Ευχαριστούμε και ευχαριστούμε για το 4ο πρόγραμμα της My Christmas Art Journal series. Η ευκαιρία για σήμερα έρχεται από αυτή η αδωραμότητα. Αυτή είναι η one by Cezic και θα σας δώσει αυτή η λίγα άνθρωπο που είναι σκέφτη. Θα φύγετε ένα μεγάλο μεγάλο από αυτή την άνθρωπος και μετά με τρεις, ώστε να μπορείτε να μπορείτε να καταλαβαίνετε ένα λίγο σκέφτη πολύ σκέφτη και εύκολο. Τώρα, αυτή η άνθρωπο έχει ένα αδερφό μεγάλο από τελευταία, και πιστεύετε πιστεύετε αυτό το πρόγραμμα που έγινε. Αυτό ήταν δημιουργμένοι σε ένα μεγάλο 6x6 αδερφό που δημιουργεί να ευκαιρήσει το πρόγραμμα σε ένα αδερφό, όπως έγινε με το τελευταίο πρόγραμμα. Λοιπόν, μπορείτε να παίρνετε την ίδια για το νέο άνθρωπο και να δημιουργεί κάτι σχετικό, αλλά σήμερα θα πάρω για ένα λίγο σκέφτη και θα θα δουλεύω σε το My Christmas Art Journal. Θα δουλεύω με ένα σχετικό πρόγραμμα στο δημιουργείο, που είναι αδερφόρου, οπότε μπορείτε να χρησιμοποιήσεις κάτι πρόγραμμα που έχετε. Είχα αυτή για αδερφόρες, και οι αδερφόρες στον πρόγραμμα είναι πολύ σχετικο, γιατί δεν βρήκαν τώρα. Υπάρχουν νέα αδερφόρια που έχουν για αυτά τα πατώρια, αλλά δεν βοδεύω, θα δημιουργήσω το πρόγραμμα και χρησιμοποιήσω καλύτερα όλα τα γλώσματα. The two colors that I finally decided to go with for my background are a chipped sapphire, which is the darker shade, and salty ocean, just to add a touch of highlights here and there. I'm using a soft brush which is lightly damp, and I'm going to apply the color directly on the page, I haven't prepped the page with anything, no jesso, I'm just working directly on there. And once I apply the first darker layer, then I'm going to dab my brush without even cleaning it in water, and I'm going to go over the darker shade just to add some highlights here and there. This is a really basic way to create a background to get rid of that blank area. Now, if you follow my videos, you know that I am incapable of leaving white space, so I have to cover up everything. And although the background doesn't look so interesting at the moment, there are so many different techniques that you can work with to make this look more interesting. So, for example, you can spray on top. I'm using a darker shade of blue that I found in my sprays, and this is actually gloss spray, the color is Night by Dina Weekly. I love the fact that this spray is going to try permanent, and this is actually acrylic paint in a form of a spray. I'm not being very neat and I don't want to have rectangles like up there, that's why I'm using a paper towel to wipe it off and make it look more organic. I didn't like the outcome. And then finally, I'm going to use the stencil, and you can see that I have paint on top of it. I'm going to use it upside down and clean it directly on top of my page, so I don't lose any of that paint, and I do add some interest on other areas of the page. And since I cannot stay away from splatters, I'm going to use the same paint and add a few here and there. Everything I used up to now on my page dries permanent. And so first I did use my acrylic paint, then I did use the spray that dries permanent. Now I'm going over to a jet black ink, and this is archival ink, which means that it is also permanent, and I'm darkening up the top of my page. I want to have kind of a sky there, and I want that to be darker at the top. I looked through my stash and I found this rubber stamp that has lots and lots of sayings that have to do with Christmas. So it has a beholdess, merry Christmas and things like that. I'm going to ink it up with a VersaMark ink, and I'm going to stamp in different areas, mainly on the top corners, making sure that nothing is going to look as a perfect rectangle, so that I can apply some white embossing powder on top. This is going to add more interest on my background, and if you find something looks too perfect, then you can use a dry brush and clear some of that embossing powder here and there. I'm going to use my heat gun to melt the embossing powder, and I absolutely love how that white stands out against the dark background. And I did repeat the same process for the other side as well. And if you follow my videos, you already know what's the next step, so I'm going to put my art journal inside the box and I'm going to go with splashes. This time I'm using this brush that makes sure that all the splatters are going to be nice and fine. I'm using a watered-down jesso for that, and this is why it was really important for me to use permanent mediums on my background. So I used acrylic paint, distress paint, which is permanent, then on top I did use the Dina Weekly spray permanent again, and then on top I just did some heat embossing. This means that whatever I add on top, like these splashes, are not going to react with the color underneath, so they are going to stay nice and vibrant and super white just like they are now. Here is a close-up look on how the background is looking at the moment. I'm going to leave this aside to dry and let's work on the focal points. So I'm going to die-cut all the bits and pieces from the set. I am cutting out lots of trees. For that I use mixed media paper. You can see that it is kind of off-white, so you can tell.  Now looking through my stash, I found this die, which is absolutely adorable. I did use it in a previous project last year probably, and I'm going to use it on this page as well, so I get that Santa with the reindeer, which I'm going to die-cut from black cardstock as well. So just like I promised from the beginning in this Christmas Argyonal series, I am going to use a new product but combine things from previous releases from older years, things that I already have in my stash. So here I'm going to color the trees. For that I'm using the new color. This is rustic wilderness, and I did use that on the previous video that I did, and I absolutely love the results. So I am repeating the exact same process, just spraying all over the trees, making sure that I end up having some lighter and darker areas. Now, if you notice closely, I do have some bleeding through from the back of the box. I do use this box for spraying a lot, and if you notice, my trees do pick up a little bit of brown and red from previous distress oxides, just because they are not permanent and they do react and activate whenever you spray with water. But this really wasn't a problem. I think that they really added more character and interest on my trees, so that it ended up having just a flat layer of green color. Now I'm putting the trees together, just sticking the tree trunks at the center. I did cut out all the tree trunks from brown cardstock, and now I have a bunch of die-cut snow that I'm going to stick on top of the trees. When these dies die-cut the trees, they are going to give you some scoring lines where you will be able to see which snow goes to where. And I'm not gonna lie, I did start really neat, making sure that I follow these lines, but in the process, I thought I won't bother at all. So we'll just stick a bunch of snow here and there, just to make sure that I cover up all the branches, and I think the finished look was better since no tree is identical with another. I want to create some snowbanks for the bottom of my page. For that, I'm just using white thin cardstock, and I'm going to tear off some strips so that I can stick one on top of the other. I am going to stick everything completely flat on my page, since this is a book and I don't want to add too much of dimension.  So here you can see, I did stack down a couple of snowbanks, but they are completely flat one on top of the other. However, I get that tiered edge that really adds something to the page. So I am going to stick down the trees. Now, if you notice, this is white on white. So to help it stand out against each other, I'm going to ink up the edge and this is a very light shade of blue. Actually, this is a speckle-tech, I believe. I'm just inking up the edges, just touch, not too much, and you will see that now it's going to stand out. And I did repeat the same process on the other side, making sure that I have a snowbank and a couple of trees there as well. Now I'm going to create a full moon. I did die-cut a circle out of my mixed media paper so you can see this is already off-white. I'm going to add some splashes. That was the stress oxide spray and the color was white honey. With my brush, I'm going to spread them out. I'm also going to spray water on top. I will dab it with my paper roll to pick up any excess color and now I'm going to call my moon done. The main reason I decided to go with the moon for my layout was to help my Santa stand out. So my Santa is actually cut out from black cardstock and if I place black cardstock on top of a dark navy background, it's not going to show at all. However, by placing the moon and the Santa on top, you can perfectly see the silhouette. I'm also going to help him by adding a little bit of inking on the top. So as if it is lighted from the moon and later on I'm going to use my white gel pen and you will see a big difference there as well. When I have a big element that has to go on both pages, I like to cut it in half so that I can stick one on one page and then just put them together like a puzzle on the other page. This way you make sure that when you open and close the book, they are going to stay put. Now it's time to stick the little elf on the page but you do see that it doesn't stand out against the dark background. Of course, you can do the little tips and tricks that I showed you for the Santa so you can ink up the edges and use a gel pen later on. However, I'm going to take it a step further that you can easily add color on a silhouette like this one.  