 Hello everybody and welcome to the third video of the free online version of the fusion research lecture We are in chapter one and as you might remember in the last video I introduced the major Properties of Tokamak and Stellarator. It gave a brief historical overview and explained why we need twisted magnetic field lines Today we are looking at the nuclear fusion process itself. So today's topic is the nuclear fusion process and Again, I'd like to start with a very brief historical overview and the first important date to name here is certainly 1919 because as you might remember I said that already two videos ago I think in the very first video that the first fusion process in the lab was initiated at that date. So that was the first fusion process in lab By the New Zealand physicist Ernest Rutherford And what he did is he shot or he bombarded Alpha particles onto nitrogen and He observed that The positively charged party was created the proton here and the second important Date here is probably 1938 because in that year beta and white-sacca Independently explained the Sun's energy source. So in that year beta and white-sacca Explained Sun's energy source and what they explained was There are two processes responsible for the Sun's energy source one is the proton-proton chain this is the proton-proton chain and Two This is the CNO cycle also called beta White-sacca cycle for obvious reasons And we will talk about those two processes in detail now so let's first look at the proton-proton chain often just abbreviated with proton-proton chain and That is responsible for approximately 85 percent of the released energy of their released energy by the Sun of Release energy sorry and In the reaction equations on the left-hand side, you can see what is going on there So first of all we have one proton fusing together with another proton now this fusion process can only happen if During that collision one of the protons undergoes a beta decay and that was explained by beta Partly for partly this was the reason why he achieved the the Nobel Prize in 67, I think So anyway, so if the two protons fuse together one of the proton undergoes a beta decay forming a neutron an electron Neutrino-antipositron and this is why this reaction is so unlikely to happen and for a single proton to fuse together with another Single proton it takes approximately 10 to the 10 years in the Sun. So this is really highly unlikely to happen In the next step the Deterium which has been created fuses together with the proton This is much more likely to happen takes only something like four seconds forming a helium-3 and then One possible ways and that is the more likely way that another that one helium-3 fuses together with another helium-3 that takes roughly 10 to the 5 years and form a helium-4 and two protons The other path, which is more which is well less likely is that a helium-3 fuses together with the helium-4 Undergoes a few steps in the end. However, it also creates a helium-4 and two protons So the result is in the end of the same now in the equation on the bottom you see that four protons form a helium nucleus to Positrons and to electron neutrinos and release an energy of 24.8 mev This energy is distributed to the partners on the right-hand side of the equation However, we have to suspect from that the energy of the neutrinos because the neutrinos are basically not interacting with anything So minus 2 point minus sorry two times 0.26 mev Which is from the neutrinos by the way the neutrinos Have only been measured in 1992 in the galax experiment, which was in principle the first proof that this Theory of how the Sun is releasing its energy is really correct then we have to add the Anihilation of the electron and the positron which releases energy so we have to add two times Then the inhalation energy 1.022 mev this is from the Electron positron of sorry positron electron annihilation annihilation and The overall result a result. Sorry is then twenty six point three four four mev and you can see the overall reaction process sketched in the right figure the first step the two protons fusing together So the first step here the two protons fusing together then we have the deuterium and the proton and here we have the Helium-3 nuclei fusing together finally creating the alpha particle The other process was the CNO cycle CNO cycle and This is more important in heavier stars. So this is more important More important if the mass of a star exceeds or is larger by 1.3 times the mass of the Sun so an hour star does not play a major role However, the net reaction the overall reaction is the same as in the PP chain and the proton-proton chain as you can see in the Equation on the very bottom of this figure. So the net reaction is the same net Reaction is the same as in the PP in the proton-proton chain Meaning that four protons so four protons are basically forming in Helium nucleus or an alpha particle and some additional constituents However here as you can see In the left hand side Carbon acts as a catalyst So this is a major difference here. So carbon here is not consumed or anything else. It just acts as a catalyst carbon as catalyst But we will not talk much more about this process as as I said It does not play a major role in the Sun in the Sun the PP chain is responsible for 85% of the released energy Now when we talk about fusion one important question is of course how to overcome the Coulomb area how to overcome the Coulomb barrier since we have positively charged nuclei which we want to bring together Okay, so to understand this Let's start first with a simple drawing. So let's draw Diagram Something like this maybe where we have here the distance are your potential energy now what I try to draw is the potential of a potential energy of a proton proton to proton protons Approaching each other so the potential energy will increase and increase and increase even further Let's continue this year with some dots until they are very close to each other and they are so close That the distance between them is on the order of the nucleus radius and then the strong nuclear force starts to act Binding them together and this is then why the potential energy drops and starts to strongly drop Now this is supposed to be the potential of two protons and When we have energy Which is above that? Step with we