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Benjamin Alexander Jorns: Well, welcome everyone to the early career lecture for mitzi it's a great pleasure to introduce a personal friend and colleague of mine, Dr justin little who's an assistant professor in the aeronautics and astronautics department, the University of Washington.

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Benjamin Alexander Jorns: Dr little has a had an impressive career to date working formally as a private company exploring alternative methods for propulsion and transitioning a few years ago to the University of Washington.

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Benjamin Alexander Jorns: He received his bachelor's degree from the University of Colorado California Irvine and a PhD from princeton university mechanical and aerospace engineering.

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Benjamin Alexander Jorns: Dr little has quite a few research interests, but in particular has been focusing on looking at low temperature plasma physics and how that ultimately influences the performance and design of novel electric propulsion technologies.

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Benjamin Alexander Jorns: Particularly is doing some very exciting work looking at data driven methods to explore, among other things, mode transition to so we'll be talking about today.

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Benjamin Alexander Jorns: among his many accolades he's a former recipient of the national Defense science, engineering graduate fellowship and the sag and is a current recipient of the air force our young investigator program award.

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Benjamin Alexander Jorns: So without further ado i'd like to turn it over to you justin please uh please take it away.

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Justin M Little: Thank you Ben.

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Justin M Little: Thank you for the wonderful introduction I believe I need.

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Justin M Little: To be able to screen share.

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Justin M Little: Right now, I have it disabled.

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Justin M Little: And, and also thank you, this is a great honor.

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Justin M Little: So thank you to the the.

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Justin M Little: Michigan Institute for plasma science and.

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engineering.

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Justin M Little: The creative, as of today and.

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Benjamin Alexander Jorns: look forward to.

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Justin M Little: sharing this talk with you Okay, so I think you should be able to see my screen now.

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Justin M Little: And so today's talk is going to be on both transitions in low temperature aerospace plasmas and to send this talk up this is really kind of motivated from something that i've observed.

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Justin M Little: towards the later stage of my graduate degree, and so I was probably a year for so of my PhD and I had built an experiment.

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Justin M Little: In order to test some of the theory that I was working on at the time, and so I constructed this experiment, I put it in the vacuum Chamber and I turned it on.

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Justin M Little: And this is what I ended up seeing and what we see is a very low density diffuse plasma very weak I didn't have any sort of signal on my diagnostic probes.

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Justin M Little: And I as I turned the the novena magnetic field eventually this this moment occurred, where this bright plasma formed and I was able to get signal and, ultimately, I was able to do a science that I needed to in order to complete my degree.

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Justin M Little: So there's sort of Let there be light moment kind of formed the basis of my.

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Justin M Little: Research in my PhD and I only did a research on the plasma that occurred after that moment, however, I was always very interested and fascinated by why the plasma would transition so abruptly from one state to another state.

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Justin M Little: And so what what I was observing here is referred to as a mo transition and, if you look in the literature there's not a very clear definition of mo transition, so I kind of came up with my own here.

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Justin M Little: And when I talk about transition i'm going to be referring to a sudden major transformation of the structure and dynamics of a plasma.

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Justin M Little: In response to a minor change in its operating conditions, so the plasma should have previously.

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Justin M Little: minor change in the magnetic field, the background minute field induced this major change in the structure of the plasma.

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Justin M Little: And transitions there they're commonly observed in plasmas both low and high temperature so One example is plasma processing in where.

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Justin M Little: rf plasmas exhibit know transitions from a capacitive Lee coupled state to an inductive a couple of state where.

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Justin M Little: This transition on the bottom shows is increased the coil and my or the current in my rf coil eventually that transition is going to occur so small increase can drive rapid increase in density.

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Justin M Little: In magnetically confined plasmas they they also observe mo transition from what's referred to as an elmo to an H mode.

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Justin M Little: So this is something that's very important in the operation of Tokyo Max.

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Justin M Little: And what's occurring here is, as you increase the amount of power that you're driving through your plasma starts to heat up and eventually at some point.

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Justin M Little: There is a transition where turbulence, which forms near the plasma edge is offset by sheer motion in that region.

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Justin M Little: And so you trade off this turbulence, with a sheer motion and, eventually, you can form a very steep density gradient at that edge, which creates something referred to as an edge transport barrier and you're able to.

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Justin M Little: operate within this high confinement mode and so there's a very rapid transition between those two regimes.

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Justin M Little: hall thrusters are another great example of mo transitions and, in this case it's the dynamics of the thruster which exhibit a transition.

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Justin M Little: So if you're operating in a certain mode at a certain current and voltage, as you can see in the bottom plot here, and you turn up the magnetic field.

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Justin M Little: Well, the oscillations go from a global mode, where the entire discharge channel is pulsating to a more local mode where you see these spokes.

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Justin M Little: Essentially rotating through the Channel of your actual devices so there's a very interesting transition that occurs with the operating parameters of a whole thruster.

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Justin M Little: hollow cafes which are also used for electric propulsion plume neutralization exhibit mode transitions from what's referred to as a spot mode this upper left hand picture.

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Justin M Little: To a blue moon, and this blue mode is characterized by the onset of strong oscillations as well, and those oscillations.

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Justin M Little: need to be understood in order to design and properly understand how the system operates with power supplies, for instance.

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Justin M Little: And so characterizing the transition between this spot building this blue moon is an important driver of designing.

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Justin M Little: Engineering systems for use for electric propulsion and so it's this relationship between these interesting physics and he's interesting transitions and how we ultimately go about designing a system around physics.

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Justin M Little: So my research is going to cover three topics, so the research side presenting to you today.

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Justin M Little: And the first topic is related to the video that I showed where we observed a mode transition in our silicon thruster The second topic will be related to this concept referred to as plasma magneto show arrow capture and we've discovered recently.

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Justin M Little: A theoretical velocity at which remote transition occurs and enables these systems to operate effectively in their design application.

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Justin M Little: And then finally i'll end with a discussion of some new techniques that i'm looking at that I think provide a powerful new lens with which we might be able to look at and mo transition physics.

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Justin M Little: So let's start with the beginning and motor it and discuss mode transitions in silicon thrusters.

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Justin M Little: So this work was done, as I mentioned earlier, at princeton university, where I was a PhD student and what we have was a healer can Forrester, that had a spiral antenna.

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Justin M Little: At the rear of the district channel, so this is shown in the upper left hand corner here and that spiral intended injects rf energy into a gas that we introduce into our plasma source.

