 Hello, this lecture started with the topic of neutron source. I explained to you how to tailor made the neutron spectrum inside the core using various kinds of sources. I explained to you that the thermal neutron flux is the one which is predominantly all over the reactor core but we can modify the spectrum using something called a cold neutron source to lower energy and something called a hot neutron source which will shift the spectrum to higher temperature. So, when I say shift the spectrum that means the maxwellian the total area under the maxwellian which is the total number of neutrons they remain conserved but the spectrum shifts to lower energy and then there are gains in the lower energy side of the spectrum similarly for a hot neutron there are gains at the higher energy of the neutrons. So, they don't actually act as sources in the sense that they produce neutrons but they rather re-thermalize the entire spectrum and gives us a peak which is desirable when I need low energy neutrons in the low energy side when I need hot or high energy neutrons the high energy side and this is done by a small amount of cold moderator for the cold neutron sources at a specific location inside the core which is and then the beam lines which transport the cold neutrons they look at this particular source and look at the modified thermalized low temperature spectrum and there is a gain in neutrons it can go at the to the level 10 or 20 factors compared to the thermal neutron flux in the core and similarly a piece of hot graphite inside the core at the temperature of around 2000 degree centigrade shifts the entire spectrum to high energy side. Among the cold neutron moderators liquid hydrogen, liquid deuterium, liquid methane, solid methane these have been used heavily because first these are low Z element base sources so the energy transfer is fast instead of hydrogen deuterium is preferable because D2 has smaller neutron capture cross-section compared to H2 so you don't have any absorption at the same time D2 has a smaller scattering cross-section also compared to hydrogen so the mean free path is large so you need a larger volume of deuterium so when you use deuterium it can be to the tune of 20 liters of deuterium whereas when we use liquid hydrogen it can be half a liter of hydrogen so the cryogenic load for a D2 source is more but it is worthwhile if economics that means the finance allows and cryogenic load is much higher for D2 source compared to H2 sources. Now once the neutrons are produced in the core which was a topic of discussion in the last part we will talk about neutron transport in this part so neutron transport from the core to the beam mouth happens through neutron beam lines and we can carry neutrons far away using neutron guides so beams bring out the neutron out from the core and the moderators in case of spallation there are moderators surrounding the spallation target because spallation target produces only high energy neutrons they are captured in a moderator kept strategically either above below or in the sides of the target and then from here beam lines they bring the neutrons out followed by guides if they are cold neutrons so this is the scheme for the topic today so I show you that there are different kinds of beam lines radial tangential and through tubes so let me explain to you so this is the core possibly there is one more two more circles so a beam has to come out from the core a neutron beam to the mouth and this distance is approximately to the tune of five meters so these beam lines they allow flow of neutrons through these beam tubes but the factory may in the neutron any point in the core acts like an isotropic source and when is an isotropic source the intensity of the neutron beam falls as 1 by 4 pi r square if r is equal to five meter which is 500 centimeters then this becomes a factor of 1 upon 4 pi r square is 25 into 10 to the power 4 so equal to 1 upon 4 into 3.14 into 25 to 10 to the power 4 of the order of 1 upon 4 into 3.14 is 12 so I can say 25 into 10 to the power 5 and this is 1 fourth so it goes to around 0.4 into 10 to the power minus 5 approximately of the order of 10 to the power 5 so neutron beam falls by a factor of almost 10 to the power 6 by a factor of 10 to the power 6 a million times so the factor of 10 to the power 6 when you go out from the source so the flux will be if at the source it was 10 to the power 14 neutrons per centimeter square per second so 10 to the power 14 goes to 10 to the power 7 or 10 to the power 8 neutrons per centimeter square per second when I come out from the source so this is a huge fault and this shows that neutrons are expensive and we have to do a proper neutron beam tailoring so this is the fact now the radial beam lines are the ones which look at the core radially for example this is the one whereas the tangential beam line that looks at the cores tangentially and also there are other kind of beam lines which are known as true tube the tube runs through the core now the fact remains that the tangential beam line tangential beam line beam line is longer than a radial beam line then why should I make tangential beam lines the reason being if I look at the core the gamma rays and the unmoderated fast neutrons they tend