 00:29:17.030 align:middle line:90% And so this can be the tail. 00:29:17.030 --> 00:29:18.770 align:middle line:84% And this will correspond to fast ions. 00:29:18.770 --> 00:29:25.750 align:middle line:90% 00:29:25.750 --> 00:29:27.760 align:middle line:84% And measuring fast ions is very important 00:29:27.760 --> 00:29:29.260 align:middle line:90% in magnetic confinement fusion. 00:29:29.260 --> 00:29:36.430 align:middle line:84% These fast ions might be due to things like rf heating, 00:29:36.430 --> 00:29:40.390 align:middle line:84% or they might be due to runaways being produced 00:29:40.390 --> 00:29:44.360 align:middle line:84% by inductively driven electric fields, or other cool physics. 00:29:44.360 --> 00:29:48.170 align:middle line:84% So it's nice to be able to measure those fast ions as well. 00:29:48.170 --> 00:29:50.190 align:middle line:84% The main problem with this technique, of course, 00:29:50.190 --> 00:29:51.190 align:middle line:90% is it's line-integrated. 00:29:51.190 --> 00:29:53.800 align:middle line:84% If I have my detector set up like this, 00:29:53.800 --> 00:29:58.340 align:middle line:84% I'm collecting all the particles in this region 00:29:58.340 --> 00:29:59.420 align:middle line:90% that come down here. 00:29:59.420 --> 00:30:03.360 align:middle line:90% 00:30:03.360 --> 00:30:05.150 align:middle line:84% And so you don't really know exactly where 00:30:05.150 --> 00:30:06.720 align:middle line:90% those particles have come from. 00:30:06.720 --> 00:30:08.137 align:middle line:84% And so we have the same problem we 00:30:08.137 --> 00:30:11.560 align:middle line:84% have with all of our other line-integrated diagnostics. 00:30:11.560 --> 00:30:13.473 align:middle line:90% But it's pretty free. 00:30:13.473 --> 00:30:15.640 align:middle line:84% We don't actually have to put any effort into making 00:30:15.640 --> 00:30:16.660 align:middle line:90% neutrals in the center there. 00:30:16.660 --> 00:30:18.730 align:middle line:84% We just let the fact that we have a crappy vacuum 00:30:18.730 --> 00:30:20.270 align:middle line:90% chamber do the work for us. 00:30:20.270 --> 00:30:22.060 align:middle line:84% So this is a nice way to do it if you 00:30:22.060 --> 00:30:24.387 align:middle line:90% don't have a neutral beam. 00:30:24.387 --> 00:30:26.470 align:middle line:84% Any questions on that before we put a neutral beam 00:30:26.470 --> 00:30:27.137 align:middle line:90% into the system? 00:30:27.137 --> 00:30:34.980 align:middle line:90% 00:30:34.980 --> 00:30:35.480 align:middle line:90% Mm-hmm. 00:30:35.480 --> 00:30:38.835 align:middle line:90% AUDIENCE: [INAUDIBLE] 00:30:38.835 --> 00:30:42.152 align:middle line:90% 00:30:42.152 --> 00:30:45.420 align:middle line:84% JACK HARE: Oh, you would just have a magnetic field here. 00:30:45.420 --> 00:30:49.950 align:middle line:90% 00:30:49.950 --> 00:30:52.498 align:middle line:84% And frankly, the magnetic field of your tokamak 00:30:52.498 --> 00:30:53.790 align:middle line:90% does a pretty good job of that. 00:30:53.790 --> 00:30:54.520 align:middle line:90% But yeah. 00:30:54.520 --> 00:30:57.571 align:middle line:90% 00:30:57.571 --> 00:31:00.238 align:middle line:84% AUDIENCE: How does it depend on the material of the [INAUDIBLE]? 00:31:00.238 --> 00:31:04.550 align:middle line:90% 00:31:04.550 --> 00:31:06.050 align:middle line:90% JACK HARE: How does what depend? 00:31:06.050 --> 00:31:10.040 align:middle line:84% AUDIENCE: Like, how many does [INAUDIBLE]? 00:31:10.040 --> 00:31:10.780 align:middle line:90% JACK HARE: Yeah. 00:31:10.780 --> 00:31:12.657 align:middle line:84% I mean, we tend to be thinking about-- 00:31:12.657 --> 00:31:14.990 align:middle line:84% we still tend to be thinking about these neutrals coming 00:31:14.990 --> 00:31:19.090 align:middle line:84% from the edges being hydrogen. So when we have the hydrogen 00:31:19.090 --> 00:31:21.657 align:middle line:84% plasma-- by hydrogen, I mean deuterium and tritium, our fuel. 00:31:21.657 --> 00:31:23.740 align:middle line:84% So when we have our fuel in contact with the wall, 00:31:23.740 --> 00:31:27.220 align:middle line:84% there will be a layer of low ionization 00:31:27.220 --> 00:31:29.578 align:middle line:84% state, partially neutral gas around the edge, 00:31:29.578 --> 00:31:31.370 align:middle line:84% just because it's in contact with the wall. 00:31:31.370 --> 00:31:33.430 align:middle line:84% And so most of this will be coming from. 00:31:33.430 --> 00:31:36.627 align:middle line:84% I don't know what happens if you start looking at this 00:31:36.627 --> 00:31:38.710 align:middle line:84% and you start looking at all the neutrals as well. 00:31:38.710 --> 00:31:41.230 align:middle line:84% Presumably, you now need many more coefficients to calculate. 00:31:41.230 --> 00:31:42.520 align:middle line:84% And probably, if you're doing it properly, 00:31:42.520 --> 00:31:44.110 align:middle line:84% you should take into account those. 00:31:44.110 --> 00:31:47.080 align:middle line:84% But I think, although impurities can dominate things 00:31:47.080 --> 00:31:51.770 align:middle line:84% like line radiation, this really depends on the ion number. 00:31:51.770 --> 00:31:53.530 align:middle line:84% So we're going to be thinking, probably, 00:31:53.530 --> 00:31:57.147 align:middle line:84% about-- the impurities probably don't have a higher number 00:31:57.147 --> 00:31:59.230 align:middle line:84% density than the fuel, or if you've done something 00:31:59.230 --> 00:32:00.397 align:middle line:90% very wrong, that's happened. 00:32:00.397 --> 00:32:03.660 align:middle line:84% So I think you're still going to be dominated by your fuel ion. 00:32:03.660 --> 00:32:05.140 align:middle line:90% Yeah, cool. 00:32:05.140 --> 00:32:06.230 align:middle line:90% Yes? 00:32:06.230 --> 00:32:08.480 align:middle line:84% AUDIENCE: So if you start with the neutral at the edge 00:32:08.480 --> 00:32:12.450 align:middle line:84% and then it goes into the plasma for charge exchange, 00:32:12.450 --> 00:32:16.920 align:middle line:84% then the new neutral that leaks out was an ion in plasma, 00:32:16.920 --> 00:32:19.410 align:middle line:84% and then you're measuring that neutral that leaks out. 00:32:19.410 --> 00:32:24.420 align:middle line:84% How do you know that you're only measuring both [INAUDIBLE] ion 00:32:24.420 --> 00:32:26.573 align:middle line:84% and the neutrals at the [INAUDIBLE]? 00:32:26.573 --> 00:32:27.240 align:middle line:90% JACK HARE: Yeah. 00:32:27.240 --> 00:32:29.430 align:middle line:84% So the question was, how do we know that none of our signal 00:32:29.430 --> 00:32:30.720 align:middle line:84% is due to the neutrals at the edge? 00:32:30.720 --> 00:32:32.710 align:middle line:84% Well, the neutrals at the edge are very cold. 00:32:32.710 --> 00:32:34.420 align:middle line:90% So their energy is very low. 00:32:34.420 --> 00:32:36.870 align:middle line:84% So we probably will have a spectra that 00:32:36.870 --> 00:32:41.730 align:middle line:84% looks like this or something, with some noise up here, 00:32:41.730 --> 00:32:44.637 align:middle line:84% or some spurious signal that's due to other neutrals 00:32:44.637 --> 00:32:45.220 align:middle line:90% in the system. 00:32:45.220 --> 00:32:48.340 align:middle line:84% So I'll just start my fit at some nice high energy, 00:32:48.340 --> 00:32:51.600 align:middle line:84% which can't be due to any of these cold ions-- 00:32:51.600 --> 00:32:53.160 align:middle line:90% or cold neutrals from the edge. 00:32:53.160 --> 00:32:58.150 align:middle line:84% Has to just be due to the core ions instead. 00:32:58.150 --> 00:33:01.235 align:middle line:90% Any other-- yeah. 00:33:01.235 --> 00:33:21.083 align:middle line:90% AUDIENCE: [INAUDIBLE], 00:33:21.083 --> 00:33:21.750 align:middle line:90% JACK HARE: Yeah. 00:33:21.750 --> 00:33:24.810 align:middle line:84% So I mean, that's what's very challenging about this 00:33:24.810 --> 00:33:26.460 align:middle line:84% here, because in fact, this will be, 00:33:26.460 --> 00:33:28.500 align:middle line:84% like, the sum of a load of lines which will 00:33:28.500 --> 00:33:29.740 align:middle line:90% be weighted by their density. 