Good afternoon, ladies and gentlemen. And it gives me really, genuinely pleasure to introduce Howard Rosenberg to you. Howard is one of this year's last visiting lecturers, and so we're grateful to the two travel funds which allowed him to come and spend a week here working and talking to members of my group. And I think this is also counting as as a physics colloquium. So. So we're actually getting two tools for this. For the price of one cup of tea, which is good value, I guess.
Now, how his parents lived in Niagara Falls, Ontario. And one day they drive across the Lewiston, Queenstown Bridge, I believe it is, but I don't know the exact date. But very shortly after they drove to Niagara Falls, asleep at Niagara Falls, New York, and very shortly after Howard was born.
And this shows the degree of ingenuity and full science, which they clearly bequeathed to Howard, because it enabled him to have a have two passports, which proved useful later, and I suppose in today's climate may prove useful again. I went to the university, my master, and did a bachelor's degree in engineering. He did his Ph.D. at Princeton in Astrophysical Sciences and then to the Bell Labs before joining University of Maryland in, I think, 1988.
And he joined the Institute for Physical Science and Technology, which is in electrical engineering. And he still has some part in there. But he's also the major part is in physics. I think I have that right. And he's won many awards, including Presidential Young Investigator Award, John Dawson Award from the American Physical Society, and he's a fellow of the American Physical Society. If I may, I'd like to say a word or two about how I got to know Howard, like many of you.
I like the way you would have learned about your academic colleagues on Earth, about Howard through his papers, and in particular, in the 1990 to mid 1990s, he wrote a series of really elegant papers on an ingenious way of guiding very intense laser pulses through long lengths of plasma. And if by very intense, I mean on a scale of 10 to 24 watts per square metre, which is sufficiently high that the electrons in matter move with relativistic energies.
And by long, I mean long compared to the range on the scale of 100 radio ranges, that sort of number. And a little bit later I became interested in the same sort of idea and rather foolishly tried to do it in a different way. And more recently I realised that of course Howard Howard's method was perhaps superior in some ways. And we've been thinking again about this with perhaps a little twist on it, and I'm talking about it this week, and it's truly an interesting area.
But the reason I mention it is, is that I've been forced to read those papers again before. I've wanted to read those papers again. And and in doing so I just realised how beautifully written they are and how they're absolutely jam packed for the physics. Every paragraph causes you to think a little bit and you learn a lot by thinking hard about it.
And so I feel that today in his talk you'll find his talk, which is on optical vortices, a different subject, although there is a connection, will be jam packed with the physics, and I'm sure you're going to enjoy it. So with that, I want to hand over to the Howard. Well, thank you, Simon, for that over-the-top introduction, which used up 5 minutes of my speaking time. So I will I will speak faster than I already do.
So I guess jampacked means he talks too fast and there's too much on the slides, so I hope you don't find that. Anyway, I'd like to thank my students here. My students are just fantastic and every few years I tell my students are about to graduate. So these guys are graduating the next six months. I say it's the end of a golden era that I that I await the next set of students to come in.
And, you know, I'm a little hesitant, I'm a little nervous, but, you know, they always seem to be really good. So the new newsletters coming in right now, if they match these guys, I'll be I'll be lucky. I mean, these guys are fantastic. In fact, I told them I'm going to delay giving them their fees and I'm going to step offices for a quarter of my life as a poet, whatever. And in fact, they're like one of the doors, professor.
Okay, just stay here now getting paid more. I know that that's a better story. The work is funded by a wide range of agencies. I was telling Simon, depending on where they I'm in the talk, I showed up in the crowd and I said to the bank, Depends what I'm talking to. So so I don't know what your feeling is about military funding in Britain, but I thought it was up to the French just in case it should be that.
Let's see. The other thing is my students work on a bunch of different projects so continuously, so they tend to get of quite a few papers by the time they graduate. And a number of agencies are involved in funding these projects. So so it's not like I just submitted the same proposal to all these agencies and just changed a few of them. You know, what we're seeing here is that these students are all on different projects on this.
In fact, this isn't funded and this is something that just came out of following our noses in the lab. So let me go to the next slide. Okay. So let me just give you the punchline of what I'm going to say today. And that's that this this vortex phenomenon that's making the first slide stoves, stoves without the it's a universal structure that accompanies all self-driving beings. And we discovered an airflow limitation. And I'll show you how that happened.
