Particle Accelerators Reimagined – with Suzie Sheehy

In 1927, a tall man from New Zealand, called Ernest Rutherford, stood not far from this location at the Royal Society. And as the new president of that institution, he had this to say– that he desires a copious supply of atoms and electrons which have an individual energy far transcending that of alpha and beta particles. Now the reason he was saying this is because awhile before, in his lab, they'd been doing the so-called famous gold foil experiments, where they had taken alpha particles from radioactive decay and impinged them on a piece of gold foil. Now those of you who know the story know that what they were expecting was that these alpha particles would kind of go straight through and some of them would be deflected a little bit. And what they actually found was that just a few of these alpha particles pinned straight back at them in the direction they were firing them.

And that was a real surprise. And now we know that they had discovered the nucleus of the atom– the tiny nucleus at the center. But Rutherford understood that in order to learn more, in order to dig deeper into the atom, in order to understand our universe at a deeper level, he was going to have to find something with a bit more energy– some projectiles which went a little bit faster. And so, effectively, what he was asking for at that time was the particle accelerator. And boy, did he get some. So 90 years on, this is what we think of now when we talk about a particle accelerator. This is the Large Hadron Collider, in case you're not familiar with it. It is a 27 kilometer long ring underneath the border between Switzerland and France. And now we think of these machines as a sort of huge behemoths, really. They are incredible feats of engineering, design, science, and even culture– breaking down boundaries between different countries.

But the question is, are these things useful? I mean, when you think about what we're looking at there and what Rutherford was looking at with the atom– atoms are tiny. And there are loads, and loads, and load of them in anything useful. So in the universe, for example, if I was to add up all the stars in the universe, there would be 10 to the 29 in scientific notation. So that's 1 with 29 zeros after it. That's the same number as the number of atoms just in the people sitting in this room– not even in the chairs and the ground. So there are as many atoms in us– in this room– as there are stars in the entire universe. Remember that the universe is 13.8 billion years old and pretty massive. So atoms, being very, very tiny, it doesn't immediately make sense that they're going to be that useful. And especially the particles inside them– the subatomic particles– it's not entirely obvious that they're going to be useful either.

And actually, if we go back further in history, we find that the initial people who worked with other types of particles were also skeptical about their use. One of the famous Friday evening discourses here was given by J.J. Thomson, the physicist, where he demonstrated the particle which later became known as the electron. And he actually came back. And this isn't that well-known– but the Royal Institution kindly dug through their archives for me and they gave me this document beautifully titled– allthediscoursesever.xls. And there was a whole host of lovely information. And one of them that they found for me was this, from J.J. Thompson. And he says– and I'll have to read up here because my screen is tiny– "if there are any among my audience, any who, 20 years ago, listened to the announcement I made here of the existence of electrons, they will, I think, admit that they would have been skeptical if they'd been told they would, in another 20 years, be listening to another discourse on the commercial application of these electrons.

For electrons are so small that it takes about 1,700 of them to give a mass [INAUDIBLE] out of an atom of hydrogen and they move at such a rate"– blah, blah, blah. "So such properties appear rather transcendental and not promising from a practical point of view." How wrong he was. And in fact, there was a toast that famously went around the Cavendish Lab– it's J.J. Thomson's favorite quote– "to the electron… May it never be of any use to anybody." So I thought, with particle accelerators, what I'd start with is to show you how we can actually make some particles. So I have here a very small particle accelerator rather like the one that J.J. Thomson would have used. And to power it, over here, I have a high voltage oscillator, which is actually an induction coil, which Faraday– himself presenting in here– would have been very proud of. So I'm going to switch this on and it actually converts a DC from a battery here to a very high voltage AC. And then over this side– fingers crossed my camera is working.

If we dim the lights a little– perhaps I can move that on there. There we are. OK. So that's is actually generating a beam of electrons. So to generate electrons is quite easy. You, more or less, apply voltage to a piece of metal and they start jumping out. So this is what's called a cathode ray tube. And some of you will be familiar with those because they were in the back of televisions for many, many years, before we had flat panel ones. So this has some of the basic components of a particle accelerator. So it starts with some particles. And then the next thing we have to do is give it some energy. And in this, all I'm doing is applying a high voltage across the terminals to rip the electrons out of one side and attract them to the other side. Now the other thing I can do with this beam of particles is I can actually move it around. And that's an incredibly important part of a particle accelerator– being able to control the beam of electrons.

