Hello everybody and welcome to video number 26 of the online version of the Fusion Research Lecture. In the last video, we started with chapter 5, Collisional Transport and I tried to explain you how the transport or how we will describe the transport based on random walk processes and we just started to talk about the classical transport last time. And in this video, we will start to talk about neoclassical transport because you might remember I told you that the Fusion Reactor just being based on classical transport would have a size which would fit on your table and you know that this is not the case and one of the reasons why this is not the case we will see in this video. So it is about neoclassical transport. So as I said last time, neoclassical transport, the expression neoclassical just means that we have a toroidal magnetic field geometry, toroidal B field geometry. The expression neoclassical just came from the fact that this is more than just classical transport and it is maybe a bit of an unfortunate expression because it sounds somewhat fancy but neoclassical transport does means having a toroidal field geometry. As you know from the chapter particle trajectories, having a toroidal field geometry means there are different type of particle trajectories possible. We have passing particles. We have particles on banana orbits and in Celerator for example, we also have helically trapped particles, helically trapped particles. All of these different orbits and different particles contribute to the neoclassical transport in a different way as we will see. And in this video, we will start to talk about passing particles. We start to talk about passing particles. And passing particles, the transport residing from passing particles is also referred to as Fersch-Schlüter transport, Fersch-Schlüter transport. So again these two important names, Fersch-Schlüter transport, so it is very likely that these names will be asked, that you will have to say these names in the exam. Now just as a reminder, having passing particles means that the particles do not stay locally on the flux surface. On average, yes, but locally they can deviate from it. And this displacement is what we will use as step size because also for the neoclassical transport, we will use the random walk approach, meaning we need a step size and a stepping time. And as a step size L, so this is a step size L in the random walk approach, we will use data P, which was the displacement of the guiding center, displacement of guiding center from the flux surface, from flux surface. And we call it these orbits, you might remember the drift orbits, the drift orbits. So it is basically the displacement of the center of the drift orbit with respect to the flux surface. And just to be precise and sure here, L, this is the step size in the random walk description that we are using. Okay, and we get the maximum displacement if, well, let's say the next quantity, we need the two quantities for getting a diffusion coefficient based on the random walk approach, the step size and the stepping time. So and we get the next step for the stepping time, we distinguish two cases. First of all, we get the maximum displacement if the collision time is much longer than the transit time. So we get the maximum displacement, maximum displacement which is data P if the electron ion collision time is longer than the transit time, transit time. This means that we allow the particle to fulfill or to make the orbit, the full orbit such that it can experience the maximum displacement from the flux surface. If the particle would collide a lot, then it would not experience a full displacement from the flux surface. This is why at a first as a first this distinguish, we have, we get the maximum displacement if the collision time is longer than the trapping, sorry, than the transit time. And this then results in a diffusion coefficient P s for first Schlüter, which simply reads data P squared, so the stepping time squared, a squared, sorry, the stepping size squared over two times tau electron ion where we have used, where we can now insert for, oops, sorry, for data P, the displacement, this was the Poloid-Lama radius times epsilon the inverse aspect ratio and the Poloid-Lama, sorry, the Poloid-Lama radius, this was given by the energy of the particle basically M times V over the charge and the Poloid magnetic field. Now if we insert these quantities, we get the following expression, we have one over two times tau EI, the collision time, then we have M V over Q B and then times yota bar as you will see, and this squared and this is basically, so this expression here you might remember, this expression corresponds to the classical diffusion coefficient as we had it in the video last time, just this expression. So this is then the classical diffusion coefficient times one over yota bar squared and we have used here the expression which we had, I think one or two times in the video that yota bar can be written as R naught over R and then B theta over B, meaning we now have an expression for the, or we can now get an expression for the particle diffusion coefficient in the Schluter regime, in the first Schluter regime and this is usually often abbreviated with D for NIO and then NIO in the index and the subscript sorry, so for neoclassical being the sum of the classical diffusion coefficient plus the Schluter diffusion coefficient and since we could express the Schluter diffusion coefficient in terms of the classical diffusion coefficient, we can now write the classical times and then parenthesis brackets one plus and now there's a two over yota bar squared, just if you're wondering where this two comes from, so this one, this comes just from the fact to make this simple description, this equation agree with the literature value, okay? So this then is proportional to the collision frequency since the classical diffusion coefficient is proportional to the collision frequency, meaning that we have again a linear scaling, linear dependency and maybe we just write that down here as a reminder this factor of two, this is to make our simple description, to make simple description agree with literature, so with a properly derived rigorously, I should say with a rigorously derived diffusion coefficient. Now we have an equation for the diffusion coefficient in the neoclassical regime, what does that mean? Let's have a look, so if we assume a typical value of yota bar of 1 over 3, then we get neoclassical diffusion coefficient on the order of if you insert this here on the order of 20 times the classical diffusion coefficient, okay? So the neoclassical diffusion coefficient is larger by a factor of 20 than the classical diffusion coefficient and this is just due to the toroidal magnetic field geometry, just due to the toroidal magnetic field geometry, so quite significant. Now in the beginning of this slide in the top, we made the case or the requirement that the collision time should be much larger than the transit time. Now what is if this is not the case? So what happens in the case of a collision time being smaller than the transit time? Collision time being smaller than the transit time, then the displacement is reduced, oops, then the displacement of the particle is reduced, which means that the diffusion coefficient is also reduced and the displacement is reduced because the particles drift now only between two collisions, so they do not fulfill a full orbit. So it is reduced basically due to the fact that the particles now drift between two collisions only such that the displacement is given by the drift velocity times the stepping, sorry times the collision time. Instead of what we had before, we had the drift velocity over the poloidal transit time but since the particles now no longer make a full poloidal orbit due to the short collision time, we have to replace that by the drift time and as you know by now probably the drift velocity simply mv squared over qrv. Inserting this results in a diffusion coefficient for Schluter equal to we have the drift velocity times the collision time and then this needs to be squared. So this is the step size, now the stepping time is the same 2 times tau ei, so it's the same expression. Now inserting this for the drift, inserting for the drift velocity we can write mv squared over qbr squared times tau ei over 2, since one of the ti cancels out, of course if you have a look here so this ti cancels out and one of the ti's in the nominator cancels out and this means now interestingly that the diffusion coefficient scales inversely with the collision frequency. So this means that the diffusion coefficient in the Schluter regime now decreases with increasing sorry collision frequency between electrons and ions. If we have a plasma which has short collision time and these plasmas often referred to as collisional plasmas, so the diffusion coefficient in the Schluter regime decreases with increasing collision frequency in a collisional plasma. Okay so that's it for the neoclassical transport being based just on passing particles and we call the resulting transport first Schluter transport and we have to distinguish between two cases. One case if the collision times are long meaning we have very little collisions because then the particles can fulfill the full poloidal transits then the other cases if the collision time is shorter than the transit time the particles can no longer fulfill their the full poloidal orbits and these two distinguished cases resulted in different scalings the first one where the collision times are long so where we have very little collisions very little collisions going on. The diffusion coefficient increased linearly with the collision frequency and for the other case when we have a lot of collisions the diffusion coefficient decreased so it increased with one over the collision frequency and the important result is that the particle diffusion coefficient in the first Schluter regime when we have little collisions going on when the collision time is long is approximately 20 times the classical diffusion coefficient so much larger. Okay that's it for this video see you in the next video.