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Justin M Little: The rf energy breaks that gas down and it forms a plasma and the idea here of a silicon thrusters to then expand and accelerate that plasma through a magnetic nozzle and that allows us to obtain.

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Justin M Little: thrust from that, and so this was mounted inside of a large vacuum Chamber that we pumped down using the fusion bumps.

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Justin M Little: And the goal My thesis was mainly to understand how plasma expansion and detachment from the magnetic nozzle occurred, and so I won't go into those topics in detail today, those were the main topics into PR papers that I published one in 2016 and one in 2019.

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Justin M Little: But, as I mentioned, I was always curious about these mo transitions that we were seeing and these these were things that had been observed.

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Justin M Little: In the literature and there's there's a wealth of literature on this subject, but I wanted to to really understand how that.

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Justin M Little: phenomenon mapped back on to the design and operation of a propulsion systems, specifically.

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Justin M Little: And so i'm showing here three different modes the E mode or the capacitive mode the H mode or the inductive mode.

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Justin M Little: And the w motor the healing mode and for electric propulsion you really need to operate in this w mode, because it gives you the highest ionization percentage.

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Justin M Little: And the other two modes are not ionizing all of your propellant that means you're not accelerating at all, and so you have a low mass utilization efficiency.

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Justin M Little: So the w mode has the highest ionization efficiency, it has the highest density is as well, and what we observed, is that our w mode in this specific experiment was occurring for very low.

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Justin M Little: currents in our magnet so a low background magnetic field and so that's what this this.

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Justin M Little: plot on the right here shows, and so, eventually, as we turned up the magnet current we would transition either into the mode, or sometimes directly into the mode as well, so we can only turn up our magnetic fields so much before we lost this desirable w.

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Justin M Little: And the fact that this the transition or the silicon mode was observed at low magnetic fields that something that's supported by the literature so Chen and the floor did characterization of E liquid plasma source where they saw this mode occurring at low magnetic fields.

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Justin M Little: However, it's a very interesting phenomenon and something that's important to understand for electric propulsion applications, because, as you increase the magnetic field.

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Justin M Little: You reduce the amount of plasma energy that's lost to the wall so magnetic field helps you control the diffusion within your device.

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Justin M Little: And so you want to keep that plasma away from the wall and the magnetic field allows you to do that, and so this plot on the right here is for a helix thruster.

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Justin M Little: And it shows the thrust on the y axis first the magnetic field current or the magnetic field strength on the X axis and they see that Okay, as you increase the magnetic field you're increasing the thrust and, eventually, you can approach this Green theoretical line here.

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Justin M Little: So the idea is you want to increase your magnetic field, however, if you have this phenomenon, where you transition out of the desirable wave mode with increasing field.

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Justin M Little: Then you're moving away from a regime where you're able to operate a thruster efficiently, so the physics here are tied to the engineering.

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Justin M Little: And so the question that I wanted to answer was how does the mo transition field strength scale with our thruster parameters, because those that's ultimately at the end of the day, what we're trying to use to design a system.

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Justin M Little: And I use data that I took during my PhD and I ultimately analyze this data it took me, I think, five years to finally come back to it, but I ultimately found that.

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Justin M Little: I was.

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Justin M Little: pretty good at record keeping, and so I kept a record of the mo transition field strength as a function of the power that I was putting into the thruster and also the mass flow rate.

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Justin M Little: And so I had this database available to me, and I had that database available for multiple configuration, so in this experiment i'm.

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Justin M Little: Ultimately, varying the back plate location of the thrusters so I can change the length of the thruster discharge channel, and so this was a capability that I built into the thruster that ultimately allowed me to have greater flexibility on.

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Justin M Little: The operation of the experiments that he's see that different lengths here in the pictures in the upper.

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Justin M Little: upper portion of the screen here, and then the mo transition field strength data in the lower portion and so, in general, we see an increase in the mo transition field strength as we increase power.

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Justin M Little: And then we also see an increase, as we increase the mass flow rate.

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Justin M Little: And so we have this idea that okay now powers, allowing us to push this this magnetic field further and mass flow rates allow us to push this magnetic field further so what's going on here.

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Justin M Little: One thing to point out, too, is the when we look at the literature, the maximum magnetic field that has been seen for this low field.

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Justin M Little: Wave mode is around 100 gals and, in our case we're seeing magnetic fields this mode being sustained that magnetic fields upwards of 800 cows or so so we're going to understand that as well.

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Justin M Little: So our specific problem was to really understand how the mo transition field strength scales.

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Justin M Little: In the presence of a converging magnetic field so here the the magnetic fields converging towards the exit of the device, and we have this spiral and.

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Justin M Little: The literature oftentimes You used a different Internet geometry, and we had a a different geometry compared to what's been observed before that's kind of our guiding criteria here for trying to understand the field strength.

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Justin M Little: So if you want to model mo transition in the plasma that's something that's it's actually a fairly well known process and.

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Justin M Little: I encourage you to look at the text physics of radio frequency plasma, if you want to learn more and basically you can you can understand mo transition in an rf plasma.

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Justin M Little: by completing the rf absorption mechanism, a model for the rf absorption to a global model for how your plasma is operating in her case we have a thruster so we have.

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Justin M Little: The propellant being created, we can heat it and then eventually expand, so if we can couple the rf absorption to a global model of the thruster we should be able to model, the transition.

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Justin M Little: So i'll step you through how we do that for this specific system so rf absorption is modeled by looking at the.

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Justin M Little: dispersion relation of the waves that are created by the antenna within this w mode and so this is some of you might recognize this as a dispersion relation, for a whisper with in the presence of some sort of conditional damping where the damping is given by this new effective.

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Justin M Little: gilligan's our whistler waves in bounded plasma.

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Justin M Little: And we can model, the effective collision frequency and this is, according to the reference by Chen as the son of just collisions due to electrons and ions.

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Justin M Little: and also a wave induced collision frequency, so this is basically an effective collision frequency due to land out damping of the wave by the electron population within the plasma.

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Justin M Little: So we can apply that model and plot, the effective collision frequency versus density that's what we do on the right hand side.

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Justin M Little: And look at the variation of that curve with magnetic field, and we see this kind of shark fin.

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Justin M Little: structure to our curve where that shark fin comes from this wave damping mechanism.

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Justin M Little: And as we increase the magnetic field strength that fin shifts to higher and higher densities.

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Justin M Little: Well, when we super impose the this effect, using a model for the absorption of plasma through this collision effect with a loss curve for the losses from our plasma, which are generally expected to scale linearly with the density we get the following curve.