And to do that, we actually use magnets. So I have, literally, just a simple bar magnet here. And I can show you that the beam bends when I bring it near. So this is just a simple magnetic field. I hope you can see that up there. I'll do that again. And this is a basic property of charged particles in a magnetic field. They will bend around a corner. So if I hold the magnet the opposite direction, then, as predicted, we should get the opposite effect. So we'll turn it around a few times there. So that has a few of the basic components of a particle accelerator. And I'll just come back over here. But I think you might not be surprised to hear that they get a little bit more complicated than that. And we'll get onto that in a little bit. I'm just going to switch that off.

A lot of people think, when you start talking about particle accelerators, that we should start from the very start– from generating particles– and then build up how we get to the very high energies at the speed of light. But actually, when we design accelerators, we start from the other end. We sort of start with, what would you like a beam of particles to actually do? So it might be, for example, that you would like to sterilize medical products. And in that case, what you'd need is actually a 10 megaelectron-volt beam of electrons, so quite a bit higher in energy than this one. And in that case, a high intensity beam of electrons is sent through all of the medical products that go into your hospital. So syringes, bandages, and that kind of thing are sent through on a conveyor belt, irradiated with electrons, and that's actually able to kill any of the germs– every single germ or bit of bacteria that might be on those products when they;re generated.

So that translates from a use back into the design of the accelerator. And that's a commercial system that's sold on the market to do that. Or maybe instead, I want a beam of something to, say, scan some cargo. In that case, you could start with a fairly similar system with electrons, use those electrons into a heavy metal target to generate x-rays, and send the x-rays through your cargo, and by doing so, map out the density and if there's any contraband or whatever that's inside cargo. And these are used as well. And there's another option, actually, at the moment of potentially using neutrons to do the same kind of scanning. So that's another thing. Perhaps you might want to treat cancer. Are you getting the impression there's a couple of uses here of particle accelerators? I hope so.

You might want to treat cancer. And actually, radiotherapy– LINACs, as we call them, linear accelerators– are some of the most ubiquitous accelerators around. There's five or six of them in most major hospitals. And this is actually just a small electronic accelerator. Again, it smashes electrons into a metal target, generates x-rays, and that's what's used to treat cancer in something like 40% of successful treatment cases. So that's a huge application. Now I think it's fair to say J.J. Thomson did not predict that. We've come quite a long way. And that's sort of electrons, but we can also move on to other types of particles. We know how to generate beams of protons and use those to generate other things as well, with our understanding of isotopes.

So one other area in medicine where we use protons in particular is to generate radioisotopes. And one example of where they might be used is in PET scans– positron emission tomography scans. And they're great because they actually also use our understanding of anti-matter. So in a positron emission tomography scan, if you don't know, someone is fed a small amount of what's called fluorodeoxyglucose. It's a sweet liquid. And into that is a tiny bit of radioactive fluorine-18, which is being generated by a particle accelerator, using a beam onto a target to generate that radioactive isotope. When it's inside the body, it emits positrons. It's a beta emitter. Now positrons, being anti-matter, when they come in contact with normal matter– electrons– they annihilate.

So they literally disappear and, instead, generate two photons– two particles of light– in exactly opposite directions. So we're able to then catch those photons, going in opposite directions, every time they happen and build up a picture of what's happening inside the person's body. And because this fluorodeoxyglucose actually concentrates in high metabolic areas, that means you're more likely to map out areas where there might be cancer, heart disease, et cetera. So that's another potential use. So if you add them all up, far from just being particle physics machines, there are loads and loads of those things. So there's over 35,000 particle accelerators in the world. And I've just sort of given a bit of a pie chart of how they're broken down. So something like 45% of them are used for radiotherapy and then most of the rest of them are used for industrial use– so whether that's treating things, scanning things, treating radial tires, changing the properties of gemstones, treating dirty drinking water to clean it up. All kinds of different things.

So you might get the idea that, actually, these things are pretty useful machines. And for me, working on them, I'd really quite like to see what else we could do with them. But before we go into that, we're going to have to understand a little bit more about how they work. So in the cathode ray tube before, I had just a single voltage supply– just a single voltage that the particles are moving through and gaining energy as they did so. But that's quite limiting because you can only gain as much energy as that voltage gives you. But the other way you can do it is you can take a voltage and try and re-use it again and again. And that's what this little demonstration here is supposed to show you, in one second. So this is powered by a Van de Graaff generator, which, I should say, Van de Graaff accelerators were one of the original types of particle accelerators. They use a rubber belt to build up static electricity, which goes on the top of the dome. And then I've attached that high voltage, which is about 30,000 volts on this device, onto my plastic bowl here, onto four strips which are crossed in the center. So those four strips in the center get charged up and the other ones around the outside– I've kept those at ground.

