I'm supposed to talk about that and give you an introduction about how plasma is, how you make it on at the end, basically how to hold it.
Because what I do is fusion.
So what we try to do is basically keep it together for long enough that we can get it to be hot enough to get fusion out of it.
Seasonality out of it turns out that we had a title before I ever started doing the presentation.
And of these three things that I don't know how to make it because I might theoretician.
So this was my when I get there but I just play a little bit how they come about.
All right. So let me tell you what I'm going to do in this first book.
First of all, I would like to explain why we need I mean, that is what we need to understand.
And really and there are sort of reasons why the astrophysical plasmas, that is manufacturing plasma, that is plasma supports space propulsion.
There is a bunch of publications I do fusion. So what I just plain and put forward is that is very important for fusion anything, right?
So that will be the first part of the top.
Then once we understand we need one one of these plasma outrageous bling, how, what they are, what their basic properties are.
And basically because I'm I do theory how you model them what is the the equations that you use to actually describe them.
And at the end because this is actually going to be in a way very slightly to what fusion I'll talk about one particular type of plasma,
which in my book feel is really strong and that the classification of particular way because we're holding it with those magic fields.
All right. So let's talk a little bit about why we need for fusion.
This about burning, right? When you are burning coal or oil or anything to get energy, what you are doing is breaking balls, right?
You play to get energy out of the bonds that form the molecules that are solid,
that the bonds that form all for molecules are actually much less energetic.
That the bonds of the nucleus.
Right, the nuclear nuclei, these very specific and bonds, usually you can relate them to the automatic forces, not quite,
but most of them you can make that that those bonds are due to this the forces that are so that the nuclear force,
the strong force is much stronger than that.
And you can see that just by thinking that it overcomes the repulsion that you have between two, two nuclear arms.
Right. So if we're able to break those nuclear bonds, we can get much more individual reaction.
This could be really a good thing to do.
Now, when you are trying to to to bond, you need to take into account what you need to do to achieve that bonding.
Right. I mean, when you are burning coal or oil or wood.
Right, just spontaneously do that. You have to become a warrior on your overcoming this this this initial barrier.
If you are getting a lot of energy out of it, usually have to overcome a much bigger battery of them.
If you are bottom in, for example, to study a molecule, the molecular bonds, you got to have the reaction.
That is the easiest amounts. The the nuclear fission reactions are the one we try to achieve.
We have two isotopes of hydrogen, deuterium and tritium. And then if you hit them hard enough with each other, they fuse and you get helium.
That one alpha particle basically on underneath them and you get huge amounts of energy of your of tens of mega electron volts,
which is a million times what you would get from are from a typical reaction,
a chemical reaction right now, because we need to overcome the barrier to actually get that fusion there,
which we need sufficient energy in the particles that when they collide, you can overcome that barrier.
Right. Turns out that when you try to do this, it implies that you have to have a nobody trinity one of these basically temperatures.
So what you need is to have a temperature that is high enough to actually get these reactions going.
But when you're modelling something is not sufficient to actually have a temperature,
you have to make sure that the energy you produce in these reactions.
If they see that when you are burning something, you feel water, right?
It basically you kill the forest just like you are evaporating water and you are getting
into the of the system and that energy doesn't go back into keeping reactor flowing.
Right. So what we need to make sure is that we ice to ice isolate the system thermally to make sure that we produce close body to the system,
keeps it hot and we keep getting reactions. Right. So that means we describe that in the, in the, in the field by a time we get it in cycles,
which is how long you can keep the kind of these basically how long it takes for a particle that you put in the model to basically want it off,
to be out. And then not only that, you want to get this going, you have to have enough fuel.
So you have to have a number of particles on.
And then that basically place like you need a density number of particles for them to get cubed to to get your your body going.
If you actually try to see what that implies, if you want to make this commercial, you get this number.
The first one is pretty daunting at 150 million degrees to get this going.
This is ten times the capabilities of the sun, which means that the hottest place in the solar system is deep enough.