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Justin M Little: So here we're showing power on the y axis density on the X axis and what we see is that, under certain conditions there's three.

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Justin M Little: intersections between these curves the green intersection here might represent some sort of capacitive mode, whereas the blue intersection would represent a wave mode where effectively coupling energy into the with the wave absorption mechanism.

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Justin M Little: This red dot that's not a stable mode, because the slope of the of the difference between a Boston the absorption curves is in the wrong direction, so can operate stable in that mode.

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Justin M Little: This is for a certain background in that field and, as I increased the background magnetic field, I see that sharkfin start shifting to the right and eventually I lose the ability to sustain the plasma at a high enough density.

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Justin M Little: With the wave mode of operation, so we see a w E mo transition occurring, and so we only have one stable mode of operation for this device.

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Justin M Little: Well what's happening here is, as I increase the magnetic field strength, the phase velocity of my healer con wave or this with whistler way it is increasing.

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Justin M Little: and eventually it's moving so far in velocity space that I no longer can couple The wave energy to the electron population via land out damping so that's what's occurring.

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Justin M Little: I can no longer positive energies into my electrons in order to sustain the plasma at the higher densities, that would be required.

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Justin M Little: So we can take this view of mo transitions and he look in thruster and apply it to the case of a.

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Justin M Little: spiral antenna thruster and what we ultimately need to do is pull out a relationship between the maximum.

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Justin M Little: magnetic field that we can operate in the w mode and the parameters of the plasma and that's what I show here in the bottom where.

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Justin M Little: The maximum.

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Justin M Little: Wave absorption occurs at this be APP which depends on the density and the electron temperature and the the geometry of the device.

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Justin M Little: And on the upper right here what I show is these kind of stable modes were at a given magnetic field strength, I will the intersection of those curves can exist at a certain location.

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Justin M Little: And so, lower magnetic fields that can be in both this E w Mons adventures I increase the magnetic field.

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Justin M Little: It transitions out and this be star that's really what I was observing when I plotted that experimental data, so I wanted to understand how this be start.

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Justin M Little: relates to the operating parameters of my device so Now I understand how the star relates to the densities, and the temperatures.

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Justin M Little: Well, I don't really know those are priori so I need to invoke a global model in order to relate mass flow rates powers, etc, to those parameters and so that's where the mass flow, where the global model comes in.

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Justin M Little: And this is really just an exercise and accounting of energy and power of power and mass within the the discharge channel.

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Justin M Little: So we can write out our power loss equation, as the sum of kinetic power exhausted into our propellant particles, the amount of power of the news to the wall.

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Justin M Little: and also the amount of power that we're putting into just creating the Ionized particles in the first place, and so, when we apply that power loss equation, to the overall power balance we can also invoke a mass balance that brings in the.

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Justin M Little: reaction rate for ionization.

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Justin M Little: We apply and approximations to this function here, which I call F F, which is function of tea, which is.

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Justin M Little: Basically, the square root of tea over the reaction rate as a function of tea, and when we apply that approximation, we can solve for.

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Justin M Little: An equation for the electron temperature as a function of the parameters of the experiment so that's what's shown here on the right.

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Justin M Little: And so I can combine those two results into a nice neat equation for be star, which is equal to some constancy one which depends on the on physical parameters.

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Justin M Little: And then we have a linear dependence on the rf power i'm putting into my plasma and a dependence on the mass flow rate to the one over and we're and comes from this fitting.

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Justin M Little: We also have the geometry dependence, so the radius of the plasma appears in this and then also a mass dependence on our ions.

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Justin M Little: So we have no way to predict where this mo transition is going to occur as a function of the parameters of my system, and so I can re scale.

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Justin M Little: The data that I showed previously using this lens of being able to understand what this mode prediction might be so.

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Justin M Little: here on the left is be not star as a function of prf so the power and putting in for my different cases.

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Justin M Little: Where here i'm not really distinguishing between the different mass flow rates, this is just the raw data, and when I re scale this X axis.

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Justin M Little: To be now as a function of prf times and L to the one over N, which comes from the scaling law that we arrived, we see that, now that the different colors start to collapse on to one curve which.

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Justin M Little: is promising and it gives us an indication that Okay, maybe are scaling law is correct and then, finally, when we correct for the fact that we have a diverging magnetic field.

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Justin M Little: And so the field near the antenna is different than where the field is at the Center of the magnetic coil we get the following curve and all of these data sets collapse nicely onto a single line.

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That.

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Justin M Little: Ultimately, overall governs how this transition is going to proceed according to this this theoretical model that we've developed.

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Justin M Little: So what this tells us is it suggests, at least, that the transition is occurring in this plasma when land on damping of our way of energy, so the.

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Justin M Little: antenna induces a way of in the plasma in that way of is deposited its energy into the plasma through land damping well when that can no longer that process can no longer be sustained, then the plasma can no longer be sustained in this mode.

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Justin M Little: And so that's ultimately what we discovered through the application of this theoretical model to the experimental data.

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Justin M Little: So we can apply this to other systems as well this isn't something that's unique to our F power supplies or a plasma supplies or rf thrusters.

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Justin M Little: And this is something that came up recently in our theoretical analysis of a concept referred to as plasma to capture so let's discuss that now.

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Justin M Little: So there's been numerous proposals that seek to develop technologies that use the force of a Ionized flow against the magnetic field in order to generate forces and thrust, in particular so magnetic sale sale is one example where.

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Justin M Little: A spacecraft would deploy this large magnetic coil form a big magnetic field around the spacecraft and then ultimately use.

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Justin M Little: The the flow of the solar, wind and then the charged particles that are in the solar, wind in order to essentially propel itself through space.

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Justin M Little: Well, one of the big challenges with this concept is you need a very large coil with a very large magnetic field.

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Justin M Little: And so it would require on orbit construction of the device and really prohibitive costs another concept was put forward called the plasma magnetic sell or end up to.

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Justin M Little: Where instead of having the magnetic field being generated by coils the magnetic field would come from currents that were induced in a plasma.

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Justin M Little: And so the idea here would be that you'd be able to essentially inflate this plasma, which would then allow currents to be driven through it and create a larger magnetic field, and you might be able to use a physical coils.

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Justin M Little: But this was very sensitive to the the your ability to such a hold on to the plasma particles, as the plasma particles diffused away you're in the same challenge of need to provide significant amounts of energy in order to sustain a large scale magnetic field at this time.

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Justin M Little: So instead of using this concept for thrust a new concept was proposed by Dave curtly who's a Michigan alum and actually want to Dean Gala moore's PhD students former PhD students.