So what happens here– and it's a very, very simple model of an accelerator– is I have a ping pong ball covered in conducting paint. So it picks up the charge on the charge strip and gets pushed away. And then it rolls around a bit, dumps the charge on the grounded strip, but keeps rolling. So every time it goes over a charged strip, it gets a little bit of a kick. And so you saw, when I turned it on, it started in the middle and slowly, it built up some speed, built up momentum, and now it's limited by friction as to how fast it could go. Otherwise, I'm sure it could reach the speed of light. I'm sure. I'm sure it could. So this is a very basic model of a particle accelerator, but there's a little bit of a problem with how that one in particular operates. I'm just going to switch him off.

So one of the flaws in that demonstration actually– and it is lovely, but it's flawed– is that I've just got a single voltage there, which I'm really using again and again. But in order to do that, I actually have to change the charge on the particle. And real particles don't change charge, sadly. So we have to come up with another way. And in the real world, we actually use radio frequency cavities, which I'll show you in a moment. But this was the idea that Ernest Lawrence had when he invented a type of particle accelerator called the cyclotron. So what he was doing was taking a single, oscillating voltage and using it again and again. And the particle would gain energy. And because it was in a simple magnetic field, it would spiral outwards as it did.

So as you gain energy, the particle's going to spiral outwards. And so these machines were limited, in terms of energy– physically, by their size. So this is a 1 electron volt, I think, proton machine that he built with his graduate student, Milton Stanley Livingston, who did a lot of the practical work. And cyclotrons really became the cornerstone of nuclear physics research for a long time. And they're still used today, especially in things like radioisotope production and actually new forms of cancer treatment as well. So that's the cyclotron. The other type of accelerator I'd like to introduce you to– because there's two circular types which are related to my work. That's one of them. The other type is the synchrotron.

And this now is the type of machine that we use to reach higher and higher energies. The cyclotron was limited by the size of the magnet that you could use. So instead, we had to come up with another idea of how we can reach higher energies but without having to have these huge, huge magnets that were just incredibly heavy. And then a guy called Marcus Oliphant– an Australia, actually– invented the machine called the synchrotron. Now this machine's a bit different because it looks quite different from the cyclotron. It just has a single large ring of a series of different magnets around the ring. So what we have to do is we have to ramp up the strength of those magnets in time with the acceleration of the particles in order to actually keep everything synchronized. And that's where it gets its name from me. That's where the synchrotron actually comes from. And there are three main components of that– there's dipole magnets, which do the bending, quadrupole magnets, which we'll come onto in a minute, and then there's these RF cavities that I alluded to before. So I've just got a little video here. Here we go.

So this is what a radio frequency cavity looks like on the Large Hadron Collider. And that thing's probably about this tall. This thing operates at 400 megahertz, so the oscillations in that are 400 times per second. And it's fed by a high voltage radio frequency signal. So inside that cavity, effectively, there's an electromagnetic wave goes up, and down, and up, and down 400 million times a second. And as the particles go through that, they have to be timed exactly in order that when the field is up and in accelerating mode, it gets a kick forward. And when the field is down, they're not seeing the field because we can't always have the field up. So that's quite a large one. That's 400 megahertz, so they're quite big cavities. I actually have here the world's smallest radio frequency cavity, which I'm lucky to have one. This was developed for a new project at CERN called the Compact Linear Collider.

So that was 400 megahertz, that one. This one is 30 gigahertz– so very, very high frequency. So the particles would travel through the center of this device. And the RF is fed in through some wave guides, which are on the top, and these ones are really tiny. And inside there is where the particles actually gain some energy as they go through. But it's not very easy to see exactly what happens inside of there, so I've got a really simple demonstration to show you, which is how a sort of radio frequency electromagnetic feel can give some energy to some particles. So if we can dim the lights a little bit? I have a plasma ball here, in the center. I know it's pretty, but ignore the plasma bit. It's generated using a 30 kilohertz oscillation, which is emanating electromagnetic waves outwards, which is what's forming the plasma.

But also, those waves continue outside the confines of the plasma ball, which means that if I put some particles in the way, those particles actually get accelerated. And you'll notice that, actually, I'm not touching that. And actually, I can ground it as well. So I can sort of turn it on and off– sort of creating a little bit of a circuit. So it does work if I touch it, but, actually, one of the main things I want to show you is the sort of RF waves coming out here, accelerating the particles. And that's why it actually switches on and off, just in proximity. A new party trick for you. So yes. So that's how we give particles energy now. But we need to go a little bit further than that. And we need to understand how particles are focused as well. So it would be easy to assume that all you have to do is get the particles, give them energy, bend them round in a corner, job done.

