Deciphering The Child Langmuir Illusion: Advanced Plasma Simulations with Dr. Dan Faircloth & VSim

TWSS2023_DAN_FAIRCLOTH: [00:00:00] Hello and welcome to TWSS 2023. We’ll go ahead and get started for today. My name is Colleen Dunn. I am the sales coordinator here at Tech X Corporation. Welcome back to day two of our annual user conference.

Our first presenter today is Dr. Dan Faircloth. Dan Faircloth was born in Cambridge in 1974. He received his PhD in high voltage electrical engineering from the University of Manchester Institute of Science and Technology in 2000. In 1999, he had joined the National Grid Research Laboratory in Surrey, UK, where he ran research projects into online condition monitoring, intelligent data analysis, and explosive failure of porcelain clad bushings.

In 2002, he joined the ISIS Neutron Source Rutherford Appleton Laboratory, Harwell, UK, where [00:01:00] he was involved in caseated, high current, negative pinning ion source development. 2014 he formed the Low Energy Beams Group, Isis Neutron, and Muon, gosh, Muon Sores, the Rutherford Appleton Laboratory. This group delivers beam for Isis 24 7 operations, operates four accelerator test stands, and has extensive expertise in high voltage engineering, RF, vacuum, modeling, Large scale simulations, accelerator technology, and plasma physics.

Physics. He has collaborated with CERN Firm Lab, Batavia Illinois. US in, the us SNS. Oak Ridge. Oak Ridge the Los Alamos National Laboratory, the Chinese Academy of Sciences, IPP Garing. Wow. Dan, a lot of places and universities all over the world. He teaches at the CERN Accelerator School, the Cock Rec, Institute, and the Johns Adams Institute.

That is an amazing introduction. We are so excited to have you, Dan. And on that note, I will let you take over. Go ahead and share your screen. Thank you, Colleen, and [00:02:00] thank you for this great honor to talk at one of the TechX World Simulation Summits. Yes, so good morning, afternoon, good evening, everybody, wherever you are.

I’m going to give this is basically the talk I gave at the recent IonSource. conference in Vancouver last month. It yeah, that was held in Victoria sorry, rather than Vancouver on, yeah, September the 18th. And it’s about, some, the Something that we’ve long held close to our hearts in the Childe Langmuir equation and the Childe Langmuir effect, and it’ll be interesting to see how much everyone else knows about this.

I’m sure probably everyone has heard about this. It’s named after Childe and Langmuir [00:03:00] two Americans 100 years ago, came up with the theory of space charge limited extraction. And they were looking at, the charge the electrons being extracted from, hot filament, an electron emitting material.

And. They came up with this equation that defines the current density that you can extract from an electron emitting surface, and how it works the thing that’s limiting it is the space charge of the beam itself, so you apply a voltage. Between the anode and the cathode and that creates an electric field on the surface, the emission field, and that causes the electrons to start being pulled out.

And as the electrons pulled out, they have their own charge their own queue [00:04:00] and that charge that space charge cancels out the electric field and you eventually get to this self limiting the space charge limiting Maximum current where you can’t pull any more current out of the surface. Yeah if you solve the equations, you get this v to the three over two dependency of the extra, the current that you extract from an an electron gun is dependent on V to the three over two.

Now this formulation of this equation. Is one dimensional and they never intended it for it to be applied to ion sources. They only ever intended this to be applied to it for electron emission. So I’m not saying child like Langmuir effect is wrong. It’s just that how we’ve been applying it to ion sources for the last decades is wrong.

And as you’ll see, it’s just an [00:05:00] illusion. There’s no V to the three over two dependency. From when you vary the extraction voltage, on a single voltage sweep. Oh, this is what, sorry, I wondered why this didn’t do this. This is why I paused earlier. I thought I’d put this animation, but there’s the animation of it in.

I thought I’d added that in for you. But we’ve just talked this through anyway, so the assumptions, there are these several six assumptions really for the child Lang Muer. Equation to be true. And for I this is the these are all pretty much true for iron source for electron guns. But for iron sources, there are not infinitely many particles available to be emitted.