So I'm going to follow some of those lines and cut out bits and pieces so that I can do some paper piecing. So here you can see I cut out the hat and I will do the same thing for the rest of the parts so you can see here I'm cutting out bits and pieces that I can use to decorate the hat with white areas. I'm going to use the green for his pants so I do separate the legs as well and once I have all the pieces ready I'm going to do a little bit of paper piecing sticking all those colorful ones on top of the black one and here is the little guy all ready to go if you want to add even more details like I do and I can never stop adding details you can use some patterned paper to create a scarf.  But again remember you don't have to go through the whole process of adding all those details on him you can just stick him on top of the page by being completely black and adding highlights with your gel pen all with a little bit of thinking. However, this is me, I'm having fun here and I absolutely love playing with paper and especially paper piecing that's why I had to go all the way. I'm going to stick him down again I'm using my Nouveau Deluxe glue and although he does have a lot of layers he's not bulky at all since I didn't use any foam tape so I'm not adding any bulk on my book. A really important step especially for the black celibates is to add the highlighting as if they are lighted by the moon this is going to help them stand out against the background and they really make a big difference make sure to check the photos at the end of the video. And as you already know I absolutely love that look so I'm going to add some highlights here and there not only on the Santa but also on the tree trunks on the branches as well as on my little elf. The pen I'm using for the highlights is the Jettyroll 08 you will find it linked down below. Also the highlight lines that I'm adding are really sketchy and I'm not paying any attention or where the source of light is I'm just adding highlights here and there wherever I feel like it. I'm also going to bring in a fine liner in black and I'm going to add some sketchy black lines on his scarf this is going to help add some shadow there and it's going to help it stand out and this is where I don't know where to stop when it comes to details so here I'm going to add another piece of that patterned paper at the top of his scarf just to make it fluffier and coming more up on his face this way I will be able to add just a couple of dots for his eyes without having to draw his nose and mouth and finally it's time to add the coat for that I went with It's All Fun and Games until Santa checks the naughty list I think that was really hilarious and I think it's the perfect quote for this page with that little elf having fun in the snow while Santa is coming over by the way lately I like to use my label maker to print out my quotes and as a finishing touch I'm adding my gel pen to add some sketch lines around my stickers so that was the project for today I hope that you had fun and that you got inspired just like always you will find a full list of all the supplies that I used down below in the description area Don't forget to comment, like and subscribe if you haven't done so already Thank you all so much for spending some time with me today and I'll see you all next time


In the last couple of years, communities throughout the United States have chosen to manage traffic using roundabouts. Hello, I'm Dusty Peerpoint of the Lacey Police Department. I would like to take this opportunity to introduce a transportation concept that might be new to some. It's called a roundabout. Simply stated, modern roundabouts move traffic through an intersection without the aid of traffic signals. Compared to signalized intersections, roundabouts have some distinct advantages. For example, roundabouts help decrease vehicle emissions, increase roadway capacity, and improve traffic circulation. But the most significant advantage is safety. Roundabouts reduce the number of serious traffic injuries because roundabouts reduce vehicle speeds. Although modern roundabouts are not appropriate for all situations, they do provide communities with another tool to address traffic congestion. So, what are the rules of the road? How do we drive through a modern roundabout? And who has the right-of-way? During the next few minutes, we will answer these questions. In addition, you will see firsthand how roundabouts circulate traffic, but more importantly, you will learn how to safely negotiate a roundabout. Please join me for an important look at roundabouts. One of the most important concepts of a roundabout is the yield principle. All vehicles must yield to traffic inside the roundabout, as well as vehicles exiting. Drivers should only enter after sufficient space is available to maneuver safely into the roundabout. Defensive driving is appropriate in all situations. Make sure you are aware of other vehicles within the roundabout, and be alert to drivers entering and exiting. When approaching a multi-lane roundabout, drivers must choose either the left or right lane before entering. The appropriate lane choice is based on the driver's desired exit or intended destination. For the multi-lane roundabout shown in this video, the left lane allows left turns, straight-ahead movements, and U-turns only. All right lane maneuvers include immediate right turns or straight-ahead movements. In all cases, signs will direct drivers to the proper lane. Drivers using the left lane have the following options, left turns, straight-ahead movements, and U-turns. Remember when driving in the left lane, always maintain your lane position until you exit. Drivers using the right lane must make an immediate right turn or a straight-ahead movement. Remember to maintain your lane position until you exit. For a roundabout to function properly, everyone must follow the rules of the road. As you are about to see, failure to observe these rules will create unsafe conditions for you and other drivers, before entering always yield to traffic within the roundabout. Everyone without sufficient space will cause an unsafe condition. In this situation, the vehicle in the right lane cuts off the driver in the left lane intending to exit. Be aware of other vehicles in the lane next to you. They may be unaware of your intended exit. Never change lanes while inside the roundabout. This car in the outside lane is attempting an improper U-turn. Drivers are only allowed in the left lane. Some roundabouts are specifically built with truck aprons to accommodate the turning radius of large trucks and trailers. Although truck aprons are provided, drivers should be aware that trucks may straddle both lanes. That is why it is important to never drive adjacent to or pass trucks while maneuvering through a roundabout. If you follow a truck into a roundabout, do not attempt to pass. An emergency vehicles approach always give them the right of way. If you have not yet entered the roundabout, pull over to the right, allowing emergency vehicles to pass. Never stop while inside the roundabout. Instead, continue to your exit, then pull over to the right shoulder of the roadway, allowing emergency vehicles to maneuver around you. A roundabout crosswalk functions the same as an unsignalized crosswalk. Before entering the crosswalk, pedestrians should always look in the direction of oncoming traffic. Find a gap in traffic and then cross, although you have the right of way. Forcing traffic to stop suddenly can create unsafe conditions for both you and the drivers entering or exiting the roundabout. Most roundabouts include refuge islands, providing pedestrians with a safe route across opposing travel lanes. Bicyclists are encouraged to use crosswalks by walking their bikes, only experienced bicyclists should ride through the roundabout. If you choose to enter a roundabout, the same rules of the road apply for a bike as an automobile. Now let's review the key points. As you approach a modern roundabout, remember these basic principles. Yield principle. Yielding to all traffic circulating within the roundabout before entering is the single most important rule. Lane choice. Drivers must make the appropriate lane choices based on their destination before driving through the roundabout. After you enter the roundabout, never overtake other vehicles or change lanes. Slow down. Modern roundabouts are designed for speeds of 20 miles an hour or less. Drivers should be aware of the posted speed limit signs and slow down to safely enter. Large trucks and trailers. Give special consideration to large trucks and trailers. Never pass or drive adjacent to a truck within a roundabout. Driving behind large trucks is preferred. Emergency vehicles. Do not impede emergency vehicles. Pull over to the right if you are not in the roundabout. Or move through and exit the roundabout to ensure emergency personnel get to their intended destination without undue delay. Pedestrians. Utilize the modern roundabout's refuge island. This allows pedestrians to cross both directions of traffic safely. Bicyclists. Bicyclists should use the pedestrian crosswalk. Only experienced bicyclists should ride through the roundabout. Following these rules of the road will help you drive through a modern roundabout correctly and safely. Thank you for joining me in this informative look at roundabouts. If you would like more information on local road projects that include roundabouts, please contact your city or county government as well as the State Department of Transportation. Thank you for your time and please drive safely.


