1 00:00:08,010 --> 00:00:17,430 It's a great privilege to be here. I gave a theoretical physics colloquium last week where I presented the theoretical underpinnings of today's talk. 2 00:00:17,790 --> 00:00:23,520 So today that would be very little theory. A more focussed on experimental program. 3 00:00:26,060 --> 00:00:30,250 Let's see. Fusion. 4 00:00:30,760 --> 00:00:38,260 If you want to do fusion, not atmospheric pressure, you need a confinement time of the order of seconds. 5 00:00:38,320 --> 00:00:45,570 The confinement time is the energy of the plasma divided by the heating power that you need to sustain this energy. 6 00:00:45,580 --> 00:00:51,100 So it's the characteristic time scale on which the plasma would cool down if 7 00:00:51,100 --> 00:00:54,340 you turned off the heating needs to be of the order of a couple of seconds. 8 00:00:57,220 --> 00:01:06,820 And to achieve fusion, you need a temperature of ten KB or so, which means the thermal velocity of the ions exceeds 2000 kilometres per second. 9 00:01:07,390 --> 00:01:13,300 So if you don't confine it there, the lifetime of confinement, I would be less than a microsecond. 10 00:01:15,540 --> 00:01:24,540 Therefore you use magnetic fields. As I'm sure you know, the magnetic field charge charges can essentially only move along the field. 11 00:01:24,870 --> 00:01:25,679 Across the field, 12 00:01:25,680 --> 00:01:35,790 they move in tightly wound spirals with a jar radius of the order of equal to the perpendicular velocity component divided by the gyro frequency, 13 00:01:35,790 --> 00:01:43,229 which is charged ten times field of a mass. So the magnetic field confines the particles in two of the three dimensions. 14 00:01:43,230 --> 00:01:50,460 And the obvious way to provide confinement in the third dimension is to is to band the magnetic field into a ring. 15 00:01:52,290 --> 00:02:02,640 But that doesn't quite work. If you do that and you max, the radius of the field capital are be much larger than the gyrus gyro radius obviously. 16 00:02:03,120 --> 00:02:08,310 So you have a small parameter rho store which is in practice of its orbit and to the minus three, 17 00:02:09,420 --> 00:02:15,719 then the magnetic field is necessarily non-uniform, so the particles do not anymore. 18 00:02:15,720 --> 00:02:19,820 Exactly. Follow follow the three lines. Plus a gyration. 19 00:02:20,420 --> 00:02:24,250 In addition, the velocity vector, 20 00:02:24,290 --> 00:02:32,270 the time average velocity vector consists not only of the parallel velocity and only the fields of B or C undetectable on the field. 21 00:02:32,750 --> 00:02:38,360 There is also a slower, slower by a factor rho star drift. 22 00:02:39,410 --> 00:02:43,040 Perpendicular to the field lines and perpendicular to the field strength. 23 00:02:45,400 --> 00:02:53,560 So that's a slow drift. We're just starting to see orders of magnitude slower than done the pilot motion. 24 00:02:54,550 --> 00:03:02,110 So if you just band the field into a ring, it will the particles will slowly drift in the vertical direction. 25 00:03:03,280 --> 00:03:09,380 This gravity is obviously directed inwards in doing so. That's a conserved quantity that we like to say. 26 00:03:10,030 --> 00:03:14,740 It's the magnetic moment of the current loop that the particle makes. 27 00:03:16,390 --> 00:03:21,910 So the confinement time for such a device would then be, roughly speaking, if the length, 28 00:03:22,480 --> 00:03:29,080 the device divided by the drift velocity, which is one factor roast, are smaller than the thermal velocity. 29 00:03:29,120 --> 00:03:32,350 But so you've gained three orders of magnitude in confinement time. 30 00:03:32,710 --> 00:03:39,680 But you need another to order something or to. So the way to get sacked. 31 00:03:39,910 --> 00:03:43,360 So what we need is second order confinement. Second order in row. 32 00:03:47,020 --> 00:03:51,460 The most popular way of achieving that is to bend the magnetic field. 33 00:03:54,210 --> 00:04:00,990 It's so that it spirals around a Troilus surface, such as it's called the Tokamak. 34 00:04:02,280 --> 00:04:10,860 The idea is, was due to Tom and Sakharov in 1951, but others conceived of the idea simultaneously. 35 00:04:12,600 --> 00:04:17,280 So in a tokamak, you drive a current of order of mega amperes, 36 00:04:19,260 --> 00:04:27,600 which then produces a pole oil field that adds to the toroidal field and makes the field spiral around the plasma. 37 00:04:30,370 --> 00:04:34,680 What then happens can be illustrated by my movie here. 38 00:04:34,690 --> 00:04:38,110 So. So this is a movie about a part of an orbit. 39 00:04:38,560 --> 00:04:45,220 So as you see, the particle orbit, the particle state follow the magnetic surface, trace off by the field lines of magnetic fields. 40 00:04:45,490 --> 00:04:51,250 It's colour coded to it's colour coded out. 41 00:04:51,700 --> 00:04:58,300 The the drift is vertical, but, but the particle drifts into the plasma as much as it drifts out of it. 42 00:04:58,930 --> 00:05:04,290 And in this way, you get the second order component. But. 43 00:05:04,300 --> 00:05:12,670 Yeah, but you have to drive this current. And there is no obvious way of driving a car in steady state and a plasma. 44 00:05:15,020 --> 00:05:20,250 And that current can, of course, can be the source of instabilities, of violent instabilities. 45 00:05:21,300 --> 00:05:29,400 The Tokamak was not what was not exclusively invented by Tom and. 46 00:05:30,090 --> 00:05:37,860 Several other people have the same idea because in the 1950s, the fusion program in Russia of the Soviet Union, 47 00:05:37,860 --> 00:05:44,669 in the UK and in the US was classified, which had the consequence. 