00:33:29.740 --> 00:33:31.530 align:middle line:84% So I think it is difficult to interpret 00:33:31.530 --> 00:33:33.150 align:middle line:90% the passive version of it. 00:33:33.150 --> 00:33:35.253 align:middle line:84% Of course, if you go high enough out in energy 00:33:35.253 --> 00:33:37.920 align:middle line:84% and you can still fit a bit of a straight line, you can be like, 00:33:37.920 --> 00:33:40.050 align:middle line:84% there is some part of my plasma-- 00:33:40.050 --> 00:33:41.760 align:middle line:84% because you'll have different slopes. 00:33:41.760 --> 00:33:44.438 align:middle line:90% 00:33:44.438 --> 00:33:45.980 align:middle line:84% And there will only be one slope that 00:33:45.980 --> 00:33:48.355 align:middle line:84% still extends all the way out here, because each of these 00:33:48.355 --> 00:33:49.920 align:middle line:84% will eventually sort of drop off. 00:33:49.920 --> 00:33:52.670 align:middle line:84% So if you're like, aha, still out here, there's some region, 00:33:52.670 --> 00:33:54.402 align:middle line:84% then that's probably your core ions. 00:33:54.402 --> 00:33:56.360 align:middle line:84% So you might have a chance of identifying them. 00:33:56.360 --> 00:33:58.652 align:middle line:84% But in general, your signal will look more complicated, 00:33:58.652 --> 00:34:01.980 align:middle line:84% which leads me very neatly on to using a neutral beam to do this 00:34:01.980 --> 00:34:02.480 align:middle line:90% instead. 00:34:02.480 --> 00:34:22.393 align:middle line:90% 00:34:22.393 --> 00:34:24.060 align:middle line:84% So this actually is very similar to some 00:34:24.060 --> 00:34:26.610 align:middle line:84% of those active spectroscopy diagnostics 00:34:26.610 --> 00:34:28.050 align:middle line:90% we talked about before. 00:34:28.050 --> 00:34:30.929 align:middle line:84% We've, again, got our vacuum chamber and our plasma 00:34:30.929 --> 00:34:34.380 align:middle line:84% like this, but now, we have a neutral beam 00:34:34.380 --> 00:34:35.535 align:middle line:90% going through the plasma. 00:34:35.535 --> 00:34:39.590 align:middle line:90% 00:34:39.590 --> 00:34:43.810 align:middle line:84% And if we have our detector oriented perpendicularly 00:34:43.810 --> 00:34:48.489 align:middle line:84% to this, now, we know that the majority of the neutrals 00:34:48.489 --> 00:34:49.900 align:middle line:84% are being born by charge exchange 00:34:49.900 --> 00:34:53.199 align:middle line:84% between the neutral beam and this small core region 00:34:53.199 --> 00:34:55.480 align:middle line:84% here, which overlaps the field of view 00:34:55.480 --> 00:35:00.490 align:middle line:84% of our detector and the neutral beam here. 00:35:00.490 --> 00:35:05.050 align:middle line:84% And so now, we know very well, when these particles come out, 00:35:05.050 --> 00:35:13.110 align:middle line:84% that we are detecting f of i Vi r about 0 from the core here. 00:35:13.110 --> 00:35:17.930 align:middle line:84% So this allows us to actively probe that central region here. 00:35:17.930 --> 00:35:19.010 align:middle line:90% It's the localizers. 00:35:19.010 --> 00:35:28.930 align:middle line:90% 00:35:28.930 --> 00:35:31.360 align:middle line:84% And this is often convenient because we often 00:35:31.360 --> 00:35:32.230 align:middle line:90% have neutral beams. 00:35:32.230 --> 00:35:34.150 align:middle line:84% As we said, these neutral beams are already 00:35:34.150 --> 00:35:39.080 align:middle line:84% being used for heating and for current drive. 00:35:39.080 --> 00:35:44.693 align:middle line:90% 00:35:44.693 --> 00:35:47.370 align:middle line:84% Of course, the neutral beam has the same problem 00:35:47.370 --> 00:35:49.080 align:middle line:84% that we found out when we were talking 00:35:49.080 --> 00:35:51.750 align:middle line:84% about how far these neutrals can penetrate. 00:35:51.750 --> 00:35:54.450 align:middle line:84% If you have a density that's high enough inside your machine, 00:35:54.450 --> 00:35:56.370 align:middle line:84% you're not going to be able to use a neutral beam to heat 00:35:56.370 --> 00:35:57.453 align:middle line:90% all of your current drive. 00:35:57.453 --> 00:35:59.010 align:middle line:84% So neutral beams tend to be limited 00:35:59.010 --> 00:36:01.860 align:middle line:84% to lower-density machines, which is why we've never 00:36:01.860 --> 00:36:04.430 align:middle line:84% had much use for them on devices like CMOS, 00:36:04.430 --> 00:36:06.930 align:middle line:84% where the magnetic field and the density is very, very high. 00:36:06.930 --> 00:36:09.770 align:middle line:84% But for other devices, you may well have a neutral beam already 00:36:09.770 --> 00:36:10.270 align:middle line:90% there. 00:36:10.270 --> 00:36:12.690 align:middle line:84% So this is, again, kind of a freebie 00:36:12.690 --> 00:36:14.160 align:middle line:90% to have this as a diagnostic. 00:36:14.160 --> 00:36:16.960 align:middle line:90% 00:36:16.960 --> 00:36:19.510 align:middle line:84% Let's talk about some other things 00:36:19.510 --> 00:36:22.120 align:middle line:90% you can do with a neutral beam. 00:36:22.120 --> 00:36:25.100 align:middle line:90% 00:36:25.100 --> 00:36:28.400 align:middle line:84% So there's a very nice technique which is called-- 00:36:28.400 --> 00:36:30.950 align:middle line:90% 00:36:30.950 --> 00:36:31.960 align:middle line:90% where's my green? 00:36:31.960 --> 00:36:34.970 align:middle line:90% There we go. 00:36:34.970 --> 00:36:43.680 align:middle line:90% Charge exchange spectroscopy. 00:36:43.680 --> 00:36:48.370 align:middle line:90% 00:36:48.370 --> 00:36:50.230 align:middle line:84% This technique has developed a number 00:36:50.230 --> 00:36:51.940 align:middle line:84% of acronyms in the literature, which 00:36:51.940 --> 00:36:55.370 align:middle line:90% are all identical in meaning. 00:36:55.370 --> 00:36:57.910 align:middle line:84% So some people call it charge exchange recombination 00:36:57.910 --> 00:37:02.740 align:middle line:84% spectroscopy, and some people call it charge exchange 00:37:02.740 --> 00:37:04.917 align:middle line:90% recombination spectroscopy. 00:37:04.917 --> 00:37:07.250 align:middle line:84% So if you see an acronym that looks something like this, 00:37:07.250 --> 00:37:09.375 align:middle line:84% they're probably talking about the same diagnostic. 00:37:09.375 --> 00:37:11.300 align:middle line:84% These are not two separate diagnostics. 00:37:11.300 --> 00:37:14.120 align:middle line:90% They are the same thing here. 00:37:14.120 --> 00:37:17.440 align:middle line:84% So the idea of charge exchange recombination 00:37:17.440 --> 00:37:21.860 align:middle line:84% spectroscopy is, within our plasma, 00:37:21.860 --> 00:37:25.170 align:middle line:90% we will have some neutrals. 00:37:25.170 --> 00:37:27.810 align:middle line:84% Sorry, we will have some ions which are impurity ions. 00:37:27.810 --> 00:37:28.570 align:middle line:90% Sorry. 00:37:28.570 --> 00:37:36.690 align:middle line:84% So impurity, like A. We'll just use 00:37:36.690 --> 00:37:39.480 align:middle line:84% the symbol A. I'll make it clear what it is in a moment. 00:37:39.480 --> 00:37:43.470 align:middle line:84% These impurities will the things like oxygen or carbon or boron. 00:37:43.470 --> 00:37:46.920 align:middle line:84% And although these impurities have many more electrons 00:37:46.920 --> 00:37:50.370 align:middle line:84% than the hydrogen, they are, in the center of the machine, 00:37:50.370 --> 00:37:51.480 align:middle line:90% probably fully stripped. 00:37:51.480 --> 00:37:53.140 align:middle line:84% They've lost all of their electrons. 00:37:53.140 --> 00:37:55.950 align:middle line:84% So they no longer can produce any light, 00:37:55.950 --> 00:37:58.080 align:middle line:84% so we can't detect their presence in the machine. 00:37:58.080 --> 00:38:00.470 align:middle line:84% So we don't know where these impurities are. 00:38:00.470 --> 00:38:02.400 align:middle line:84% So the idea of charge exchange recombination 00:38:02.400 --> 00:38:04.380 align:middle line:84% spectroscopy is, we put our neutral beam 00:38:04.380 --> 00:38:10.090 align:middle line:84% through the machine, and we end up charge 00:38:10.090 --> 00:38:11.630 align:middle line:90% exchanging on these impurities. 00:38:11.630 --> 00:38:18.930 align:middle line:84% So we have some neutral beam and some impurity in a state Z 00:38:18.930 --> 00:38:24.420 align:middle line:84% plus where it's ionized at times, and this charge exchanges 00:38:24.420 --> 00:38:30.240 align:middle line:84% and gives us a neutral beam ion plus an impurity 00:38:30.240 --> 00:38:35.580 align:middle line:90% in a state Z minus 1 plus. 00:38:35.580 --> 00:38:37.607 align:middle line:84% And most importantly, it's likely 00:38:37.607 --> 00:38:39.690 align:middle line:84% that the impurity will end up in an excited state. 