The particles do not have zero initial velocity. One good thing for at least they’re non relativistic in iron sources. They’re definitely not yet right relativistic. The electrodes are not infinite. [00:06:00] There is not a constant spatial distribution of particles perpendicular to the direction of the beam propagation, and there is not a zero electric field at the emitting surface.

However, even with all that stuff, we’ve been going on about this for ages. This is the accepted wisdom that ion sources, there’s two regions on a voltage, extraction voltage. Sorry, I’ll get a better pointer up. Pointer options, laser pointer, that’s a bit better. As you vary the extraction voltage, the current goes up, and this bit at the front.

Where it goes up, we like to fit V over 3 over 2 curves to this bit, and we call this the space charge limited region. And then eventually you get to this bit that is emission limited, the perviance limit, where you can’t get any more beam out of the plasma, we like to say. And here’s three different cases of three different, of a high plasma [00:07:00] density, a medium plasma density, and a low plasma density, but they all have this rise at the front.

And this is in books. And in fact, if anyone’s been to any of the CERN accelerator schools, I’ve been talking about this for the last decade as well. I, put these graphs up and talk about V to the 3 over 2. So yeah, there is our, dogma that in the space charge limited region, the extracted current varies of V over the 3, 2.

And as I said, I am guilty of putting these V over 3, 2 curves. There at NIBS is a recent example, the negative arm beam conference. Look, there it is. published a nice VOV to the three over two fit. There we go. There’s an ISIS a bit longer ago, but again, there I am fitting a V to the three over two curve to my data.

However, the true cause of this observed power law is not space charge limited extraction. It’s meniscus focusing and then collimation. On the extraction [00:08:00] electrode on the puller electrode. And we’ve recently done some work with the University of vascular to prove this. And we published this year just in July this year in plasma sources, science and technology.

And basically, we did some experiments and we did some modeling. They pretty much confirmed that the observed power laws is convoluted caused by meniscus focusing and collimation. I’ll just give you a brief summary of the experiments. So it’s a very simple, ion source. It’s a filament driven hot filament, arc discharge plasma, and it’s an argon plasma to keep the chemistry as simple as possible, single hole extraction.

And then. a gridded extraction. So instead of a hole, we just have, we had a grid. So that’s pretty close to trying to deliver on an infinite parallel plane extraction. That’s as good as we can [00:09:00] get. And then underneath that, the Faraday cup for measuring the Faraday cup, we had a segmented Faraday cup. So you can measure the divert.

You’ve got a very good. fundamental measurement of the divergence of the beam. And you can see here, the beam, as it hits different, the different, as you vary the voltage, the different, the beam gets larger and smaller as it’s focused, as the beam is focused smaller, as you increase the extraction voltage.

And if you add up all those segmented things, there’s no V to the three over two law there for the, currents. So experimentally, we didn’t see this this V to the three over two, when we look really closely, and we wanted to model this. Now, how do you model beam extraction from plasma? There’s two options, really.

There’s PIC codes, VSIM and then there’s all the ones that the universities and various collaborations and, people have developed over the years as well. But the problem has been to model [00:10:00] the meniscus, you need to resolve the Debye length because it’s the Debye length feature. So to do that.

For reasonable plasma densities, you need a tiny mesh density. But then… We go and extract over, say, 20 millimetres, and to maintain that mesh density over that distance is impossible. It’s not computationally tractable. Up until recently, it hasn’t been computationally tractable. Or the other option is, gun codes.

These are, Plasma equations coupled with tracking codes and IBCMU, I recommend, is used, developed by University of Uvascular and is open source, but there’s commercial ones, iGUN. But the problem with this is, these GUN codes, is do they really reproduce the plasma dynamics properly? Or there’s the combined approach, and this was recently done by us.

In our paper that we published earlier this year, this was what we did the previous year, [00:11:00] where you have a tiny little region where you model the plasma and then you model the meniscus and a bit of the propagation. You then pass the particles on the boundaries to a tracking code and track them across the rest of the gap.