48 00:05:44,670 --> 00:05:49,170 That work was parallel. Work was paralysed. 49 00:05:49,350 --> 00:05:54,090 The same invention, the same ideas were conceived in many different places. 50 00:05:54,840 --> 00:06:03,270 It also had advantages. If you talk to people from that era, they will tell you you never had to go to conferences, didn't have to publish. 51 00:06:04,110 --> 00:06:07,530 You didn't have to fight for recognition because there was none. 52 00:06:09,690 --> 00:06:15,580 The only thing that mattered was to get the right answer. There was no government, so there was no. 53 00:06:20,610 --> 00:06:28,610 So most of the ideas infused in the world at that time were held by several people independently of each other. 54 00:06:28,620 --> 00:06:32,460 But there was one one exception. 55 00:06:33,330 --> 00:06:40,320 This clever chap, Lyman Spitzer of 36, was head of astrophysics in Princeton, 56 00:06:41,130 --> 00:06:47,430 and so great pioneer of the study of the interstellar medium and also the father of the Hubble Space Telescope. 57 00:06:47,430 --> 00:06:53,100 Later, he had a unique idea that nobody else had the quality to stellarator. 58 00:06:54,780 --> 00:07:03,630 In the stellarator. You also twist the magnetic field lines, but you do it with the help of external coils, not by a plasma current. 59 00:07:04,560 --> 00:07:10,490 So this is the classical stellarator of of Spitzer. 60 00:07:11,100 --> 00:07:13,259 The magnetic field is produced by two kinds. 61 00:07:13,260 --> 00:07:21,270 Of course, you have these toroidal magnetic field coils, just as in the Tokamak, which produces quite a few like this. 62 00:07:21,810 --> 00:07:28,709 And in addition, you have these helical coils which carry current in alternate directions like this that makes 63 00:07:28,710 --> 00:07:36,060 the magnetic field lines twist around the Taurus like this so that they trace out the surface. 64 00:07:37,750 --> 00:07:43,830 And on the surface, the magnetic particles move and just seem to talk a lot. 65 00:07:45,610 --> 00:07:49,840 They are confined because the drifted approximately vertical. 66 00:07:50,500 --> 00:07:58,210 The particle, the particle drifts into the magnetic surface. 67 00:07:58,300 --> 00:08:02,260 That's the surface trace off other fields as much as it drifts out. 68 00:08:03,710 --> 00:08:10,580 So you don't have to drive a current in the place where you have a steady state confinement device for plasma. 69 00:08:11,780 --> 00:08:16,820 But it is a bit counterintuitive that that would be possible at first. 70 00:08:16,850 --> 00:08:27,020 First of all, if we are so the magnetic field is twisted, as you saw in this in this figure, this twisted if I take this magnetic surface. 71 00:08:27,850 --> 00:08:32,680 This purple surface. And unwrap it. So this is the toroidal angle. 72 00:08:32,770 --> 00:08:37,590 That's the long way around the quartz to follow along a following feedline periodically. 73 00:08:37,690 --> 00:08:43,270 So you follow the feedline like this. It comes back here and it gradually winds around the tours. 74 00:08:43,690 --> 00:08:49,570 I can define a rotational transform. Spitzer called it as the winding number of those few nights. 75 00:08:50,200 --> 00:08:54,189 But it is counterintuitive that that should be possible for. 76 00:08:54,190 --> 00:08:58,090 Let's consider this this picture again. 77 00:08:58,720 --> 00:09:09,660 Let us. Integrate the magnetic field around such a contour since there is no current in the plasma. 78 00:09:10,830 --> 00:09:18,110 The answer is zero. Suggesting that there is no average magnetic field in this direction. 79 00:09:19,420 --> 00:09:26,020 And yet. Spitzer realised the magnetic field lines do spiral around the Taurus. 80 00:09:27,320 --> 00:09:32,750 So what is the average feel then? Well, it turns out that there are two kinds of averages. 81 00:09:33,620 --> 00:09:39,080 This average is different from the eye out on the winding number average. 82 00:09:39,920 --> 00:09:41,780 If you write it in a clever set of coordinates, 83 00:09:41,780 --> 00:09:49,250 you find that one is the average of the covariant pull of vital component and the other is the average of the contraband component. 84 00:09:52,090 --> 00:09:55,180 Another way of seeing this is to go back to the Tokamak. 85 00:09:55,360 --> 00:10:01,689 It's a field in the Tokamak. And let's define an integration contour that starts on a few lines and goes 86 00:10:01,690 --> 00:10:07,540 perpendicular to two of the few lines until you come back to the original field, 87 00:10:08,410 --> 00:10:11,620 and then you go back to where you started along the V line. 88 00:10:12,850 --> 00:10:18,390 So it runs perpendicular to be up to here and then it goes along. B. Now again, let's calculate. 89 00:10:19,580 --> 00:10:25,520 This can be integral or be. It must be clear to me, you know how steam closed current. 90 00:10:26,510 --> 00:10:32,900 But the first bit of the control, the one that goes from here to the here, which is perpendicular to be, makes no contribution. 91 00:10:34,100 --> 00:10:43,460 So you realise that the lengths that you have to go along the field is proportional to the current, then to the current. 92 00:10:45,300 --> 00:10:51,900 So in a stellarator this means that the perpendicular is closed on themselves. 93 00:10:52,260 --> 00:10:56,960 There is no such aspect. So purely a geometric way of formal, 94 00:10:57,240 --> 00:11:05,470 formal acting spritzers inside is that if you draw the field lines on the magnetic surface and the perpendicular ice, 95 00:11:06,200 --> 00:11:13,010 then the field lines spiral around the Taurus. If you follow a few line here, you'll notice that it's started by as well as the cross. 