And we've done experiments and simulations for this, but it also applies to relativistic. So focusing on actual levitation in plasmas, which is the basis for the most successful version of laser acceleration. We are also we are really quick simulations for that, very sophisticated simulations, but we're also setting up to do experiments. So that's why I have this at a later time. We have done those experiments here. So here's a picture of what this looks like. This is meant to be a time machine.
That's not not a bunch of these pulses coming out of some source. So what happens when you generate a bunch of these things is that you have a total structure. This is phase circulation and where the centre of circulation is and there's a field of so that's sort of depicted by this noble intensity region. And this thing moves at the good velocity of the pulse and the total.
The object as depicted here has total angular momentum of zero, but there's not zero angular momentum density in this object. So that's it is so the kinds of vortices that you're familiar with are so-called maybe familiar with our own orbital angular momentum vortices.
And for instance, a Gaussian being that's higher than the lowest order basically can be thought to have Orbital gaining momentum around its propagation axis and that shows up in the expression of their gas and then as a phase suppression around chance of beating the odds by space when you move into now here's a different structure and this is just the limitation of my power point scale. So it's not a real action. This is actually a pulse. So imagine something that's more teardrop shaped.
This is a field over the centre and there's now a phase circulation which exists in space time. So front to back as time up and down is this transverse. Position or in the frame of the polls, you can look at this as being a local space killer. So the first circulation is is in space time. It's a one dimensional story in the sense that that field is what do. So this is, again, a repeat of what I showed before. This is this is in 3D and the circulation is in space time.
Now, let me just maybe make this go down a little easier by showing some questions you may be familiar with. This is a low order guessing game. So this part of the familiar with that's the radial Gaussian fall off. This contains the voice case and also whatever other face you have in the game. And this is the transverse phase which we can write is either a plus or minus sign. So this is a space phase situation. Now, in the time domain, what we're going to do is to find a local space coordinate.
So this is space coordinate moving also. And you can divide by the good velocity. It is a local time orbit and you can do exactly the same thing. You can have this pre factor. We have this radial Gaussian falloff. Now we can say, well, we have a Gaussian temporal dependence. We have the same sort of additional phase factors here. But we have this piece, as I said, and this could be written this way. So this is a spacetime situation that this would describe.
In fact, this one here is a linear stone. So that that expression to describe the structure is not like this, but like this. Okay. So just to repeat, go back to what I showed earlier. Well, I'm going to show experiments and simulations for two systems simulations in the classical case. In this case, I'm going to show results for here. So. In November, I'm going to show results for air and.
Okay. Yeah. Okay. So in here, this whole process arises from the sole focus on the amount of evidence and so far saying is arrested by ionisation and the cell focusing in arrest process is what gives rise to this. What is is in plasmas the nonlinear to the causes of cell focusing is as relativistic. I talk about that and the arrest of another area of the termination of dominant area occurs due to cavitation. So the electrons are forced out of the lightest way by the mode of pressure.
So that's what term. And so there's always a self focusing process in the termination process and that's what gives rise to these new structures. Okay. So let me start with some limitation in value of an electron system. So this uses linear. So just to review at low intensity, a CW laser pulse diverges when it propagates. And that's just because it's a wave.
And the characteristic length of divergence is the so-called rather edge, as defined to be the distance over which the intensity drops after two. If you use a lens, nothing changes you just short on the spatial scales. But the same same physics is involved. Things change the locks. When you go to short pulses of a few molecules, I'm talking a lot of people who are short pulses shortly.
But what happens in the lab and this was really made possible by the mid 1992, people were able to find our way as a result of other 50 seconds pulses with a few black holes and the next person standing took place in Michigan outside of Hollywood and it was laboratory. And I'm quite confident that he didn't call it the safety people that the game just down the hallway and this is right out of the pulse compressor if you if you know what that is but it's right out of the laser.
And after propagating a couple of metres, it just collapsed. And then what happened was this long extended, high intensity region whose diameter is equivalent to many really ranges and propagation and electron gestures were limited to about a 10th of atmosphere and a 10th of a 10th of a percent of that of atmospheric density. And the intensity was limited to about 10 to 14 watts for sure. So it's a self-limiting process.
Once you generate some electrons here, it tends to refract between and the structure just propagates through for a long distance. What limits it can get into too much detail in the of the range of the original object, which is obviously much, much longer. It's a much wider diameter. When you get some free things here, you get electrons generated. So there's a vision that we could see some of them die within the electron column and have a giant capacitor here and run on electrons all over.