No. We actually have to keep them focused as well. And we have a problem with that because the types of magnets we use– and any type of magnet– can't focus a beam of particles in both dimensions at once. So if I squeeze it horizontally, it's pulled apart vertically. And I'll solve this dilemma for you in a little while, but first, I just want to show you– this is a real, physical quadrupole magnet over here. It weighs about 30 kilos, so I wouldn't try picking it up. But this one is for a fairly medium energy electron beam. But once we get up to the very, very high energy– say, proton beams– we need much, much stronger magnets. And that's why you get these huge ones at the Large Hadron Collider. So all of that then in the synchrotron has to be synchronized together. So we have to have the accelerating cavities, we have to have the bending magnets, and we have to have the focusing system all acting on the beam in perfect timing in order to accelerate the beam. And on most synchrotrons, we use something like a sinusoidal cycle of the magnetic field and we link everything to that.

So this is just showing you what that cycle would look like. We would inject the beam at the low point of the cycle. As the particles are accelerated, the field increases. And then we would extract the beam at the top. Now that's a limitation for the synchrotron because it means– great as they are and they can reach whatever energy you want, as long as you have strong enough magnets– they have a cycle limitation. They only cycle– most of them– often once or a few times a second. The rapid cycling versions are up to sort of 50 to 70 times per second. So that's a limitation that will become important in a little while. Now backtracking a little while– at the start, I was showing you lots of applications. We face many, many challenges today, especially in the 21st century. And as a scientist, like me, you don't have to go very far to pick a challenge, you just have to sort of watch the headline news. This morning I wrote down– what was there? There was climate change, overpopulation, food and water shortages, incurable diseases, aging populations, security and terror threats, or our planet being destroyed by an asteroid– not an astronaut, sorry.

An asteroid. Don't get too depressed though. Yet I've chosen to work on these. I've chosen to work on particle accelerators when all those glorious challenges are out there. And the reason is because I believe and I want to use what we've learned from this field and these machines to help solve some of these real challenges facing us today. Now the next generation of accelerators for particle physics could take any form. So we're researching lots of different options– whether that's a very long, straight line linear accelerator, whether that's a circular accelerator, or even a more exotic one, colliding different types of particles– say particles called muons, which are like the heavier version of the electron.

And they're brilliant and that's really pushing our technology forward. But there are other areas of accelerated science which are pushing us in a slightly different direction. So in the accelerator world, we talk about there being two frontiers. There's the energy frontier– and, in particle physics, that's where we're going with that. We're trying to get to higher and higher energies in order to reach heavier and heavier mass and more rare and exotic particles. But there's also something called the intensity frontier. And that's the one that I work on. And the intensity frontier tends to lead us towards different applications. It could also lead us towards a new particle physics applications. But one of the main ones is actually to generate neutrons using a high intensity beam of protons and then use those neutrons to do other things. In the UK especially, people are really good at that because we have a spallation neutron source called ISIS, which is at the Rutherford Appleton Lab in Oxfordshire.

And that's been going for more than 30 years. And it's generating wonderful science from all kinds of fields using neutrons to investigate matter, and materials, and biology, and aircraft wings, and oil part blockages, and how to save babies with [INAUDIBLE], and all kinds of amazing science. So on the one hand, we need to understand, to generate more science that way, how we can generate more neutrons using a particle accelerator. But there's actually other challenges which are pushing our field further, and further, and further. And one of those is how we might be able to deal with the nuclear waste problem or parts of the nuclear waste problem. And there's an idea out there called accelerator driven subcritical reactors. Some of you may have heard of this already. Now this idea is to take a very high intensity proton beam, smash it into a target, generate neutrons in the same way we do in the ISIS accelerator, and then, using those neutrons to drive existing nuclear waste– especially minor actinides, high level nuclear waste– through their cycle in order to reduce the lifetime of that they would have to be stored for.

So one particularly popular idea is to mix in an element called thorium. And thorium is actually a fertile element, not a fissile one– unlike parts of uranium. But thorium is about twice as abundant in the earth as uranium is and you don't have to refine it. So if you mix in thorium and then you mix in these existing types of nuclear waste from existing reactive fleets, you would be able to bombard it with neutrons from the accelerator, transmute the nuclear waste, and get rid of it. If you did it in the right way and within enough power coming in, you could generate energy from that process as well. But this is an incredibly, incredibly challenging application. So let me give you kind of where we're at versus where we'd like to be. This is a plot, which is often used in my part of the accelerator field, which shows the beam power of different accelerators, which I'll explain a little bit at the moment. But all you need to know is the energies are on the x-axis and the beam current– so how many particles per second– are on the y-axis. And we can see sort of different generations of machines there.