96 00:11:13,340 --> 00:11:16,580 But the perpendicular do not spiral. They're closed on themselves. 97 00:11:18,320 --> 00:11:22,820 And this is the slightly counterintuitive fact that this should be possible. 98 00:11:24,680 --> 00:11:29,450 It is an early realisation of what later became a geometric phases in physics. 99 00:11:29,570 --> 00:11:34,010 The Berry Face is the most famous example of it, but there are others that are even ones. 100 00:11:34,250 --> 00:11:40,130 But this is one one of the first. It's not the first realisation of it, but it's it's one of the first ones. 101 00:11:40,340 --> 00:11:41,270 The same thing happens, 102 00:11:41,270 --> 00:11:53,479 I believe if you send polarised light down a and an optical fibre which you twist in space when it and if you make it come back to itself, 103 00:11:53,480 --> 00:12:02,530 the polarisation has shifted by an angle so you can prove mathematically that are exactly three ways of twisting magnetic fields. 104 00:12:02,540 --> 00:12:04,250 This follows just for maximum sequential. 105 00:12:04,880 --> 00:12:13,940 You can you can calculate this winding a number iota up close to the innermost feeling called the magnetic axis as an integral. 106 00:12:14,150 --> 00:12:20,660 And you can show that in the right ones around the Taurus, and you'll find that this one number is the sum of three terms. 107 00:12:21,020 --> 00:12:27,260 The first one is the current. That's what's used in the Tokamak to twist lines. 108 00:12:27,500 --> 00:12:33,319 But then there are two other terms. So just the current density here. First you have Tao. 109 00:12:33,320 --> 00:12:37,160 Tao is the course of this innermost magnetic field line. 110 00:12:37,940 --> 00:12:47,780 So the torsion is a concept from differential geometry that characterises how much a curve deviates from lying in a plane. 111 00:12:50,220 --> 00:12:52,880 So capped by here is the curvature vector, which points inwards. 112 00:12:52,890 --> 00:13:01,290 If you take the curvature vector and cross it with the with the tangent vector, you get a vector that's perpendicular to both. 113 00:13:01,530 --> 00:13:05,700 And if, um. Um. 114 00:13:06,480 --> 00:13:16,340 Well, if you do this, you get that to get the torso. The third way of twisting a funny line is the following. 115 00:13:17,840 --> 00:13:26,080 If you cut the magnetic surface like this, it's necessarily necessarily elliptical in the centre with a major axis and a minor axis. 116 00:13:26,090 --> 00:13:31,400 If you left a cross section of that ellipse, rotate as you go around the Taurus. 117 00:13:32,890 --> 00:13:37,600 Then so do you. Here is the angle, the tilting angle of the ellipse. 118 00:13:37,900 --> 00:13:48,160 If that, um. If if there's ellipticity on that tilting angle, that tilt moves systematically in one direction. 119 00:13:48,160 --> 00:13:53,020 It drags the fields field with it. You can understand this by thinking of water. 120 00:13:53,050 --> 00:14:01,360 That's a perfect mathematical analogy between three lines and streamlines, you know, in in an in an ideal fluid. 121 00:14:01,930 --> 00:14:13,360 Suppose you build a pipe with elliptical cross-section and you you make that cross-section rotate along the pipe, then the then the streamlines. 122 00:14:13,580 --> 00:14:19,480 The water will also rotate. Although even if there's no vorticity in the water. 123 00:14:21,080 --> 00:14:25,340 Miles can rotate without vorticity. Magnetic fields can rotate without current. 124 00:14:25,760 --> 00:14:40,180 It's a perfect mathematical analogy. So knowing this now that it's how to twist magnetic fields, people went off and built stellar reactors. 125 00:14:40,210 --> 00:14:48,220 Now you can do anything your heart desires. You can think of all sorts of weird, stellar ideas. 126 00:14:48,220 --> 00:14:52,660 This is the largest one in the world. Prior to our experiment. It's called a large helical device. 127 00:14:52,930 --> 00:14:58,000 It's in Japan. What you see is a magnetic surface here with the field strength colour coded. 128 00:14:58,180 --> 00:15:01,690 This is the set of coins that produces it. So you have. 129 00:15:02,500 --> 00:15:07,180 So this is not a classical stellarator. It's not if debate with Spitzer's idea. 130 00:15:07,180 --> 00:15:09,190 There's no there are no Royal Enfield coins. 131 00:15:09,190 --> 00:15:16,540 Instead, there are these pull oil field calls, this circle of things, and there are two helical coils carrying current in the same direction. 132 00:15:17,200 --> 00:15:21,790 That also works has the largest stellarator in Europe. 133 00:15:21,790 --> 00:15:24,880 Prior experiment. It's called T.J. two. It's in Madrid. 134 00:15:26,860 --> 00:15:32,650 This is the. A magnetic surface with the strength colour coded again. 135 00:15:32,740 --> 00:15:36,580 This is the strange set of coins that produces it. 136 00:15:39,040 --> 00:15:43,390 It's rather artistic. So this is from the country of Salvador Dali, of course. 137 00:15:45,790 --> 00:15:56,920 So this film, this it's created by by a red and blue card in the cemetery which are tightly wound around each other and by this circular green course. 138 00:15:57,490 --> 00:16:02,840 In addition to the large football field courts. So you can go. 139 00:16:03,200 --> 00:16:05,450 So there are wonderful, stellar writers around the world, 140 00:16:05,840 --> 00:16:15,050 but they all suffer from a basic problem that has to do with particle or particle orbits that are different from the ones I showed you earlier. 141 00:16:15,860 --> 00:16:22,489 Remember, the magnetic moment is constant and these perps squared over to be the perp is 142 00:16:22,490 --> 00:16:26,330 the component of the velocity vector that's perpendicular demographically. 