have to overcome for example here. Let's say one proton approaches each other Then it will just simply be reflected at the Coulomb wall. So this is the Coulomb repulsion and What we now want to do is we want to estimate the height of that Coulomb all for that we need to make a few assumptions first of all we need to Know or roughly estimate the nuclei radius or the nucleus radius Since as I said the strong force starts to act in if they are So close that the distance is on the order of the nucleus radius. So this is can be estimated with our not a to the power of 1 over 3 where our not is a constant of approximately 1.3 femtometers so times 10 to the minus 15 and a is the the mass number mass number Furthermore, we have two nuclei Let's try to write it a bit more general each with the charge number that one that two and This now allows us to estimate the Coulomb potential Long potential then can be estimated as first of all we have the Coulomb factor e squared by 4 pi epsilon not and Then the charges that one that two and now We and we have to write down here the distance of the two nuclei. So are you are this is the distance of the approaching nuclei Now we enter the Estimation for the nucleus radius which we have written above in the top right. So this is our not then times A1 so the first nuclei plus a 2 and both to the power of 1 over 3 and This allows us now to calculate for the proton proton Fusion process of the Coulomb area and that is on the order of 0.6 Mev 0.6 Mev and As you might know, this is much larger than the Sun's core temperature Sun core Which is as we know from thermodynamic considerations on the order of 1 kev Now the question is how is fusion possible? It's possible due to two things or two processes First is quantum tunneling. So we don't need to actually Overcome the full Coulomb area, but if we are close to it then Tunneling can set in so if we are in the wave picture and say the partly supporting the other Then this can tunnel through the Coulomb area and then fusion can be possible. The other factor is that we always have a Maximum maximum distribution here since we are considering thermo nuclear fusion meaning we have a thermal plasma So we have the distribution of the energy of the electrons or more importantly of the ions So we said fusion is due to two processes processes so fusion is due to One hand side is the tunneling Tunneling which was first described by gamov in 1928 and The other one is the Maxwellian tail Maxwell tail As we are talking here about or as we are considering your thermal nuclear fusion as I said Okay, now let's try to make another drawing to illustrate that a bit better probably something like this Then here Something like this Now what do we have here, this is the easy energy and let's first have a look at Maxwellian, sorry at a Maxwell-Boltzmann distribution. This might look something like this It goes down Was an exponential write an exponential read more or less like an exponential. Yeah, so this is FM and FM is supposed to be a Maxwell-Boltzmann distribution often just in short a Maxwellian distribution And that is proportional to Velocity squared and then to the energy factor where we have e to the power of minus e over t the temperature and By the way on the y-axis, this is something like a probability here and Now the probability for fusion If we would draw it on the same scale, we would hardly see it So we just now draw here the fusion cross-section, which is proportional to the fusion To the probability for fusion to occur and we try to draw it with the Dashed line something like the higher the energy This somewhat increases. This is supposed to be Sigma fusion This is the fusion cross-section so sigma Fusion This is the fusion Cross-section This is a quantity or a measure for the probability that the fusion will take place when two particles collide and the Convolution of these two quantities of the Maxwellian and of the fusion cross-section this gives us a measure for The fusion rate of our fusion rate coefficient. So this will look something like I try to draw it Something like this. So it is a convolution that increases and then you decrease this again Maybe something like this and this is often or this is abbreviated usually with a digmer fusion times you the velocity and this is the fusion rate coefficient What is that that is the convolution? Convolution of the Maxwellian distribution and then let's write it like this for indicating convolution and the fusion cross-section Okay Now I have introduced the fusion rate coefficient being the convolution of the Maxwellian of the Maxwell-Boltz von distribution and The fusion cross-section now which depends on the energy. So let's just quickly write that down So we have the fusion rate coefficient Coefficient Sometimes also called fusion reactivity And this is sigma Fusion times you Being proportional In proportionate to the integral of er the relative energy of the two particles approaching each other then the Maxwell-Boltz von term and Then the fusion cross-section sigma fusion, which is also a function of the energy and then d er Please note that on the left-hand side We have these brackets Indicating that we take an average here since we have the Maxwellian the Maxwell-Boltz von distribution Meaning there's a distribution of velocities and energies. So we must take an average here so er is to be complete here er is the relative energy the relative energy of the colliding colliding ions you is the relative velocity relative Relative Velocity of colliding ions and t is the ions temperature. So this is ion temperature Now how to get the fusion power from this? Quantity or from this measure might be an important question. So let's just quickly write that down the fusion power if you want to estimate that Fusion p And we also need that later on This is the number density of one species the number density of the other species and then the fusion reactivity, so the sigma fusion times you or fusion rate coefficient Both are valid names for it and then the energy Released in the fusion this gives you or allows you to estimate the fusion power Okay Now the fusion cross section it depends on the particle species. It depends on the action fusion process you're looking at We have talked so far only about the proton proton reaction going on in the Sun However, there