And previously you’ve run the, your electrostatic GUM code. to work out what the boundary conditions were on your particle and cell model. So this requires parsing between models, but it does work and it works very well. We got really good comparison when we use VSIM and IBSIMU to do the tracking. You can see the positions of the meniscuses for different, three different extraction voltages here.

They’re very close. They both predicted Pretty nice jobs on, on, on the position of the meniscus. And you can see they, the experimental results measure, match very nicely with the IBCMU, pure IBCMU, and the pure and the, IBCMU [00:12:00] VCM combination. But the problem, Is that there’s still doubts with that really isn’t there?

Because when you’re combining models how do the models interact? And you’ve got to transfer the boundary conditions. How many times around you iterate the boundary conditions to be sure you’re right. Thankfully in the Vsim from the late Vsim 12 and I think Vsim 11, anyway, when it started in axi symmetric, you can have a variable mesh density, which is one of Vsim’s absolute killer apps, as it were.

It’s your USPs. It’s brilliant. No one else can do a variable mesh. And that’s allowed us to model the entire. Extraction, plasma, meniscus and tracking in a 2D3V cylindrical symmetric model. And we basically had a, it’s a cylindrical symmetric. So we had our plasma electrode. We had our plasma production region where we were literally just birthing [00:13:00] argon plus ion, plus one ions and electrons at a birthing rate.

And this was the only variable in the whole model. This was the only knob. You could vary the rate at which we birth particles. And what we did is that for a, for a two sorry, four KV extraction voltage. That is the voltage where all the beam goes through the extraction electrode, the puller electrode, and you measures on the Faraday cup.

And we use that. So there’s the point where we then set the load density in this in the model so that the beam current we measured matched the, the beam current that we measured in the in the in the PIC model matched the experimental and then we and then that’s all then we varied the, extraction voltage.

So there’s the mesh a very aggressive [00:14:00] go Change, but a smooth, a smoothly aggressive change, but that allowed us to get the plasma and the post gap of this, or the acceleration gap, the extraction gap measured in resolved in 383 by 448 mesh cells. So we basically just ran it. There’s the argon ions at the top and the electrons at the bottom.

And there’s three KV example here. And we ran it, until it converged, until it stabilized. So ran to equilibrium. And that was by about 25 microseconds in the model. That took about 16 weeks on a 32 core machine. But the electron energy distribution function, Was nicely resolved. You can see that it’s about one just under one volt plasma potential and you can see that little peak there on the electron energy distribution is there.

The [00:15:00] electrons are accelerated to the wall of the plasma chamber there. Anyway, we ran this for loads of different extraction voltages and recorded the total current, the beam current and the emittance. After the extraction electrode, and here’s the results. So for 500 volts, so we’ve got the top of the argon ions, and the bottom is the electron density.

Here’s the current, the blue is the total current emitted through the electrode. Plasma electrode hole. And then the red is the beam current as measured by on the back of the, model there as it’s got through the extraction electrode. And then down here is the emittance. And you can see as you increase the extraction voltage, the electrons are pushed back into the plasma chamber.

The meniscus, this is the emission surface where the argon ions are essentially turned into a beam from the plasma is pushed back to KV. 3 KV. We’re now starting to get to this [00:16:00] S ing, which we’ll talk about in a moment on the beam emittance. 4 KV was our matched case. 6 KV is our now over focused.

And 8 KV, we’re out the other side, now completely over focused. And the meniscus is pretty much into the plasma production region. There’s the data. That is our experimental data. Very nice comparison between the experimental data. There’s the IBC mu, so the gun code data. That’s pretty good. That matches very nicely as well.

You try and fit a V over 3 to the curve to that. If you squint and look sideways and hope for the best, you can, which is what I did all over these years, but there shouldn’t be a V to the 3 over the 2 curve there, really. It doesn’t fit. So how do you measure a true Pervians plot?

You can either, in the simulations it’s easier in that you just look for, you’d have to get the constant meniscus at each plasma At each extraction voltage, you would need to vary the plasma density. But [00:17:00] again, the plasma density is then different, so that’s not quite a true perviance plot.