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Justin M Little: and basically what Dave proposed was well you know, there are other applications where a magnetic field can be used in order to generate forces on a system in space and one application came to mind was in breaking.

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Justin M Little: So breaking a spacecraft or slowing down a spirit spacecraft near a target destination is a significant challenge, and one of the byproducts of that high speed interaction between the spacecraft and an atmosphere.

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Justin M Little: Is a plasma and so the concept of plasma magneto shows leverages that interaction and actually augments it in order to generate more drag on a spacecraft in a planetary atmosphere.

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Justin M Little: With the ultimate goal of performative maneuver called arrow capture where you go from a hyperbolic orbit into an elliptical orbit around target destination.

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Justin M Little: And so, this was a nyack funded effort in 2011 and eventually that got funded through a phase two award and that's where my exposure to this concept began when I was working in Ms and w under that award.

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Justin M Little: And it provides a very interesting physical problem and physical system to analyze from a basic physics point of view.

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Justin M Little: So, just a quick recap, of what a magneto Shell is it's effectively a plasma parachute that allows you to arrow capture at high velocities where that arrow capture concurrent lower densities compared to arrow shells.

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Justin M Little: And in the night Program.

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Justin M Little: What they ultimately did is they performed theoretical modeling mission analysis and they found a lot of very promising results.

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Justin M Little: So, for instance, and Neptune orbiter and they found they can put 1000 kilograms orbiter in orbit around Neptune at Mars, they could put 16 metric tons of payload in orbit around Mars.

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Justin M Little: And a lot of this is enabled by the fact that your arrow captured at higher altitudes or lower densities compared to physical systems and what this allows you to do is it significantly reduces the thermal protection system requirements so you're trading off tps.

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Justin M Little: For the magnet basically and if the mass balance in the power balance of that trade off tips in your favor well this might be a good option for certain missions.

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Justin M Little: They also performed proof of concept tests or they put a basically a magnetized plasma in front of a am PDT thruster balloon.

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Justin M Little: And they saw using the thrust, in that they saw in 1000 times increase in drag over just the aerodynamic track of what they were putting in front of the stamp so very preliminary results that were shown tremendous promise for this technology.

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Justin M Little: So one of the things that I became interested in is modeling the system from an analytical perspective, and one of the early models, the original model that currently put forth.

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Justin M Little: It had a lot of room to grow, it was a very simple model that was mainly designed to to understand some scaling some early scaling see if the numbers were in the right ballpark and see what sort of forces were generated and so.

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Justin M Little: He had to make a number of different simplifying assumptions so some of those being that the magnetic field wasn't really a physical magnetic field that had certain layers to it, the plasma was just sort of the cylinder with a fixed access aspect aspect ratio.

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Justin M Little: particle trajectory effects weren't modeled and the drag area was modeled in sort of an ad hoc manner, based on the radius at which a certain alarm or radius would occur and then finally mass and energy transfer wasn't fully fleshed out.

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Justin M Little: So that the question that I wanted to answer was related to this last topic was how well is this my needle shot utilizing mass and energy from the flow.

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Justin M Little: So, from the perspective of the magneto Shell, the atmosphere is flowing at very high speeds against this magnifies plasma, are we effectively utilizing this mass and energy.

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Justin M Little: And so we developed a model that.

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Justin M Little: Basically added in additional effects, and so we modeled this as a dipole magnetic field.

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Justin M Little: Where the plateaus and dipole equilibrium so there's specific equations for equilibrium of the plasma within a dipole and we kept track of different particle trajectories, as I mentioned in a minute and we developed a self consistent drag with full mass and energy transfer.

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Justin M Little: So i'll describe to them to describe this model and, ultimately, how it leads to an interesting transition reminiscent to what we saw in the rf plasma.

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Justin M Little: So, as the the particles come in to our magnet here they're going to have a certain probability of ionizing a different location, with respect to our magnet.

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Justin M Little: And depending on where that Ion is created it's going to exhibit a different trajectory in the presence of the magnetic field, so we modeled that trajectory using just just the very simple equations of a charged particle on the magnetic field, and this is where the first.

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Justin M Little: Important dimensional paramor comes out where it's the an effective warmer radius which is shown here in the lower left hand corner.

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Justin M Little: And, depending on what that dimension was parameter is the nature of those deflections change so i'll walk you through a few different collections here, where, if a particle is born.

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Justin M Little: In front of the magnet but you know quite a bit away from it radial able deflect a little bit as we get closer that deflection becomes more strong.

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Justin M Little: Eventually, it kind of exhibit some strange angular rotations as we become online with the magnet and actually bounces off the magnetic field reflects back towards the original source.

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Justin M Little: And then eventually as we get closer and closer to the magnet eventually the particles born into these traps orbits are these confined orbits where it just orbits around the magnet.

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Justin M Little: And so here's another one shown here there's a.

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Justin M Little: kind of a peculiar feature as you go further out where those trapped orbits turn it into kind of these back and forth orbits that are kind of reminiscent of banana orbits and token X so they're also trapped, but in a different way.

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Justin M Little: And then eventually we get back out into a region where they're deflected so we took this single particle picture and we built up a map of what the particles did as a function of.

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Justin M Little: Where they were created and should be more specific, what the final velocity of those particles, the final Axial velocity doesn't have those particles were as a function of where they were created and that's what this map here shows.

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Justin M Little: So basically, this is a map that shows what the deflection was.

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Justin M Little: as a function of where the particle was created and what we see here is there's one magnetic flux surface that's what this five star star is that is a mark.

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Justin M Little: of where the boundary between trapped particles and deflected particles occurs, and so this is going to become important because we use this flux surface as a control volume when we're doing our mass and energy balance within the overall system.

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Justin M Little: So what's the point of theory if I can't put people to sleep during talks I think this is the most equation intensive slide that I have all try not to dwell on this one too much.

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Justin M Little: But basically we we have a model for how the particles deflect based on where the form, but we don't have a model yet where particles or form yet.

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Justin M Little: And so that's where the continuity equation comes in, we do a continuity equation for our stream neutrals that are coming into the system and we can make a number of assumption assumptions and put it in this very easy simple form, where the.

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Justin M Little: The neutral density or Stream is known and a little analytically everywhere, as a function of this ice of N, which is just dependent on that note topology and the distribution of our.

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Justin M Little: plasma density and then also this other dimensions parameter that appears, which we call data total.