The better part is the discharging intensity. So this is the first thing, the potential funder I think about it, NSF, one of the other agencies. But what practically speaking, you know, it's very, very difficult for the gases discharge. Again, it's the degree of strength of some people. But but in a more useful and actually on a daily basis many many groups use this process.
So this collapse leads to high intensity and very rapid temporal changes within the index for fractionalisation and through basically stretching the electrons down molecules and you get what's called some phase modulation and a very broad band radiation is generated which still haven't been fully directed. So this can be used for lots of different things. There are versions of positive lasers to capture this dark colour or fibre kind of there's some limitations on those process uses atoms.
So in everyday usage, filaments are very, very common, even though people may not understand its own mutation process. So it's is being used. And so the super containing generation is that the typical practice or they're everywhere in the organism, they're are quite small. So lots of people tend to use lenses. And so the length of these things is governed typically by the variation the lot. So typical labs they have. A few metres long.
But if you send a one and a half centimetre doing anything down a long hallway, we'll talk about that in a few seconds. These things can be 40, 50 years long. But what limits them is energy prices in terms of the divergence of the human beings. Anyway, this is my lab. This is an example of the use of tolerances of two atmospheres, you know. And so I'll describe why we use this green filaments in this cell.
And this is a nice beacon of light. And you can see this is the if you subtract off the other side of that, we get this huge bad, you know, double out of the lab and this is something like 50%. So it's capable of supporting pulses. If you want to compress it and you can use this, it's capable of assembling a double sheet up to the surface of the circumstance. Okay. So many of you have seen graphs like this is not this is a traditional graph always thrown up.
So it looks like a fancy way to start. And it gives the intensity of lasers versus a year. And there's a proliferation when you get into the mind. And because the first demonstrated laser was actually a pulse laser, nice CW laser. So things got less exciting for a few years while teeny tiny lasers came in and then it started coming back up again. So the area that we operate in is with these with these filament type experiments.
Okay. And then and then here you see the different kinds of physics that you can do with these and these towers shown. So we operate with an air filaments or any filament gas or actually filaments even in solids and these kinds of 10 to 14 to the 13 densities, you're operating between intensities, you operate between 2003 electrons. You remember I said that the in air digitisation yield is about a 10th of a percent.
So most of the air is actually neutral, it's not optimised, and yet it's exposed to direct high intensity. And so perturbation theory does not apply to the atoms that are exposed to that kind of laser intensity. And then there's because of that, there's room for lots of mischief. And I don't want to talk about this, but this is a controversy that my group got involved here, I think successfully. You know, it was the new world versus the old world.
And to give you a little time to listen to the circuit, but if anyone is interested in this, you can talk to me later. But it was a question of what the nonlinear, nonlinear, responsible adverse injury intensity feels when the atoms is organised. And so we have diagnostics, a good measure of that. And then the other part of this is the Relativistic Machine. So we've gone through about ionised electrons, let's say, from hydrogen.
So it's a bunch of protons and electrons, yet you still have a known linearity, but that kicks in when the normalised electric potential, which basically is a measure of vitamin C in some sense, is close to unity. And then you have to take into account the relativistic electron orbits and so on. So there is an electron investment. So that's sort of that that's a source of another non linearity and that's the source of relativity and so forth.
And so we'll talk about that. Okay. I'm going to give you this because we talk about filaments to burn people out. And a lot of the allegations that I added some of my editorial comments here, so clearly directed energy is not important. I think that's not controversial because you're talking about military and military intelligence. And if you have bigger beings with hundreds of molecules, they're very different to hundreds of Solomon.
So it's not like, you know, my father had a religious incident, so it's not an energy delivery device. But if want to deliver the intensity, it's actually pretty good. If people are thinking about using it for this laser induced breakout spectroscopy, this is something that's been hijacked a number of years. I think that deserves to the question that you're going to bring. Then there's other things here.
So if you're interested in this slide, there's there's actually a fairly large community trying to apply some of this to various things. I don't through all of them what I'm going to focus on actually and stuff, but my group does. So I don't know that you get a degree in checkmarks there, but it's all fun and great. So and I'll talk about how you can actually use filters for directed energy, but not the filaments.
So this is all of the air to form index of refraction structures and then those are data to hydrogen based for remote detection. I'm not going to talk about that, but if you're interested in a paper a couple of years ago in optical and and also you're not going to talk about laser acceleration of electrons, what I'm going to talk about is relativistic propagation that leads to laser acceleration, which the.