Today, whips, chains, and metal things are a part of pop culture. A 2015 survey found that 64% of women and 53% of men reported fantasies of being dominated. But if the idea of being strapped down and spanked is still a little much for you, let me assure you that you are not alone and also that bondage play can be as intense or as tame as you want. Which is exactly what I wanted to share with Hattie and Taylor. A couple curious about bondage. Hattie and Taylor, how are we feeling? I'm excited, I'm excited. I think I'm more curious and excited, but also a little scared. Well, we are about to enter into the Disney World of BDSM. Are we hyped? We're hyped. Let's do it. Let's do it! Yeah. Let's go, let's go. Enter at your own risk. Oh, wow. Welcome to Zedungeon. First impressions. It seems kind of forbidden. Yeah, it's that element of danger. It's just like naturally in the air here. What made you attracted to the world of BDSM? There's been a couple of times where I've encouraged us to go to a store and maybe play with some toys. And then when we walked in there, there was a whole different room of foreign objects and just leather and whips and stuff like that. And I think he was actually the first one to kind of teeter over into that section and start playing with stuff. And I was like, okay. Interesting. I mean, you can't help but look at it. Yeah. How kinky have you guys gotten? I really enjoy spanking there, I said it.  He met me. But there has been a time that like I did it a little too hard. And so like now you're going to put a weapon in my hand. It's like, I don't know. That seems dangerous. Hey, this guy was fun. I picked this for you. There's two acronyms that I want to talk about today. So the first is BDSM. That stands for bondage, discipline, sadism and masochism. And so bondage and discipline are obviously a very big part of what you do with this play. That's what all these tools are here for. Sadism and masochism speaks to the different roles that are at play.  But the word pain is very subjective. Yeah. Right. Yeah. I think the big misconception about BDSM is that it's about torture and a victim. Yeah. It's not. Oftentimes a person who is the dominant is actually the really nurturing one because it's submissive. It's all about them. It's about their pleasure, their boundaries, their desires, their fantasies and the dominant is there to bring those to life. Okay. I never thought about that before. Yeah. Okay. Keep playing. Show me what your eyes are drawn to. Oh, the nipple clams. Yes. Give to your church. The second acronym is RAC and that stands for risk aware consensual kink. So you actually can't consent to kink until you are aware of all the risks and that is why negotiations are so massively important and the negotiation sheet that I gave you guys, you gave me your hard nose, your yeses and your maybes. Let's talk about a few of these. Okay. Now when it comes to power exchange, Taylor, you were interested in Hattie. That was a no for you. How come? I feel like if I step into a role, I'd have a hard time kind of changing up in the middle of it. I viewed that as me like giving the power like I'd be okay with not having...  So what you're actually describing is known as a scene and that's when you step into character. So to your point, if you're starting off as a dominatrix in the scene, you may not want to switch midway through. Right. But you would be comfortable in another scene, maybe an hour later, maybe two weeks later, and in that position now you are the submissive. That I would be okay with. Okay. Then yeah, you can change my answer. I think what's great about thinking about it like scenes is that you're allowing yourself to have an alter ego. In this place, in this space, you get to become whoever it is that you want to be. And when you go home, that's not a reflection on who you're going to be later on. Right. Right. Safe words are really important in BDSM because part of the fun sometimes is saying, no, stop, don't, I can't. This is a word that's very separate that we wouldn't use in the act. So when you hear it, that really means stop. So what are your guys' safe words? I feel like you want to make it something random. I do. What? I don't know. Oh, I thought you were saying that was a safe word. No, no, no. Like, that's an incredible safe word. No, I have a feeling that I'll say that multiple times if we're in a fun scenario. Kiwi. All right. So all we've done is sit and talk. Yeah. Let's do it. More enthusiasm. Are you ready to play? Yeah. Let's do it. Let's do it. Patty, step right up. Strap me in. Is that comfortable for you? Yeah, it actually is. Okay. All right. I'm going to hand this over to you. Okay. You got the keys in your hands. I think this is a great time for the two of you to explore and for me to take my exit. Patty, thank you for trusting me. This was wonderful.  Thank you for watching Sexology. We'll see you next time.


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