So recording, got it. So today I'm going to be giving a broad overview about stellarators. I'll start from the very basics about how we can get good confinement with 3D magnetic fields. And I'll talk a little bit about the history and the current status of where our stellarator research is today. So let's see. Here's an overview. So as I said, I'll talk about how we get good magnetic confinement with these 3D fields through stellarators, what ingredients we need to get good confinement, and then how do we put those together through numerical optimization. And then at the end, I'll talk about the context of some current research in stellarators. So we're broadly interested in turtle confinement for nuclear fusion applications. We want to confine a hot plasma for sufficiently long periods of time to get net energy gained through nuclear fusion. But there are other applications that could be considered. For example, there are astrophysical plasmas that are composed of non-neutral plasmas, such as electron-positron plasmas. And these could also be studied with magnetic confinement. Magnetic confinement has also been used to produce hot laboratory plasmas used for basic plasmas studies. And the basic ingredients you need for turtle confinement is to, first of all, get field lines which lie on continuously nested turtle surfaces. Because the guiding center motion largely follows the magnetic field lines on average, if the guiding centers stay close to magnetic surfaces, then they will stay confined. So the most naive way we could think of doing this is taking something like a cylinder and then wrapping it into a torus. So we get no escape of field lines from this turtle region. And so we get something that looks like a hybrid between an onion and a donut. So we get these continuously nested magnetic surfaces. The field lines lie on these surfaces. And the guiding centers largely follow the field lines on average. And we call the short way around the torus, the poital direction, and the long way around the torus, the toroidal direction. So as you may have heard, just getting field lines that lie on magnetic surfaces is not quite enough. And that has to do with the fact that we have magnetic drifts off of field lines. So the lowest order guiding centers follow the field lines on these magnetic surfaces, but then to the next order, they start to drift away. And one of the drifts that we see in magnetic confinement devices is the grad B drift. So if you have a torus, then the field strength is naturally larger on the inboard side than on the outboard side. And that gives rise to a drift that is largely vertical. So if we have a field line or a guiding center that's lying on the surface, the guiding center is going to feel a net drift in the vertical direction. But we can try to cancel this out by getting the guiding center to go from the outside of the torus to the inside of the torus. So if I project this motion onto a plane, it's going to look something like this. So by getting the guiding center to move around the torus, we can get a net cancellation of this drift on average, and that will give us good confinement. So the way that we quantify this is through a number called the rotational transform that tells us the number of colloidal turns of a given field line per toroidal turn of a given field line. And the typical width of the guiding center orbit in comparison to the magnetic surface goes inversely with iota. So we naturally want larger values of iota because this gives us better confinement. We stay more closely to magnetic surfaces. So there are different ways that we can get this iota or rotational transform. And the way to look at this problem is to see the expression for the rotational transform when we're at the very core of the torus. So we're close to the magnetic axis, which is pictured here. So we have this formula, which is from theory by Mercier, and it tells us the ways that we can generate rotational transform if we're close to this magnetic axis. So the most obvious way to do this is by driving some current in the plasma, and this is the way that Togomex generate rotational transform. So if we have a current that lies on the magnetic axis, that gives us a component of the field that goes politely around just from the right hand rule. And so this gives us some rotational transform. The tricky piece about driving current in the plasma is that it's difficult to do in steady state. So you typically have to use some kind of transformer coil using induction. And so this can't be done in steady state. And also the current can give rise to instabilities, which can lead to sudden losses of confinement. And so this talk is going to instead be focused on the stallerator, which uses an alternative method to get rotational transform. So if we take a look at this region that's very close to the magnetic axis, then you can show that the shapes of the magnetic surfaces are actually ellipses. So like this ellipse that's pictured here. And the ellipse rotates as you go around the axis. And this is one way that we can generate rotational transform. So in this expression, delta prime, delta is the angle between the curvature vector and one of the semi minor axes of the ellipse. And so if delta prime is non-zero, this tells us that the ellipse is rotating with respect to the curvature vector. The second way that we can generate rotational transform is by having torsion of the magnetic axis. So torsion is a measure of the non-planarity of a curve. So if you have a tokamak, the magnetic axis lies on a plane. So that doesn't give you any additional rotational transform. But if you have a magnetic axis that wobbles in and out of a plane, this can give you rotational transform. And this was the mechanism that Lyman-Spitzer came up with when he invented the first stolarator. So Lyman-Spitzer was the founder of the Princeton Plasm Physics Laboratory where I am now working. And you can see here a diagram of the figure eight stolarator that he invented. It's fairly simple. It's produced by some planar circular coils that give you this non-planarity of the torus. So if we want to drive rotational transform without having current in the plasma, you can see that there's generally two ways to do this. And they both require breaking of the toroidal symmetry. So if you have a current in the plasma, you can keep your torus axis symmetric. And as soon as you want to try a configuration without current, then you start to break the toroidal symmetry of your device. And that's what we call a stolarator is a device that generates rotational transform without driving current in the plasma, but through 3D shaping instead. So one way to think about the rotational transform is it's analogous to a geometric phase that arises through the motion of the curve through parameter space. So in this animation, what I'm showing is an example magnetic axis. And the purple arrow is pointing in the direction of a nearby field line. So you can see as this arrow is rotating about the curve, it generally doesn't come back to the same position. So if you follow it around, you can see that it's coming back. In some places it rotates very quickly, but then when it gets back to the start, it's generally rotated by a finite amount with respect to the initial condition. And this is what gives rise to the rotational transform. So the stolarator concept was the basis for some early experiments at PPPL. So I discussed the figure eight experiment. This was the basis for the Princeton Model A device in the early 1950s. There were some later experiments at Princeton which tried to improve over some of the limitations of the figure eight by introducing magnetic shear. And that led to this Princeton Model C stolarator. This is a simple race track design where you have straight segments at the ends and then a helical segment at each of the endpoints of the torus. So the earliest stolarator experiments at Princeton exhibited some poor transport properties. So they found that there was some misalignments of the coils in the Princeton Model C stolarator that gave rise to bone-like diffusion. So they weren't necessarily declared an immediate success. And around this time, the Tokamak started to have some early success. So there were measurements from the Soviet, Soviets that they had been able to achieve high temperatures in their Tokamak experiment. And at this point, a lot of the energy and magnetic confinement community began to focus on the Tokamak instead of the stolarator because they had this early success. And at this point, the Princeton Model C stolarator was then turned into a Tokamak experiment. So since this time, so here's a quick timeline. So in the 50s and mid 60s, there were several stolarator experiments at Princeton, but then they were transitioned into largely Tokamak experiments at PPPL. And I think there's some resurgence in interest in the stolarator concept within the fields. And I'll talk about why that is toward the end of my talk and some new developments that we're seeing. Okay, so how do we actually get good confinement