Sports is a pyramid. Okay. This is a little review of the nonlinear and the boundary electron nonlinear atoms, the small electric field and the divergent that's just linearly polarised. The atom sensor, large electric field view of the electrons has been stretched and this is near a nearly instantaneous response. You can think of it as a spring, a simple spring model.
And so before the laser was invented, the spring responded by the early, and then later you start to stretch in the spring, and so it gets floppy or gets looser as the laser field goes up. And this curvature basically means that the effect of polarised ability of a number of a bounce electron without an electron is it scales or fields. In other words, it becomes more polarised the larger the laser is basically because of that, because the spring is getting sloppier.
So we can just see what the effect of this is. Simply call I said perturbation theory doesn't apply until I need to use it for a toilet paper. So I'm using this as a target. And so I'm expanding the polarisation at a power so that you feel in a central symmetric medium, which is, you know, typically the ensemble average over the gas that goes away and you get terms, you can group the terms like this and say saying a fraction in terms of susceptibility.
So you see the leading order response here is scaling the light intensity. And then there's what's the sign of this thing like explain in the earlier slide springs to become a flop here. So M2 as positive energy is basically related to the second rhythm that the terms that I showed you. So what is the effect of this? The effect is that if you hear the beam waste of a gas would be near the beam was the face looks like this at low intensity and here's the laser intensity profile.
But I think we've now learned that the index goes like the before low intensity index plus turn the intensity so it peaks in the centre. And so the index profile of that, does it accept that optical fibre that slows down the wave at the centre of the beam and then look at it, it just propagates more or less like it normally do on the outside of the lens that causes concavity in the face fronts and that cell phones and that will continue and that will go to the singularity.
It's a runaway process because the higher the more peak it gets, the more some location in does. And it just keeps going until something starts it. So you can derive a criterion for this, the basically requiring this process to be diffraction diffraction services president tending to spread the beam up. And so I was watching these samples. And so basically it comes down to a power critical power requirement. And to have this collapse happening in air, I need to detect gigawatts of power.
This is why this didn't have to wait till the mid-nineties to have it devastated in the air, because the time that technology was available to provide 2 to 10 gigawatts and a couple of villages and saw it, it's about a thousand times less the threshold. One divided by 26 seven times this. So, yes. You're here, Professor. The. He had the correct answer. Why is it a thousand times less unsolved than in a gas? What's the difference? What's the main difference when you solve the gas? That's it.
So as solid as America has in terms of where it. So you can think of those as fundamental springs that are present and where there's a thousand times more of an earthquake. So the question is just and in fact, this thing was discovered in the 1960s. These people were destroyed and those are not there. There's a whole debate about it, but they were actually getting ripped apart from the inside. And so this is what was going on. You don't need to go to the second puzzle to do this.
You just need a couple of second pulses to demonstrate there's an air and there's a threshold is the process is higher. Okay. Now, okay. So what are the limits of the approach to the singularity?
One of the people in the 1960s solved it by destroying the lasers, and then in the hallway with them, the second pulses you were getting, and I'm sure it was multiple times, they should probably have lunch in the laser rods in the 1960s, but in the in the 1990s it was totally ionisation or or multiple times.
It doesn't matter. It's a hydraulic process and the intensity and that gives rise to three electrons in a polarised ability of same thing and the index of a function that goes like this four or five times. But the susceptibility of the electrons of both as a delivery, which is, is negative. And so you get a negative addition to the unit instead of a positive rate.
So again, the same picture, these are profiles that face from the securitisation routeing experiments the other way that's pretty sharp in default the same. So both processes are operating and you get some kind of combination of self-focus and refocusing. And these two things are interplay and you get the same phenomenon. Now the vortex thing comes in later when I explain how the whole thing comes together.
So let's take a little break and I want to talk quickly about the response of air molecules. And this is not just to highlight of interesting. This is in some of the details. It's just to say that this is these are measurements. These are a simulation. So the way that we look at this is that here's the time evolution, here's your space. This is the response of nitrogen molecules to an intense pulse.
So this is the electrons that are the nitrogen molecules as a function of time, responding essentially instantaneously. And then a little later, the much of the nitrogen locals are talking to alignment with the driving electric field. This is a pump probe experiment, so a very short pulse, approximately 42 seconds in duration causes a strong up in the air and then that pulses off. And then there's a probe that monitors the entire response.