00:38:39.690 --> 00:38:47.560 align:middle line:90% 00:38:47.560 --> 00:38:51.570 align:middle line:84% So then our impurity, which is in some excited state, 00:38:51.570 --> 00:38:54.630 align:middle line:84% it will spontaneously decay down and we'll 00:38:54.630 --> 00:38:57.180 align:middle line:90% get out a photon like that. 00:38:57.180 --> 00:39:00.865 align:middle line:84% And because this photon will have a characteristic energy 00:39:00.865 --> 00:39:03.240 align:middle line:84% that we're looking for with our spectrometer, we can say, 00:39:03.240 --> 00:39:07.580 align:middle line:90% aha, this is from an impurity. 00:39:07.580 --> 00:39:10.180 align:middle line:84% And now, the invisible impurities are visible again. 00:39:10.180 --> 00:39:12.900 align:middle line:90% 00:39:12.900 --> 00:39:14.840 align:middle line:84% So there are a few things that we 00:39:14.840 --> 00:39:17.780 align:middle line:84% can measure from charge exchange recombination spectroscopy. 00:39:17.780 --> 00:39:22.070 align:middle line:84% We can measure the density of impurities from intensity. 00:39:22.070 --> 00:39:28.460 align:middle line:90% 00:39:28.460 --> 00:39:30.200 align:middle line:84% So you need some atomic models and you 00:39:30.200 --> 00:39:32.000 align:middle line:84% need an absolute calibration for your detector, 00:39:32.000 --> 00:39:34.208 align:middle line:84% but you can work out the density of these impurities. 00:39:34.208 --> 00:39:35.340 align:middle line:90% That's pretty useful. 00:39:35.340 --> 00:39:39.590 align:middle line:84% We can also measure Vi and V flow 00:39:39.590 --> 00:39:54.520 align:middle line:84% from the Doppler broadening and the Doppler shift, respectively. 00:39:54.520 --> 00:39:56.580 align:middle line:84% So as we discussed in the spectroscopy 00:39:56.580 --> 00:39:58.680 align:middle line:84% a few weeks ago-- or a week ago-- 00:39:58.680 --> 00:40:01.410 align:middle line:84% when we were talking about different broadening mechanisms, 00:40:01.410 --> 00:40:03.690 align:middle line:84% these effectively can be the impurities 00:40:03.690 --> 00:40:07.180 align:middle line:84% which are acting as a tracer for the flow velocity. 00:40:07.180 --> 00:40:10.890 align:middle line:84% So our bulk motion of the entire plasma around the torus 00:40:10.890 --> 00:40:12.430 align:middle line:90% and for the temperature. 00:40:12.430 --> 00:40:15.360 align:middle line:84% And again, the reason is that maybe you 00:40:15.360 --> 00:40:17.250 align:middle line:84% could rely on impurity that was very high Z 00:40:17.250 --> 00:40:19.260 align:middle line:84% and still had some electrons left. 00:40:19.260 --> 00:40:20.760 align:middle line:84% But if you've done a really good job 00:40:20.760 --> 00:40:22.590 align:middle line:84% of reducing all of the tungsten and nasty things 00:40:22.590 --> 00:40:24.923 align:middle line:84% in your machine and all you're left with oxygen, carbon, 00:40:24.923 --> 00:40:27.690 align:middle line:84% and boron, then you need to effectively give them 00:40:27.690 --> 00:40:30.280 align:middle line:84% back an electron so you can do spectroscopy on them. 00:40:30.280 --> 00:40:32.520 align:middle line:84% And again, this is a nice active diagnostic, 00:40:32.520 --> 00:40:35.520 align:middle line:84% because you can localize the region where the particles are 00:40:35.520 --> 00:40:37.980 align:middle line:84% sitting in by putting your spectrometer 00:40:37.980 --> 00:40:42.940 align:middle line:84% perpendicular to the line of sight of your neutral beam. 00:40:42.940 --> 00:40:47.890 align:middle line:84% And again, you can localize it to that region here. 00:40:47.890 --> 00:40:50.700 align:middle line:84% So this gives you these two, and they're all 00:40:50.700 --> 00:40:52.567 align:middle line:90% localized measurements. 00:40:52.567 --> 00:41:08.170 align:middle line:90% 00:41:08.170 --> 00:41:10.225 align:middle line:90% There can be problems with this. 00:41:10.225 --> 00:41:12.870 align:middle line:90% 00:41:12.870 --> 00:41:19.160 align:middle line:84% So one issue is, you get charge exchange with edge impurities. 00:41:19.160 --> 00:41:26.640 align:middle line:90% 00:41:26.640 --> 00:41:28.560 align:middle line:84% I know I said this measurement localizes this, 00:41:28.560 --> 00:41:30.060 align:middle line:84% but you could imagine that you could 00:41:30.060 --> 00:41:35.040 align:middle line:84% get light reflecting from here go back down into your detector. 00:41:35.040 --> 00:41:38.580 align:middle line:84% And you can also just have background, so something 00:41:38.580 --> 00:41:44.110 align:middle line:84% like Bremsstrahlung radiation, at this photon energy. 00:41:44.110 --> 00:41:46.960 align:middle line:84% And because there's not so many impurities, we hope, 00:41:46.960 --> 00:41:49.450 align:middle line:84% and not so many of them are charged exchanges neutral beam, 00:41:49.450 --> 00:41:51.350 align:middle line:84% the signal could be relatively weak. 00:41:51.350 --> 00:41:57.460 align:middle line:84% So there's Bremsstrahlung at the photon energy of the charge 00:41:57.460 --> 00:41:59.260 align:middle line:90% exchange with impurities. 00:41:59.260 --> 00:42:02.210 align:middle line:84% That could be a significant amount. 00:42:02.210 --> 00:42:04.810 align:middle line:84% So we may not be able to see this signal very clearly. 00:42:04.810 --> 00:42:09.587 align:middle line:84% So a really neat trick that you can do is to modulate the beam. 00:42:09.587 --> 00:42:16.050 align:middle line:90% 00:42:16.050 --> 00:42:22.300 align:middle line:84% So you take the intensity of your neutral beam 00:42:22.300 --> 00:42:27.310 align:middle line:84% and you just turn it on and off like that. 00:42:27.310 --> 00:42:32.220 align:middle line:84% And then when you look at the intensity 00:42:32.220 --> 00:42:35.790 align:middle line:84% at this specific wavelength that you're on the lookout for, 00:42:35.790 --> 00:42:42.620 align:middle line:84% you should see that there's maybe some background, 00:42:42.620 --> 00:42:46.010 align:middle line:84% but that background is being modulated by the neutral beam. 00:42:46.010 --> 00:42:48.110 align:middle line:84% And then you can do tricks like phase-locked loops 00:42:48.110 --> 00:42:50.690 align:middle line:84% and all your other favorite Fourier transform techniques, 00:42:50.690 --> 00:42:53.420 align:middle line:84% and you can isolate out which part of this signal 00:42:53.420 --> 00:42:57.970 align:middle line:84% is actually due to charge exchange 00:42:57.970 --> 00:43:02.990 align:middle line:84% and which parts of the signal is due to BREMS. 00:43:02.990 --> 00:43:04.250 align:middle line:90% That's pretty neat. 00:43:04.250 --> 00:43:09.190 align:middle line:90% OK, questions on this? 00:43:09.190 --> 00:43:09.690 align:middle line:90% Yes. 00:43:09.690 --> 00:43:16.982 align:middle line:90% 00:43:16.982 --> 00:43:24.340 align:middle line:84% So theoretically, we have just a single line like this. 00:43:24.340 --> 00:43:26.080 align:middle line:84% If all the particles were stationary 00:43:26.080 --> 00:43:28.510 align:middle line:84% and the temperature was 0, all the 00:43:28.510 --> 00:43:30.230 align:middle line:84% particles moving at the same speed. 00:43:30.230 --> 00:43:32.620 align:middle line:84% And we just have a line at omega 0. 00:43:32.620 --> 00:43:36.470 align:middle line:84% If all the particles are moving in the same direction, 00:43:36.470 --> 00:43:42.460 align:middle line:84% this will be Doppler shifted, and that Doppler shift 00:43:42.460 --> 00:43:46.930 align:middle line:84% would be adopted into the flow velocity. 00:43:46.930 --> 00:43:50.297 align:middle line:84% And if we have some broadening on top of that, 00:43:50.297 --> 00:43:52.130 align:middle line:84% because we've got non-zero temperature, some 00:43:52.130 --> 00:43:53.270 align:middle line:84% of the particles-- although they're all 00:43:53.270 --> 00:43:54.170 align:middle line:90% moving in one direction. 00:43:54.170 --> 00:43:55.878 align:middle line:84% Some of them are moving back a little bit 00:43:55.878 --> 00:43:57.140 align:middle line:90% and some are moving forwards. 