So you can see, for example, some of the high energy particle physics machines are very high on the energy axis, not so high up the beam current axis. And so when we multiply those two numbers to give a beam power, it's maybe not that high. It's maybe 0.1 megawatts. On the other hand, the optimum energy for generating neutrons is about 1 gigaelectron vote. And so you'll see on sort of the left hand, but up at the top, a bunch of facilities and machines which are more attuned to this intensity frontier, which has slightly low energy, but they're generating quite enormous beam currents. And actually, state of the art, at the moment, is to get to about 1 megawatt or just over 1 megawatt, which has being done at the SNS Spallation Source in the US and at PSI, which is in Switzerland, that's done that before.

Now where we need to be for these future applications is at least 10 megawatts, if not 100. So we need to be 10 to 100 times more powerful than we are at the moment. Now I haven't mentioned reliability yet. When you get higher in power, it's much harder to make your machine reliable, so you can leave it on all the time, run it all the time. But actually, a real application, like transmuting nuclear waste, would also require us to be switched on all the time. So we actually have to be up to 1,000 times more reliable– so less small trips and small problems than we have at the moment. And we've never designed an accelerator with that in mind. So just to backtrack a second– how might we actually do that? Which parameters do we have to play with? Well, to get to high power, which is what we need, we have sort of three pieces of the puzzle– there's the energy– but, as I said, that's kind of fixed because if we're generating neutrons, 1 GeV is about right– then there's the particles per beam– and that's a limitation which I'll get to in a little while.

And then there's the repetition rate– there's how many times per second you can run the machine– because that limits your average intensity over time. And I said before that the two machines I was looking at are the cyclotron and the synchrotron. The cyclotron is limited in energy. It can't go up 1 GeV, so it can't get to the optimum energy that we need for this application. The synchrotron is limited in its repetition rate. So in order to generate a high average current, it has to try and operate it many times a cycle or to really, really ramp up how many particles there are in the machine at one time, which is really problematic. But there is actually another option. And this it's a type of machine that I have specialized in. And this is called a fixed field alternating gradient accelerator. Right now, this isn't going to make a huge amount of sense, but the main points in that are in the title– it's a fixed field, so that means we don't ramp the magnetic field in time, and alternating gradient.

And this alternating gradient has something to do with the focusing system, which I'll explain a little bit more about in a second. So it uses the same focusing as a synchrotron so we can reach high energies, but also the fixed magnetic field of the cyclotron, which means high energies, and also no sort of limitation, and giant magnets, and things like that. So the beam in this machine, it does actually spiral outwards a little bit, but only a small amount. And we've arranged the magnetic field to increase with radius in a very particular way, so that as the beam spirals outward, it sees a higher and higher field. So it sees a field like a synchrotron, but we don't have to ramp the thing in time. And in terms of high intensity, this could be a huge advantage to us in the future. And to understand a little bit more about that, I actually want to talk about how we trap particles and how we focus.

I've kind of been alluding to this magnet that squeezed one way and didn't the other. So I've got, over here, a very sort of visual demonstration to show you how this works. So if I have my particles in a beam and they're traveling through a series of magnets, when they go through, say, a focusing magnet, they're going to say a magnetic field which controls it like this– so if it's too far that way, it'll push it back to the center. And if it's too far this way, it will push it back to the center. But unfortunately, when it goes through the other type of magnet, it will be defocused. So no matter where it is, it's always going to be pulled away from the center and defocused. Now I think, to those of you looking at this demonstration, there's an obvious solution to how we solve that problem and how we make that focusing stable.

And that is– well, in this case, we have to alternate the gradient of that focusing. That's what I mean by alternating gradient. And in this particular case, we can do that by actually physically spinning this device. It creates quite a wind. Here's the difficult bit. I have to try and trap a particle with it. Let's have a go. Thank you very much. And again, we'll come back to that in a little while as well. So if we get the alternating gradient correct, and the right speed, and the right everything, then we can trap our particles. And that's quite a fundamental thing in accelerator physics. And it leads to this principle that we call strong focusing. And this is why the synchrotron was such a great invention and allowed us to reach higher energies– because by alternating the magnets back and forth between focusing and defocusing, we were able to focus in both planes.

And not only that, but we can focus in both planes stronger than any other way we know of focusing particles because it's sort of analogous, but not quite like lenses of light. But the slight other problem though is that you can't choose anywhere. Now this is, genuinely, a plot from my PhD Thesis. I'm actually not kidding. So what I was showing to you before, with this Paul trap– I've set it to a particular speed. I set it running– this saddle shape. And I put the particle on. And it was trapped for a short while before it flew off again. But that actually only works at certain speeds. So this diagram here is showing you– on the x and the y-axis– kind of the focusing strengths, so the curvature, on one. And let's say we're looking at the speed on the other axis. It doesn't matter. There's two parameters there. We're changing a couple of them.