You know, when he's running, right? This is it.
I mean, this is the reason why we basically need a plasma at this high temperature to moderate plasma speeds, and that's why we actually need it.
Here is a typical plasma that we experience of like lightning and things like that.
All you need is to do a 20 particle spinning that you that's basically a millionth of the density of air.
So you have this very cool thing that is very unusual. So in total energy that you get in the system is just ten years.
That is, you have ten times the energy right now.
So it's not I mean, it is very hot, but it's not particularly energetic on the time that you have to be holding this together.
1 to 10 seconds. More on the second side and on the one side. But that's the ideal.
So as you can see, let me just stop by 150 million degrees.
This is not something you can teach, something easy to do.
What we need is because even though it's hard, a lot of interviews, for example, like like fission, these basically this, this.
If we take these, we get energy globally inexhaustible.
You can get most of the fuel from seawater and actually doesn't have any long leaf radioactive waste.
All right. So now these are motivation. We want to teach these fusion energy, but we need those temperatures.
We actually up with the plasma. So what?
These are plasma and sorry. Well, plasma ice things like you see neon tubes.
These lightning is basically the actual universe there.
What we see emitting that is a blossom, right? The reason that we got the name is because this guy, Langmuir,
which is an American scientist working, I think in New York, was working on these neon tubes.
And then what he noticed is that you could actually deformed if you only knew you want it.
And that luminous stuff that was in the middle just full of the tube. Right.
So he said that you could mould it and that's where plasma come from.
Is the Greek for the mould, right.
Turns out that this is normal because when you have a plasma 150 degrees, the listing thing does is actually ballpoint.
But we inherited the name and that's what we work with. So what are the properties that define what a plasma is?
It is a gas and by definition, usually we consider a plasma,
a nice gas that is dominated by long range interactions over strange interactions, and that is what you write.
These two things can be relax. People talk about astronomy called the plasma or money that plasma as well.
But in general, when we are talking about plasma, this is actually what we're thinking about.
I can discuss basically when you get hot enough, you get a plasma.
The reason for that is that once the temperature is bigger, that you only see some energy, the electricity in the system,
we just knocked it out and you begin to see some process and you get basically outgassing,
which you dissociate electrons from the nucleus electrolyte.
And that happens when your body you fact you have to be cold enough to get one
indication of energy which is an electron will basically that's 10,000 kelvin.
Once you overcome the temperature, then you get organised gas, you see emission and things like that.
We have experience of them. For example, when you look at fluorescent lights, that's a plasma in there.
It is pretty surprising to think that that thing might be at that high temperature, right?
It would seem that you wouldn't be able to contain that in in a blast you right reason for this.
But in reality what needs to be called is electrons.
But you need to have whole audience in these what you need to know to to have electricity in the dark enough that when
they collide with with an atom they knock out one of the electron and it starts to propagate all over the place.
And then getting the electrons hooked on keep it down as cold is not so difficult in fact, because the electrons are very small mass.
So what you have is like whenever you have a collision between this massive atom on an electron, it's like hitting a ball with a wall.
It just bounces. And then when it bounces, it keeps its velocity.
It basically gives you the rate. So electrons move, take momentum from their background ions but they want they want their energy.
You've you to have these very hot electrons and it is this cold.
These are in the system. This is not what happened last months because we go from 10,000, 100 million and medium Kelvin.
Right. These are very different types of plasmas.
How actually not experience how these plasmas come here you get lining is basically that you get a magnetic field in the system
and this electric flux very selective that you have around when you play these electrons in the actually for long enough that.
You have to get ready to knock out an electron. You put these two electrons, those two to each, and you have an avalanche.
And immediately you get these very violent experiences of of plasma up here.
All right. So it's on your guts. As soon as you go to the kind of temperature you have disorganisation.
What else defines a plasma? You have the comparison between long range interaction and tolerate interaction.
And I know I'm going to be a little bit I'll be more precise in a second about this,
but just to start with, to distinguish between one and the other type of interactions.
Think about the following.