in the stolarator? We saw that some of the early stolarator experiments perhaps did not have great confinement. And we'll begin to probe how we can do better as we design a magnetic confinement configuration. So one of the basic ingredients we need in stolarator confinement is magnetic field integrability. So if we take a set of coils that I'm showing here, these are coils that produce the NCSX stolarator configuration. This was a design that was partially constructed at Princeton, but it was never completed. We can just look at a Poincaré section of the magnetic field lines. So here we follow the field lines many times around the device. And every time it intersects a plane at constant throttle angle, we place a mark. And this allows us to see the motion of the field lines. So we can see that we do have some nice magnetic surfaces, but we also have some magnetic islands and some stochasticity at the edge. And here's a large view of what some of these magnetic islands look like. So if we want to have good confinement, as I outlined in the introduction, we want to have a large volume of nested magnetic surfaces because this allows us to maintain a large pressure gradient in the plasma. If we have a large region of chaotic field lines, then the pressure tends to flatten, so it's not as good for confinement. And we call the presence of continuously nested magnetic surfaces integrability, and this is because of the connection with the Hamiltonian nature of field line flow. So it turns out the magnetic field can be written as a Hamiltonian system. So we can write the vector potential in this form. We have some function chi that will act as our Hamiltonian. And we're going to use a coordinate system where rho labels constant toroidal surfaces, but these are not necessarily magnetic surfaces. We're just considering this to be some background coordinate. So we set up some surfaces of constant rho, which are toroidal surfaces, and then we have two angles which parameterize the position on this surface. So then if we write down the equation for the motion of a magnetic field line, where we're parameterizing the trajectory by phi, then we can see that the trajectories are analogous to Hamilton's equations, where chi is acting as our Hamiltonian, theta is our coordinate, rho is like a momentum, and the toroidal angle phi is taking the place of time. So this tells us that if we have a autonomous Hamiltonian, so chi is independent of the toroidal angle phi, then this tells us that we're going to have integrability of our system. So it's a one and a half degree freedom Hamiltonian. If it's autonomous, we get energy conservation, and that energy conservation corresponds to having magnetic surfaces of constant chi. So chi in that case is a surface label. So in the case of axi-symmetry, where all physical quantities are independent of phi, this tells us that we automatically have magnetic surfaces. If we are in a three-dimensional system where the physical quantities can depend on phi, then integrability is no longer guaranteed. And this is the reason that we have to start to worry about the presence of chaotic field lines and magnetic islands. So if we start with a Hamiltonian that is integrable, this first piece in green, and add a non-integrable perturbation that is scaled up by epsilon, you can see that we can start to develop a magnetic island at this 1 over 2 rational surface, and the island grows as we scale up this parameter epsilon. So the phase purchase looks very similar to that of a pendulum because of the Hamiltonian nature of the field line flow. We start to add in multiple perturbations, then we get multiple islands that exist at these different rational surfaces, the 1 over 4, the 2 over 4, and the 3 over 4. And as the widths of the islands increase, they can begin to overlap, which gives rise to a volume of chaos within the magnetic surfaces. So as we get farther away from symmetry, this is something that we have to worry about in designing the magnetic fields to preserve the necessary surfaces that we desire. So there's another benefit of axi-symmetry that we lose as we go toward stellarators, and this comes from the single particle Lagrangian picture. So if we consider the motion of a charged particle in a general magnetic field, we can study it through this general Lagrangian, and if our Lagrangian is independent of the territorial angle phi, which comes through the axi-symmetry property, then this tells us that we get a corresponding conserved momentum, which is p phi. And you can show that if you have a sufficiently strong magnetic fields that p phi is approximately constant on magnetic surfaces. So this tells us that if we have a purely axi-symmetric magnetic field, then we automatically get confinement of our charged particles, and they're essentially stuck to magnetic surfaces. So this is one of the benefits of axi-symmetry, but as I'll discuss, there are ways that we can try to preserve the interability of charged particle motion, even when we go to three-dimensional systems. So in general, we have to be careful to optimize magnetic fields in order to confine three-dimensional particle orbits. So what these pictures show on the right are the orbits of guiding center motion in a tokamak if you add on some error fields. So you start to get some particles that can come trapped in the local minimum of the magnetic field strength. That's the trajectory in pink here. And you can also get charged particles that follow these banana-like orbits in purple, but the banana tips begin to wander because of the symmetry breaking. And there's much more complexity when we go to fully three-dimensional systems on the left. This is a, you can see some particle orbits on a stalerator. Again, you can get some local trapping features and you can get transitions between different types of orbits between the trapped and the passing. And so in general, this is something we like to avoid because then it can give rise to larger diffusion. And this is something that we can study through neoclassical theory. So the drift kinetic equation allows us to study the drift, the guiding center drift motion when we add in collisions. So this is an equation for the distribution function f. And in general, stalerators tend to have larger neoclassical transport than tokamaks. And this is especially true as we go toward lower collisionality. So what this figure shows is a typical calculation of the neoclassical diffusion coefficient for a tokamak in this dashed line and a stalerator. And you can see that there are different regimes where the diffusion scales differently with respect to the normalized collisionality. As we go to higher collisionality, the scaling for the stalerator and the tokamak are pretty similar to each other. But at lower collisionality, we get much more transport in this stalerator configuration. So we get this, the scaling with one over the collision frequency. And this is especially problematic if we want to operate at high temperatures and experiment because it tells us that as we increase the temperature, then the diffusion actually gets worse. So this one over new regime comes because we have particles that get trapped in local wells and they de-correlate through collisions. We can estimate the scaling of this diffusion coefficient by using a random walk like argument. So we can take the characteristic radial step size to be something like the radial drift over the collision frequency and the typical timescale to be one over the collision frequency. And this gives us a diffusion that scales like temperature to the seven halves. So this is definitely a regime that we want to avoid when we're designing a configuration. So there's lots of ingredients we would like to include if we want to design a stalerator. So we want it to be MHD stable. We don't want any large scale instabilities that will degrade the confinement. We want to think about the bootstrap current. This is an effect that also comes from neoclassical theory. So while stalerators are designed to have to not need current in order to get rotational transform, there is a small amount of self driven current that comes through pressure gradients. And this is called the bootstrap current. So some configurations try to minimize the self driven current in order to improve some of the stability properties. We also have to think about the confinement of the most energetic particles. So these are typically the ones that are hardest to confine because they have very low collisionality and they can also experience different resonant properties that we have to take into account. The equilibrium beta limit is something that is a little bit different in a stalerator than in a tokamak. So while in the tokamak, the beta liven is often driven by stability considerations. In a stalerator, it can also be driven by degradation of the magnetic surfaces. So as you increase pressure, you can get some losses of intergrability, which has to be accounted for. We have to think about what the diverter might look like in a potential configuration. And then