143 00:16:26,900 --> 00:16:30,440 The energy source. A constant, of course. So. 144 00:16:31,850 --> 00:16:35,540 So these two conserved quantities implies that B is equal to each of the new. 145 00:16:37,350 --> 00:16:47,090 Implying that a a particle can never penetrate into a region with a magnetic field strength larger than that of AMU. 146 00:16:47,690 --> 00:16:54,630 And this is, of course, the basis for trapping of charged particles in the magnetosphere, the Van Allen belts. 147 00:16:56,070 --> 00:17:01,530 Particles with large enough, you can't go into regions of large field strength. 148 00:17:05,420 --> 00:17:08,500 If we look at the particle orbits in a tokamak, 149 00:17:08,510 --> 00:17:18,200 this means that there are orbits that do this that are reflected by the large magnetic field strength that that prevents on the inboard side, 150 00:17:18,710 --> 00:17:25,400 the Taurus, these particles, they stay on them on the magnetic surface that we see here, so that they are, well, confined. 151 00:17:26,960 --> 00:17:34,310 And bounce back and forth. But when confined by the magnetic field still, but in a stellarator, it's just different. 152 00:17:34,940 --> 00:17:43,970 So first of all, the the mathematical reason for this is that there is the third constant of the motion in addition to EMU due to the symmetry. 153 00:17:44,910 --> 00:17:53,219 So there are three constants of the motion and therefore the Hamiltonian describing this part of the most integral in a stellarator. 154 00:17:53,220 --> 00:18:00,330 It's different. Let's look at the particle of motion on a magnetic surface again in the large helical device in Japan. 155 00:18:01,140 --> 00:18:06,720 So this is the same orbit as I showed you before, and it does exactly what Spitzer realised it would do. 156 00:18:07,500 --> 00:18:13,260 But then there is this second class of orbits that we didn't think of as prime time to realise this. 157 00:18:13,260 --> 00:18:17,069 Ten, 15 years after that, the trapped particle orbits. 158 00:18:17,070 --> 00:18:22,470 They bounce back and forth along the field and they drift slowly across it. 159 00:18:23,130 --> 00:18:28,210 The drift is no longer compensated by the helical emotion and the particles drift out. 160 00:18:28,920 --> 00:18:35,580 So the trapped orbits would drift out of a generic stellarator and therefore the confinement is pretty bad. 161 00:18:36,750 --> 00:18:41,360 In practice, particles collide before they're drifted out. 162 00:18:42,420 --> 00:18:48,540 So those are shorter timescales after the collision frequency. So let's estimate the diffusion coefficient. 163 00:18:49,620 --> 00:18:56,190 So what will happen is that the particle, the particle follows a magnetic field line where the field strength bar is roughly like this. 164 00:18:56,850 --> 00:19:01,860 These little magnetic wells, when it is trapped in one of those swells, it drifts vertically. 165 00:19:03,380 --> 00:19:07,970 But then it collides with another particle and it's scattered into another type of orbit. 166 00:19:08,090 --> 00:19:09,169 Circulating orbit, perhaps. 167 00:19:09,170 --> 00:19:15,170 So then it's welcome, fine for a while until it collides again and it becomes trapped somewhere else, and then it perhaps drifts into the surface. 168 00:19:15,680 --> 00:19:19,910 And in this way the it undergoes a random walk, sometimes drifting inward, sometimes drifting outwards. 169 00:19:21,380 --> 00:19:25,100 The step length of that random walk is equal to the drift velocity times. 170 00:19:25,100 --> 00:19:33,980 The step time and the step time is sort of the collision frequency, the inverse collision frequency. 171 00:19:34,820 --> 00:19:41,020 So if you add the number of participating particles of this, the number of particles trapped in these events. 172 00:19:41,780 --> 00:19:46,730 So if you estimate the diffusion coefficient by multiplying the number of participating particles, 173 00:19:47,030 --> 00:19:52,100 when this fraction of such particles divided with the delta all squared over delta t, 174 00:19:52,550 --> 00:19:58,310 we get a diffusion coefficient that scales with a square of the drift velocity and inversely with the collision frequency. 175 00:19:59,760 --> 00:20:06,950 The collision frequency. Gives us energy to the minus three halves at high energies. 176 00:20:09,610 --> 00:20:16,870 So if he works like this, the drift velocity is proportional to the temperature or to the energy of a particle. 177 00:20:17,860 --> 00:20:24,100 So the this diffusion coefficient is proportional to temperature to the seven halves. 178 00:20:25,970 --> 00:20:28,940 So in the hot plasma, it causes enormous loss. 179 00:20:29,480 --> 00:20:35,090 So in practice, in an experiment, it means you can heat the plasma up to a certain temperature and then you just hit a brick wall. 180 00:20:35,090 --> 00:20:42,830 You just can't get it any hotter. And this has been plaguing all Stellarator experiments for decades. 181 00:20:43,640 --> 00:20:47,900 And these losses tend to predominate over turbulent losses, which are that in addition. 182 00:20:49,210 --> 00:20:55,240 You can do a proper transport theory by solving a kinetic equation for these particles, but I won't go into that. 183 00:20:56,050 --> 00:21:00,010 So our new experiment balanced on seven X in Germany. 184 00:21:00,130 --> 00:21:07,780 It's one of the largest physics experiments that have ever been constructed in Germany, and it aims to solve this problem. 185 00:21:08,620 --> 00:21:12,910 It is remarkably and perhaps uniquely theory driven. 186 00:21:15,160 --> 00:21:22,550 This is what has been done. An attempt has been to optimise the magnetic field. 