When you have a plasma is charts, and then you look at at a given point, you can see that it has some touch density and some current density, right?
You could take as much as equations.
You produce an electromagnetic field that is currently that is all over the place and interact with a piece of this here.
Right. For this piece of plasma, because of its density touch on its current density,
we interact with this little piece through mathematic fields that this one has produced.
That's what we call the long range interactions in black. Right.
But the other thing that happens is that you have two particles about charts and expulsion of they interact on a force.
Right.
And that would be the sort of the range that you can estimate how close you have to be for the particles to know that they are close to each other.
And thus by using that equation there, what you can do is take the Coulomb potential and give it at least a B,
and you have to make that equivalent to the energy of the object, which is their temperature right out of this equation.
You actually get how close you have to be to actually see another electron on the line, both of you.
Right. And you can see that that actually scales probably with energy.
The more of a you have, the more difficult. It's actually to notice that you're close to anything because you just squeeze by an elastic.
You really don't know that plasmas have very few of these interactions.
And here's how you can see the first. The first I have two, two ways of looking at it.
You have on the first one is if you take a particle and you draw on the sphere around, it would cease to be apart.
You can ask how many of the particle.
So we think that the sphere of influence right and then if you take them and particle to be much less than one this
is basically kind of particles don't see all the particles they are just very far apart from from each other.
Right. Another way of looking at the same thing, which is completely related, but there are people that like it better,
is what is called the coupling constant gamma in which you take the energy,
the kinetic energy of the particles, get the body temperature,
and you divide basically by the typical Coulomb interaction between them, which is just taking the Coulomb potential at a distance.
You put the average do something with the particles that you can estimate, even the density, right?
The density to the minus one third if you the typical distance the particle subsequently took.
That, for example, is very large. The potential between particles is tiny, but we need to get it.
And both of these numbers are related. That is actually the other one.
The other one. Right. That that makes sense. So you want to think about this in terms of, for example, got a solid to liquids, right?
What happens is that particles don't interact with each other.
They are basically a gas. If they would be closer together, then they would form.
They would form.
A lot of this stuff is what is called a plasma on form, something like it's more like a solid liquid you general effusion for sure we have.
But on the study slide, this by definition is what we call a black,
maybe fully the other type of plasma like organised gases that are extremely powerful.
A lot of basically coal is only a couple of plasmas. As you can see, we have not very imaginatively named in the field, but that's not,
you know, because these long range interactions are actually they don't belong here.
When we model these plasmas, we can think of them kind of almost like a flute, right?
What we're going to do is that we are going to take these tools of function to describe them.
And we have the distribution function that gives you basically the the number of particles in position are with the prosody that you have right now.
When we have those, by integrating in theory by number of particles, we can get the density of particles that we have.
And if we look at the and integrate over that, we get the average velocity that they have.
If you use that and you are the only species in the 64 species on the charts, this becomes the density and that here becomes the carbon density.
Right?
And then with all these we just put it in too much with equations and we can exert multiple situations and get that if my dick feels out of these,
right? So we didn't say yes, take whatever current she said.
If your current identity have in one place. I think I feel my dick feel and I see what happens.
We thought in the other place. Now we have to believe that this crucial functions there.
I need to do that. What we are saying is that if you have in this kind of deterministic way, we look at in an infinite mechanics, right?
If you have a number of particles, at one point they see an automatic field that tries to be a field of particles.
If they have the same position, extending the position and the same velocity will actually be always the same.
So what you can say is the number of particles long places, right?
That's that's basically what it is. And this is the classification.
So let's just look at the right hand side. Right.
What you have is an equation which has got to be fixed so that the value of the function
is conserved along the characteristics and these characteristics of a particle like this.
If you move,
you move in a space with a bit of TV and you move in one of these space due to an acceleration that's that comes from the little magnetic fields.
So like, if I didn't have this right hand side here, I would actually have caused the problem.
And these longer interactions will be the only thing that we have.
However, this muscle equations that they showed in the previous slide are quite small.