to go out radially so when I look at the core radially then along with the thermal or cold neutrons you have fast neutrons gamma rays which are traveling radially fast neutrons why are they traveling radially because these are the neutrons which have not undergone too many collisions generated at the core and they tend to go out radially when I make a beam line tangential somewhat like this then I am not looking at the core directly and sometimes even we go out from the core to the reflector reflector and in the reflector if it is small core like ILL granable here I have the neutron flux almost isotropic and uniform or maybe falling somewhat slowly here I can make the beam line look at a certain part of the core but a certain part of the reflector but not directly looking at the core so this reduces the fast neutrons and gamma rays and allows thermal or cold neutrons but we know that in this case 1 by 4 by r square loss will be more so it's a gain versus loss so it's a gain versus loss picture gain versus loss versus loss and accordingly you have to do I'll give an example of this picture let me just show you if you see this the top four beam lines you can see they are tangential to the core which is this lattice with the lattice of fuels at the center and the radial beam lines are at the bottom now you can see that the core wall the biological shielding wall has been reduced where the tangential beam lines are there this is to maximize the flux because in that case it is traveling a shorter distance so 1 by 4 square loss is minimized at the same time you have less number of unwanted fast neutrons and gamma rays where the radial beam lines they have all these and you have to shield accordingly now the story of true tubes why true tubes let me expand the core so if this is the core we can make a true tube run like this but then the question is from where the neutrons will come to the true tube if I run a hollow tube across the core so actually a true tube has a gap between the two parts so a true tube in reality looks somewhat like this and in between there is moderated in the core now why it should be like this reason being and then of course the rest of the biological shielding they run reason being now neutron which is undergoing collision inside the core a neutron which is bent through a very large angle can come in in the true tube and the neutron which is scattered at large angle has a chance of better thermalization so true tube true tube true tube allows thermal neutrons preferably and you can see if the gamma flux is going out radially they have less chance of coming out and same goes for the fast neutron flux so true tube and also since it is passing through the core so it is in a high flux zone high flux zone zone allows thermal neutrons preferably preferably and cuts down cuts down fast neutron and gamma so with all these properties true tube at the outlet of the true tube you will find more number of thermal neutrons less number of fast neutrons less number of gamma to shield from so with this the true tube at Dhruva it has got one beam line TT1015 on the left and TT TT is true tube 1004 on the right so so now I have completed the discussion on the types of beam lines that one can have to bring the neutron beam out which is preferably we will expect thermal neutrons to go go out and arrest the fast neutron and gamma rays to the extent possible now the fall in flux as I said showed you in my calculation so it's over the core flux so it's actually 1.8 into 14 neutrons per centimeter square per second which goes to around 10 to 7 to 10 to 6 neutrons per centimeter square per second when it reaches a beam out and we cannot avoid this because it has to travel to the beam out to the outside so radial beam lines are the shortest I explained to you why we use tangential beam lines which reduces gamma rays and fast neutrons through tubes allow less fast neutrons and allows thermal neutrons preferably and there is some bit of moderator between the two parts of a true tube as I showed you in the drawing and in Dhruva we have 100 millimeter and 300 millimeter beam lines with 300 millimeter beam lines are made their larger diameter because you can allow some insertions through these beam tubes and for experiments we use the 100 millimeter beam lines through which the neutrons come out so this sort of shows you in Dhruva the number of tangential beam lines the true tube at the radial beam lines now I will talk to you about neutron guides so as you see that if you want to go out 40-50 meters away then we can't allow neutrons to flow freely because 40 meters means 1 by 4 pi r square 40 meters becomes 4 into 10 to the power 5 so that kind of fall so that is a huge fall so it goes down to and we cannot allow the neutron beam to diverge keep on diverging because they're continuously diverging keep on diverging from the as it goes from a point source and for that what we use are known as invention from the 1970s known as neutron guides neutron guides neutron guides I will repeat again neutron guides are like optical fibers so now you can define a refractive index for x-rays and neutrons and in a very generalized statement I can say that the refractive index for x-rays and neutrons for most of the materials