So there's a probe response and then a delayed response. You can also do it with a probe into the particular orientation so that in this candle that allows us to extract some interesting stuff if you're interested, it's in these papers. But the point is that there is two timescales for molecule responses, a fast response and a slow response. This is instantaneous, isn't just it's just about electrons responding at any angle that the molecules are responding to the laser field.
And then there's a slower response as the molecules light up due to the target, the induced polarisation by the start of the laser too, we can also measure ionisation. So this is this is Krypton. So this is there's no molecular location here. And so basically we see an instantaneous response and remember that what we're actually measuring here, I guess I didn't tell you what we're measuring is the index of refraction as a function of time in space.
So this perturbation really goes like in leading order at this intensity, it goes like e squared or close, like the intensity. So this is a way of measuring the intensity profile in space. Later in time, though, we're in a higher and higher intensity as we ionised so early in time, we get the same effect. But then the last part of the pulse is shaved off and we generate electrons. So this is along the electron contribution to the index, the fraction that comes later.
Okay, so now let's get into all the important stuff. So one of the things that we did was the elements of the question, there was a history behind this, but I'm sort of repackaging it sort of as you tend to do in the slide. And so it's just the fact that you start thinking about is that after someone is long gone, what's its effect on the area?
And so from the point of view of all of the sort of physical constants of air and thermal conductivity and mass motion and all that stuff, the filament heating is like a double function. You're making electrons very quickly, rotating molecules very quickly. All of these things are sources of energy. From the point of view of the gas is like a delta function application of energy density.
And so energy density is like pressure. But at all times it's no longer in the original form that you put it in and put it in. Initially was an organisation and electron density and molecular excitation. If you waited too long to wait a few hundred picoseconds that all thought that there's recombination and then internalises turned to the gas.
So you can look at the gas as having a pressure profile at table zero where you basically equilibrate all the energy going to be done from the centre second pulse and that that would actually do the pulse of pressure source. And then the thing which is a celebration. So it's a delta of function pressure source and okay, this is important. It's relatively speaking, certainly typical plasma. A gas is a tiny neutral gas is a tiny little of activity.
So it really maintains tight, real radio confinement of all that thermal energy. So it's not like as this equilibrium, the energy moves away, it pretty much sits on the same radio. So don't worry whether the filament dumped it, except it's now purely the pressure profile of the Mitchell gas. And so this is what the illusion is.
And the folks inside this room, they don't find themselves in a cold relative to simulate sort of a different problem, but that's applicable as a hydrophone, which is this situation. So we did an experiment, a simulation of what happens to the air by nanosecond and longer timescales after the Solar Inductance Energy.
And it's very it really is of a delta function of pressure applications of constrained time at some profile and it launches, you know, within the air periodically it's one punch so you get a single serve the sound way leaving the air it's leaving and very interested there's the interest will come at this end. But the most important thing is it wants to work because one is to notice this.
This is a single cycle sound with the lever. And then once you get to the microsecond scale, what's left over is what we call a density called the depression that was pushed mass with the Soundwave. But then this all sits there and it dissipates over milliseconds because the thermal conductivity of air is low. So here's a point to go over here and do what I think you would do. You're just here's a movie. It's no, it's three.
Very good. So that's just that's an experimental it's a sequence of frames that that previous slide was made made from. Okay. So the idea here, and I don't want to get into this whole experiment except to sort of set the stage with all their stuff. So the point here was because each one of these so that part of this, if you wanted to make a teeny one and have each one of these guys for each one of these would leave a hole in the gas density for milliseconds after the so on the left.
And the idea is, well, maybe these things to fuse together. And that would have allowed in at a core. So the inside isn't affected at all that they have got sitting there. And then you get a core which is required, which is a lower density on the outside, and that is precisely the amount of the virus, except as an optimal vacuum in the air that lasts for milliseconds.
So that's the setup. This was initially a poor man's way that I could see and one of the low income people who do optics, you know, but this optical telescope, you can actually cut them with razor blades and have three stars. And it's amazing, actually, because you can throw their attention to be able to get the people to cut a couple of razor blades and turn them away and tell them the right way.
And you can put multiple five on the beam and then the focus this is a teeny one, but it collapses of the filament and makes the waveguide that we injected with 100 times the energy from the opposite direction of the gods. Here's a movie of the process. Maybe it'll cycle again. I don't know. There's no way of getting it there. So just the four of us right there. The cloud is on the other side. Yeah.