These don't have like the bleeps in electric field that you get a potential of
a smooth out those those singularities that you have that there are collisions.
They are not the dominant piece of the physics in the plasma, but they are there.
Right. And then you have to model that somehow. So what we have is a right hand side of collision operator.
Statistically, these interactions between to touch particles when they get closer.
Right now, when we go to the we come to an approximation.
It doesn't exactly mean that these collisions are actually important.
What it means is that the this is a gas that is very rare,
that three or four particles meet in one place because the volume that the particle occupies given by that B parameter,
how how far it actually gets is just really small compared to the whole volume of the plasma.
Right. And what happens is that you have two particles to come together, but three, four or five is even better.
So what happens is that the approximation turns out to be that you have only binary collisions but was quite two by two.
They never get to be three or four interacting together on.
And then that's what you get. Nobody gets out to be by linear.
You go back a little bit, you notice there is something fishy about all this,
which is that they treat in Coulomb interactions as if they were only binary collisions by the to they got before.
However Coulomb interactions actually long range. So every particle, everywhere, it's not really a particle quite.
So what has happened here that does not really matter because plasmas usually have the
other problem which is what you talk these actually the natural tendency of anything
that starts to be neutral negative particles that attract positive particles and then
things we tend to be neutral that sort of most plasma satisfies two of our is satisfied.
Well this is by definition basically these two properties, the typical tail of the plasma is violent, something which is caused by length of plane.
In a second, what it is and the frequency of the phenomena that we worry about is much less than what we call the plasma frequency.
When this happens, these natural tendency to neutrality will actually be very strong.
And what will happen is that you take a volume of plasma, it'll be neutral, there will be no charge, almost in it.
You cut it in half, there will be no chance of it, and you continue copy.
And as long as volumes are bigger than that, Debye length will still be neutral.
The plasma doesn't actually allow time specifically. Not not very much.
Why is that?
This look at what the like this what what you have is that when you have a plasma you have a bunch of positive or negative particle flow of the place.
No, I can pick up positive touch. I'm putting the needle with light.
That's my Red Bull here. Right. In an extreme case.
Yes to yes to like if it's take this.
What that does is that it takes all the positive particles, the awareness field around it, and expels them away.
And then what you have is that you have a region affected by the thoughts,
which is full of negative particles that try actually just cancel the positive touch you have in the needle.
We can estimate the size of that is here by just simple, simple math here like the estimate.
The first thing is that once this chart is sitting there, you have to set up a potential.
In this case, it's positive, right?
So the potential will be positive compared to the plasma to actually expelling positive particles or attracting another one.
What happens in the plasma is that the agents are very heavy. So usually this is done by electrons.
They are not very massive and they explicitly sucked in by.
Positive touch. Okay, so what do you need? You need actually to have sufficient potential to attract enough number of particles into the field.
If you have the potential, a different potential difference that was much smaller,
much smaller than the table of electrons with a modified velocity at the beginning.
And that is too high. I think within between now you had a potential that was much bigger than that.
Right. What will happen is that everything would collapse into into the into the touch, which kind of hovered right there with your a.
So what you have is that the jump between the outside of the sphere and the positive touch has to be of the order of the written table.
That's the.
Now that is created by the fact that you have a positive touch here and you have a bunch of electrons flying around into the sphere on the other.
The agents will be influenced or like overcome by all the negative charges.
You can then take an equation which tells you that the same of the of the potential has to do with the toxicity in the, in the plasma.
And then just by our my estimate that leprosy and you can estimate by the potential difference divided by the the square and typical toxicities,
the electron density that you played to people, the audience is the physical body that you saw.
It's good to get an estimate and then that they're blaming the dielectric constant out of this and that you can get an estimate,
which is called the dividing that actually turns out to be tiny, but usually dense enough that that actually is not unimportant.
It's a very small number. So what happens is that even sometimes a touch of period, that chart is always shielded and you don't see it.
Björn antibody length, which is tiny compared to the to the surface of the plasma and then important.