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Justin M Little: Which is basically the ionization frequency over the frequency at which neutrals will transit our magnet so as ionization increases, we would expect more reaction to occur, and so we would expect the interaction between our flow and the plasma to be stronger and so these weeks.

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Justin M Little: actually appear in the upper right hand plot when it when we plot this function, where, as we increase this data total we're increasing that interaction we're increasing the reactivity, and so we have a larger region over which this awake forms.

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Justin M Little: As I mentioned, we we've identified a boundary where we can.

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Justin M Little: attribute particles that are Ionized to the plasma itself so it's trapped within a current it's Ionized and undergoes a trap orbit that means it's going to.

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Justin M Little: Essentially, be around our magnet long enough to equilibrate thoroughly with the plasma existed there that's kind of the implicit assumption that we're making.

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Justin M Little: And so it's equation here and CAP that's just the rate at which we're adding particles to our plasma so it's basically those particles that are forming within this size star within this magnetic flux surface.

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Justin M Little: And so, once we know that we can also know the amount of power that's captured by the plasma because that's just equal to the kinetic energy times, the rate at which particles are trapped and the nice thing about this formulation is, we can.

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Justin M Little: Ultimately, reduce this to an analytical expression for the capturing of particles and power which depends only on these two dimensions parameters ro L and xena total.

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Justin M Little: And there's this function here I assign which is just a an integral function, and we can characterize easily because that's what's shown here is what the capture rate of particles is or power that's the function of these two dimensions parameters.

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Justin M Little: So we see the kind of interesting behavior where for a specific llama radius that the.

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Justin M Little: amount of power flow that we can capture increases reaches a maximum and then rapidly falls off so what's occurring here we can look at a few different points so highlighting green this maximum.

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Justin M Little: So that's occurring when the kind of the region of the wake this sort of cloud erosion of the way that's where a lot of the reactions are being driven.

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Justin M Little: Well, and that's bordering the magnetic flux surface that essentially divides track particles from those that purely deflect when that borders that are capturing the most particles, that we can buy our magnetic field.

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Justin M Little: knows I increase the reactivity, for instance, by increasing the density or increasing the temperature I fall down this curve, and so what that means is this 10 to the minus second.

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Justin M Little: curve that i'm showing here, marked by red that's being fully shadowed by the wake that's being formed by this process and so there's no reactions that are critics in this trapped region and so i'm not actually capturing the flow particles or energy by my plasma.

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Justin M Little: And so, this is ultimately going to become important when you consider the operating mode of this specific concept.

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Justin M Little: So to go back to the question of how does the magnate need a new show utilize mass and energy from the flow again we look at a power and mass balance, similar to the.

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Justin M Little: The case of the rf thruster.

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Justin M Little: So in our paper what we ultimately balanced was the power captured from our stream controls, we had a term that was representing the injected power into our dipole plasma.

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Justin M Little: And then, when you rearrange the the rate rate equations for for power for the different species, where you get as a term that represents the diffusion of electron thermal power from their control volume.

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Justin M Little: You get an effective lost due to ionization and effective loss due to the net diffusion of Ion and what we refer to a secondary neutral powers, because are neutrals that are formed in the in the control volume and eventually diffuse away.

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Justin M Little: And so, this equation exhibits a very interesting structure.

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Justin M Little: In the limit where the capture power scales linearly with the eye on density, so this capital and I here and that's something that we observed in that that previous function that I showed, and so, ultimately, what we find is a correct critical condition on the electron confinement time.

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Justin M Little: That will allow us to operate in a specific mode.

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Justin M Little: Where that specific mode, is where the the power balance to the plasma is dominated by the captured mass and energy from the actual flow.

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Justin M Little: And so, this is shown on the right hand plots were applauding a this power balance the the p out versus the p in as a function of the overall I on number within my control volume.

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Justin M Little: And i'm showing this curve for different electric confinement time so that's what this tau he represents, and so, if i'm below that TAO he my last curves too high.

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Justin M Little: And so my power losses can't be balanced by just input power from the flow at at a specific specific density and so ultimately that balance occurs.

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Justin M Little: When the power bounces dominated by the injected power into the system well at critical.

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Justin M Little: electron confinement time I start to converge these two curves and move up the slope of this input power curve rapidly and eventually three times the critical power have moved up this curve quite a bit.

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Justin M Little: So much so that what we see is a factor of nine increase in the electron confinement time led to a forward an order of magnitude increase in the power.

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Justin M Little: into the actual plasma and so we've moved from this regime where our plasmas balanced by injected power to where the plasma power balance is dominated by the power input from the actual neutral stream.

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Justin M Little: So that's where the they this comparison occurs.

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Justin M Little: Between these two devices so for the rf.

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Justin M Little: thruster when we have is rf absorption that's leading to this transition through the global model of our thruster.

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Justin M Little: In the plasma plasma magneto Shell case we have flow absorption from the initial flow interacting with our plasma and the magnetic field that's that's in the presence of that plasma driving mode transition in the global structure of the actual magneto Shell itself.

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Justin M Little: This has a significant consequence on the ability of this specific concept to actually provide benefits for arrow capture application so one thing that we're showing here on the left is the the input power and the dimension was four cents what's a fat D that's kind of your your.

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Justin M Little: Your drag force as a function of this electron confinement time and we see that this transition drives a significant increase in both of these quantities.

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Justin M Little: And our paper we mapped out a regime.

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Justin M Little: or different regimes, where these effects occur and so we've identified this effects that are described as a charge exchange regime.

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Justin M Little: And that borders, a critical ionization regime that kind of relates to Alphonse notion of the critical ionization velocity.

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Justin M Little: And depending on where you're at in terms of the ratio of the electron confinement time to your capture time scales and also the ionization energy with respect to the.

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Justin M Little: kinetic energy of your input stream, you can be operating in any of these number of different regimes so we've kind of gone through the theory and mapped out where we would expect these regimes to exist because they are crucial in terms of the performance of this device.

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Justin M Little: So we what I described so far was talking about diffusion and power balance and sort of a.

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Justin M Little: kind of a broad sense, and so we actually applied more.

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Justin M Little: Standard models to this this control volume.

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Justin M Little: layout and, specifically, we added a model for Bowman classical diffusion of electrons and an MB polar diffusion of the ions and we kind of created this big framework for the global model this plasma and actually solved the system and the presence of more fine tuned physics.

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Justin M Little: And we recreated the transitions that we observed theoretically So here we see the basically the the plasma transitioning from this Irish team to the charge exchange regime to the CIV regime based on the philosophy of the flow with respect to the critical ionization velocity.