00:43:57.140 --> 00:44:00.320 align:middle line:84% And then the width of this feature, 00:44:00.320 --> 00:44:05.720 align:middle line:84% full width of half maximum, is proportional to VTi, which 00:44:05.720 --> 00:44:08.030 align:middle line:90% is square root of temperature. 00:44:08.030 --> 00:44:09.913 align:middle line:84% So you measure the shift of the feature 00:44:09.913 --> 00:44:11.330 align:middle line:84% and the broadening of the feature. 00:44:11.330 --> 00:44:14.354 align:middle line:84% That gives you the velocity and the temperature-independent. 00:44:14.354 --> 00:44:18.050 align:middle line:90% 00:44:18.050 --> 00:44:19.268 align:middle line:90% Any other questions? 00:44:19.268 --> 00:44:22.615 align:middle line:90% 00:44:22.615 --> 00:44:23.490 align:middle line:90% Any questions online? 00:44:23.490 --> 00:44:32.290 align:middle line:90% 00:44:32.290 --> 00:44:33.385 align:middle line:90% OK, next topic. 00:44:33.385 --> 00:44:41.940 align:middle line:90% 00:44:41.940 --> 00:44:44.877 align:middle line:84% There are yet more fun things you can do with a neutral beam. 00:44:44.877 --> 00:44:45.960 align:middle line:90% Who would have thought it? 00:44:45.960 --> 00:44:59.195 align:middle line:90% 00:44:59.195 --> 00:45:01.070 align:middle line:84% Next fun thing you can do with a neutral beam 00:45:01.070 --> 00:45:17.535 align:middle line:84% is something called beam emission spectroscopy, BES. 00:45:17.535 --> 00:45:22.010 align:middle line:90% 00:45:22.010 --> 00:45:30.490 align:middle line:84% The idea here-- once again, vacuum chamber, plasma, 00:45:30.490 --> 00:45:31.210 align:middle line:90% neutral beam. 00:45:31.210 --> 00:45:34.050 align:middle line:90% 00:45:34.050 --> 00:45:36.600 align:middle line:84% As the beam goes through the plasma, remember, 00:45:36.600 --> 00:45:39.630 align:middle line:84% our beam is going to be hydrogen or deuterium 00:45:39.630 --> 00:45:41.100 align:middle line:90% or something like that. 00:45:41.100 --> 00:45:43.822 align:middle line:84% The neutrals inside here-- and these are all neutrals. 00:45:43.822 --> 00:45:45.780 align:middle line:84% So I'll just put a little 0 to remind ourselves 00:45:45.780 --> 00:45:47.280 align:middle line:90% they're neutrals-- 00:45:47.280 --> 00:45:49.200 align:middle line:84% will have some glancing collisions 00:45:49.200 --> 00:45:51.930 align:middle line:84% with the electrons and ions-- not enough to ionize them. 00:45:51.930 --> 00:45:53.820 align:middle line:84% Some of the collisions will ionize them. 00:45:53.820 --> 00:45:57.270 align:middle line:84% But some of the collisions will be enough to excite these. 00:45:57.270 --> 00:45:59.250 align:middle line:84% And so we'll end up inside our beam 00:45:59.250 --> 00:46:05.490 align:middle line:84% with excited neutral hydrogen and excited neutral deuterium 00:46:05.490 --> 00:46:07.890 align:middle line:90% or something like that. 00:46:07.890 --> 00:46:12.970 align:middle line:84% And we can then put our spectrometer down here 00:46:12.970 --> 00:46:14.920 align:middle line:84% or our detector down here, and we can 00:46:14.920 --> 00:46:17.435 align:middle line:90% look for the characteristic-- 00:46:17.435 --> 00:46:19.060 align:middle line:84% we actually have some drawings of this. 00:46:19.060 --> 00:46:21.460 align:middle line:90% 00:46:21.460 --> 00:46:21.960 align:middle line:90% No. 00:46:21.960 --> 00:46:22.470 align:middle line:90% OK. 00:46:22.470 --> 00:46:25.600 align:middle line:84% We can look for these characteristic decays here. 00:46:25.600 --> 00:46:27.240 align:middle line:84% And if you remember before, we talked 00:46:27.240 --> 00:46:31.960 align:middle line:84% about the Lyman-alpha and -beta, and the Balmer series, as well. 00:46:31.960 --> 00:46:33.960 align:middle line:84% So we know very well-defined what 00:46:33.960 --> 00:46:38.070 align:middle line:84% these energies of the photons coming out are going to be. 00:46:38.070 --> 00:46:44.720 align:middle line:84% Now, the neat thing about this is the intensity of these lines 00:46:44.720 --> 00:46:47.030 align:middle line:90% is proportional to-- 00:46:47.030 --> 00:46:48.922 align:middle line:90% or is-- I'll make it stronger. 00:46:48.922 --> 00:46:51.130 align:middle line:84% It's directly proportional to the number of electrons 00:46:51.130 --> 00:46:55.540 align:middle line:84% in the plasma, because this is a collisional excitation process 00:46:55.540 --> 00:46:58.030 align:middle line:84% and we know that that is proportional to Ne, 00:46:58.030 --> 00:47:02.920 align:middle line:84% and then whatever the relevant collisional excitation 00:47:02.920 --> 00:47:03.910 align:middle line:90% cross-section is. 00:47:03.910 --> 00:47:04.450 align:middle line:90% OK. 00:47:04.450 --> 00:47:09.150 align:middle line:84% But the main thing is it's proportional to the density. 00:47:09.150 --> 00:47:14.810 align:middle line:84% So the neat thing is if I now have density fluctuations-- 00:47:14.810 --> 00:47:16.780 align:middle line:84% so this is-- we've got some background density, 00:47:16.780 --> 00:47:19.490 align:middle line:84% but the density is fluctuating on top of that. 00:47:19.490 --> 00:47:25.660 align:middle line:84% So Ne 0 plus delta Ne of T. Then that's 00:47:25.660 --> 00:47:29.795 align:middle line:84% going to give me an intensity fluctuation as well. 00:47:29.795 --> 00:47:35.420 align:middle line:90% 00:47:35.420 --> 00:47:38.380 align:middle line:84% So by carefully measuring the intensity of these lines-- 00:47:38.380 --> 00:47:41.110 align:middle line:84% and again, we can localize this relatively well 00:47:41.110 --> 00:47:44.210 align:middle line:84% because I have a specific field of view for my detector 00:47:44.210 --> 00:47:47.653 align:middle line:84% and I know where this beam emission is coming from. 00:47:47.653 --> 00:47:49.320 align:middle line:84% So I can localize it to a little region. 00:47:49.320 --> 00:47:51.170 align:middle line:90% I could have multiple detectors. 00:47:51.170 --> 00:47:53.500 align:middle line:84% And I could have another one looking here. 00:47:53.500 --> 00:47:55.930 align:middle line:84% I can measure density fluctuations 00:47:55.930 --> 00:47:57.700 align:middle line:90% in very precise regions here. 00:47:57.700 --> 00:47:59.690 align:middle line:84% And density fluctuations are very important, 00:47:59.690 --> 00:48:01.510 align:middle line:84% especially in magnetic confinement fusion, 00:48:01.510 --> 00:48:04.570 align:middle line:84% because these fluctuations lead to transport-- 00:48:04.570 --> 00:48:06.290 align:middle line:90% turbulent transport. 00:48:06.290 --> 00:48:09.667 align:middle line:84% So we really, really want to be able to [INAUDIBLE]. 00:48:09.667 --> 00:48:11.250 align:middle line:84% So beam emission spectroscopy, I think 00:48:11.250 --> 00:48:12.833 align:middle line:84% this is the only slide I have on this. 00:48:12.833 --> 00:48:14.070 align:middle line:90% Yes. 00:48:14.070 --> 00:48:16.360 align:middle line:84% Well, I have another one that's related. 00:48:16.360 --> 00:48:18.450 align:middle line:90% This is a very cool technique. 00:48:18.450 --> 00:48:23.450 align:middle line:84% The trouble is that what I just said here 00:48:23.450 --> 00:48:25.460 align:middle line:84% about just being proportional to density here, 00:48:25.460 --> 00:48:27.600 align:middle line:90% this is rather simple. 00:48:27.600 --> 00:48:30.060 align:middle line:84% It's not actually true in reality. 00:48:30.060 --> 00:48:34.190 align:middle line:84% So what we actually have to do is 00:48:34.190 --> 00:48:39.380 align:middle line:90% include all relevant processes. 00:48:39.380 --> 00:48:41.340 align:middle line:84% This is going back to spectroscopy again, 00:48:41.340 --> 00:48:44.750 align:middle line:84% where if you're not quite in a simple equilibrium, 00:48:44.750 --> 00:48:47.150 align:middle line:84% you need to include lots more processes. 00:48:47.150 --> 00:48:53.130 align:middle line:90% 00:48:53.130 --> 00:48:56.857 align:middle line:84% And you also need to include the beams' attenuation, 00:48:56.857 --> 00:48:59.190 align:middle line:84% because of course, the point of launching a neutral beam 00:48:59.190 --> 00:49:02.010 align:middle line:84% into your system is not to hit the far wall of your vacuum 00:49:02.010 --> 00:49:03.600 align:middle line:84% chamber and melt it, but it's actually 00:49:03.600 --> 00:49:05.280 align:middle line:84% to charge exchange with the plasma 00:49:05.280 --> 00:49:06.880 align:middle line:90% and heat it and drive current. 