 If you want to make electrons go super fast, say close to 5-10% the speed of light, then all you need is a few thousand volts applied between two metal sheets kept close to each other. But what if instead of an electron, you wanted to make a proton go super fast? Well, since protons are way more massive compared to electrons, with a few thousand volts, they don't gain much speed. Now for them, you need to provide millions of volts, which is hard to do. And so the goal of this video is to think about how can we use low voltages and accelerate heavy particles, like protons and other heavy nuclei, to very high speeds. Alright, let's think through this. So protons won't gain much speed over here, right? But what if we could somehow make these protons turn and re-enter the electric field? Then maybe we could re-accelerate it and make it go faster. But you might say, wait a second, if it re-enters like this, then it's going to decelerate because it's going in the opposite direction of the electric field, right? So what we can do is as it re-enters over here, we could just flip the direction of the electric field. Now it will get accelerated again and the proton will go faster. And then as we can make it again turn and come back over here and again flip the direction of the electric field, re-accelerate it and make it go even faster. So by doing this, I can keep on making the proton go faster and faster and make it go super fast. But the question we have is, how do you make charged particles turn like this? Hey, we've seen this. Magnetic fields can do that. So now we have the working principle of a cyclotron. So what we can do, so the whole idea is we use electric fields, electric fields to speed up our proton. But we use magnetic fields to make them turn back and re-enter that electric field. So that we can accelerate it over and over again. Remember magnetic fields do not change the speed of the particles. Why? Because magnetic force is always perpendicular to the direction of the motion and so they do no work. And if you're confused about this, we've talked a lot about that in our previous videos in great detail. You can feel free to go back and check that out. But anyways, using this setup, we can use low voltages and accelerate our heavy charged particles to very high speeds. Now of course, one small thing that we just saw is that our electric field needs to keep flipping its direction. And so the electric field we need over here is an oscillating electric field. So this needs to be an oscillating electric field. And therefore this particular voltage source is not a DC but it's an AC oscillating source, usually depicted by a sine wave. Now that we have the working principle, let's look at things a little bit more practically and make our cyclotron a reality. The first thing that comes to my mind is we need to cut holes inside these metallic sheets so that the protons can go through it. So if I were to show you from the side, we'll cut holes in them. The simplest way to do that is make small rectangular holes so the protons can go wherever they want. Okay, are we done? No, there are more problems. Second problem is there could be, there is air everywhere. We don't want that because protons will collide with the air molecules and decelerate. So we need to enclose this whole thing in a vacuum chamber. All right, we'll do that. Are we done then? No. There's one more problem that we haven't considered yet. See, if we had infinitely long sheets, then electric field would only exist in between them. But our sheets are not infinitely long. And as a result, there will be electric fields existing outside over here as well. And why should I care about that? The reason I should care about that is because that means when the proton is over here, notice it will experience a deceleration. The same thing would happen when the electric field flips and comes over here. It would experience a deceleration. We don't want that. So we need to find ways to make sure that there are no electric fields in these regions. The proton shouldn't experience electric field over here. How do we make sure of that? Can you pause the video and think a little bit about this? Well, remember that metals cannot have electric fields inside of them. So to kill this electric field, all I need to do is make sure that there is metals over here. That's why in cyclotrons, we use semicircular metallic discs. So if there's metal over here, electric fields cannot penetrate. And so you won't have electric fields over here. You only have electric fields in between. Of course, there'll be electric fields from outside, but that's not going to affect us because the protons are going to be revolving over here. And so cyclotrons usually have these hollow metallic discs for the protons to revolve inside where there'll be no electric fields. And since these shapes represent the English alphabet D, they are literally called the D's of the cyclotrons. So these are metal D's of the cyclotron. They're hollow and their job is to ensure there are no electric fields over here. So are we done now? No. We have to put the magnetic field. We haven't done that. So here's my question to you. Imagine the proton is over here. It is moving to the right. We want it to turn up, let's say. So what direction should we be putting the