Experimentally, you could look again, you could try and measure the point where it starts hitting the extraction electrode. So this is the current on the extraction electrode, so you could say that point there is the matched point, and therefore what you would put the V to the 3 over 2 curve on if you really wanted to fit one to it.

Okay, so moving swiftly on, as I know I’ve only got nine minutes left just looking at the emittance phase space S shape. We’ve got really lovely evidence now for what causes that S in the phase space. If we look again, this is just exactly the same results. This is at 500, 700 volts, extraction voltage.

You can see here’s the electrons bulging out the meniscus. But if you look at the, now we’re plotting here, the radial velocity, and that is what really defines the emittance of a beam. It’s how much the velocity outwards, be it [00:18:00] X and Y or radial or whatever, the radial ion velocity is the emittance, and you can see it’s got quite a high positive radial ion velocity here, because it’s divergent.

The beam’s very divergent. But as we increase it, What happens is very interesting. Here, this is the point it starts to happen. When the meniscus comes inside the plasma electrode, the corner of the hole, the outside hole of the plasma electrode, You can see the sharp pointy corner of it, and that creates, as you can see here, a blue on the bottom here, the radial electric field.

It starts to reveal itself, and that radial electric field is what gives the beam, you can see here, blue, a strong radial kick, and the emittance has just jumped up as well here, because you’re getting, you can just begin to see the start of this s, they’re very faint, but that becomes more clear, there’s the s, and you can see The larger field here [00:19:00] on the outside edge has been revealed more kicking down of the more s ing is caused by this.

The particles that are emitted from this part of the meniscus, they see a strong radial field and give it a real s shape to your remittance plot. And there we go, carrying right on six and then eight kV. And in fact, looking at it with no plasma, with the really high extraction fields, it’s the field is basically the same as if there was no plasma there at all.

The emittances cover match pretty well between, VSIM and the gun code. They at least follow the same sort of shape. The numbers are a little different, but not a million miles away. The temperatures, this is going back to one of the assumptions. Emitted with constant temperature, zero velocity.

Not only are they not emitted with zero velocity, as you increase the extraction voltage, that meniscus eats into the ambipolar [00:20:00] expansion from the plasma production region. And so the particles are emitted at different ion temperatures. As it eats into the ambipolar expansion of the ions, which is going up and down in the extraction voltage there because it’s a quite a nice little picture of it, of how the meniscus is pushed back into the plasma expansion region.

I tried varying the plasma density. This is just an interesting point that. On this rising edge, there is a very there is very sensitive to the plasma density. And in fact, as you increase the plasma density at 2. 3 KV, because it causes the meniscus to bulge out. Your then beam is more defocused, and you’re losing more on the extraction electrode.

And so as you increase the plasma density, the beam current actually goes down. The beam current drops and [00:21:00] drops because the beam is going further and further out. And you can just see these points here with them varying, that as you increase the plasma density down here, the beam current drops.

Whereas up here, as you imagine, the plasma density increases the beam current. The limit of 2D, so I’m hoping, so this was run on 32 cores, and I’m hoping, I haven’t yet got my models to scale onto all our, we’ve got four and a half thousand licensed cores, I’m hoping to be able to reach the higher current densities that will allow us to get milliamp, tens of milliamp beam classes, because obviously we’re interested in, say, 50 milliamp beams.

I am almost finished. There we go. I’m just going to show the variable mesh, which is now up and running. In, and then 3D model up and running as well, because I want to look at negative extraction, which is going to require magnetic fields and dumping of electrons. So in summary, the front end bit of a, of these [00:22:00] voltage current plots in iron source is not the child Langmuir charge limited extraction region.

It’s the divergence limited region. Now, I didn’t get a chance to show these at ISIS, but I did have some, oh, we’re hiring. Quick job advert. If anyone wants to come and work for us email me and I will, yeah we would love you to come and work for us. We’ve got two positions open at the moment.

I am open for questions as well. A couple of minutes, but I wanted to show you these videos because I didn’t get to show these. What happens at low extraction voltages? I worry about if these are physical because the by length is not fully resolved in the gap, but I get these beautiful movies at the top is the electron is the argon ions.