187 00:21:24,050 --> 00:21:33,620 The magnetic field near Taurus is defined uniquely by the surface of the of the boundary. 188 00:21:34,670 --> 00:21:41,750 If you can close a magnetic field in a trial, in a trial region with the boundary of given shape, you have uniquely defined what the few lines are. 189 00:21:45,340 --> 00:21:53,110 So you can you can play with that boundary, see what you feel you get, and try to reduce the number of particles that drift out of the device. 190 00:21:54,590 --> 00:22:04,280 Until you are and when you are happy with that feed, you can on a second surface find the current distribution that would produce that feed. 191 00:22:06,510 --> 00:22:14,340 There's always such a current distribution that you can be scrutinised, that kind of distribution to find magnetic field coins that will do it. 192 00:22:15,410 --> 00:22:23,780 This is the result for Palestine seven x. So the result that is the shape of a plasma with feedbacks that you are happy with. 193 00:22:25,030 --> 00:22:28,720 And magnetic field coils that produce this shape. 194 00:22:29,470 --> 00:22:34,000 This only became possible with the advent of super quantum computers in the late eighties. 195 00:22:38,250 --> 00:22:46,190 So in London's time, seven x an attempt has been made to optimise the field for small transport, but not only for that. 196 00:22:46,190 --> 00:22:52,229 There is also a list of other criteria. One of the once good nested magnetic surfaces. 197 00:22:52,230 --> 00:22:57,139 How to show you a picture of that in a minute. Good finite pressure equilibrium. 198 00:22:57,140 --> 00:23:03,799 The plasma influences equally. It changes the occurrence in the plasma that affects the magnetic field. 199 00:23:03,800 --> 00:23:07,310 One wants to minimise the back reaction of the plasma on the field. 200 00:23:07,850 --> 00:23:16,760 One wants to optimise stability and one wants to end up with coins that are buildable that are not too complicated. 201 00:23:16,880 --> 00:23:24,800 Their shape. You might think these are very complicated, but they are very simple compared with some other types of satellite records. 202 00:23:25,790 --> 00:23:29,179 And they are modular, unlike those of the classical stellarator. 203 00:23:29,180 --> 00:23:34,110 They don't go all the way around the Taurus. So they are much smaller. 204 00:23:34,110 --> 00:23:37,530 They can be put on the back of a lorry. They don't have to be wound on the side. 205 00:23:40,920 --> 00:23:47,310 To try to convince you that this works. Let me show you particle orbits on the magnetic surface in this device. 206 00:23:47,670 --> 00:23:51,480 So here again, it's a little orbit that circulates around the tourists. 207 00:23:52,140 --> 00:23:55,380 Again, it's very well confined. It stays on the surface. 208 00:23:55,860 --> 00:24:05,240 It started to pop. But let's now zoom in on a trapped particle orbit in orbit that just gets reflected by the stars. 209 00:24:05,480 --> 00:24:14,510 It doesn't drift out to the device. It drifts around and stays on average on the magnetic surface where it started. 210 00:24:17,190 --> 00:24:24,479 And in this way. So then that happens for the great majority of all orbits because make it happen for for all orbits. 211 00:24:24,480 --> 00:24:27,990 One can show that mathematically you can make it happen for the great majority of them. 212 00:24:29,700 --> 00:24:36,520 And in this way one can reduce the diffusion. Can efficient. Can you reduce it enough? 213 00:24:36,600 --> 00:24:45,090 Well, there is a technique that will always be a temperature above which those few unconfined orbits will dominate the transport. 214 00:24:45,460 --> 00:24:55,770 You can calculate the the temperature above which that diffusion coefficient gets larger than a previous time values like one square metre per second. 215 00:24:55,780 --> 00:24:59,370 That's typically what turbulence does for the plasma anyway. 216 00:25:00,000 --> 00:25:05,790 And you find the prediction is that you one should get up to five KB or so depending on the density. 217 00:25:06,510 --> 00:25:10,860 I remind you that this diffusion coefficient we found was inversely proportional to the density. 218 00:25:11,130 --> 00:25:15,900 It's all the same proportion to the square of the magnetic field strength and the radius of the device. 219 00:25:16,440 --> 00:25:23,040 So this transporter is small enough that if one scales it up to the size which a fusion power plant would have to have, 220 00:25:23,340 --> 00:25:24,630 the confinement is good enough. 221 00:25:30,390 --> 00:25:38,790 The device is not had not only been optimised for good confinement magnetic field on some trajectories without much coding system, 222 00:25:39,210 --> 00:25:48,630 they can be chaotic. Of the few lines that correspond to particle orbits with particles of zero mass, so they are therefore Hamiltonian. 223 00:25:48,630 --> 00:25:54,980 And as Hamiltonian systems they can exhibit chaos that can. 224 00:25:55,760 --> 00:25:59,970 The defeat came from Ireland. So that that happens if you don't watch out. 225 00:26:00,000 --> 00:26:10,110 So this is this is a puncture plot to carry a plot of the field in a cross-section of abandoned flights of the next where we have optimised the field. 226 00:26:10,860 --> 00:26:16,200 You see chaotic felines in the edge here and you see a chain of magnetic islands. 227 00:26:16,770 --> 00:26:23,910 So. So here the particles can move freely from the inside of the island to the outside of the island, along the beach and around the course. 228 00:26:24,720 --> 00:26:28,230 So the red region here doesn't provide any confinement. 