Let me do it one more time. I don't know if you excited that early in time there was this red dot and that's when the satellites collided. So there's two places you can actually get a guiding structure when the sideways is alive in the centre. Let's go again. Okay. And then later. That's on a nanosecond timescale. Then later you get it when you. Yeah, that's right. It's right there. So there's, there's the collision of the subway and later this thing develops.
Okay. So this is just a demonstration of guidance that we got, and this is paper versus the paper, if you're interested. But this was, I think 25 pages or something like that. It might have a number, but it's quite efficient, 75% efficiency. And so that's the source of a lot of the experiments we're doing now. And so the idea is to extend that that way so that I show it was about a metre reader.
How long I forget exactly. I think it's about a metre, but now they're in the 50 metre moment to set something like that. So we need, we got the local guys in the drills to drill holes in our wall and we've got all the safety folks to sign off on this. We run this experiment the middle of the night and we put the laser pictures up everywhere, the police and the housekeepers and blah, blah, blah. That's all. It's all the all the documents are saying they're doing this.
Right. And and so one of the fascinating things about all of this is that when you propagate metres away, you still have this structure. So this is a super continuous of a collapsed tier one property. You have one, one mode, but part of the super continuous generation process is massive formations, huge. So why do you still have these things separating fact we set up a parameter at the end of the rule. All these things are still surrounded by a single box. Why is this?
So that told us. Well, we've got to find out what's going on inside the. So when we set up data for either the room or down the hallway so that it ended or it was just freely propagated and that's what we did in case we want a little bit in the middle of it. So this is we're seeing really very nice results. So there's no incentive to there. But okay, this is the motivated question. So we did a bit of a detour. We were redeveloping a laser.
We didn't have enough energy to go down all the way. So during the time we developed the laser, we decided to go after this question. And so we set up an experiment which would allow us to look inside of film. Now I'll show in the next slide how we do that in terms of the real world. But if you were to have an interface between air and helium and then the air ended abruptly and you would have the ideal situation as you would be. So this is essentially the full blown linear process development.
The m2 of air is high enough so the station. But then when you get to this interface, we encounter the atmosphere that's 20 times less than air. And the reason is that electrons are quiet by the time we want us to. Electrons are not floppy, floppy spreaders. We need a time. So at this interface you can literally image everything that you collect at that, at that interface.
So you collect the intensity and the phase. And so what we do downstream is we deliver that rather than just measure all the stuff. Here's this, okay? You don't have to look at it too closely except to note the cell is the only answer. And here's the film. Some of it is it starts somewhere down here. It just propagates a couple of metres and this helium, so it terminates inside this nozzle.
The way this works that we overpressure this slightly compared to the atmosphere and the helium just flows out very nicely and there's a couple of millimetre transition and then that nozzle and we've simulated that essentially it acts like an interface stop, start, stop. That's going to be so that's all good. And so what we do is we move the helium so up and down on this thing and we adjust the energy between zero and five individuals at each position.
So we have a huge base space of filling that information. And I'm just going to show you part of it. But but wherever Filament exists, this stuff is is. The idea for this came from 2010 is now at Merrill Lynch, but he used it just for intensity purposes. We made it useful for Facebook profiles as well, and there's a lot of knowhow out there in terms of how we prepare the game using other spacial filters before the compressor and others before and after the compressor.
So means that there's something on here. Anyway, here's the here's the results at one particular position. So the human cell is 187 and we scan the laser energy between zero and ten units of critical. I forget exactly what it is at that point, but you can see that at this magic place of five, incredible, it could have been 4.3 or 6.25 for this particular position. You see a phase jumps of almost exactly to five.
You just look at the red dots and several blue dots. But we've basically averaged over we have a moving average of several hundred shots over here. And this this is just scattered because we're going into a lot of problems and it's just that sensitive. And we see this everywhere in the film. And so we could park at 120 and 120 this transition. Then we actually have a higher peak as you're forcing it to collapse earlier.
If we brought this to play farther away, then this transition would be a lower characteristic because it's allowed to propagate farther before it collapses. So this is a universal thing and there's a pipe to partition. Anyone who's done interferometry will say, well, is this just a phase on the right or something like that? Let's see what's not. So just keep this in mind. It's essential that we said, as we said, what's going on with that?
And we start to see simulations. We can see you're doing them simultaneous. And there was this thing that we had seen before and we didn't ask to understand what it was, but then we started getting this data and you know, these things sort of come together. And it's also very powerful to have students who also considerations, people who are also doing simulations so that the communication pathways is very, very shortly after about three flights of stairs to talk to the theorists.