And at the bottom is the electrons. And at zero extraction voltage, the plasma, it seems to be blowing bubbles. It’s blowing low temperature bubbles into [00:23:00] the extraction gap. It, with zero extraction voltage. I’d like to hope this is maybe physical, but it could be because of a Debye length resolution problem, and I know that things do tend to blow up once you don’t resolve the Debye length, and here it is with a hundred volts.

A hundred volts is essentially suppressing the electrons back a bit, but it still tries to blow bubbles, which is very sweet. Still blows these little rainbow bubbles of cold ions. There they go. And I didn’t show this at the conference and I’m glad, but here we are amongst Pick friends.

So you can maybe tell me that is non physical. But yes, thank you very much. I am open to questions. Yeah. It looks like we have a few and if anyone has questions, you can type into the Q and a box on the bottom of your screen. Oh, okay. Shall I answer those? I see. And I’ll, if you want, or I can read them to you, it’s up to you, whatever’s easier.

Okay. So the audience, so I’ll do the [00:24:00] first one. It just says, does your. Extracted space charge screens does your extracted space charge screens applied voltage? If it does, you get CL. Does your space charge screen the applied voltage? Yeah it, it, does. But yeah the if you don’t get child Langmuir because at zero extraction volts, you still have a current.

So it’s, there’s no child Langmuir really from plasma. Extraction. And then there’s a second one again from Igor. Have you tried using Pierce focusing electrodes to remove the S shape? So in, in, practice, yes, we have, but I am still, so we built Pierce electrodes for our Penning negative minus source.

And we did improve the emittance. And we did have problems with overheating electrodes because of [00:25:00] the electron current. I haven’t yet tried it. I’ve got a whole load of things I want to try with the PIC model and that is going to be one of them. I want to shape the plasma electrode. I want to try all this stuff.

So it’s going to be very interesting to look at. And then, Joseph says, thank you. Angie. Oh, sorry, Colin. He said, thank you for the amazing presentation. And you are in Istanbul and being so gracious, but we have a whole crew of people here in Colorado that have really enjoyed this and you haven’t, we’ve been on mute, so you haven’t heard it, but this has been a fantastic presentation.

And so there were some, Oh, glad you enjoy it. Good. It is nice to see this presentation. Do you think pierced geometry and rounding the edge of the PE could eliminate the S shape of the emittance? Yes, I think it will have a good effect. But what is so interesting is as whatever shape you’ve got, and I want to try a 4.

45 [00:26:00] degree on angle on the outside of the plasma electrode. I want to try a curve and I want to try a pierce, angle on there as well. It’s gonna be because you can’t, what happens is as the meniscus recedes

inside the plasma chamber. The electrodes are revealed. And so whatever electrode shape you’ve got there is is going to cause a, if it’s got some tangential field, it’s going to create some focusing, which will affect the emittance now. If you design your ion source to only work at one extraction voltage, then you can design whatever you like.

But as is shown, if you try varying that extraction voltage, that the root point of the meniscus will just work its way round whatever shape you’ve got. You’ve, made the exterior geometry of your [00:27:00] plasma electrode shape. So yes it’s really interesting. I’m looking forward to experimenting with different geometries if it can be optimized in different ways.

And then

a couple of questions, please. Ah then John Kerry wants to ask you some questions directly. Yeah. First of all, wonderful talk. Really enjoy it. It’s always been great to work with you over the years. So what’s your maximum grid variation? And how many iterations did the Poisson solver take to converge?

It was quite a brutal grid variation actually there, John. I wanted to go as brutal as I actually possibly could. Like I wanted it to be more brutal. Actually, I wanted to go over a couple of orders of magnitude. So yeah, it’s going over four to four microns to 500 microns. So that’s going over.[00:28:00]

Yeah, it’s going over two orders of magnitude, the change in the mesh density there. Yeah, I and how many iterations did that take to solve? This was running on vc, I think this was doing on, was this running on 12? I think it was running on version 12. I’d have to have a look, John, I’ll email you.

But I think it was… To tens hundred something like that. I think I’ll have to have a look. We noticed that when we get more grid variation, the convergence number of iterations to convergence goes up. So I’m curious to see what you’re experiencing, but still, even at 100. You have a large number of particles per cell.