magnetic field is a question for you? Can you pause and think about this? Remember, the magnetic force F is given by Q times V cross B. All right. Now, since we want the proton to go up, we need a centripetal force that's directing towards the center, which is somewhere over here. So you want the force to be upwards. The velocity is to the right. And so we need to use our right hand in such a way that V cross B gives you F, the thumb points in the direction of the F. So what I do is I take my right hand and I ensure my thumb is pointing in the direction of the F. My four fingers are pointing in the direction of the velocity. And so notice if I have to cross it, the magnetic field needs to be somewhere into the screen. And therefore, the magnetic field will be directed into the screen over here everywhere. And so if I look from this angle, it is into the cyclotron. So the magnetic field will be into the screen like this, so into the cyclotron. And how do we put this magnetic field? Well, you can use magnets, but today we use electromagnets, coils of wires which are electrified that also generate magnetic fields. But don't worry too much about that. That's on the focus of the video. We can produce magnetic fields. And so the question now is, are we done? Now with these magnetic fields and oscillating electric fields, the protons can keep accelerating forever and ever and ever and you can get super high speeds, right? As much speed as you want, right? No, we've missed one small detail. See, when the proton accelerates again, once we flip the field from here to here, it is faster than it was over here, right? Which means it will now take a bigger circle over here. It will go in a bigger circle. Why? Because if it has more speed, the magnetic field finds it harder to turn. It's harder to turn it and therefore it tends to go in a bigger circle. And in fact, in a previous video, we've derived the expression for the radius. Do you remember that? Well, let's quickly go ahead and do that again. The way to do that is we realize that the force that's making it go in a circle, the centripetal force, is provided by this. So the magnitude of this force should equal the centripetal force. The magnitude over there is QVB sine 90 because VNB are 90 degrees apart. That equals the centripetal force. And that's it. Now, if I just simplify, I get it to be MV by QB and that's the expression for the radius. And again, if you need more clarity, then we've done this in much more detail in a previous video. Feel free to go back and check that out. But what you see is that the radius increases with the velocity. And so the particle, as it accelerates again from here to here, it goes in a bigger circle. And this keeps going on. And as a result, you can see the particle will end up spiraling outwards as it goes faster and faster. Why is that important? That's important because eventually the radius will be equal to the radius of the D. And once that has happened, I cannot make it go any faster because if I do, then it'll go and hit the wall. And that's not something that we want. And so that means once the radius equals the radius of the D, that's the maximum and then we need to let it go. And so there should be some way over here, some hole, some guided way over here to shoot it out. And so once it has that maximum radius, the particle is shot out with whatever speed it has over there. And so you can immediately see that there is a limit to how much you can accelerate it. That limit depends upon how big the cyclotron is. Bigger cyclotrons, that means you can accelerate it to faster speeds. And there we have it. We've finally built our cyclotron. So long story short, how do cyclotrons accelerate heavy particles using relatively low voltages? The whole idea is, although these electric fields speed up these particles just a little bit, the magnetic fields turn them back and make them re-enter that electric field. And by flipping the electric field at the right moment, we ensure that every time it enters the electric field, it'll keep speeding up just a little bit. And so the speed keeps adding up over and over and over again. And finally, once it has gathered enough speed, we shoot it out. Now, before we wind up, there are a couple of interesting questions I want you to ponder upon. First one is, the crucial part of this is that the electric fields need to flip at the right moment, isn't it? So how do we ensure that? I mean, the way I'm thinking is, as the particle spirals out, it'll take more and more time to enter that electric field, right? So should it be like initially it should spin, it should flip faster and then it'll flip slower and then it should flip slower and so on and so forth? Wouldn't that be hard? How do we manage that? So how do we ensure that the electric field flips at the right moment? That's question one. The second question is, for a given cyclotron, if the size of the cyclotron is fixed, how can we increase the speed at which the particle shoots out? There are two options and I want you to think about it. One is we could either increase the electric field strength or we could increase the magnetic field strength. Which one would ensure that the proton shoots out faster? Ponder upon this brainstorm with your friends and we'll explore this in a separate video.