And you're right there. So it was was a very fast convergence of understanding. And so this is a phase picture from the film. The propagation of the beam is going this way. So here's the intensity and there is the phase field. Does that occur? And there's phase circulation around this field right now. People doing these kinds of simulations in this field really looked at the phase. They just looked at this kind of thing. They were interested in the intensity of how intense you look at the phase.
You see these structures and there is two pilot phase circulation around each one of these vortices. Where are these forces from? That's the question. And I'll talk about actually where these two guys come from with our first question. There's actually another step. The simulation, again, is a moving window, but the pulse is a phase of moving. This shows them developing. And, you know, they go. Yeah. There's one coming here and there's another one that these two are going to annihilate.
See, that's the first time I used the word denial. We're going to have to explain what I mean by that. And and there's one that's right there. And this is some propaganda. The false this all goes away. And then you have died and some guy with this thing attached to it. So what is going on? What is all this stuff? Okay, so here is a toy ball, which is a kinematic model at first glance. But but it really is a dynamic one because it has to be some physical substance that's that's driving this.
So just imagine that we have what I call a half plane. So here's the plane for the planes. And imagine that the intensity down here is very low and the intensity above is dotted. But that's dash. It is fine because the time of the motion of the plane and this thing's propagating from left to right. So after some distance that you're going to start getting a redshift, I should say.
This is a nonlinear level pointed out before, which is proportional to the square of the concealed, but it accumulates over the propagation distance. So with some propagation distance, you get reach out to the front, inclusive to the back, very little ship down here because remember that the square diagrams very well. You get a what's called an edge dislocation.
You get to a place where there is a vibration and actually a lot and this was observed or discussed in some detail in this classic early paper where dislocations by variability and try to explain. So I think there's something in there because somehow something like that, more sound waves and then you propagate a little farther and this thing splits into two.
Now there's actually no first circulation here, but you go around here, there's two parts minus two, five circulation plus two primary circulation. So the phase gradient integrated over the top gives to five. Here is a plus or minus one. And these have so called typological charges and forecast with a to kind of an index of energy. So this thing in the development of this edge, this location gives rise to the plus or minus one of all again.
So again, this appears to be kinematic but it's really dynamic is something is giving rise to dispersion some material the. Here's a simulation of our pulse. So this is our simulation that comes later. This is a fluid simulation. So here's the pulse propagating. It starts the cell focus picks up at the centre, it starts it's a runaway process, so it picks up even more.
And then it starts by analysing the gas and there's more force, even more phase slippage between the space that is going on between the centre and the outside. So you can think of this to happen to play with the low intensity part of the star intensity bar. And then another dose right here and this is a little refraction to the intensity. This continues at the bottom. So you don't show the more.
Detailed simulations here. This is basically the same instead of just looking at the full being cross-section. So this is phase and this is intensity. What we're doing here is we're following a plane. This is a plane moving with the pulse. And we know having done the simulation where the null is going to appear. So we're just following that plane from the beginning and then seeing what happens.
We know it's actually the real world here at that plane. So initially we have a Gaussian being going it. So this is the log of the capsule. It starts to focus on this peaks up and then you start developing this field. Now, when you have a phase zero between the inside and suddenly there's the phase development, pretty flat phase inside of what's called the core. We're going to call that region inside this. No, that is the core of the region outside the periphery.
And a little later, you get this. So this shifts very rapidly. And as the vortex starts to move and now it goes completely out of the supplied coffee and it looks like it's out of focus. So there's a lot of very fine action taking place basically in in this region right here. Okay. This is data. So this is experimental data. And this is for one particular value of the field. So we're parked. We're near where the collapse occurs at the peak of the picture at 4.4.
And we see a range of different behaviours. We see something where it has collapsed. The slight fluctuations in laser intensity are affecting whether it collapses or not. Severe intensity phase. Nothing exciting here. It's collapsed. And we see a now and the phase here is pi here we see around it all in the phase. Here is why this part in the phase difference between here and here is too violent.
Now, people who have done the phase extraction interference have occasionally encountered the field of phase of the universe. And so we wanted to verify that this is not a phase. And so we did a of a measurement essentially of the phase transition between the periphery of the core, which we're going to find to be inside the outside of the cradle. And this is just a smooth change between the background and the inside of the of the dark. So it's always inside versions of the outside of the inside.