one of the major challenges is how feasible it is to build the coils. So to get the rotational transform in a stalerator configuration, we have to get the twisting of the field lines by twisting the magnetic surfaces. And this generally requires some magnetic coils that are quite complex in shape. And it's non-trivial to actually construct them in practice. So we have to take into account these type of engineering considerations in our design as well. Okay, so these are the basic ingredients we would like. And so how do we actually put these together? So we want to get intergrability of the guiding center motion. And the surprising thing is that we can actually design our magnetic field to get intergrability, even if we're far away from axisymmetry. So the way to see this is that if we take our standard Lagrangian for charge particle motion and take the limit of strong magnetization, then we get this modified guiding center Lagrangian that only depends on the position on a magnetic surface through the magnetic field strength. So here I'm using a set of coordinates where psi labels magnetic surfaces, and then theta and phi are some set of coordinates on these magnetic surfaces. So if this tells us if we have a symmetry of the magnetic field strength in this particular coordinate system on surfaces, this again gives us a corresponding conserved momentum. So note that the symmetry of the field strength on the surface does not mean that the magnetic surfaces themselves have to be symmetric. It's a separate property. So again, we can show that this conservation of momentum tells us that the charge particles stay confined to magnetic surfaces on average. So there's two terms in this P phi expression. The first is relatively small if we're strongly magnetized. And so we again get confinement to magnetic surfaces analogous to the axi-symmetry case. And we call this property quasi-symmetry. So there are several different varieties of quasi-symmetry. One is quasi-polatal symmetry. So here we have contours of the field strength in this coordinate system that wrap around the torus poloidally. So this this figure that I'm showing is the QPS experiment that was developed at Oak Ridge. So you can see that the shape of the torus is nowhere close to being symmetric, but we still get near symmetry of the magnetic field strength in this coordinate system. And the coils can be quite complex in order to confine this magnetic field. We can also get quasi-helical symmetry. So these are contours of the field strength that wrap around in a helical direction. And the black lines here indicate the approximate symmetry direction. And this is a visualization of the helically symmetric experiment at the University of Wisconsin. So this is currently the only operating experiment that is testing the quasi-symmetry idea. We can also get quasi-axi-symmetry. So this is more analogous to axi-symmetry as in a tokamak. So we get the field strength contours that wrap around the long way around the torus, toroidally. But again, you can see that the shape of the surface is very far from being symmetric. So we know we want to get this quasi-symmetry property, but actually finding magnetic fields that have this property is not in trivial. So to find these magnetic fields, we have to use optimization tools. So typically this takes place in two steps. So in the first step, we try to optimize an MHD equilibrium to get confinement properties that we would desire. So we specify the shape of the boundary of our plasma, like this one that's pictured in yellow. And given the shape of that boundary, the magnetic field everywhere inside is completely determined. So we can use the shape of the boundary of the plasma as our degree of freedom in the optimization problem. So we optimize in this space to try to find magnetic fields that have good confinement properties. So once we find this boundary of the plasma that we would like to build, we can then go and find the coils that support this equilibrium. So this is again an inverse problem. It's an optimization problem. So we want to find the coils that give us b normal on the surface, which is close to zero. So we want the magnetic field to be approximately tangent to the surface when it's provided by these coils. And in the second step, we also have to take into account how complex these coils are, how how buildable they are in practice. So this two-stage optimization approach has been tested experimentally and verified. So I mentioned the helically symmetric experiment to HSX at Wisconsin. Here's another picture of the device. And they've tested that with the quasi-symmetric configuration, you can actually improve the neoclassical confinement. So they have a mirror configuration where they add in some additional coils, which degrade the quasi-symmetry. And here you can compare the mirror configuration to the quasi-helical configuration. And you can see that the thermal diffusivity is actually reduced in the experiment with the optimized configuration. They can also compare with the theoretical calculations of the neoclassical transport. These are the lower lines here. And you can see that in the experiment, there's generally enhanced transport in comparison to theory. And this has to do with microturbulance and turbulent transport that gives rise to additional diffusivity in practice. But nonetheless, we're able to confirm that using this two-stage optimization approach, you can find equilibria with this quasi-symmetry property. So one of the largest advances in the Stellarator is the design and construction of the Wendelstein 7x experiment. This is an experiment in Greifswald, Germany. And it was designed not with quasi-symmetry, but with a related optimization approach called Omnigenity. And so this device just came online in 2015. It was designed for several criteria. So they wanted to have stable equilibria up to high beta. They wanted to have improved fast particle confinement in reducing the plasma bootstrap current. So I'm just going to play a short time-lapse video so that you can see this impressive feat of engineering in the design of W7x. Let's see if this will go through. So here you can see, this is the vacuum vessel for the main chamber. You can see some of the modular coils they're putting in place now. So this is just one half period of the device. You can see the various ports that they used to have experimental access. So on W7x, now that they've turned the machine on, they've been also able to demonstrate that the optimization actually worked. And so what they did is they measured in the experiment the heat flux. And they normalized the heat flux that's computed theoretically from neoclassical theory to the total heat flux that's actually in the experiment. And you can compare the actual W7x experiment, which is neoclassically optimized to configurations that aren't neoclassically optimized like LHD. So in this picture, you can see that this normalized heat flux is actually less than one. And again, this has to do with the large amount of turbulent transport in the experiment. But what you can see is that if you try to support the same temperature and density gradients in an unoptimized configuration, there'd be no way that these gradients could be supported in the experiment because the neoclassical heat flux largely is much larger than what they actually measure in the experiment. So this tells us that it's actually, it paid off in the end, all the work that went into designing this equilibrium and engineering it. They're able to now achieve record-breaking discharges due to this neoclassical optimization. So now I'll place accelerators in context a bit. So there are two leading approaches to magnetic confinement, the Tokamak and the Stelerator. So while the Tokamak enjoys automatic particle confinement because of its Tertile Symmetry, you get automatic guiding center integrability. You also get automatic integrability of the magnetic field because of the Tertile Symmetry. The coils are relatively simple in a Tokamak. You can see they're planar. That doesn't mean they're necessarily extremely simple to build, but they're at least simpler than something like W7X. The problem with Tokamaks is that they require a very large plasma current, and this can give rise to instabilities, sudden losses of confinement. And writing this current in steady state is challenging from a technical point of view, but it's also inefficient because that means in a reactor that you have to take some of the energy from your fusion reactions and put that back into driving a current. And so the Stelerator tries to address some of these problems by avoiding the current. So the advantage is that you get low recirculating power in a reactor. You also don't have to worry about plasma terminating disruptions due to current driven instabilities. Stelerators also have the advantage that they have a softer pressure or beta limit. So it's often due to degradation of the equilibrium rather than a large scale instability. But the challenges that we require careful optimization of the confinement and the