are less than 1 it is marginally less than 1 around 1 minus delta and this delta is around 10 to the power minus 5 for x-rays and 10 to the power minus 6 for neutrons so I can say that neutrons and x-rays undergo total external reflection at very low angles so if I have a surface let us say most commonly used guide material was nickel so if it is a one angstrom neutron then it will undergo a total reflection up to six arc minutes that means one tenth of a degree up to one tenth of a degree point one degree it will undergo total external reflection that means a neutron beam falling below six arc minutes angle will undergo reflection and now the guides use this principle of reflection and as I show you here so up to a certain angle which was six arc minutes for one angstrom neutron for nickel it undergoes reflection and so critical angle for external reflection nickel six arc minutes per angstrom so if I want to take out a cold neutron or a low energy neutron typically let us say four angstrom this four angstrom neutron will have a critical angle which is four into six 24 arc minutes that means up to 24 arc minutes I can totally reflect this neutron and then we can make something like a nickel guide here I show in this drawing it's a rectangular cross section for a nickel guide and the inner wall so a nickel guide has a rectangular cross section rectangular cross section like this like this and the inner wall of this is basically let me just show you the side view is something like a float glass which is a very very low roughness glass coated with the so far as elements are concerned nickel will be best nickel will be best coated with a core nickel and this nickel coating is around point one micron thickness so around point about point one micron that is 1000 to 2000 angstrom now my neutron guide or the optical fiber has two elements on two surfaces on that side and if the guide the neutron enters gets reflected from the surface and then starts traveling so basically this picture the neutron gets reflected and travels and hits the next element and I keep putting element of the elements so this is one element this is one element followed by another element followed by another element so this is how it goes each is around one meter long so if I put 30 such elements I can take the neutron sideways 30 meters but now by doing this the neutron is traveling through total external reflection through this thing of course this has to be a cold neutron because if it is a thermal or hot neutron the critical angle will be very low so very less number of hot neutrons can come out but for cold neutrons this angle is reasonably large for cold neutrons for cold neutrons and they will get transported the way laser beam gets transported through an optical fiber and it travels through the guide and that it is not now suffering from a 1 by 4 pi r square loss node so the transmission depends on the length of the guide and how good we align them because now we are talking about such small angles it is important that the alignment is proper so the cold or low energy neutron travels through reflection similar to optical fiber in Dhruva we have nickel coated float glasses and there are nickel not nickel coated but multiple coatings known as neutron super mirrors will expand shortly which has got even larger critical angles and these can be used to carry neutrons up to hundreds of meters and they have a transmission overall transmission much better than 60 or 70 percent now the fact is that if you can take it 100 meters out then you can go out from the reactor hall or the target hall in case of a spallation neutron source or react hall in case of a neutron nuclear reactor and when you go out from the reactor then your background gamma and the background fast neutrons they fall drastically by three to four orders of magnitude so even with a 60 percent 70 percent transmission you can see I have got if I started with one neutron at the source so I have got say 0.6 neutrons for per neutron whereas the background has gone down by a factor of four so you can see this gives a very large signal to noise ratio and preferable and also the guides and the gaps in guides allow us to put a number of experiments on the same guide which will be difficult to accommodate in a reactor I will show you the photographs then you will realize so this is the basic principle of the guide total external reflection from a coated glass and then it can carry like this if you want to take the neutrons far the intensity falls as 1 by 4 power square if you just allow free flow but here neutron guides are optical fibers for neutrons so alignment of neutron guides are extremely critical another factor I must mention that because the neutrons are traveling hundreds of meters you need to evacuate the guides because otherwise you have around four percent typically four percent absorption absorption in air if the guides are filled with air then our purpose is lost because after one meter you have 96 percent of the beam if you have 100 meter guide then I will have very few neutrons out so we have to align the guides align them with very high accuracy because you can see the angles I'm talking about are arc minutes so guide elements are one meter long typically so you