00:49:06.880 --> 00:49:10.320 align:middle line:84% So this beam is going to be getting less and less intense 00:49:10.320 --> 00:49:11.958 align:middle line:90% as it goes through the plasma. 00:49:11.958 --> 00:49:13.750 align:middle line:84% And so if you want to do all this properly, 00:49:13.750 --> 00:49:16.110 align:middle line:84% you also need to track the beam attenuation, 00:49:16.110 --> 00:49:20.100 align:middle line:84% because this density is also proportional to the number 00:49:20.100 --> 00:49:23.990 align:middle line:84% of beam particles as well-- the number 00:49:23.990 --> 00:49:25.650 align:middle line:90% density of beam particles. 00:49:25.650 --> 00:49:27.380 align:middle line:84% So we need to track the beam attenuation. 00:49:27.380 --> 00:49:32.918 align:middle line:90% 00:49:32.918 --> 00:49:34.710 align:middle line:84% But if you can do that, this is potentially 00:49:34.710 --> 00:49:36.377 align:middle line:84% a very powerful diagnostic for measuring 00:49:36.377 --> 00:49:38.190 align:middle line:84% density fluctuations, which are otherwise 00:49:38.190 --> 00:49:41.190 align:middle line:90% quite challenging to measure. 00:49:41.190 --> 00:49:44.147 align:middle line:84% Questions on beam emission spectroscopy? 00:49:44.147 --> 00:49:44.980 align:middle line:90% AUDIENCE: Professor? 00:49:44.980 --> 00:49:47.710 align:middle line:90% JACK HARE: Yes. 00:49:47.710 --> 00:49:51.760 align:middle line:84% AUDIENCE: So do you need to specialize or neutral beam 00:49:51.760 --> 00:49:54.430 align:middle line:84% for these kind of readings, or is 00:49:54.430 --> 00:49:56.680 align:middle line:84% this something you can do while using the neutral beam 00:49:56.680 --> 00:49:58.000 align:middle line:90% as a heating source already? 00:49:58.000 --> 00:49:58.270 align:middle line:90% JACK HARE: Yes. 00:49:58.270 --> 00:49:59.950 align:middle line:84% The nice thing about all of these things 00:49:59.950 --> 00:50:02.590 align:middle line:84% is you tend to just be able to use your standard neutral beam. 00:50:02.590 --> 00:50:04.630 align:middle line:84% So some people do have specifically 00:50:04.630 --> 00:50:05.980 align:middle line:90% made diagnostic neutral beams. 00:50:05.980 --> 00:50:08.590 align:middle line:84% So on eta, they have several neutral beams specifically 00:50:08.590 --> 00:50:10.150 align:middle line:84% designed for heating, and they also 00:50:10.150 --> 00:50:11.540 align:middle line:90% have diagnostic neutral beams. 00:50:11.540 --> 00:50:13.990 align:middle line:84% So the heating beams are up at megaelectronvolts, 00:50:13.990 --> 00:50:16.270 align:middle line:84% and the diagnostic beam is at a lower energy. 00:50:16.270 --> 00:50:17.800 align:middle line:84% And I believe that lower energy is 00:50:17.800 --> 00:50:19.930 align:middle line:84% because it gives you better cross-sections for all 00:50:19.930 --> 00:50:20.870 align:middle line:90% of these processes. 00:50:20.870 --> 00:50:22.570 align:middle line:90% So I'm not sure. 00:50:22.570 --> 00:50:24.460 align:middle line:84% An amusing example of that is that there 00:50:24.460 --> 00:50:28.300 align:middle line:84% was a diagnostic neutral beam developed for the National 00:50:28.300 --> 00:50:30.410 align:middle line:84% Compact Stellarator Experiment at Princeton, 00:50:30.410 --> 00:50:31.258 align:middle line:90% which was canceled. 00:50:31.258 --> 00:50:32.800 align:middle line:84% And that diagnostic neutral beam then 00:50:32.800 --> 00:50:34.383 align:middle line:84% went on to be the heating neutral beam 00:50:34.383 --> 00:50:35.988 align:middle line:90% for a much smaller device. 00:50:35.988 --> 00:50:37.780 align:middle line:84% So you can build a diagnostic neutral beam, 00:50:37.780 --> 00:50:39.988 align:middle line:84% but at the end of the day, it's still a neutral beam. 00:50:39.988 --> 00:50:41.770 align:middle line:84% It can do whatever you normally want. 00:50:41.770 --> 00:50:44.450 align:middle line:84% And this is going to be coming in at 300 keV 00:50:44.450 --> 00:50:46.087 align:middle line:84% or whatever energy you can generate. 00:50:46.087 --> 00:50:48.170 align:middle line:84% And all these processes are going to be happening. 00:50:48.170 --> 00:50:51.590 align:middle line:84% And the fact that the beam slows down and converts into ions 00:50:51.590 --> 00:50:53.450 align:middle line:84% and does all the heating relies on all 00:50:53.450 --> 00:50:55.760 align:middle line:84% of the same atomic processes that we then 00:50:55.760 --> 00:50:58.335 align:middle line:84% use to observe beam emission spectroscopy and charge exchange 00:50:58.335 --> 00:50:59.460 align:middle line:90% and all that sort of stuff. 00:50:59.460 --> 00:51:02.300 align:middle line:84% So those processes have to happen for the beam to work. 00:51:02.300 --> 00:51:04.610 align:middle line:84% And now, you're just observing the obvious consequence 00:51:04.610 --> 00:51:05.570 align:middle line:90% of them occurring. 00:51:05.570 --> 00:51:06.675 align:middle line:90% Yeah, good question. 00:51:06.675 --> 00:51:07.800 align:middle line:90% AUDIENCE: Great, thank you. 00:51:07.800 --> 00:51:08.925 align:middle line:90% JACK HARE: Other questions? 00:51:08.925 --> 00:51:20.740 align:middle line:90% 00:51:20.740 --> 00:51:24.175 align:middle line:84% Now we're going to be done early. 00:51:24.175 --> 00:51:26.410 align:middle line:84% The final thing, as we discussed it the other day, 00:51:26.410 --> 00:51:28.120 align:middle line:84% is the motional stark effect, which I'd 00:51:28.120 --> 00:51:29.750 align:middle line:90% forgotten was to do with this. 00:51:29.750 --> 00:51:31.150 align:middle line:84% And in fact, I was looking through my notes today 00:51:31.150 --> 00:51:33.638 align:middle line:84% and I was like, oh, I actually wrote several pages of notes 00:51:33.638 --> 00:51:35.680 align:middle line:84% on the motional stark effect and then told people 00:51:35.680 --> 00:51:37.100 align:middle line:90% I had no idea what it was. 00:51:37.100 --> 00:51:38.830 align:middle line:84% So that just shows how good my memory is. 00:51:38.830 --> 00:51:41.072 align:middle line:84% So now, you will have the pleasure 00:51:41.072 --> 00:51:43.030 align:middle line:84% of learning about and then instantly forgetting 00:51:43.030 --> 00:51:44.870 align:middle line:90% about the motional stark effect. 00:51:44.870 --> 00:51:46.120 align:middle line:90% No, it's actually really cool. 00:51:46.120 --> 00:51:54.860 align:middle line:90% 00:51:54.860 --> 00:51:57.230 align:middle line:84% This is often abbreviated as MSE. 00:51:57.230 --> 00:52:00.210 align:middle line:90% 00:52:00.210 --> 00:52:04.498 align:middle line:84% So we already talked about the stark effect. 00:52:04.498 --> 00:52:06.290 align:middle line:84% And in the stark effect, we said that there 00:52:06.290 --> 00:52:08.315 align:middle line:90% was an electric field. 00:52:08.315 --> 00:52:09.690 align:middle line:84% And I'm going to continue writing 00:52:09.690 --> 00:52:11.430 align:middle line:84% electric with this weird curly E's 00:52:11.430 --> 00:52:14.160 align:middle line:84% because we're going to have some capital E's for energy later 00:52:14.160 --> 00:52:16.000 align:middle line:84% and don't want us to get confused. 00:52:16.000 --> 00:52:22.560 align:middle line:84% So this is the electric field, which shifts 00:52:22.560 --> 00:52:29.010 align:middle line:90% the energy levels of some atom. 00:52:29.010 --> 00:52:32.963 align:middle line:90% 00:52:32.963 --> 00:52:34.630 align:middle line:84% So we could do this just in a laboratory 00:52:34.630 --> 00:52:36.588 align:middle line:84% with a strong electric field and a neutral gas. 00:52:36.588 --> 00:52:39.330 align:middle line:90% 00:52:39.330 --> 00:52:42.570 align:middle line:84% And we then considered what this does inside a plasma. 00:52:42.570 --> 00:52:49.260 align:middle line:84% So in a plasma, we have lots of electrons moving around, 00:52:49.260 --> 00:52:50.190 align:middle line:90% as we said. 00:52:50.190 --> 00:52:53.520 align:middle line:84% And those electrons will be colliding with our ions, 00:52:53.520 --> 00:52:56.320 align:middle line:84% so our atoms that have bound electrons. 