So that's basically what a plasma you call the plasma when the plasma size is going to be by length.
If that's not the case, you could call it an another plasma.
You actually not only need to have a plasma bigger than than the than the size of the of the device length,
you also need to have the phenomenon that you're studying to be its frequency, to be as one of the brightness.
You have to allow the electrons to move within the sphere.
If it's too fast, electrons coughing, it's to kind of move the kind of shield, right?
So what you do is to estimate the time you take the electron thermal speed and
you say how long it takes for electron to go from the outside of this year. To these you make that estimate,
you will always call the plasma frequency and then you frequencies have to be more than the frequency, usually satisfied as well.
And then the last one, which is very important later so that it works out really nicely, is you only need to be first to know the electrons they have.
There has to be electrons in this field. If there is no electrons, they won't be able to come in a still, right.
So what you have to do is take your particle, make us feel around it with the size of the device length and see how many electrons you have in there.
And if you want shielding, there must be enough of them.
So you have to have this number, the number of electrons, this is the electron density to be bigger than one.
And you remember the coupling parameter gamma and finally four.
Turns out that that has to be big for plasmas two to be quickly couple so that
that number when that's big you have plenty of electrons in the device for you.
All this has to do with the fact that both excellent potential and device for you to have to do with the reality constants,
densities, temperatures and all works out to be like that.
So when you have our we can double platinum which is very useful.
We have literally have plenty of electrons to fuel and that actually solve our problem about the long
range interactions because what happens is that through long range that action should talk to everyone,
but they don't get farther than device length because the particle, any particle outside of the device length won't see another particle.
Right? So our expansion actually turns out to be based on the fact that we have enough filters in the
device length to shield any charge and then the interaction that's gone beyond the device length.
With that in mind,
we can actually they got equation and divided into the motion due to long range on these binary collisions due to the typical long interaction.
Okay, we have a plasma, we know why it works like more or less.
And then we want actually to get fusion and this is where we're going to magnetised plus.
So how can we get I said that you need some temperature, some timescale in which particles have to stay in the plasma.
And we need actually some of this. Right. And there are different approaches you can imagine by doing this, you have the do not confine approach.
If you cross and you get energy fast enough out of it, you don't need to worry about how long it takes to get it right.
He is what unreachable is. So we get future these the beginning of one of the beginning of those tests there.
So there is a lot of energy in the actions. What they do basically is they they they brutally explode an atomic bomb to compress completely steam
fast enough to get these things to compress and get the temperatures to get the reaction going.
And that's how things are done.
There is a side to that is like another approach to nuclear fusion energy, not not bombs, but this is usually the same idea.
But instead of using an atomic bomb to compress, they use lasers. And that in the second point in fusion approach.
Right. That's one one thing one would think, well,
I can actually try to find out a material to hold this thing together in it and keep it keep it in place of having to do something.
That's why you going to start. Turns out that that's not possible, not only because materials more than like 100 million degrees in general,
they usually get damaged and stuff like that is because you actually kind of get that high.
What happens is that you have this very dilute plus a lot of energy.
They not only bomb the material, but all that energy sucking through the material and you basically lose everything.
So I actually at some point before working on fusion, I work on plasma thrusters for space propulsion.
And in both cases you had a wall that was containing the plasma.
You actually get at most of 100,000 Kelvin in those cases.
So it's very difficult to get to the hundred million.
That is a factor of a thousand between what you can get without containing it on what you can get into in places like these or what.
I talk later. Another possibility is gravity.
The that will happen in the stars. You have a stellar size kind of object.
You can get fusion out of it. Obviously, that's not both feasible on earth.
And then we have the last one mighty confinement, which is, I think the best one,
not only because the work within that there is that is good reasons to to argue for it.
And it is basically other thing you have beyond probably on this for me, you're wrong or I stop.
So how does this work? It works because once you have a very strong magic feel in your plasma, they behave differently.
And I will talk about how how different that how that behaviour is different, you know, in a second to make connection to what they say.