And only for certain sets of those parameters is it stable. The green and the red show that it has to be stable in two different ways. So if I set this running again– and those of you, especially if you're higher up, you might be able to observe this quite closely. I have to feel exactly when it's in the right spot. There we go. So if you were to observe that closely– whoa. I'll try again– you would actually notice that there's a couple of different types of oscillations. There's sort of one round this way, a sort of radial one, and then there's also a vertical one. And both of those have to be correct in order for it to stay put. So let me just put that back on there again. Oh, I think that's the sweet spot. There we go. I'm not the best at doing that. We have other people who are better at it.

Otherwise, if it's not rotating at the right speed or if it's not in the sweet spot particularly, it goes flying off. So for example, if I do it much, much slower– a little bit too slow. Come on– and if I pop it on then, I think, based on just intuition, you can probably tell that that's not going to work. But I'll give it a fair try anyway. So more or less, it just builds up and comes straight off. And I'll do the same thing at an incredibly dizzying speed. Full power? Yeah. Yeah? All right. Full power. Woo. It gives off quite a wind. All right. I'll pop that back on there. And again, complete rubbish. Completely unstable. And that's because, as this diagram shows you, you can only be stable in particular dimensions.

And the fascinating thing is that the mathematics that describes this saddle shape and the mathematics that describes are focusing in a particle accelerator are pretty much identical. And this thing has a name. It's called a Paul trap. And I'll come back to that in a little while. So we have to set up our accelerator with a focusing system in a very specific way so that it sits in one of these stable regions. We usually use the region which is on the sort of bottom left corner of that plot because it's fairly easy to reach with normal magnet strengths and things like that. But you can see that it's a relatively small area, so we can't just put magnets anywhere. We actually have to choose them and design them very, very carefully. But I showed you before, with this device here, that when we do that, we set off oscillations. Now in physics, in any system which has an oscillation, there's one problem which we're always going to run into, which is the problem of resonances.

Now when I say the word resonance, I'm sure most of you know what I'm talking about. If you have a system that's oscillating, and you occasionally kick it, and you kick it in the same way every time, it builds up and builds up exponentially, and you get a resonance, and, in this case, your beam goes flying into the wall of your particle accelerator, which isn't such a good thing. So this diagram is showing you, on the x-axis, say, the oscillation rate of, say, one of these oscillations. So maybe that's the one around this way. And the vertical axis is showing you the oscillation rate in the other direction. So they interact as well. And so one of the reasons why I can never get this thing to stay more than about 30 seconds is because the turntable isn't precisely flat because there's imperfections in the building up. Not that it's imperfect– it's beautiful.

It's beautifully made, but it's not submicron level, just saying. So we will always have little imperfections which build up. So when we're designing an accelerator, we have a really tapped choice to make, which is, what value do I choose for those oscillations to keep my beam in the machine? And that's why I've shown you this diagram because it's pretty tough to spot. Your guess is, literally, as good as mine, in that case. But we do– we choose a specific point in that diagram. We might choose a few. We have some flexibility, so we might operate the machine in slightly different ways. And usually, we try and place that spot as far away from any and especially the crossing over points, where different orders of resonances actually cross over. And they can be driven by magnet misalignments, they can be driven by magnetic fields having a slightly wrong shape– all kinds of things.

So that sounds kind of like a disaster, but we do, in fact, as I said, operate 35,000 accelerators quite successfully. Thank you very much. But we have always designed accelerators to stay away from these resonances until a couple of years ago when we came up with a new type of accelerator, which was one of these fixed field alternating gradient machines that I talked about before. But we actually simplified it right down. The machine I showed you before had quite a complicated magnetic field shape. And someone said, well, what happens if we just simplify the field and just use these– just use these so-called quadrupole magnets, which have a nice, linear field shape? And everyone said, well, you'll get resonances. Yeah. OK. So what we found was that we have resonances all the way through the acceleration cycle. But we let it do that intentionally because one of the things you need to know about resonances is they need time to build up.

So this type of machine– and it's same was EMMA, the Electron Model for Many Applacations– was, literally, the first of its kind in the world where we intentionally crossed through resonances in the acceleration cycle– major resonances, which everyone else said, that's never going to work. But the theory was, if we went quickly enough, we'd be able to cross through them because there wouldn't be enough time for those resonances to build up and destroy the beam. And that's what we demonstrated and published back in 2012. And the plot on the bottom left of the screen there, the lower half of that plot just shows a red and black line coming down. That's our measurement of what we call the tune– that is, the oscillation rates– in this accelerator as they're going to the acceleration cycle. So you can see that it sort of decreases over time. And that was our demonstration that we were, indeed, crossing through resonances. And we did, indeed, manage to accelerate particles, get them out the other end, and show that, actually, if you go fast enough, this system works. Now unfortunately, that machine can't be applied to very high intensity very easily.