are much more possible future actions Here I have drawn The most important ones so here you see the fusion reactivity as a function of the ion temperature and you can see there is one Reaction the blue curve, which is the most likely it has the highest reactivity parameters over a large range of Temperatures and here approximately is the maximum achieved and this tells us that often this diagram We basically conclude a conclude that the Deuterium fusion which corresponds to the blue curve the deuterium trisium fusion is the most attractive Candidate for fusion on earth on earth for fusion on earth There are few other fusion reactions drawn in this diagram included in this diagram One important one might be the purple one where you have helium 3 plus helium 3 This is the purple one here this one you see however that over a large temperature range it has orders of magnitude lower reactivity as the other values and only if you achieve very high temperature this becomes Achieve is reasonable reactivity values I've just included it here because the helium 3 fusion is something which you often find in sci-fi literature The proton proton chain reaction is not included here in this diagram because the reactivity is just so Incredibly low. I told you that for a single proton diffuse with another proton together It takes 10 to the 10 years in the Sun However, it does not really matter It's not a problem for us as the Sun is so incredibly large and also has a very high density at the core On earth, this is something which is however not attractive on earth the deuterium trisium fusion reaction is to the most attractive candidate so let's Spend a few more words about that reaction. So it's the terium plus trisium Which is basically heavy hydrogen plus very or super heavy hydrogen and that fuses together to an helium 4 particle so to an alpha particle Which has an energy of 3.25 and EV and a neutron which has an energy of 14.06 MeV and To talk a little bit about the abundance of the terium trisium Deterium has the very big advantage that it can be simply extracted from seawater. So the terium can be extracted from seawater and There is so much Deterium on earth that it is sufficient to To supply the human mankind with energy for every time scale you can imagine Trisium however is radioactive with a half time of 12.3 years So trisium is actually very rare. So this is why we need to breed trisium. So trisium breeding Happens in lithium blankets. So lithium Blankets are used to breed the trisium Which means that the neutron which is created in the fusion process is Needed for breeding the fusion fuel. So this is needed for breeding The helium nucleus the alpha particle as we will see later on is used to further heat up the plasma Heating since if we have a magnetically confined plasma since the helium nucleus is a charged particle It is also confined by the plasma by the magnetic cage The neutron is not confined this immediately hits the wall Where it's supposed to create a in the lithium blankets more trisium and it's supposed to make the wall hot And this is how the energy is extracted from a fusion reactor So blankets are something very important and there are two processes how the trisium can be created The first one is from lithium 7 plus a neutron this generates and helium nucleus Plus a trisium and the other one is using lithium 6 where Also an alpha particle is created and A trisium and in the top one, so I forgot another neutron which is also created there now while the first one might Look more effective to do the additional neutron created there the second one has actually orders of magnitude higher Probability to happen so the cross section is much higher much larger And this is therefore the one which is favored in fusion actors and will be used there although a lithium 6 is the rarer Isotope it has only an abundance of 7.6 percent isotopraction whereas lithium 7 is on the order of 20 s or a 92.4 percent In addition to lithium and the blankets, there's often beryllium you did as used as an additional neutron multiplicator So the blankets we also often have beryllium as a neutron Multiplicator There have been only very few experiments with trisium so far namely two experiments only two Experiments with sorry, I meant with trisium not with lithium with trisium This was one t f t r, which was located in Princeton the tocker mcfusion test reactor And the other one jet, which I have introduced already in the last lecture Tftr is no longer running jet is still running and jet is at the moment prepared for another Tftr campaign, which is scheduled for this year Okay, and as for the last slide we have a very brief reminder on the nuclear energy Source, so what is actually responsible for releasing the energy? So the nuclear energy source and this is something Which you probably know from your high school physics that is the binding energy binding energy and the famous equation e equal to mc squared and You see that on the left diagram illustrated. I have drawn there the binding energy Per nucleon as a function of the atomic mass number and you can see that this increases starting from hydrogen It increases until it reaches a maximum at something at nickel 62 then it decreases again And if you now come from the right-hand side and making Your nucleus in a way like decreasing the mass number. Let's say this is fission because in that way you can Release energy because then the binding energy per nucleon is higher in your core if you go into this direction This is the fission direction If you however go along the fusion direction You also increase the binding energy per nuclear and release this energy in the fusion process so you're going along this path and the gain Per nucleon or the gain sorry the gain of energy. I wanted to say the gain of energy in Fusion the gain of energy per nucleon in fusion is Generally larger as you can see that from this diagram then the gain of energy Nucleon in Fission Although the gain of energy per reaction in fission is often higher or is generally higher just because the atomic mass number is so much higher Okay, that's it for a brief introduction about the nuclear fusion process and the most important Yeah parameters Involved there and in the next video we will talk about key parameters in fusion research. See you hopefully in the next video