shaping is produced by rather complicated magnets. So on this plot, I'm comparing some large Stelerators and Tokamaks with respect to the triple product. So the triple product tells us that if we have this critical value, then we can get ignition. So the losses from thermal conduction balance the energy that's produced through fusion. And so the vertical axis in this plot is the triple product and the horizontal axis is the duration of the pulse. So really we would like to be in the top right corner of this plot. So what you can see is that for the Stelerator discharges LHD and W7X, we can more easily operate toward the right because it's easier to go in steady state. And we'd also like to push to to hire triple product in the Stelerator. So currently the Tokamak has the the record for the triple product in a turtle confinement device. But the Stelerator is not too far behind. So these yellow dots show some of the recent discharges from the early campaigns in W7X. In an upcoming campaign, OP2, they're helping to push up a little bit further and get closer to the envelope of what the Tokamak has been able to achieve. So what are some open questions and new frontiers in the Stelerator community? So as I've emphasized, we're now able to reduce the new classical transport of the collisional losses in the Stelerator. And there's still a lot of losses that occur due to micro turbulence. And since we have a lot of degrees of freedom in designing a Stelerator, we would like to use those degrees of freedom to reduce the turbulence. We'd also like to understand better the properties of Stelerators as they go to high pressure or high beta. And then we'd also like to take advantage of some innovations and optimization to improve confinement. So how can we design a Stelerator with reduced turbulence? So one approach to this is to reduce this trapped electron mode that MJ discussed in the previous talk. And so one way to do this is by by manipulating the sign of the derivative of J parallel, which essentially tells us the direction of the drift motion, such that the trapped electrons cannot resonate. And it turns out that W7X was able to be constructed with this so-called maximum J principle. It wasn't actually part of the design, but they realized it after the equilibrium had been finalized that W7X has this property. And so in the experiment, they can show that W7X can operate in a so-called stability valley. So there's a valley here where you can see that the growth rate is minimized. So as you start to increase the temperature gradient, the ITG drive gets stronger. And as you start to increase the density gradient, the TEM gets stronger. But in the middle, you can operate in a stability value. And favorable conditions can be achieved for confinement with this maximum J configuration by using pellet injection. So as you increase the density gradient, this can stabilize the ITG. And you can see that the largest triple product shots that have been achieved so far have been using the pellet injection technique. So this plot is showing the triple product as a function of the density in some W7X shots. And this green dash line is the record that was achieved in LHD. So at the top, these are the shots that have been achieved with pellets and the stars. And you can see that they're pushing up to very large triple products. So this is a potential scheme to reduce one of the modes that gives rise to some transport and magnetic confinement. But of course, there are other modes that we have to think about when we're designing a configuration. And so there's a lot of work in the community on developing reduced models that can be used for designing a configuration that can operate at reduced turbulent transport. So one of the surprising features of a stalerator is that when you cross a predicted pressure gradient boundary that's predicted from MHD theory, that we don't see a sudden loss of confinement. And we don't see a large scale instability in the plasma. And this has been seen in the large helical device in Japan. So what this diagram shows, the pressure gradient and the pressure on the horizontal scale and this black dash line tells us the predicted mercier instability thresholds. And you can see that there's a bunch of discharges that we're able to operate above this threshold. However, when the growth rate gets too large, then you can see that there's not as many discharges that are able to operate. So it appears that the stability threshold is more like a soft boundary. There may be some increases in transport, but it doesn't give you a sudden loss of confinement. And this is quite different from what you would see in a tokamak. And one of the reasons for that is as you go to increasing beta, then you get losses of integrability, the pressure can flatten, and this reduces some of the drive for the MHD modes. But we still need to do some more theory to understand this basic feature of accelerators and understand how we can design a accelerator to be able to self heal at high beta. So that means as we increase beta, the currents that come from the plasma would actually heal the islands rather than degrading the integrability of the fields. And this would give us a configuration that could potentially operate at higher beta. So a lot of improvement has been made in the past years by taking advantage of innovations in optimization. And one of these is in finding magnetic fields that can get much closer to this quasi symmetry property. So in the bottom right, I'm showing some figures of the field strength contours in a bunch of devices that were designed to be quasi symmetric. So if we had perfect quasi symmetry, all these contours would be exactly straight in the plane. And you can see that they're approximately straight, but they're not exactly precise. And here's just another way of visualizing this data. So on the y axis, this is a measure of the quasi symmetry as a function of the radius. And you can see it's on the order of 10 to throughout the device. Just within the past year, we found some new configurations that get much closer to quasi symmetry. So if we look at the field strength contours, they by look exactly straight. And when you actually measure the quasi symmetry, you can see that it's improved by orders of magnitude over the previous configurations. And this property is actually really important when we want to confine the most energetic fusion boron alpha particles. So with these new configurations, we can show that the confinement of the guiding center losses is analogous to or is comparable to what you would get in a tokamak. And so this has been able to demonstrate that accelerators really do have the confinement that's needed for a future reactor. And one of the ways that we've been able to improve in the optimization of stellarators is by taking advantage of tools that have been developed in related areas of physics and engineering. And so as I've highlighted, the stellarator optimization problem is really a problem of optimizing a shape. So we want to optimize the shape of the boundary of the plasma or the shape of coils. And there are very related areas that arise in, for example, aerodynamic engineering, you want to optimize the shape of a car or an airplane to reduce the drag. So in these fields, there have been tools developed to more accurately and efficiently evaluate these kind of problems. So we've been able to take advantage of concepts, which are called the shape gradient and the adjoint method, which allows us to very easily get sensitivity information without directly preserving the shape, but by taking advantage of some underlying self-adjointness property of the equations. So what I'm picturing in this figure is the shape gradient for the drag. So this is a measure of the local sensitivity to perturbation. So it tells us if we were to push the car inward in the red region and outward in the blue region, we could reduce the drag. And we can get an analogous figure for the stellarator. This tells us how we would perturb the boundary of the stellarator in order to push the rotational transform towards some target function. So by taking advantage of these adjoint methods, we've been able to more efficiently push configurations toward quasi-symmetry. So there's a graduate student at Princeton who was working on this project with me. So for obtaining these precise QH and QA configurations, I showed a few slides ago. This can take on the order of 10 to 4 CPU hours, but by taking advantage of advances in numerical methods, we can push this down to something like 10 CPU hours. And so we can more easily scan the space of quasi-symmetric configurations to find some interesting designs. And I think there's a lot of excitement in the field of stellarators now. So there's a design that's currently under construction, which will be likely the first quasi-symmetric design. This is the CFQS device. So it's in collaboration with NIFS. And so the physics design is complete. And I think they've started breaking ground and they're putting the device together, and hopefully we'll see