And there's an extra complication. When we have charged particles and they're all in the same place, we have, in physics, the Coulomb force– literally, the repulsion of different charges against each other. It might not have occurred to people to think, well, hang on, there's all these particles, they're really dense, they're going through this tube– aren't they repelling against each other? Yes. They are. And you know what? It's a real pain. If it accelerators were like this we had one particle– one, like this– life would be a dream. Unfortunately, the more particles we try and cram in there, especially in high intensity machines, the worse our problems get. Because instead of them having one oscillation period– instead of having one tune– all the particles are interacting with each other.

They're also, mind you, interacting with the beam pipe, with the magnets. There's a lot of electromagnetic fields going around there. And so when we have that diagram where I said before we choose a point– it ain't a point anymore. Instead, our beam becomes this spread of different particles where every particle has, more or less, a different tune. And this is really what limits us when it comes to designing higher and higher intensity machines. The more particles we cram in there, the bigger this spread gets, the more resonances we run into, the more beam loss we create, and the more risk we have of, literally, melting the beam pipe of accelerator, which we can't afford to do. So there's a couple of different ways that we could potentially think about solving that. And one way is to design the type of machine that I work on, which is this fixed field alternating gradient accelerator. But another one is something a little bit wackier, which is to take a synchrotron and add a special insertion of magnets, which kind of does away with the existence, in the physical questions, of resonances, which sounds rather confusing.

It is. It's a very theoretical concept. It's called an integral optics accelerator. And that's being driven by Fermilab in the United States. So there are a couple of ideas. There are also, of course, other ways you could do this. You could use a giant linear accelerator, although I work on circular ones because I think, in the future, the linear ones will be too large and costly. And I think we ought to be looking at a generation of smaller, circular machines. So that's when we have to come back to this device over here because understanding how those accelerators work is really hard. If I try and run a simulation of billions– literally tens of billions– of particles in one of these machines interacting with each other, interacting with the beam pipe, interacting with the magnets, generating secondary particles, doing all kinds of– this takes weeks and weeks, on huge clusters of computers, in order to run a single simulation to see what my beam is doing.

If I try and study it in a real accelerator, it takes weeks and weeks of beam time. And I showed you before that these machines are in use all the time. So the ISIS neutron source, for example, when that's on, it runs 24/7. There's very little time for someone to do a beam study. And there's, particularly, no time for anyone to intentionally lose any beam because we can't because it would generate radiation. So a few years ago, I was wondering, how can we study very intense accelerators in the future without building the accelerator first? Because it's a pretty big job. And that's when I came across this idea for the first time of the Paul trap. And I came across some papers from a group from Hiroshima university in Japan, who I now collaborate with. And they are using these devices to actually study beams of particle accelerators and intense beams, in particular.

So this is, I promise, the only slide I have in here with some serious equations in it. This describes the Hamiltonian of beam motion. This is on the lower side. And on the left, that's the Hamiltonian for beam motion in an accelerator. Now a Hamiltonian sort of describes the overall motion in a system– the physicist will be familiar. If you're not, all I want you to recognize in that equation is how similar it is to the other one. So the other equation is the Hamiltonian for what we call a Paul trap. And if you sort of compare all the different pieces of that equation, you'll see that they're very, very similar in form. And what these colleagues at Hiroshima University had realized is that they could actually use a Paul trap– a small one rather than a large one, like this– to actually study the physics of the beams of accelerators. So just to point out a few terms in that equation– on the left, the pxpy, that's momentum, and then there's a focusing term, which is the k term, and then x squared minus y, squared, which is the sort of the hyperbolic shape here.

And then, on the far right hand side, there's this phi sc. And on the left, there's a phi as well. This phi is what we call a space charged term. That describes this defocusing, weird, annoying effect from all the high intensity interactions between the different particles. So this device I discovered was able to not just simulate the beams in just about any accelerator– because we, literally, can dial it in– but it was also able to simulate the intense dynamics of those beams. And that was very, very exciting to me. So the first thing I did was I had to learn what the system is like. I'm an accelerator physicist. I don't I don't use these things usually. So this is an electric quadrupole trap. So the top right there shows an image of the quadrupole mode excitation of one of these traps, where we apply an electric RF field at 1 megahertz and we change that in time– kind of like we were changing this or like we change this in time, as we spin it.