00:52:56.320 --> 00:52:58.180 align:middle line:84% And as those electrons get close, 00:52:58.180 --> 00:53:01.440 align:middle line:84% they will be shifting the electric field, 00:53:01.440 --> 00:53:04.360 align:middle line:84% and therefore, the energy level in the vicinity that atom. 00:53:04.360 --> 00:53:07.680 align:middle line:84% So we saw there that we got a change 00:53:07.680 --> 00:53:11.910 align:middle line:84% in the energy of the photons being emitted, which 00:53:11.910 --> 00:53:15.420 align:middle line:84% was proportional to the electric field. 00:53:15.420 --> 00:53:18.390 align:middle line:84% And that electric field was proportional to density 00:53:18.390 --> 00:53:19.230 align:middle line:90% for the 1/3. 00:53:19.230 --> 00:53:23.520 align:middle line:84% And this was just an electric field 1 over r squared argument. 00:53:23.520 --> 00:53:26.610 align:middle line:90% This should be 2/3. 00:53:26.610 --> 00:53:28.480 align:middle line:90% There we go. 00:53:28.480 --> 00:53:30.570 align:middle line:90% And this was from collisions. 00:53:30.570 --> 00:53:38.250 align:middle line:90% 00:53:38.250 --> 00:53:43.250 align:middle line:84% But this whole picture here required a thermal plasma 00:53:43.250 --> 00:53:46.590 align:middle line:84% with lots of particles moving in all sorts of ways here. 00:53:46.590 --> 00:53:48.050 align:middle line:84% So this was with the distribution 00:53:48.050 --> 00:53:53.890 align:middle line:84% f of V Ve that was exponential of, I don't know, 00:53:53.890 --> 00:54:00.500 align:middle line:84% minus V squared over V thermal e squared. 00:54:00.500 --> 00:54:06.670 align:middle line:84% But in this case here, for a neutral beam, 00:54:06.670 --> 00:54:09.260 align:middle line:84% we have a very peaked distribution function. 00:54:09.260 --> 00:54:17.220 align:middle line:84% So our distribution of neutral beam ions 00:54:17.220 --> 00:54:19.440 align:middle line:90% is roughly a delta function. 00:54:19.440 --> 00:54:20.850 align:middle line:90% So they're all at VB. 00:54:20.850 --> 00:54:24.090 align:middle line:90% 00:54:24.090 --> 00:54:26.430 align:middle line:84% So we don't expect to see a broadening. 00:54:26.430 --> 00:54:28.650 align:middle line:84% What we would expect to see, maybe, 00:54:28.650 --> 00:54:32.310 align:middle line:84% is some sort of shift in a single direction 00:54:32.310 --> 00:54:35.930 align:middle line:84% here but where is the electric field coming up 00:54:35.930 --> 00:54:38.690 align:middle line:84% from in a plasma like this, where we're just talking 00:54:38.690 --> 00:54:39.925 align:middle line:90% about our particles moving? 00:54:39.925 --> 00:54:42.050 align:middle line:84% Because here, we argued this was the electric field 00:54:42.050 --> 00:54:44.270 align:middle line:84% from particles close in within the Debye sphere. 00:54:44.270 --> 00:54:47.370 align:middle line:84% But on large scales, we don't see this electric field. 00:54:47.370 --> 00:54:50.210 align:middle line:84% But what we do have is a magnetic field. 00:54:50.210 --> 00:54:54.210 align:middle line:84% We have a magnetic field B, like this. 00:54:54.210 --> 00:54:59.870 align:middle line:84% And so we have some beam velocity 00:54:59.870 --> 00:55:04.540 align:middle line:84% V cross B. And in the frame of the particle, that creates 00:55:04.540 --> 00:55:07.840 align:middle line:84% an electric field, which is equal to minus V cross B. 00:55:07.840 --> 00:55:10.420 align:middle line:84% So this is our Lorentz transform. 00:55:10.420 --> 00:55:17.410 align:middle line:90% 00:55:17.410 --> 00:55:19.210 align:middle line:84% So in the frame of the lab we see 00:55:19.210 --> 00:55:21.370 align:middle line:84% particles moving with velocity V beam, 00:55:21.370 --> 00:55:22.645 align:middle line:90% and we see a magnetic field. 00:55:22.645 --> 00:55:25.640 align:middle line:90% 00:55:25.640 --> 00:55:27.350 align:middle line:84% But in the frame of the particle, 00:55:27.350 --> 00:55:29.948 align:middle line:84% when we do the Lorentz transformation, 00:55:29.948 --> 00:55:31.490 align:middle line:84% the particle, of course, doesn't know 00:55:31.490 --> 00:55:33.820 align:middle line:90% it's moving within its frame. 00:55:33.820 --> 00:55:35.920 align:middle line:84% And instead of seeing a magnetic field, 00:55:35.920 --> 00:55:40.360 align:middle line:84% it sees this electric field instead. 00:55:40.360 --> 00:55:42.310 align:middle line:84% And so that means that now, we're 00:55:42.310 --> 00:55:46.030 align:middle line:84% expecting to get energy shifts delta e, which 00:55:46.030 --> 00:55:51.060 align:middle line:84% are, again, proportional to the electric field, which are now 00:55:51.060 --> 00:55:59.970 align:middle line:84% proportional to V cross B. And I just want to point out-- 00:55:59.970 --> 00:56:02.268 align:middle line:84% and Hutchinson goes into this in some detail-- 00:56:02.268 --> 00:56:03.810 align:middle line:84% we've assumed here that we're talking 00:56:03.810 --> 00:56:07.660 align:middle line:90% about the linear stark effect. 00:56:07.660 --> 00:56:10.250 align:middle line:84% And depending on exactly what's going on 00:56:10.250 --> 00:56:11.800 align:middle line:84% you may need more complicated things 00:56:11.800 --> 00:56:13.190 align:middle line:90% like the quadratic stark effect. 00:56:13.190 --> 00:56:15.220 align:middle line:84% But this is the linear stark effect. 00:56:15.220 --> 00:56:18.310 align:middle line:84% It turns out the linear stark effect is good 00:56:18.310 --> 00:56:20.425 align:middle line:90% when this delta E is large. 00:56:20.425 --> 00:56:24.120 align:middle line:90% 00:56:24.120 --> 00:56:25.910 align:middle line:84% So as long as you have sufficiently large 00:56:25.910 --> 00:56:27.902 align:middle line:84% magnetic fields and beam velocities, then 00:56:27.902 --> 00:56:29.360 align:middle line:84% you end up with this linear regime, 00:56:29.360 --> 00:56:35.415 align:middle line:84% which is much easier to analyze here OK. 00:56:35.415 --> 00:56:36.790 align:middle line:84% I'm going to erase this because I 00:56:36.790 --> 00:56:38.082 align:middle line:90% want to keep that on the board. 00:56:38.082 --> 00:56:52.220 align:middle line:90% 00:56:52.220 --> 00:56:57.570 align:middle line:84% Now, some voodoo magic happens, and we find out 00:56:57.570 --> 00:57:02.260 align:middle line:84% that each energy level splits into multiple energy levels. 00:57:02.260 --> 00:57:05.280 align:middle line:84% So this is reminiscent of the Zeeman splitting again. 00:57:05.280 --> 00:57:09.390 align:middle line:84% So each energy level splits into energy levels whose energy is 00:57:09.390 --> 00:57:12.550 align:middle line:90% given by 3nK. 00:57:12.550 --> 00:57:16.030 align:middle line:84% I'll explain what all of these symbols mean in a moment. 00:57:16.030 --> 00:57:28.560 align:middle line:84% Electric fields over ze over 4 pi epsilon 0 A0 squared. 00:57:28.560 --> 00:57:30.090 align:middle line:84% I haven't got, in my notes, what A0, 00:57:30.090 --> 00:57:32.423 align:middle line:84% is and I've forgotten what it is off the top of my head. 00:57:32.423 --> 00:57:35.430 align:middle line:90% So that's not very useful. 00:57:35.430 --> 00:57:38.590 align:middle line:84% Some constant is the most important thing. 00:57:38.590 --> 00:57:42.610 align:middle line:84% All this times the Rydberg energy, which you all remember 00:57:42.610 --> 00:57:46.180 align:middle line:90% is 13.6 electron volts. 00:57:46.180 --> 00:57:52.810 align:middle line:84% And this electric field is V cross B modulus of it. 00:57:52.810 --> 00:57:56.545 align:middle line:84% OK, so n here is the quantum number. 00:57:56.545 --> 00:58:01.240 align:middle line:90% 00:58:01.240 --> 00:58:04.540 align:middle line:90% n equals 1, 2, 3. 00:58:04.540 --> 00:58:07.270 align:middle line:84% And K, here for each quantum number n, 00:58:07.270 --> 00:58:14.230 align:middle line:84% can take multiple values, K equals 0 plus or minus 1, 00:58:14.230 --> 00:58:23.260 align:middle line:84% plus or minus 2 up to plus or minus n minus 1. 00:58:23.260 --> 00:58:26.290 align:middle line:84% So for n equals 1, K can only take the value 0. 00:58:26.290 --> 00:58:28.090 align:middle line:84% At n equals 2, it can take three values. 