some of the results coming out in the next few years. There's also an influx of private money into the fusion community. And this has had an impact on the stellarator as well. So there is a new stellarator company coming out of Princeton, which is taking advantage of some innovations in magnet design. So their idea is to not have complex modular coils, but to have some small dipole-like coils that give you the confinement. So you can have very simple toretal field coils that are easy to construct and large sets of small dipole fields that give you the confinement and are not too challenging and can also give you some experimental flexibility. There's also a private company based out of Wisconsin that is also taking advantage of some advances in magnet technology. So they're planning to use high temperature superconductors to construct their coils. And they may produce a quasi-helical or quasi-isodynamic device in the next few years. And so I think this is one of the areas where there's a lot of area for development is seeing how we can use improvements in magnets to improve confinement in the stellarator. So I'm going to be moving to Columbia in the new year and I'm also going to be developing my own little experiment to be a future testbed of optimization. And the goal of this experiment will also be to demonstrate some new magnet technology through HTS tape and demonstrate that we can use simple coils to produce a confined equilibrium and maintain some simplicity in previous designs that were at Columbia. So if you're interested in learning more about the background of stellarators and a little bit of the physics, I wanted to point you to a text that I've been working on with some of my collaborators. And so the goal of this document is to really start from first principles and to build up to the concepts that you need to understand the confinement in the stellarator and how they're designed. So we're working on publishing this as a book, but for now it's available on the archive. Anyone is welcome to check it out and please give us feedback or questions if there's anything that comes up. So I think I'm coming to the end of my talk. I want to make sure that I have plenty of time for questions. But I think as a community, we're really looking toward pushing the stellarator toward a fusion power plant. And so the community recently put out a strategic plan for the US, which is pushing toward a national program that is leading to the design of a compact power plant. So there have been previous attempts at designing stellarators that can be pushed toward a fusion power plant. This is the schematic of the area CS design. And there have been many innovations since this time that could really push the stellarator further. So I'm excited to see what progress will be made in this area in the coming years. So thank you for your attention. I'm happy to take questions at this point. Thank you very much, Elizabeth, for an absolutely excellent talk. And I'm sure that the strain and interesting world of stellarators is introduced to the participants, maybe for many of them for the first time. And I'm sure that there was a very high transformation and translation of information from your talk to the people. So I encourage anyone of you to ask a question. I mean, I'm sure that many of the things you have heard for the first time, so it's not very easy to ask question, but if there is anything you can ask. So Elizabeth, I'm going to ask you in the afternoon, we normally get together and have an informal session where the participants can ask questions. Today, would you be able to join us? What time is this? We are meeting at two o'clock? You are two thirty. Somewhere around between two and two thirty. Yeah, two o'clock. Around two thirty. Okay, I will put that on my calendar. I think I should be able to join, yeah. Okay, so then I mean, I think that I will try to give them a joint perspective of various things just in more or less in the way that you started, but maybe a little bit more simply with a little bit more of algebra and then we can all try to kind of make some kind of an impact on this entirely new audience to this field. But I mean, they are already, to some degree, introduced to tokamak confinement, but not really, not in any fundamental sense. So we'll go through the whole notion of confinement in a in a somewhat general manner. Okay. And I'm sure Professor Paul will greatly contribute to that. And as she said, she's moving on to Columbia to build an experiment. Congratulations for that. And we'd be looking forward to the results that you produce. Thank you. Yeah. So I will be sure to join in the afternoon and also please feel free to send me an email if you have any questions that come up later on. Okay. Wonderful. Thank you. Okay. Bye.


When you put a loop inside of another loop, we call that a nested loop. For example, here we're given the code I'll write to draw one triangle with sides of length 100 pixels using the repeat times block set to 3, once for each side of a triangle. But we want to draw six triangles. In order to do that, we're going to take that loop and place it inside of another repeat times block. Pretty cool!


Live from Las Vegas, it's theCUBE. Covering VMworld 2017, brought to you by VMware and it's ecosystem partner. Okay, welcome back everyone. Live here in the VM village at VMworld 2017, it's theCUBE's exclusive three day coverage, day three. Kicking off, we're here with Robin Matlock, CMO of VMware, great to see you. With my co-host, Dave Vellante, how are you? Good, hi guys, great to be here. Day three, we noted, you got the same thing down this whole VMworld cadence. Day two is always a great networking night, a lot of different events going on, and then you kind of make it like a light morning, no keynotes by design, I'm sure. Yeah, thanks for that. Well, and the attendees really, to be honest, they want the breakout sessions in the lab. So you give them, you know, when we do keynotes, they don't have that opportunity to do that. So Wednesday and Thursday, there's no come, you know, not very little to compete with that. They can get to those breakout sessions, so. Okay, great, give us some of the inside, the numbers, attendees, what's going on this year, what's different about this year? If there's anything different that's the same formula, give us some of the data. Yeah, you know, it's going to be interesting as we kind of leave the event and get a little bit of more post-mortem insight, but my perception being in the middle of it is, the energy this year is, there's a tipping point. There is, we are at some inflection point in this industry, and you can just feel it here at VMware and VMworld. I think that, you know, kind of some of the partnerships that we highlighted on stage has just changed people's perspective about what's really going on in this industry and really what's VMware's role in it. Yeah, a new vibe too, I mean, VMware, we were talking about the transformation of VMware as a company, and from its roots to where it is now, and then just in the ecosystem, just in the past two years alone, you're seeing, it was almost like the eye of the storm, and then all of a sudden now a new ecosystem vibe is here, which is clarity. They kind of know what's going on, the cloud thing has decided, they know what to expect there, and so people see the beginning back down to business. Yeah, I think, first of all, the ecosystem is such a vital part of VMware's culture and success and history, but when any market goes to a massive disruption, it impacts everything, right? It starts with the customer and what they're trying to do with their business, but then all of us on the technology side, we're having to shift and adapt and change, and that means also our relationships with each other is shifting and adapting, you know, I think you're right. I think there is a lot of historical legacy and many of our relationships are very strong, and I think those are going to continue to be very strong, but you're seeing a lot of new brands step in, you know, whether that's the Googles or the Amazons, you know, kind of taking it to a different level. There's a new blood both on the ecosystem and also employees within VMware, we noticed some new keynote folks on stage, some great women in tech now, a lot of ladies in tech going on at VMware, you guys done a great work there, just want to give you a prop on that. Yeah, you know, actually thank you for acknowledging that because it's so important that we drive diversity and inclusion in our industry, and we all know, as an industry, we're not performing particularly well in that department. Actually, I was told by my CUBE guest one time, it's actually been changed, it's inclusion and diversity now, they kind of move the eye first. Yeah. That's what I was schooled on, but no, but this is important, inclusion has always been part of VMware, but you guys are doing more of it now. And we're working hard, and trust me, those were conscious choices about thinking about who is the messenger for our narrative and our story, from