And that changing quadrupole field does exactly the same thing that our focusing in the accelerator does. But this is fixed in space, so it's like a tabletop experiment. So in the accelerator, our beam is traveling through. It's going through magnets like this, it's going through RF cavities. And it's experiencing these focusing and defocusing forces. In this trap, we take argon ions, which we ionize with a little gun of electrons, and then we do the same thing, but we actually do it in time instead of in space as the beam travels through. And so that means that we can't necessarily look at all the acceleration based effects, but we can look at all these beautiful oscillations, resonances, and high intensity effects as well. And so I started working with these guys a couple of years ago. And the first thing we looked at was to actually recreate the EMMA experiment that I showed you before and the resonance crossing that happens in that. So that brings me now to what I'm working on at the moment as well as designing new types of accelerators.

I'm also building one of these Paul trap devices. And one of the things I find really incredible is how, in physics, the mathematics and the description of these systems actually translates between lots of different physical systems. So the beam in the accelerator, the beam inside one of these Paul traps, and the beam or the particle on this Paul trap as well actually all have the same equations of motion. And we can relate them to one another and use it to study. So this is a picture of my Paul trap. It's called IBEX– intense beam experiment– which we're building at the moment. And this is a picture of the design and then the manufacture. And I'm proud to say that this is really an up-to-the-minute discourse because this is a photograph I, literally, took yesterday. I went up to [INAUDIBLE] Laboratory up north and I took this photograph of this chamber, which actually just blew me away. It's so beautiful. It's cleaned for ultra high vacuum.

And inside that, is mounted this Paul trap mechanism. And into that, very soon, we'll also have a load of electrical connections, and put the lid on, pump it down, and then we'll be able to start running experiments to explore the intensity frontiers of accelerators with that. So I want to come back, just for a moment, to sort of speculate because I've shown you, all the way through, the design of particle accelerators– how they work, how they're accelerated, how we bend the beam, how we focus, and how we supply voltage. And there's a load of technology that's come a long, long way in decades and up to the present day. And alongside that, of course– alongside the development of technology and driving the development of that technology– is the field of particle physics, which a couple of you in the room are familiar with.

But let me go through very quickly some of the discoveries that we've made. So I talked before about the discovery of the electron– J.J. Thomson, in this theater. Well, the particle which later became known as the electron because, apparently, his nemesis named it, not him. And then we we're looking at the discovery and understanding of the photon. And then other types of slightly stranger particles. So there's muons. Now I mentioned before, muons are like heavier versions of the electron. There's also an even heavier version of the muon, called the tao, which is further down there, in sort of medium blue, which was only discovered in the late '70s. So there's three generations of matter that we've discovered. We don't quite understand why there's three. And as well as those particles– the electron, muon, and tao– there's all the ones that make up the rest of our matter. So there's ones that make up the protons and neutrons and those are the quarks. So on the left hand side there, there's is down, strange, up, charm, bottom, and, eventually, top, as they were discovered in series.

And those are the six different types of quarks which go in– and only the up and down versions of those quarks go into making our normal matter. Again, there's three generations. We don't know why. And then, of course, there's all the other force carrying particles– things like the photon, which does all the electromagnetic forces that we've been playing with, the gluon, which is holding the proton and neutron together with those quarks, the W boson and Z boson do other sort of weak contractions, and then, of course, recently discovered as well, the Higgs boson, which is the fundamental mechanism of how things get mass. That's a very quick rundown of the standard model of particle physics. And then, of course, there's other things in there which exist– there's neutrinos as well. They're really mysterious particles. And those are the ones, for example, that we could generate with the next generation of intense beam accelerators.

And so we have these different strands of particle physics going into the future. But what I'd like to ask you is, well, going back to the start of my lecture, and looking at J.J. Thomson, and his inability to predict what we were going to use the electron for, and, admittedly, his complete inability to predict– I think we're at an interesting place in history at the moment because of our slight inability, ourselves, to predict how we're going to use all of this knowledge in the future. So I've shown you a few applications of protons. There's lots of other applications of ion beams and things. Maybe there's applications of muons in the future. But I want to sort of leave you with the thought that having learnt to understand and control these beams of particles, it opens up the question of, exactly what could we do with these beams of particles and these accelerators in the future? So in the future, if someone's going to give a toast in my presence, I'd like it to be something like this– I'd like it to be, "to the particle accelerator… May it be of use to everybody." Thank you very much. I also am aware of people from the high energy physics community investing in plasma whitefield technologies– not only for high energy, actually, but also further applications.

I just wondered if you had any comments on that? Do you think it's a runner? Should we be worrying more about that? Or is it interesting? .