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Justin M Little: We map this out over a range of conditions, so a range of velocities magnetic field strengths and we ultimately kind of built up an intuition, of what was going on, so one of the things that we observed, is that the transition from this Irish team to this charge exchange regime.

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Justin M Little: Basically it didn't always occur, so if the magnetic field was too low, as this red curve indicates that we didn't observe a transition, then, as we increase the magnetic field, we would see that transition occur, which is shown by this dotted orange line.

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Justin M Little: And then, as we increase the field further that transition which shift towards lower and lower velocities.

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Justin M Little: And so, these are results from that global model, and when we map those onto this mapping, we see that.

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Justin M Little: Our theory was able to accurately predict these regimes.

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Justin M Little: Point your attention to this red curve, so the red curve starts to approach that boundary but eventually works its way away so never reaches the condition is required for that mode transition the orange curve was we increase velocity the.

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Justin M Little: epsilon I on so that the normalized ionization energy starts to decrease and eventually we hit that regime where we're able to.

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Justin M Little: move transition into this charge exchange regime, and as we increase the magnetic field strength, while that's shifting us up in this curve, because our electron confinement, time is increasing.

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Justin M Little: And so that allows us to approach this boundary at higher higher velocities or i'd lower and lower velocities and transition into this regime.

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Justin M Little: Okay, so at this point we've knocked this cow about as much as we could from a theoretical standpoint and we wanted to go back to some of the mission design and determine how this performance.

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Justin M Little: performance was changed through these additional effects, so we looked at this Neptune orbiter example and we compare our model to kirklees original model.

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Justin M Little: And we saw that the scaling agreed well at higher densities, the magnitude was off by about a factor of two with the scaling and read well.

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Justin M Little: But as we decrease density this mode transition became front and Center and so became very apparent that this is something that you need to account for when you're going through the mission design and analysis of this concept for arrow capture applications.

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Justin M Little: So we applied this to the development of flight on the globe, so we developed a way to create a flight on the loop for this specific concept, and so this is.

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Justin M Little: Some work that was presented at the 2019 IPC where the flight on the loop is sexually BAP bordered by a minimum of velocity and then a range of altitudes or a range of density is where this is going to work and so.

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Justin M Little: Depending on what mission you're looking at if this flight envelope was outside of the parameters of this mission, this is not feasible concept for arrow capture, so it allowed us to build up those capabilities.

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Justin M Little: So the question can be asked well okay there's added mass added complexity of the magnet are the benefits still there.

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Justin M Little: and, more recently, we applied our analysis to a Neptune mission and Neptune design and architecture and compare the results to this other arrow capture concept called adapt.

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Justin M Little: So that's showing the lower left here where it's basically it's a carbon fiber structure that spreads out and then eventually it sheds, and so it goes in and spreads out and then it sheds that.

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Justin M Little: That structure and exits as this capsule shown in the lower left here.

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Justin M Little: And so we used our model to essentially map the performance of the magneto Shell, as it was going through.

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Justin M Little: A specific trajectory so we see it coming here and a certain velocity minus you know manual shells on providing drag we get a decrease in velocity deactivates and then it goes out.

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Justin M Little: This blur this look kind of blue blur in the upper left hand corner that's our mode transition so that blue blue or shifted to.

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Justin M Little: intersect to this trajectory we would have a mission failure because we weren't generating drag anymore, and so we would ultimately leave the region too early and continue on in a hyperbolic trajectory.

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Justin M Little: So when we run the numbers what we saw was a 70% increase in the payload mash compared to the design mission.

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Justin M Little: Reduction in the arrow capture system massive 30% reduction in the peak heat flux of 30% total heat load of 45% and a 16 times improvement in the ability to vary the drag during the orbit and this last aspect is actually really critical when you're designing missions for Neptune.

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Justin M Little: So.

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Justin M Little: One thing that.

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Justin M Little: That mission planners need to contend with is uncertainties at target destination, and so this might be hemispheric uncertainty is approach trajectory uncertainties sensor uncertainties there's all these uncertainties that conspire to.

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Justin M Little: Basically.

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Justin M Little: create a scenario where you might come in at the wrong angle, with respect to the atmosphere in order to perform arrow capture so ultimately what's.

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Justin M Little: What results from this county of uncertainties is this notion of a quarter with it so it's the angle, with which you can come in at and still have a high probability of this being a successful maneuver.

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Justin M Little: And so it's been shown is having control or variability of your drag within that that that arrow capture maneuver allows you to increase that quarter with you can you can come in with less precision.

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Justin M Little: And so, one of the interesting things about this concept is by varying the magnetic field that allows you a degree of control over the.

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Justin M Little: Effective diameter of your drag generating element, and also the amount of drag that you are achieving in orbit.

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Justin M Little: So basically the idea of the system would be you come in to an atmosphere at a target destination you deploy the the magneto Shell here.

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Justin M Little: And you can then very the magnetic field in a manner that you can adjust your drag in such you react to changing conditions and eventually jettison this maybe she'll post maneuver.

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Justin M Little: Okay, so Finally, how do we test, a concept like this.

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Justin M Little: Well, show here is a map of where the magneto shall flow test conditions exists and Reynolds number mach number stagnation temperature and dynamics pressure space.

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Justin M Little: compared to existing wind tunnels and what we see is that really it's not feasible to recreate the conditions that are observed in this technology using these wind tunnels and so.

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Justin M Little: Basically, our one of the things we're doing right now is looking at.

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Justin M Little: retreating these conditions, using plasmas and so i'll show here a an experiment where we're forming a plasma plasma impinges on a neutralizing plate, and we get a neutral beam that then send towards a.

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Justin M Little: mock up of the manual show i'll just show this real quick, this is our plasma magneto show that we've created in lab, and this is a pendulum where we're using it to measure the forces on the actual negative.

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Justin M Little: here's another video of the plasma striking this plate, and eventually deflected into this region.

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Justin M Little: So very plenary results were using this to ultimately try to.

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Justin M Little: recreate these conditions and lab and test some of these concepts Okay, so I think i'm starting to run out of time, so very quickly go through this last topic, and this topic is basically concerned with.

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Justin M Little: Looking at how this mo transition is basically.

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Justin M Little: A balance between microscopic processes that are occurring in the plasma and how the plasma organizes itself in a macroscopic sense.

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Justin M Little: And so oftentimes you observe a macroscopic change in the plasma and you don't know what the driving physics are behind that macroscopic change.

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Justin M Little: So the technique that i've been looking at recently is referred to as sparse optimization response identification of nonlinear dynamics and I won't go into this technique and much depth, but basically it's a way to analyze time dependent data of a system.