It tends to be small compared to the product mode. Is that still true for you? Yes. Yeah. Yeah. So to get to the plasma densities that I’m trying to get to, which is what I’m targeting, the really high plasma densities. You’ve got so many particles to get the statistics [00:29:00] in the, electric field.

Yes, I’ve got the, particle push step is still a significant chunk of the, solve each step. Yes. I’ve just got two more things and I promise I’m not going to take too much of my privileged position here to keep asking you questions because we can always communicate later.

But, yes, very much to the new decomp when you get 12 to 1, you’re going to be able to improve your speed much faster because of the particle load balancing, which the guys here worked hard on getting. So I look forward to your experience with it. The knee in the transition that you see you have a lower part where it slopes up, then you have a part where you are space charged.

If I were to believe the red curves and the red dots, can we remove that Q and a or move it aside if I were to believe the right guy? [00:30:00] So the red if I were to believe Those for the beam then, you know the lower part where it’s coming up almost parabolically I don’t know what that regime is, but the next regime where it shoots up real fast that’s of course space charge limited and then over on the right you’re getting into the emission limited regime right because when you put more voltage on it, you can’t get any more.

So that means you’re probably emission limited. At least that’s what we find in another case. So that’s the preface to this question, which is that if the knee is the transition from space charge limited to emission limited, couldn’t you look for it by saying, Hey, where is my current equal to my birthing rate?

I love the birthing rate term, by the way. But whatever you call it, it’s the emission, yes, yeah. The emission rate, but the birthing rate is nice. Gives it a human character. There is no [00:31:00] child Langmuir. It doesn’t seem to be space charge limited. This is the, emission divergence limited.

It is It is because the beam is so divergent, because of the highly prolapsed meniscus, the highly, convex meniscus, that you then collimate it all, and so this front bit here is not child Langmuir, this front bit here, Is focusing meniscus focusing and collimation on the puller this bit here and even if you were to do it with full grid extraction, you can attract everything extract everything.

You still don’t see any V to the three over two. There’s no child Langmuir on the plasma, not in this regime anyway, not in this iron source currents and densities. [00:32:00] Okay thank you for. Very much. It was a very inspirational talk, which caused me to think about this problem a lot more. So thanks again.

Pleasure and thank you for having me and I’ll happy to talk to anybody. Email me whatever set up meetings and I’m really looking forward to carrying on this work with Tech X. It’s we’ve got a lot of great stuff coming up in front of us. I’m very excited. Hey, Dan, this is Seth Weitzer. I just had a really quick question for you.

How are you defining the the edge of the meniscus? Is that some small percentage of the average plasma density? Or is that two sigma from the from the density? So there’s beautiful. How am I defining the meniscus as in how am I plotting it or how am I finding where the edge of the meniscus is? Oh it’s different.

So there’s different ways you can plot it. So you could plot, it as the zero potential equi [00:33:00] potential line. You could plot it as the you could plot it as, here is the electron density. And of course, as the electron density gets higher and higher your Debye length is so short, the meniscus is, so it’s pretty much where the electrons stop.

You could do it, you could do it looking at the electric field. You could do it looking at the plasma potential. So yeah, the voltage. I quite like the meniscus being defined as the point where the voltage equals zero or sorry, the voltage is the same as the plasma electrode voltage. So if you take the plasma electrode equipotential.

And plot that I’d call that the meniscus, I think it’s a Dubai length and you’ve got this. I’m looking forward to studying this pre sheet. There’s a lot of theory that people have gone into it, and I’m actually a simple engineer. I’m actually electrical engineer, so I’m not. I don’t understand the [00:34:00] plasma physics.

Really? I’m just doing this with brute force computational stuff. And I look forward to just seeing what I see. And I’ll happily define the meniscus how anyone wants to define it, but I think it’s a zero volt equipotential open to discussion. Thank you so very much, Dan. We really appreciated this.

That’s all the time we have for questions today. We are going to take a brief break and we will be back in about seven minutes with our next talk. All right. Thank you. Thanks everyone. Bye.