The plasma ice is very important for Magnetisation but the plasma is quite a neutral.
Right. If you were to take just like you have naked charges and you had problems with it and you
estimated how much the magnetic force is compared to the to the to the electric force.
Naively, what you would find is they are related by the level of the of whatever you are worried about, divided by the speed of light.
Right. Which would mean that in general, we don't have a lot exotic particles.
Usually in the confinement. These would be really tiny.
The fact that have tons of lead,
basically shielded to be too weak of extent means that the electric field is more than you expect and you can make that light,
which is very important that you have washing in these in these cases.
So what we're going to play now is how do plasmas behave once you have a properties beacon of competition on the scale and on a small Antarctic,
which is more on a certain frequency, and that's when the plasma is magnetised.
So what happens is that once you have a strong magic feel, the particles go and they go what is called a motion.
I'm pretty sure you probably saw this. A lot of you saw this at some point.
These are competition between a situation in which you particles don't have a cinematic feel and a situation in which you have a uniform,
a straight line, maybe feel going through the plasma. And you obviously have these particles.
You see any force, if one might feel they're just going straight lines to the wall, bounce back and forth, back and forth.
Right. If you put a strong feeling system, what particles tend to do in this one is straight is just.
They have galaxies around them. Ideally lines on are basically trapped within.
Right. If you see what these looking is composed of is basically a circular motion in the plane to the magic feel and a free motion parallel to it.
The reason for that is that the magic feel doesn't accept any force along it,
so the particles will just be free to flow along them on and then across of it.
But these are a force that is perpendicular to the velocity. Yes, I reminded of how to estimate the general radiation.
What you do is that you estimate the centrifugal.
You basically get the centrifugal force of having a superior motion, a plane with a radius rule that you have to determine.
Right. And then you make that equal to the mighty force that you have in the system.
By making that estimate, you can actually get what is the radius, which is the size, the reason, duration of those galaxies.
And you can see now why magnetised the commoditized plasmas, if you have a mighty strong enough,
you can make these already small enough compared to essentially the machine.
And then what you see is kind of the particles are like beads that are for the magnetic field and they just go back and forth.
You might feel on this the cold air that you have your plasma, 15 million degrees is very hot, actually.
The more mighty food you need to keep it together.
And that's why in experiments we get to some of the highest magic philosophy for because we'd like a five Tesla student, ten Tesla sometimes.
Right. But that's that might be pretty excessive. You cannot to estimate how long does it takes for a particle to do one of these cycles.
And that is called the gyro frequency, which is problematic field facilities.
So what you need is to make sure that the length of your plasma, the cyclical plasma this large compared to the radius on that,
you don't have any frequencies that can interact with to get a frequency. And then in principle.
You'll be know if you can find plus one, but not quite.
What happens is that there is not the magic pill. Some of these traits are not uniform on very small business, monolithic feel that we are consistent.
And those actually change the motion in a particular way is very is very important and you need to account for in these systems,
which is what we call this as an example I have here, they just drift.
Yes. Just describe the geometry I have my dick feel like is coming out of the ball towards you.
And then in principle,
for particularly the magnetic field in this case and I am positive charts and then they move in this direction with your radius and roll.
Given my ability right now, I put electric feel in the system, which is perpendicular to the mighty field.
Okay. So what happens with motion and this is this is actually going to be the surprising thing.
You start here in motion and you put a target in the electric field.
Just popped up when the particle was here. Then as you go up, the electric field is doing work on the particle and then you're getting in it.
That means that you have a velocity that is bigger, like expect you to be on it,
but obviously you have coming to higher velocity means in terms of of forces,
if you want to think about it that way,
more a difficult force or that you need more than three but very which are two which means then that for the same force the mind.
If you have intent, you actually need to have a bigger radius of direction.
And what you get is something like that, which I tell you. I mean, this would happen with every scientific field.
We don't have such a strong electric field in the system. Now, when you come down here, you would actually start to work against the electric field.
You are looking at it when you lose energy, right?