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Justin M Little: And essentially form a matrix of that data that you can then perform regression on in order to identify what the driving physical terms of.

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Justin M Little: Of the physics, of the system where, and so you can go through and form from these data sets.

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Justin M Little: Do a sparse regression on that and then ultimately pull out coefficients that represent the dragon dynamics, so this is that system applied for Lorenz system where it can pull out what he the dragon parameters of that system where.

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Justin M Little: So i've applied this to the Elder age mode transition that I I mentioned earlier, where, as you transition from the hell mode into the H mode.

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Justin M Little: The plasma undergoes what or purchase limit cycle oscillate oscillations, and so it goes through these oscillations where there's a trade off between turbulence growth in damping through.

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Justin M Little: Shared velocity effects and what effectively what i've done is taken a model for this transition the dynamic model, and this was the model of Kim and diamond.

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Justin M Little: And i've gone through and applied the results from this model to this Cindy algorithm.

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Justin M Little: And so I don't think I have time to go through this model much detail, but this is basically a balance between turbulence intensity where turbulence is driven through linear instabilities and then has various saturation mechanisms, the I am pressure gradient.

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Justin M Little: The zonal flow share.

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Justin M Little: And the main flow share So these are the the parameters are evolving as a function of time and the input parameter into this model is the input power.

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Justin M Little: And so, all the physics, all the macroscopic physics are baked into the parameters that you put in front of these other driving mechanisms.

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Justin M Little: And so, if you can understand what these these coefficients are you might be able to get a better lens into what those basic physics arm and so if we provide a simple test data have a.

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Justin M Little: input power ramp here Q into the system, we can see the these various quantities evolve and so what we see is a.

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Justin M Little: Early on, we have this elmo where turbulence grows and then eventually the sheer flow takes over, and it goes through these limits cycle oscillations and then eventually transitions into this age mode where you have as higher I am pressure gradient balanced by this year flow.

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Justin M Little: So can Cindy be used to find the coefficients using data from this model and so that's what i'm showing here where basically we form this.

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Justin M Little: matrix of candidate functions here and I expect that the dynamics of a given parameter that I have data on will be reflected in the coefficients of these functions so, for instance, for an.

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Justin M Little: We have this coefficient C one C two and then Q, also have a dependence on teeth and what we see is that this algorithm is able to actually pull out those coefficients in those dinette as the associated with those different dynamical terms.

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Justin M Little: And we also apply this to additional terms that might represent unknown physics, so this is.

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Justin M Little: Some other strange term that you know I don't really have any physical intuition, of what this might represent we can add that into the mix here and we would expect here a point five, to show up.

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Justin M Little: In this position in the matrix and so when we run this well sometimes you get garbage and you find a bug in your code you're up till 3am and eventually you fix that, and you can obtain the result you're looking for.

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Justin M Little: And so, this is a very interesting technique and again it's only something that i'm starting to look into now, but I feel like it has a lot of progress, especially in the.

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Justin M Little: Age of more data better diagnostics higher quality data this technique.

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Justin M Little: In my mind can can ultimately be used to identify these macroscopic scale physical drivers that are associated with mode transitions and then from the coefficients that result.

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Justin M Little: If you build up enough understanding of those coefficients you can link the macro scale to the micro scale and ultimately come up with this powerful way to.

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Justin M Little: analyze multi scale physics, using the this this high quality data that we might have.

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Justin M Little: Okay, so i'll leave you with just three quick conclusions, the first is that plasmas oftentimes exhibit these bizarre.

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Justin M Little: mo transitions and it can really be fascinating but also are very important when it comes to designing space technologies, because.

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Justin M Little: We can't always control the conditions of a space technology in orbit and so, if we're going to run into one of these mode conditions and we're running out of our.

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Justin M Little: Operating regime, then that can be detrimental into our mission and, finally, I think there's a lot of exciting new data science methods on the horizon, that are going to allow us to really leverage these transitions and learn more about plasma physics, in the process.

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Justin M Little: Okay, I think i've talked for enough so Finally I want to again thank mitzi Julia phalke of its key chain for really just organizing everything all the great communication Professor Mark Fisher as well, for helping organize this again, this is a great honor to present to you all today.

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Justin M Little: The funding for the helikon work was through an air force our fellowship again the space her a lot of the work on.

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Justin M Little: arrow capture was done with a PhD student of mine Charlie Kelly, who is funded through a NASA space technology research fellowship.

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Justin M Little: And then finally funding from the air force our young investigator program which is enabling me to look in some of these interesting data science methods okay that's enough, I will be happy to.

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Justin M Little: Take.

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Benjamin Alexander Jorns: Questions from you.

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Benjamin Alexander Jorns: Thanks justin pick up a half of the audience i'll do a virtual round of applause, thank you for an excellent talk and.

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Benjamin Alexander Jorns: I think, to your questions, we could either you can unmute yourself and suppose directly into justin or if you'd like to throw up in the chat box to that would would work.

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Benjamin Alexander Jorns: I can lead us off with one question justin which had to do with your absorption model for the first first phase, first part of the talk.

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Benjamin Alexander Jorns: Where you show the collision frequency that you're using.

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Justin M Little: Okay.

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Benjamin Alexander Jorns: yeah and, specifically, I recognize that you have this wave based model for the effect of absorption of the the healer con waves, which is based off of Landau resonance.

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Benjamin Alexander Jorns: And that that makes sense to me in so much as it can predict a transition to and from w mode, but I mean now you.

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Benjamin Alexander Jorns: Remember that each modes are characterized by capacitive and inductive coupling where the waves aren't propagating per se it's just kind of maybe even a localized effect nearly the interface with the antenna.

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Benjamin Alexander Jorns: So does this model kind of capture that interaction is that also baked into new, effective, or is it.

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Justin M Little: No that's that's just.

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Justin M Little: it's a very good point so so I didn't do that for this model so that's why you see in the lower end here, this this curve kind of continues.

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Justin M Little: And I cheat a little bit because it flares up here and that's just a way to capture this this capacity mode, so if there weren't that flare up there wouldn't be this other mode.

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Justin M Little: That were that this would be able to exist in we would only be able to exist in this mode and then eventually no other stable solution would exist and we couldn't.

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Justin M Little: We couldn't operate staveley, so this is kind of a general form of how the capacity of mode works that has it this one over and dependence, where it kind of trends upwards and and, eventually, you can kind of catch on to that mode through different damping mechanism.