229 00:26:28,950 --> 00:26:32,880 So the field has been carefully designed to avoid such things happening. 230 00:26:34,200 --> 00:26:40,530 And this is the result. This is the result of a heroic German engineering effort that's been made. 231 00:26:41,790 --> 00:26:46,200 But. To construct this device. 232 00:26:46,260 --> 00:26:51,040 It's. The plasma vault. So this is a normal size person. 233 00:26:53,000 --> 00:26:59,460 It has a plasma volume of 30 cubic metres. It's a major radius of five and a half metres metres. 234 00:27:00,190 --> 00:27:04,540 A minor radius ten times smaller. A magnetic field of three Tesla. 235 00:27:05,290 --> 00:27:14,169 So the field energy is nearly gigajoule. This field is created by these superconducting coils, weird shapes. 236 00:27:14,170 --> 00:27:20,290 There are 70 of them. 50 non-playing, their coils and 20 additional play. 237 00:27:20,290 --> 00:27:28,540 They're quite strong. Experimental flexibility to the device. They are superconducting so they can produce plasma for up to 30 minutes. 238 00:27:29,260 --> 00:27:34,230 It's just a cooling plasma that that limits the life. 239 00:27:35,160 --> 00:27:42,569 The cell sets this this limit. The plasma heated by various heating systems, 240 00:27:42,570 --> 00:27:49,320 most mostly microwaves of two different frequencies resonating with this electrons and the subsequent electrical motion. 241 00:27:52,730 --> 00:28:00,300 And this is what it looks from the inside. I'll try to explain. So explain the device. 242 00:28:00,330 --> 00:28:05,150 So first there is the plasma surface, right? 243 00:28:05,540 --> 00:28:09,339 That's the shape. Powered by optimisation. 244 00:28:09,340 --> 00:28:15,460 So this is where the theoreticians job is done. So I feel qualified to talk about everything that comes now. 245 00:28:17,850 --> 00:28:22,210 So in well-defined places, the field lines hit the wall. 246 00:28:22,750 --> 00:28:29,170 Somewhere, the energy must come out of the of the device that happens at these so-called diverter targets. 247 00:28:30,970 --> 00:28:36,640 They're actively cooled to withstand heat fluxes up to ten megawatts per square metre. 248 00:28:37,240 --> 00:28:46,360 That's a fifth of the energy flux on the surface of the sun, but it can be done by pumping a lot of water, essentially. 249 00:28:48,400 --> 00:28:49,990 So this is the way it happens. 250 00:28:51,040 --> 00:28:59,680 If you take a cross-sectional magnetic field and a puncture plot, the magnetic islands at the edge, which have been designed to be there, 251 00:28:59,950 --> 00:29:07,120 and they are and they are cut by this diabolical place, by these target plates for the plasma when it leaks out to the field. 252 00:29:07,120 --> 00:29:11,919 Here it comes on to on to a few lines corresponding to these islands. 253 00:29:11,920 --> 00:29:15,880 And they hit these flights, which are designed to withstand. 254 00:29:18,330 --> 00:29:21,870 So yeah, I'm going to think I should add that that's a category. 255 00:29:22,470 --> 00:29:34,550 Then that's the vacuum vessel, of course. The vacuum vessel is a piece of our of welding art, one can say. 256 00:29:36,710 --> 00:29:52,010 Fantastic feat of engineering. I think outside the vacuum vessel cover is odd because this is the most expensive chip of the device, €80 million. 257 00:29:52,010 --> 00:29:55,040 I think they cost the 70 of these magnetic field coils. 258 00:29:57,440 --> 00:30:03,710 Niobium, titanium. Which was just about fit around the vacuum. 259 00:30:04,370 --> 00:30:07,430 So they had to be threaded upon it carefully. 260 00:30:08,210 --> 00:30:12,740 Huge forces on on these coins. 261 00:30:14,330 --> 00:30:18,920 Hot water, 100 tons. So they are own bolted into this central support structure. 262 00:30:19,930 --> 00:30:28,190 Steve. Then is a cry a start to keep to the field. 263 00:30:28,790 --> 00:30:32,600 The coin's cool, of course. So this is another. 264 00:30:34,090 --> 00:30:39,159 Piece of engineering that almost more holes in this stuff than there is metal. 265 00:30:39,160 --> 00:30:45,040 It's a very wobbly thing. Is there 254 ports? 266 00:30:46,430 --> 00:30:47,280 It looks like that. 267 00:30:47,300 --> 00:30:58,360 So which then to go to both the outer vessel on the inner vessel of three metres long and this is what the device looked like a few years ago. 268 00:30:58,370 --> 00:31:00,380 So you see here that the inner. 269 00:31:01,930 --> 00:31:12,670 Vacuum vessel, the coils, lots of cooling pipes and the aftermath after cries that you don't miss in a misguided effort to save money. 270 00:31:13,570 --> 00:31:16,720 The crisis that was made as small as possible. 271 00:31:18,160 --> 00:31:25,390 Which seemed like a good idea at the time, but it left almost no room for for all the pipes that had to go. 272 00:31:26,380 --> 00:31:33,070 So then then a team of 20 people had to use cat software to root these pipes so that 273 00:31:33,070 --> 00:31:37,060 they don't collide with with each other when the when the device is cooled down. 274 00:31:41,710 --> 00:31:45,820 This is slightly like the one that Chrysler has been added. 275 00:31:48,440 --> 00:31:56,569 There's certainly some rather difficult working conditions that you can set a war plan that's obviously protecting what you see. 276 00:31:56,570 --> 00:32:01,610 Some of the cooling pipes here. Lots of scaffolding, of course. 277 00:32:05,250 --> 00:32:10,740 The device was started to be commissioned in the middle of 2014. 278 00:32:12,930 --> 00:32:17,040 I'll show you a little movie of the assembly. 279 00:32:20,300 --> 00:32:24,520 Let's see. The device is pentagonal. 280 00:32:24,520 --> 00:32:27,180 It consists of of of five modules. 