00:58:28.090 --> 00:58:31.210 align:middle line:84% At n equals 3, it can take five values like this. 00:58:31.210 --> 00:58:33.830 align:middle line:90% 00:58:33.830 --> 00:58:35.980 align:middle line:84% And because these energy levels are all split-- 00:58:35.980 --> 00:58:38.350 align:middle line:84% and I'll draw some now so that you get 00:58:38.350 --> 00:58:39.625 align:middle line:90% some feel for what's going on. 00:58:39.625 --> 00:58:42.390 align:middle line:90% 00:58:42.390 --> 00:58:45.470 align:middle line:84% Let's see if I've got space to do it here. 00:58:45.470 --> 00:58:57.050 align:middle line:84% We start out with n equals 1, n equals 2, n equals 3. 00:58:57.050 --> 00:59:00.740 align:middle line:84% This n equals 1 will just be split when n equals 1 level. 00:59:00.740 --> 00:59:04.460 align:middle line:84% The n equals 2 will be split to three levels. 00:59:04.460 --> 00:59:08.105 align:middle line:84% And the n equals 3, we split to five levels. 00:59:08.105 --> 00:59:12.340 align:middle line:90% 00:59:12.340 --> 00:59:13.990 align:middle line:84% And each of these levels is going 00:59:13.990 --> 00:59:18.510 align:middle line:84% to have an energy, delta E, between them, which 00:59:18.510 --> 00:59:20.440 align:middle line:90% is given by this formula here. 00:59:20.440 --> 00:59:22.470 align:middle line:84% And so by measuring this splitting, 00:59:22.470 --> 00:59:25.590 align:middle line:84% we can measure the magnetic field, 00:59:25.590 --> 00:59:28.292 align:middle line:84% because most of the stuff in here is just a constant. 00:59:28.292 --> 00:59:31.000 align:middle line:84% We should know our beam velocity because we're the ones injecting 00:59:31.000 --> 00:59:31.800 align:middle line:90% the neutral beam. 00:59:31.800 --> 00:59:33.420 align:middle line:84% So the only thing we don't know is 00:59:33.420 --> 00:59:36.440 align:middle line:90% the size of the magnetic field. 00:59:36.440 --> 00:59:40.715 align:middle line:90% So we could try and use-- 00:59:40.715 --> 00:59:42.340 align:middle line:84% so again, this is still a neutral beam, 00:59:42.340 --> 00:59:43.640 align:middle line:90% so we've got one electron. 00:59:43.640 --> 00:59:46.480 align:middle line:84% So we could try and look at transitions from here 00:59:46.480 --> 00:59:48.770 align:middle line:90% down to here. 00:59:48.770 --> 00:59:52.880 align:middle line:84% And there should be a triplet of transitions all coming out 00:59:52.880 --> 00:59:54.440 align:middle line:84% with slightly different energies. 00:59:54.440 --> 00:59:56.458 align:middle line:84% What is the problem with using this? 00:59:56.458 --> 00:59:58.250 align:middle line:84% first of all, does anyone remember the name 00:59:58.250 --> 01:00:00.710 align:middle line:84% for this transition, and what's the problem with using it? 01:00:00.710 --> 01:00:07.060 align:middle line:90% 01:00:07.060 --> 01:00:08.710 align:middle line:84% AUDIENCE: Is it a forbidden transition? 01:00:08.710 --> 01:00:10.752 align:middle line:84% JACK HARE: It's not forbidden, but good question. 01:00:10.752 --> 01:00:15.730 align:middle line:90% 01:00:15.730 --> 01:00:21.100 align:middle line:84% Hydrogen. Transition from the first excited 01:00:21.100 --> 01:00:24.850 align:middle line:84% state down to the ground state is the Lyman-alpha. 01:00:24.850 --> 01:00:28.050 align:middle line:90% 01:00:28.050 --> 01:00:32.140 align:middle line:84% What's the wavelength of the Lyman-alpha? 01:00:32.140 --> 01:00:34.330 align:middle line:90% Yeah it's 121 nanometers. 01:00:34.330 --> 01:00:37.370 align:middle line:90% 01:00:37.370 --> 01:00:39.915 align:middle line:84% So this is what's called vacuum ultraviolet. 01:00:39.915 --> 01:00:42.040 align:middle line:84% And the reason it's called vacuum ultraviolet is it 01:00:42.040 --> 01:00:43.340 align:middle line:90% only propagates in a vacuum. 01:00:43.340 --> 01:00:44.720 align:middle line:84% So it's a real pain to deal with. 01:00:44.720 --> 01:00:47.620 align:middle line:84% So we don't want to work with this transition here. 01:00:47.620 --> 01:00:51.100 align:middle line:84% Instead, what we want to do is use a transition from n 01:00:51.100 --> 01:00:52.957 align:middle line:90% equals 3 down to n equals 2. 01:00:52.957 --> 01:00:54.415 align:middle line:84% What's the name of this transition? 01:00:54.415 --> 01:00:57.150 align:middle line:90% AUDIENCE: H-alpha BALMER 01:00:57.150 --> 01:00:59.990 align:middle line:90% 01:00:59.990 --> 01:01:01.820 align:middle line:90% JACK HARE: Yeah, H-alpha BALMER. 01:01:01.820 --> 01:01:06.220 align:middle line:90% 01:01:06.220 --> 01:01:08.890 align:middle line:84% This is where the forbidden transitions that were mentioned 01:01:08.890 --> 01:01:09.860 align:middle line:90% come in here. 01:01:09.860 --> 01:01:13.210 align:middle line:84% So these have an angular momentum quantum number 01:01:13.210 --> 01:01:21.850 align:middle line:84% nm of 210 minus 1 minus 2, 1, 0, minus 1 like this. 01:01:21.850 --> 01:01:25.120 align:middle line:84% And the selection rule for these that tells you 01:01:25.120 --> 01:01:28.300 align:middle line:84% whether this transition is forbidden or not is delta m 01:01:28.300 --> 01:01:30.777 align:middle line:90% is equal to-- 01:01:30.777 --> 01:01:32.110 align:middle line:90% have I got it written down here? 01:01:32.110 --> 01:01:35.340 align:middle line:90% 01:01:35.340 --> 01:01:36.240 align:middle line:90% Yeah. 01:01:36.240 --> 01:01:38.010 align:middle line:90% 0 and plus or minus 1. 01:01:38.010 --> 01:01:40.850 align:middle line:90% 01:01:40.850 --> 01:01:45.060 align:middle line:84% So from any given level here, for this one, for example, 01:01:45.060 --> 01:01:47.660 align:middle line:84% the m equals 0 and the n equals 3, 01:01:47.660 --> 01:01:53.090 align:middle line:84% we can have a transition down to 0, down to minus 1, 01:01:53.090 --> 01:01:54.650 align:middle line:90% and down to 1. 01:01:54.650 --> 01:01:56.300 align:middle line:84% We get a triplet of lines from that. 01:01:56.300 --> 01:01:58.550 align:middle line:84% We'll also get another set of lines-- 01:01:58.550 --> 01:02:00.800 align:middle line:84% you can see this starts to get quite complicated quite 01:02:00.800 --> 01:02:01.520 align:middle line:90% quickly-- 01:02:01.520 --> 01:02:04.217 align:middle line:90% like this. 01:02:04.217 --> 01:02:05.800 align:middle line:84% There is no transition down to minus 2 01:02:05.800 --> 01:02:07.010 align:middle line:90% because it doesn't exist. 01:02:07.010 --> 01:02:12.720 align:middle line:84% And then finally, we'll have-- well, the minus 2, could guess, 01:02:12.720 --> 01:02:13.785 align:middle line:90% can go to minus 1. 01:02:13.785 --> 01:02:16.800 align:middle line:90% 01:02:16.800 --> 01:02:27.190 align:middle line:84% And the m equals 1 can go down to m equals 0. 01:02:27.190 --> 01:02:29.410 align:middle line:90% And m equals 1-- 01:02:29.410 --> 01:02:31.620 align:middle line:90% I'm running out of colors-- 01:02:31.620 --> 01:02:35.220 align:middle line:84% and the m equals 2 can go down to here. 01:02:35.220 --> 01:02:35.730 align:middle line:90% Sometimes. 01:02:35.730 --> 01:02:37.730 align:middle line:84% So you see there's all sorts of different lines. 01:02:37.730 --> 01:02:40.927 align:middle line:84% But you notice that their spacings of these levels 01:02:40.927 --> 01:02:42.510 align:middle line:84% are the same as the spacings of these. 01:02:42.510 --> 01:02:44.070 align:middle line:84% No, it's not, because n is different. 01:02:44.070 --> 01:02:46.898 align:middle line:84% Yeah, you're going to get clusters of different lines 01:02:46.898 --> 01:02:48.190 align:middle line:90% at slightly different energies. 01:02:48.190 --> 01:02:49.830 align:middle line:84% So you need a very nice spectrometer 01:02:49.830 --> 01:02:52.090 align:middle line:84% to be able to distinguish between these lines. 01:02:52.090 --> 01:02:54.040 align:middle line:84% So as you increase the magnetic field, 01:02:54.040 --> 01:02:57.030 align:middle line:84% the energy gap gets bigger, and so you need a less and less nice 01:02:57.030 --> 01:02:57.780 align:middle line:90% spectrometer. 01:02:57.780 --> 01:03:00.663 align:middle line:84% So your resolution requirements go down 01:03:00.663 --> 01:03:01.830 align:middle line:90% for a bigger magnetic field. 01:03:01.830 --> 01:03:04.080 align:middle line:84% But in general, you're going to see a forest of lines. 