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Benjamin Alexander Jorns: Okay, and that was that was incorporated into the new effective kind of that.

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Benjamin Alexander Jorns: No so in a loaded.

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Justin M Little: It was incorporated just into this.

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Justin M Little: kind of the license.

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Justin M Little: But it wasn't incorporated into this new effective if it were, it would add kind of a similar thing here.

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Okay, thank you.

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Mark Kushner: This is this is mark Thank you justin for that great talk know in semiconductor manufacturing, there are also these either ah transitions in the effectively couple plasmas and.

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Mark Kushner: In some ways the transition is a friend in that in pulsed systems where you're very electro negative during the interpol's period, all the electrons just attached way.

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Mark Kushner: And you just can't restart and in an adaptive mode, so the fact that you start in a capacitive mode gives you the voltage you need to strike the plasma and then you transition into the H mode.

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Mark Kushner: So do you anticipate a similar effect that, as you have, as you start deploying these wave wave heated devices that if you turn them off, you know you have a hard time turning back on.

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Justin M Little: yeah it's a.

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Justin M Little: very good question and I think.

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Justin M Little: Absolutely and that's something that i've observed experimentally, where.

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Justin M Little: There is this sort of history, SIS effect so experimentally, when I when I would turn on my plasma source, I would have to turn up the magnetic field, starting in a passive mode and then turn it down in order to get to this inductive mode.

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Justin M Little: And so what that means, from a space technology standpoint is you need to be able to number one add that capability into your system you can't.

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Justin M Little: necessarily rely on a fixed magnetic field if if that's something that you need to be able to do and then number two you need to be able to send switch motor in so whether or not that's through the smart matching network or measurements of your your sw are.

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Justin M Little: You need to be able to have that sensing capabilities, so I think that's the fact that there's this history says here it's good from a sense that well, you can actually operate in this w mode in certain regimes, but you actually need to be able to know which regime you're in.

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Mark Kushner: In in.

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Mark Kushner: Typical missions now is there that.

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Mark Kushner: tune ability in matching, for example, my my senses most.

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Mark Kushner: Most missions, or I have very little dynamic range in the thrust, so the the matching electronics are not that sophisticated and here, are you probably talking about some more more sophisticated matching electronics.

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Justin M Little: yeah i'm not too sure what's being used in practice right now there's a company called Phase four which is developing this type of thruster for small satellite applications and.

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Justin M Little: I know that they they've really pushed that technology forward quite a bit I don't know what the current state of the artists.

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Justin M Little: But one of their their main selling points kind of gets back to your initial question is the startup of EP devices can oftentimes be complex and even destructive on certain types of devices, so you only have a certain amount of on off cycles and rf thrusters.

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Justin M Little: You know, while they might exhibit different modes and history cysts and they tend to be a little bit easier to start in practice and less harsh, so I think one of their their marketing claims is they have sort of infinite on off cycles.

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Mark Kushner: Okay, thank Thank you.

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Benjamin Alexander Jorns: justin there's a question for you in the chat box.

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Justin M Little: yeah sorry, let me just see if I can find it.

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Benjamin Alexander Jorns: I can read it aloud to.

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Justin M Little: No, I haven't okay.

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Benjamin Alexander Jorns: So the question is from Ryan Sandberg.

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Justin M Little: Also, about the absorption model if we end up damping is the absorption mechanism is it possible to see Lando growth.

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Justin M Little: Or the Lando ECHO phenomenon before collisions.

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Justin M Little: erase that information that's a good question I don't know if.

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Justin M Little: If that's been seen before my intuition, is that the.

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Justin M Little: These these plasmas are at a high enough.

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Justin M Little: density compared to experiments where where those effects have been observed.

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Justin M Little: That, I think any.

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Justin M Little: Any of the information of the wave and the the electron distribution function gets washed away very quickly, so you know you're observing your way of energy or.

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Justin M Little: Your flattening your electronic distribution function in that region, but then collisions are going to kind of.

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Justin M Little: You know, get rid of that information very.

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Benjamin Alexander Jorns: quickly.

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Justin M Little: So imagine it's it's it's a.

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Justin M Little: high enough of a collision.

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Justin M Little: rate within the the plasma that you wouldn't you wouldn't see that.

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Benjamin Alexander Jorns: I think we have time for one more question.

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Benjamin Alexander Jorns: No, no takers um I just have a practical on for you, which is related to your simulation of high energy neutral beams when you're running the plasma into that plate.

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Benjamin Alexander Jorns: And i'm guessing, the idea is to increase density, but also you want to maintain velocity.

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Benjamin Alexander Jorns: It seems like you would lose quite a bit of energy there that'd be a pretty non elastic process in neutralizing the beam and.

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Benjamin Alexander Jorns: Have you had already characterizing the speed of those neutrals and is it commensurate with what you're hoping for.

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Justin M Little: A very.

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Justin M Little: Good question, we have no idea.

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Benjamin Alexander Jorns: Yet.

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Justin M Little: How we're going to characterize the speed, I think we might try time of flight method.

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Justin M Little: In the literature they've done.

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Justin M Little: Basically, they put a plate.

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Justin M Little: A small plate in front of the flow and measure the heat or how the temperature rises that plate in presence of the game in order to try to make energy and then they can back out the velocity that way, I think, in an ideal sense if I had a system, I would.

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Justin M Little: use.

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Justin M Little: laser nice fluorescence or something like that, but we don't we don't have a system like that.

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Benjamin Alexander Jorns: So.

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Justin M Little: we're we're still trying to.

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Justin M Little: answer that question but you're totally right it's.

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Justin M Little: There is a lot of losses.

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Justin M Little: That are creating that plate, so we have a fairly high power rf.

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Justin M Little: system that that's creating this plasma and.

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Justin M Little: it's really uncertain at this point, whether or not gonna.

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Justin M Little: be able to maintain both the densities, and the loss of these that we need in order to reach that smooth transition regime regime that we're looking for.

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Justin M Little: So that's kind of the big question right now is is will this experiment allow us to reach that regime.

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Benjamin Alexander Jorns: Well, I think, on behalf of everyone who's in the seminar series, like to thank you again.

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Benjamin Alexander Jorns: for joining us today, and congratulations on being or early career lecture.

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Benjamin Alexander Jorns: wish you wish you the best and mark I don't know if you have anything else to add to close this out.

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Mark Kushner: But just to add my thanks to that have been and hope that we will see you out here in person late to summer or next academic year, so we should good health.

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Justin M Little: Right Thank you again, I look forward to visiting.