It's always a partnership publication between these two. It's a two part threshold. So that is basically the measurement of the vortex. Now, we've done simulations that also are so that we can calculate the point and character in the frame of the moving pulse. And it is very interesting. It depends on the radio phase at all in two dimensions in this space like dimension, and then the dynamic dimension and the final dimension. It depends on the media, the loss of exposure.
So I'll start with our case of error because data is so small, but it is proportional to the gas density. So this term is actually quite small. This is what it looks like. So ahead of the pulse. So here's this is the outer. This is the axis of the mean. This is, by the way, the galaxies. There's energy getting sucked in. This is the cell focusing. And this is the default in the vortex, basically is the self-consistent structure, which is basically described.
And you can say, well, it's describing the focusing of the refocusing, but once it gets going, it actually starts to dominate the energy flow of the focus energy this focusing. So this is our case in here and in a plasma that's dense enough, there's negative changes. So you can show that that sort of disturbance starts to dominate. So it picks up the vectors just to go up and down sideways as well. And it spirals this way and in a positive energy and sounds.
We've done these measurements recently and last and verify that this is this is this is happening to us. Okay. So for a forward this is this is a rapidly converging one. And so let me quickly speed up. Here's the solar wind collapse where the wind collapsed. And one can describe the that basically like this is an impulse which has an intensity where the location of the vortex is focusing on the front deep, focusing on the back. And this is that this structure is propagating with it.
So the question really is how important is this thing? Is this just a matter? That is a description of what we're doing for three eight or is it some dynamically important object? We believe it's a dynamically important object. We've done simulations in that area, but I'm going to show you simulations in all in plasmas that sort of reinforce this. So relativistic filaments, what is the source of the nonlinear relativistic system?
That is really nothing of the driven electronic speed to the speed of light. So that means that the sinusoidal oscillation of the electrons are more rounded off or reduced in just a simple minded view of this. And this gives rise to a nonlinearity which is scale in the same way as it does with electrons, and it also scales inverse to the fourth power of the laser driver, which makes CO2 lasers, for instance, very interesting for this kind of thing and then for the mid-range as well.
So here's a picture of the simulation, and many of you are familiar with the cell phone TV. So we simulated this in to the lab geometry. This was three groups. One of those was, I guess from the material was a very complicated idea to do this. But here's a laser pulse moving through a hole in ionised hydrogen gas and it cell focussed in a generator farther away.
So this thing collapsed under a lot of pressure generating these plasma and crests in the middle class before it starts to accelerate and beam. And we're going to examine this thing in a little more detail. And when you do, just that will fly on the field for the purposes of this display, you get this dislocation. So the question is, is it important? It's there. Is it important? Certainly. It's really an elevator. And transport is about 80% of the spectrum of your life field.
That is potentially lower, but is limited by our simulation. So here's the novel and we're going to now again, is this mathematically just something out of the hundreds and important? Well, there's 40% of the energy outside the location of it all radially. So it's a significant amount of laser energy. So I've just suspected it's there. What does it do? Well, propagates a little farther and here you go. We've got the plus and minus one phase circulation is two pi farther.
The minus one is left so that the simulation went up, the minus one went backwards. And the here's the plus one of propagation loss. And now here it is in 3D. That was a slab geometry in three D that first appears at some location. It's off axis, possibly due to some distant numerical thing, maybe feels a little higher there after some of the propagation. And then so the block is the location of the field.
And I'm just advancing this. It just grows. And eventually, if you get a minus one, that leads to the plus one in forward. So even in the 3D case, you get this situation. Now, how important is this? We did a simulation where we set up a very high density plugging along the path of the relativistic wave self guided impulse.
So here's the location in a that this is the is the main part of the laser pulse energy blocked the stone block this we're testing this big cloud of electron density and slowly it just it just goes away. On the next one, we lost everything, but we left the stone on the outside go by. And this thing reforms that stream. So this is our evidence so far that it's just a spectator, but it's really a switch or pointing flow that is robust enough to reform the propagation structure.
So let me conclude and I think the most important thing to me is that self guide is synonymous with these vortices. There they are to both lenses. So consistency to the overall field structure. And I would go beyond that and say that they're robust enough to actually control the fate of any of the solar panels and then various other things and then some, some fairly motivated because we're still thinking about this set of applications for these these kinds of orders.
And so you can ask about those very same answers. That's it. Thank you.