281 00:32:27,190 --> 00:32:37,720 This is the first half module is in the vacuum vessel and the and the cords being threaded upon it one by one by this special machinery. 282 00:32:38,970 --> 00:32:43,380 One after another. So there are seven coins in one half module. 283 00:32:44,280 --> 00:32:50,580 Now the first half module is ready. Lifted it somewhere else, bolted into another half module. 284 00:32:50,970 --> 00:33:02,420 And then the cooling pipes are added. I'll do the entire module as it is being lifted into the Taurus. 285 00:33:02,420 --> 00:33:07,220 Who comes into the vacuum vessel? The lower part of the vacuum vessel here. 286 00:33:07,970 --> 00:33:10,970 The top pockets are dead. It's put into position. 287 00:33:10,970 --> 00:33:25,540 This is from above. You see a lot of activity in module after module coming into place this year as another bit of the year of the Christ. 288 00:33:25,540 --> 00:33:34,140 And that's the last module. Lots of scaffolding, lots of pipes, lots of ports being run to the sea from above again. 289 00:33:34,620 --> 00:33:45,770 And you see how many? So that that that took ten years. 290 00:33:48,110 --> 00:33:51,590 That was ten years. And one minute if this. 291 00:33:57,930 --> 00:34:09,020 So then about a year ago, the most dramatic moment I think, of the commissioning went away when they started cooling down the Croisette. 292 00:34:09,690 --> 00:34:16,440 So it's 530 tons of mass to that is to be called the cryogenic temperatures. 293 00:34:16,830 --> 00:34:21,480 It's a11 and a half megawatt helium cooling, cooling, cooling plant. 294 00:34:23,400 --> 00:34:30,240 And then you hope that there are no cold leaks. But afterward, there are 5000 welds in the cryo stuff and each of them has to be tight. 295 00:34:31,140 --> 00:34:35,430 And co leaks are the other worst nightmare of leaks that only appear when the 296 00:34:35,430 --> 00:34:39,930 device is cold and disappear when you heat up the device to go look for them. 297 00:34:41,520 --> 00:34:46,980 But it all went very smoothly in one month's time. It cooled down the device. 298 00:34:47,160 --> 00:34:50,220 Everybody was was terribly nervous. 299 00:34:52,170 --> 00:35:00,600 And this was the final plunge the following week, down to four Kelvin, ten to the minus seven millibars. 300 00:35:00,690 --> 00:35:06,680 Ice pressure. No leaks. There were leaks afterwards in the quiet start. 301 00:35:08,420 --> 00:35:16,310 In the in the there there were there were leaks in, in less critical components like the pumping ducts. 302 00:35:17,480 --> 00:35:22,549 Um, that, that we knew could be repaired afterwards. 303 00:35:22,550 --> 00:35:26,870 So that, so that, that, that only took a few weeks. 304 00:35:29,300 --> 00:35:38,180 And then in the summer, filling measurements could be made. So these magnetic everything has been mounted with mm. 305 00:35:38,180 --> 00:35:50,210 Precision. To make sure the magnetic field is is as close as possibly possible to the design value and it can be measured. 306 00:35:51,980 --> 00:35:56,360 This shows this picture shows the principle of it. So here are a few lines. 307 00:35:56,780 --> 00:36:05,860 The coin points, obviously, if you insert a cathode into a low pressure, but not desperately low pressure vessel. 308 00:36:05,870 --> 00:36:12,380 So you have to have some gas in it. You don't need much more than that to keep inside a cathode. 309 00:36:12,440 --> 00:36:17,030 It will emit an electron beam along the feet, which you can detect. 310 00:36:17,870 --> 00:36:27,500 For instance, if that's enough gas, that gas will light up along the field line where the electrons travel. 311 00:36:27,860 --> 00:36:32,329 Or you can put a fluorescent rod intersecting the beam and make your point. 312 00:36:32,330 --> 00:36:38,990 Carry a plot of the field. Then you can swing the electron emitter and the fluorescent ROC and see what happens. 313 00:36:39,000 --> 00:36:42,280 So this is the device we have these manipulators. 314 00:36:42,550 --> 00:36:50,410 So you're inside a cathode with one of them, a fluorescent rod or not with the other one. 315 00:36:51,790 --> 00:36:58,790 And you see what the electron beam does. And you get pictures like this. 316 00:36:58,810 --> 00:37:03,790 So this is a picture of an electron beam propagating in the in the air, 317 00:37:03,790 --> 00:37:11,710 essentially moist air at low pressure on the toys that goes up around the mile 25 times around the Taurus. 318 00:37:12,140 --> 00:37:17,270 You can actually see the magnetic field. We have funded projects. 319 00:37:17,460 --> 00:37:20,460 So it looks like the fee lines are noted. 320 00:37:21,730 --> 00:37:28,110 So some of these pictures look really strange. You can compare this with with your predictions, of course. 321 00:37:28,470 --> 00:37:32,880 Or you can do it. You can have this fluorescent rod. 322 00:37:36,090 --> 00:37:40,440 That lights up when when the electron beam intersects it. 323 00:37:41,980 --> 00:37:50,920 And you can take pictures of these feedlots and the price and load with long exposure targets to get pictures like this. 324 00:37:51,460 --> 00:37:58,170 So here you see magnetic felines going around the tourists and an intentionally created magnetic island. 325 00:38:00,170 --> 00:38:06,440 Five over six Ireland. So this is when the when the winding number is exactly equal to five over six. 326 00:38:08,340 --> 00:38:18,520 This provides an extremely. Accurate measurement of that magnetic field line component down to one part, ten to the minus five. 327 00:38:19,330 --> 00:38:25,000 To my knowledge, it's the first time that the topology with magnetic field has been measured that accurately 328 00:38:25,990 --> 00:38:33,160 the topology of a magnetic field that's 30 metres across measure to this position. 