01:03:04.080 --> 01:03:10.150 align:middle line:84% You're going to see, instead of just your h-alpha line that you 01:03:10.150 --> 01:03:12.700 align:middle line:84% had originally, you're going to get-- 01:03:12.700 --> 01:03:16.460 align:middle line:84% I'm not going to try and draw this accurately-- 01:03:16.460 --> 01:03:17.870 align:middle line:90% a set of lines like this. 01:03:17.870 --> 01:03:21.080 align:middle line:84% And then you might get another line over up here, 01:03:21.080 --> 01:03:22.940 align:middle line:84% and you might get another line down here, 01:03:22.940 --> 01:03:24.440 align:middle line:84% and all sorts of things like that, 01:03:24.440 --> 01:03:28.310 align:middle line:84% and other sets of triplets and doublets different places. 01:03:28.310 --> 01:03:35.090 align:middle line:90% 01:03:35.090 --> 01:03:37.540 align:middle line:84% If that's not quite right, it's not completed. 01:03:37.540 --> 01:03:38.855 align:middle line:90% OK, cool. 01:03:38.855 --> 01:03:41.600 align:middle line:90% 01:03:41.600 --> 01:03:42.980 align:middle line:90% Why are we bothering with this? 01:03:42.980 --> 01:03:44.900 align:middle line:84% This looks an awful lot like Zeeman splitting. 01:03:44.900 --> 01:03:47.270 align:middle line:84% Couldn't we have just done Zeeman splitting? 01:03:47.270 --> 01:03:50.720 align:middle line:84% So the main thing about this is this delta E 01:03:50.720 --> 01:03:53.724 align:middle line:84% is much, much larger than we get for Zeeman. 01:03:53.724 --> 01:04:00.990 align:middle line:90% 01:04:00.990 --> 01:04:03.580 align:middle line:84% By "much, much larger," I about 10 times larger. 01:04:03.580 --> 01:04:06.300 align:middle line:84% So it's much easier to distinguish between the lines. 01:04:06.300 --> 01:04:11.640 align:middle line:84% And once again, we can use our neutral beam that we already 01:04:11.640 --> 01:04:13.090 align:middle line:90% have to do this. 01:04:13.090 --> 01:04:15.570 align:middle line:84% So this is a very nice use of a neutral beam. 01:04:15.570 --> 01:04:18.990 align:middle line:84% Now, we talked about, with Zeeman before, 01:04:18.990 --> 01:04:20.760 align:middle line:84% it's not actually super useful to be 01:04:20.760 --> 01:04:23.910 align:middle line:84% able to measure the strength of a magnetic field in a tokamak, 01:04:23.910 --> 01:04:25.115 align:middle line:90% because we know what it is. 01:04:25.115 --> 01:04:26.490 align:middle line:84% It's the toroidal magnetic field. 01:04:26.490 --> 01:04:29.020 align:middle line:84% Basically, the poloidal magnetic field is very small. 01:04:29.020 --> 01:04:31.620 align:middle line:84% So this is our condition that the poloidal 01:04:31.620 --> 01:04:34.470 align:middle line:84% is much, much less than the toroidal 01:04:34.470 --> 01:04:36.180 align:middle line:90% that we have in a tokamak. 01:04:36.180 --> 01:04:38.550 align:middle line:84% And the nice thing about this is that each 01:04:38.550 --> 01:04:41.640 align:middle line:84% of these different transitions has a different polarization. 01:04:41.640 --> 01:04:44.140 align:middle line:84% And this is going back to what we were talking about before, 01:04:44.140 --> 01:04:47.910 align:middle line:84% where we had these high polarizations and sigma 01:04:47.910 --> 01:04:49.260 align:middle line:90% polarizations. 01:04:49.260 --> 01:04:51.310 align:middle line:84% And I'm running out of room to draw it. 01:04:51.310 --> 01:04:53.640 align:middle line:84% But if you go back to the notes that we 01:04:53.640 --> 01:04:57.690 align:middle line:84% had on Zeeman spectroscopy here, this polarization, for example, 01:04:57.690 --> 01:04:58.305 align:middle line:90% will come out. 01:04:58.305 --> 01:05:14.910 align:middle line:90% 01:05:14.910 --> 01:05:17.010 align:middle line:84% We've got some magnetic fields here, 01:05:17.010 --> 01:05:21.530 align:middle line:84% which is the toroidal field plus the poloidal field. 01:05:21.530 --> 01:05:30.020 align:middle line:84% We'll have the pi polarization coming out of the plasma 01:05:30.020 --> 01:05:34.920 align:middle line:84% perpendicular to B. And we'll have the stigma polarizations 01:05:34.920 --> 01:05:41.300 align:middle line:84% coming out parallel to B. So by having 01:05:41.300 --> 01:05:44.030 align:middle line:84% two spectrometers with two different polarizers 01:05:44.030 --> 01:05:46.340 align:middle line:84% cross of each other and measuring the relative strength 01:05:46.340 --> 01:05:48.260 align:middle line:84% of these two lines, you can actually 01:05:48.260 --> 01:05:51.030 align:middle line:84% determine the angle of the magnetic field. 01:05:51.030 --> 01:05:54.110 align:middle line:84% And then from that, you can work out the size of this B poloidal 01:05:54.110 --> 01:05:54.890 align:middle line:90% component. 01:05:54.890 --> 01:05:57.630 align:middle line:90% 01:05:57.630 --> 01:05:59.490 align:middle line:84% And from the B poloidal component, 01:05:59.490 --> 01:06:01.980 align:middle line:84% you can start to guess at distribution 01:06:01.980 --> 01:06:05.420 align:middle line:84% of current inside your tokamak, which is very, very 01:06:05.420 --> 01:06:07.920 align:middle line:84% important, especially when we're doing things like bootstrap 01:06:07.920 --> 01:06:11.010 align:middle line:84% current, where we need very specific current profiles 01:06:11.010 --> 01:06:12.540 align:middle line:90% in order to induce it. 01:06:12.540 --> 01:06:16.670 align:middle line:84% So basically, emotional stark effect 01:06:16.670 --> 01:06:21.170 align:middle line:84% here is very useful for magnetic reconstruction. 01:06:21.170 --> 01:06:33.830 align:middle line:90% 01:06:33.830 --> 01:06:34.550 align:middle line:90% Questions? 01:06:34.550 --> 01:06:38.570 align:middle line:90% 01:06:38.570 --> 01:06:39.805 align:middle line:90% Yes. 01:06:39.805 --> 01:06:45.190 align:middle line:84% AUDIENCE: Is [INAUDIBLE] always there [INAUDIBLE]? 01:06:45.190 --> 01:06:47.770 align:middle line:84% JACK HARE: So the Zeeman effect requires 01:06:47.770 --> 01:06:50.110 align:middle line:84% certain electronic configurations 01:06:50.110 --> 01:06:51.470 align:middle line:90% to actually occur. 01:06:51.470 --> 01:06:54.460 align:middle line:84% And I believe that you don't get Zeeman splitting in hydrogen, 01:06:54.460 --> 01:06:55.310 align:middle line:90% normally. 01:06:55.310 --> 01:06:57.640 align:middle line:84% So this motional stark effect is therefore 01:06:57.640 --> 01:07:01.120 align:middle line:90% more useful in that case. 01:07:01.120 --> 01:07:02.330 align:middle line:90% Yeah. 01:07:02.330 --> 01:07:04.880 align:middle line:84% And this motional stark effect is particularly big 01:07:04.880 --> 01:07:08.180 align:middle line:84% because we're talking about very fast-moving neutral beam 01:07:08.180 --> 01:07:08.730 align:middle line:90% particles. 01:07:08.730 --> 01:07:12.500 align:middle line:84% So this isn't useful in a plasma-- 01:07:12.500 --> 01:07:14.090 align:middle line:84% in just looking at the thermal ions, 01:07:14.090 --> 01:07:15.920 align:middle line:84% because all these velocities are in different directions 01:07:15.920 --> 01:07:17.240 align:middle line:90% and they're relatively small. 01:07:17.240 --> 01:07:19.130 align:middle line:84% So all that will give you is a broadening. 01:07:19.130 --> 01:07:22.320 align:middle line:84% The point is that this V is large and all in one direction. 01:07:22.320 --> 01:07:24.350 align:middle line:84% So you get a big splitting and it's consistent. 01:07:24.350 --> 01:07:26.630 align:middle line:84% Every single particle is emitting light 01:07:26.630 --> 01:07:27.931 align:middle line:90% with the same spectra. 01:07:27.931 --> 01:07:30.098 align:middle line:84% And so you can actually stand a chance of measuring. 01:07:30.098 --> 01:07:34.310 align:middle line:90% 01:07:34.310 --> 01:07:35.225 align:middle line:90% Any questions online? 01:07:35.225 --> 01:07:41.070 align:middle line:90% 01:07:41.070 --> 01:07:42.397 align:middle line:90% All right. 01:07:42.397 --> 01:07:43.730 align:middle line:90% You can have a quarter of your-- 01:07:43.730 --> 01:07:45.350 align:middle line:84% quarter of an hour of your lives back. 01:07:45.350 --> 01:07:46.340 align:middle line:90% Do whatever you want. 01:07:46.340 --> 01:07:49.120 align:middle line:90% And happy Thanksgiving. 01:07:49.120 --> 01:07:52.000 align:middle line:90%