That means that you are actually getting less difficult force and you get that you you can actually get bigger.
It's more of a reinterpretation. And when you do one cycle, you end up this place, which is back to where you were.
The important thing of this is not the size. This is completely exaggerated.
Right. Usually we don't have that big displacement. What is important is that each segment.
You continuously as you go on and on and on, you get something like that.
So you stop it somewhere. You want to go find this particle and unavoidably this particle population, you break the great symmetry that it made.
It goes on itself and they just signally move away. These will be culprits.
And in particular this one is because we drift on.
This is basically what we do in mathematics.
We actually study how these these drifts, these velocities interact with the with the automatic fields and decide how the mighty things work.
I want you to notice this is an interesting piece of physics.
We kind of went back 24 billion mechanics in that the velocity is proportional to the force, not acceleration is proportional to the force.
And with a little twist in that, you actually move your particle perpendicular to the force, not actually parallel to it.
Right. So things are a little bit different.
Now, how do we treat this? Theoretically, what you do is you actually do it to a scale expansion in time scales.
What you have here is actually two scales, the one of the motion, which is very fast,
and you have the pay scale of the fields in the background that that that are basically get in the street.
Right. So what you do is you you define to normalise times one normalise to the general
frequency across time scale and the other one normalise to another frequency,
which is the one of the, of the mind fields.
Then the particle position depends some time through those two not normalised variables.
Right. And what you can do is separate the motion into the slow motion of the centre of a simple plus, a superior motion that is really fast.
Right. And then you have corrections.
I mean, once you begin to include more and more tension, it is not circular, is elliptical well, not political, is somewhat triangular.
And you keep correcting and correcting incorrect and you can get the circular motion out of this.
This was proposed. I mean, that was scale expansion.
Classical already did it in the sixties. Peter Cato is is actually the person that proposed the easiest way of of of doing this system.
And it actually works quite well.
What you can do then is that once you look at the system, right, you can actually obtain equations for this low dependence of these things.
This is the position of the centre of the city. Paul And this here is the reading of the simple right.
So you can see how slowly the centre of this pragmatically line because there is no force along it.
So you can, you can move it along on it drifts slowly across.
You can actually see how the circle as it goes around it becomes larger or smaller as we're moving the particle around.
Aren't that part of the velocity actually can be affected by electric fields and all that I know it affects.
The final thing that you get is that you are moving around rings of stars, right?
With these three simple out of the velocities and then you get up again a hit equation
in which you actually the characteristics of it are the most of the particles.
And you get things like these. This is a might if you like. I think what you have is that you have a ring of charts.
That move moves mostly parallel to the Magic V line, but they slowly can drift across.
And you have to finish. This is not only a nice expansion into scale of and stuff like that, it's actually extremely crucial to our machines.
We have to take into account these three because otherwise they wouldn't work on.
I have here two samples. The first one is the Tokamak, which is a isometric between configuration, which looks like a doughnut and what you have.
A magic film produced by the Royal Magnets, which is a magic filler, goes along the long length of the of the light.
In principle, you would think that that's enough. But it turns out because of the separately so that a small parallel is right, they never stop.
You actually need to have an almighty feed such that this in the short direction of the doughnut so
that the composition of it looks like that it's kind of lying along along it to keep the particle seen,
to avoid that from killing you, that actually requires a cover into the system.
I won't go into details of that, but that is expensive and that is actually can be dangerous for instabilities and stuff like that.
So there were some people that thought that what the the current you want to create a system of magnets
that easily form in such a way that you get the same effect as you couldn't pick them up from the current.
These are very smart idea so that you can prove that you kind of work in electric motor device.
That's why these these devices have these we are shapes. It turns out that if you forget about the drifting systems, they don't work at all.
And it's being the case that. Until probably the end of the age of the nineties.
People were designing these things, not pursuing their dreams. None of them work well.
As soon as you can prove them for this, they were fantastic.
Well, not as good as that one, but it's getting close.
So that's it for me for now. If you have any questions.