329 00:38:37,330 --> 00:38:44,469 And you can of this is this is this is a pop culture plot done with experiment. 330 00:38:44,470 --> 00:38:47,350 And you can compare that with your calculations. 331 00:38:48,130 --> 00:38:57,760 The feed the build machine has to be carefully been scanned, put in to the computer so it can calculate what the field should look like. 332 00:38:59,440 --> 00:39:02,650 And it. And it agrees. Exactly. 333 00:39:03,920 --> 00:39:09,950 Then you can crank up the debt. You can increase the current. For the coins, the coins are subject to huge forces. 334 00:39:11,900 --> 00:39:21,860 They don't. And they try to be more become more planar as you increase the the current the state of lowest energy is a circle is a plain circle. 335 00:39:22,100 --> 00:39:30,290 That's what they want to be. And you do that when they become more plane, that reduces the widening number, the rotation and transform the field. 336 00:39:30,590 --> 00:39:38,750 And these islands move the surface on which the widening number is equal to five six moves outward when you do that. 337 00:39:39,410 --> 00:39:44,750 So this here you see this chain of magnetic islands with different field strengths. 338 00:39:45,770 --> 00:39:50,420 You see if moving out from the red one to the green one as you increase the field strength. 339 00:39:51,900 --> 00:40:03,250 And you can compare that with the calculated elastic, the formation of the cards, and see that they deform as you expect them, 340 00:40:03,270 --> 00:40:09,150 that they are properly bolted onto the central support structure and that also increase. 341 00:40:09,930 --> 00:40:16,530 So that's quite an element model of the entire US built machine where this can be done. 342 00:40:19,540 --> 00:40:30,760 And then we finally, after waiting for six months or more, most got permission from the radiation protection authorities to have first class mass. 343 00:40:32,380 --> 00:40:39,260 So on the 9th of December. We had invited the press to come and look at our first plasma. 344 00:40:40,350 --> 00:40:47,540 We had made some the night before, actually, and there were 11 camera teams in the control room. 345 00:40:47,550 --> 00:40:56,820 You don't want to. So this is the first pass by a temperature of a million degrees, 180 lifetime for 20 milliseconds. 346 00:40:56,820 --> 00:41:06,149 So the there are lots of impurities, lots of impurities in the walls that you need to get rid of by successive plasma 347 00:41:06,150 --> 00:41:11,820 so that those impurities flow into the plasma and to extinguish it after a while. 348 00:41:14,550 --> 00:41:20,430 This is a movie. It's very faint. It's from last week of a more recent plasma. 349 00:41:21,870 --> 00:41:24,749 You see the plasma rotating like this, 350 00:41:24,750 --> 00:41:32,820 which is like from from hydrogen and from from from impurities that move inwards and eventually extinguish the plasma. 351 00:41:34,910 --> 00:41:43,920 I'm. My Final View graph are just the parameters achieved to date as of yesterday or so. 352 00:41:44,970 --> 00:41:48,850 So. The heating power is up to five megawatts. 353 00:41:48,850 --> 00:41:55,540 It will be much higher in the future. Plus, my lifetime output of 15 times longer than the first estimate. 354 00:41:55,580 --> 00:42:00,310 Estimation gets cleaner and cleaner. And extreme temperatures up to eight kilowatts. 355 00:42:01,740 --> 00:42:06,389 I am temperature's about a 10th that so the all the heating is in the electron 356 00:42:06,390 --> 00:42:11,130 channel and the items get heated by the electrons because of the large mass ratio. 357 00:42:11,490 --> 00:42:18,450 The temperature equilibration time between the electrons on the ions is longer than the discharge time. 358 00:42:18,450 --> 00:42:22,440 So for densities up to ten to the 20. 359 00:42:25,830 --> 00:42:32,390 So this is an example of a series of temperature and density profiles across the plasma. 360 00:42:32,420 --> 00:42:43,470 So you see in the beginning. So you have temperature locked out and then the temperature rises, the density first goes up and then it goes down. 361 00:42:43,500 --> 00:42:48,810 So the best for after 200 milliseconds or so is the. 362 00:42:49,880 --> 00:42:58,400 It's this light blue one where you have a whites ten to the 20 metres per square and particles per cubic metre. 363 00:42:59,370 --> 00:43:06,830 That's just what you want for fusion. You want it to be about three times hotter than that we have here. 364 00:43:07,640 --> 00:43:11,900 So you see the temperature of that being about four kilowatts. 365 00:43:11,900 --> 00:43:15,230 And for those of you a plasma physicist, we may even see it. 366 00:43:16,250 --> 00:43:23,510 To find that pressure with the plasma making the field expand its potential problem of shift because this this. 367 00:43:24,440 --> 00:43:28,340 China is recording a high temperature on the central line. 368 00:43:30,960 --> 00:43:39,570 So to summarise then, the Stellarator concept will now be put to a definitive test and the voltage line seven x. 369 00:43:41,790 --> 00:43:44,880 The device has been completely decommissioned and taken into operation. 370 00:43:45,300 --> 00:43:49,860 Last month we will have a first hydrogen plasmas. 371 00:43:49,890 --> 00:44:05,160 Next week we invited a physical chemist to push the button. We hope that this will verify that the fusion great plasma confinement device can be 372 00:44:05,160 --> 00:44:10,530 provided by a STELLARATOR And it will be very interesting to compare confinement, 373 00:44:10,620 --> 00:44:14,970 turbulence and general performance to that of other fusion devices. 374 00:44:15,570 --> 00:44:15,930 Thank you.