customers to employees, and want to make sure that we're representing the diverse world that we live in. So I got to ask you a question, I was already having an interrupt, but Sanjay was on, he was talking about the relationship with Amazon, now you've got Google, I interviewed Sam Ramjay yesterday after his keynote here, and VMware goes to the Amazon events, you don't see Microsoft going to Amazon events and Google going to Amazon events, so VMware is going to all the now cloud events. Kind of changes how you do the community as people start collaborating with Google now, you've got Microsoft, you have Amazon, how is that changing some of your marketing tactics? If any, does it change at all? I think it's, first of all, our marketing tactics are always grounded in one thing, what is the business outcome we're trying to drive? What's our business strategy? And then we think about what's the right marketing strategy to get us there? And look, we've been very vocal and very consistent, we believe the world will be made up of multiple clouds, right? We believe in a multi-cloud world, we think our customers are going to consume cloud services from a variety of cloud providers, and what we're all about is creating a common operating environment that lets you run, manage, connect, and secure clouds, workloads on any cloud, right? Consume by any device, and that means we've got to be present when these other clouds and their customers are engaging, VMware needs to be present, so that's what's driving my strategy. So that's really clear, the clarity is a really real theme to me, anyway, of this year, but when you think about maybe a related question on the marketing and the narrative, the broader narrative, you know, the lows in this industry sometimes are low because of external factors, sometimes they're self-inflicted and the highs are really high, and you guys are on a real high right now, so it's like your North Star is sort of that customer focus, that value piece. So when you think about the changes that are going on in the ecosystem, and it's reforming, do you try to sort of capture that momentum and ride it, or do you sort of try to stay steady stream from a marketing pro's perspective? No, I think absolutely we want to ride momentum, and I think, but first you have to have your fundamentals, right? I think all of it, we believe we create momentum. We create our own momentum, and we're not responding to momentum, we're creating it. Now, are we doubling down, are we paying attention to what is resonating, and what customers are saying, that's important to me. Well, yeah, then we'll kind of be agile and invest and really accelerate in particular areas. I do think VMware has tremendous momentum, but I think we've been working on that for a long time. I don't think it's some short-term thing that's happened. We've been building great momentum now, quarter after quarter for quite a while. Sort of a self-powered machine is essentially what you're saying, but I do feel as though, and tell me if you agree, that the clarity with respect to, say for instance, the AWS announcement, and the customer clarity, we've been talking about it all week with the notion that, I'm not just going to bring my data into the cloud. I've got to bring the cloud to my business model, and I think there's a reality that is set in. Have you seen those two factors sort of help you, help customers understand your vision better? I mean, I wonder if you could comment. Yeah, I think first of all, there's some level of just maturity that is happening. These things have been, three years ago they were so new, and we've gotten really involved, and we've started playing around, and we've started trying some things, and testing some things, and listening to more customers, and I think customers are going through their journey. So all of us, I think, are kind of on our spectrum of maturing, and that helps drive clarity. I think VMware has a vision, and it's consistent. It really hasn't changed for many, many years. We were advocating hybrid cloud long, long ago, and so now what you're seeing is the delivery against that vision. So clarity, you can start getting more and more focused because you keep making the next step forward in delivering on the vision that you set. Well, the bets come through. You can see which, as it shapes, which bets are happening, which ones are not, and then you get, okay, that's not working. Let's keep this going. And Dave, just your point about customers, I think for us we're always really deeply committed to saying connected to our customers. So the validation that customers are putting on stage and talking about, that's really evidence of just that they've validated our strategy and that as we're making these next milestones, they're in it with us. And I think that's a really important thing that we're constantly being responsive to what are their requirements as they learn more and digest this stuff more. One of the challenges that comes up with communities that are robust as VMware's has and VMware's communities have always been the strength and the ecosystem's part of the community is as the world grows, open source is growing, communities are growing, there's always been the talk that, oh, reinvents the new VMware world and then VMware world just never goes away. It's still a robust show. You guys continue to do a great job but now you start to see these communities come together. Reinvent and VMware world. Google now putting the olive branch out there with you guys. I still haven't seen the Microsoft piece come together yet but it's clear that Amazon web services and VMware have synergy. Andy Jassy's on stage with you guys. So you have to challenge the team to still be collaborative with the cross the communities. How do you balance that from a marketing standpoint? Because they still, they do compete. Amazon, Microsoft, Google kind of compete. Yeah, but if you look at VMware's position in that landscape, I mean, we are the common operating environment that lets you run, manage, connect and secure any work late, load on any cloud. And sure they're going to compete and they're going to compete fairly and they're going to go try to win in the market. Our job is not to help or break that. Our job is to elect customers, decide which of those clouds makes sense for their business and ensure they have a common operating environment. I think we used the word arms dealer yesterday with Sonja. I don't think he was going for that one pretty well. But you, VMware hasn't. That is not going to pass the marketing test. We like it because it's a good cube material. But VMware has a point of view and you have to assert that point of view as a leader or you have to be subservient to those other leaders and it doesn't appear that you want to be subservient and there is a stack war that's emerging and you are at the center of that and you can either lead it or you can follow it. And I think we all bring a different set of strengths to the table. At the end of the day, VMware has had incredible success in the enterprise and within the enterprise data center and that is our forte and we're going to leverage that and what we are, the experiences, the training, the expertise that our customers have, they want to capitalize on that. They don't want to throw that out the window and they don't need to. We're going to enable them to capitalize on that and use that in these other cloud environments and get the benefit from those cloud providers while not giving up some of the benefits they've been enjoying for years. Well, the technology matures very quickly and we're seeing that and you guys address some of the cloud native stuff but the people process stuff doesn't mature nearly as quickly. Somebody said the other day and I thought it was a great quote, you're moving at the speed of the CIO which is really underscores that you can't get out ahead and over rotate or you're going to lose that customer base. I would argue that the CIO probably needs to pick up the pace a bit because he's got to move or she at the speed of business. It's hard. And that's fast as Pat was saying. This is the slowest day of your life going forward today and the next day is going to be faster. Props to Pat, we'll have him on at one because he's having a great year. Congratulations for really VMware.  We've never been afraid of being decisive and making big bets, you know? That's what staying relevant's all about. Well Robin, we made a bet on VMworld years ago, you made a bet on us and we're proud to work with you and thanks for your support for theCUBE and Andy Jassy the same with AWS. We made a bet on them when they were like didn't understand it now, here it is, and soon it'll be Google so thanks so much for your support. All right, well here's to adapting and being versatile in this crazy industry of ours. How about making the bets? Here at VMworld 2017, that's the theme, making the choices are clear, make the bets. This is theCUBE bringing you all the action from VMworld 2017. We'll be back with more live coverage after this short break.