have to align the guides using very accurate alignment procedure within microns and also we need to evacuate the guides to avoid the loss of neutrons in the air absorption once you do that we're ready with a neutron guide and they can take neutrons far away so alignment of neutron guides are extremely critical actually it has a long process but it is possible to align mechanically that is not a any technological challenge neutron guides can be curved also if you curve the neutron guide can be curved also if I curve a neutron guide let me just continue it is a continuous source if I curve a neutron curve a neutron guide like this a long guide basically while I am curving actually what I am doing actually element after element I give a little bit of angle between the elements the next element will have some some small angular displacement will curve the guide if you have a curve guide then the guide allows the neutrons to follow the curve path but it does not allow the gamma or the fast neutron so that curve guide will allow clean transport of beams with very good drop in background neutrons and gamma rays and very high transmission for the desirable neutron so curve guides are also used many times to reduce the background so after saying this this is a one assemble neutron guide you can see the picture this is it has to be held tight because it has to be free of any vibration so you can see it's on a large piece of rail and these are the neutron guides which are the typical element that I said there are about one meter long I can show the neutron guide you can see this long path these are the guides this is in a source you can see the this is a guide hall and you can see all the spectrometers and what is to be seen actually this guide hall is jam packed with instruments we can't put all these instruments in a reactor and this is a guide hall as I showed you that if we avoid the direct line of vision to the reactor core it reduces the fast neutrons and background gamma ray background it also acts like a band pass filter depending on the coverage of the guide there is a critical angle so transmission versus lambda if I plot it goes somewhat like this so it acts like a band pass filter theoretically above a certain wavelength that means below a certain energy and cuts of the neutrons which are below this critical angle for the guide this critical angle it depends on the curvature so in a curvature curve guide not only that you have less number of fast neutrons and gamma rays it is also acting as a band pass filter it will not allow neutrons of higher energy to pass through it and only low energy neutrons are allowed so this is another example usually in a single beam path because the beam path as I told you it is 100 meters diameter 300 meter diameters where these guides are typically this width is around not more than a centimeter or maybe 2 centimeters at best 1 centimeter 1.2 centimeters so in that beam mouth you can put number of guides and then take the beams away in a divergent way so that you can see the distance between the guides are increasing as they go out at a 40 meter 50 meter distance you will have large gap to put experiments in between the guides so what I mean to say here is this that if I take the guides far away far away from the same beam line with a schematic then the gaps you can put instruments in this gap there can provide a gap where we can put instruments maybe another instruments here maybe instrument there maybe an instrument here so you can accommodate large number of instruments on a single guide and a number of guides away from the reactor core and that's the big help for experimental setups because we can increase the number of experimental setups and accommodate more number of instruments using a guide more number of guides so that's what I was showing you in this picture there are lots of instruments on a single guide this is the guide hall in Dhruva this is the left top photograph is when the guides were just installed there are two guides and there are two gaps in this guide one is 28 plus 8 36 meter long the other one is 21 meter long and here we have got three instruments one is a medium resolution small angle neutron scattering instrument here and sans instrument conventional sans instrument at the end of the guide as I showed and then polarized neutron reflectometer here and there's a spin eco instrument supposed to be installed on another guide the there are two these are curve guides one guide has a radius of curvature 1.9 kilometers or 1916 meter the other guide has a radius of curvature of 3.5 kilometer approximately which is 3452 meters more the curvature larger is the value of the critical wavelength cutoff wavelength so for the smaller radius of curvature the critical angle is larger 3 angstrom and for the less curve guide whose radius of curvature is larger if it is straight it will be infinite we have got the critical angle of 2.2 angstrom and this has got 27 meters then there's a gap then three meters then there's a gap and in these gaps we have instruments that are lined up so this is so this is all that I had to talk to you about neutron beam production and transportation and in the next lecture I will take over other elements of neutron scattering devices