 In the previous lecture, I told you how we tailor made the beams inside the reactor and how we can transport the beams outside the reactor and even outside the reactor hall or the target hall using guides. So this is about neutron transport from the core and also neutron transport to far places. In this lecture, we will be discussing the various components like filters and the collimeters that we use in the beam line and also the kind of monochromotors we use in tailoring the neutron beam. The next part of the lecture where the beam tailoring with respect to wavelength and with respect to removal of unwanted components are concerned. So I have discussed with you in the previous lecture up to beam lines and now we will be talking about in-pile collimeters, filters, solar collimeters and monochromotors and then most importantly I will take one lecture on neutron detectors and monitors that are used at various sources. So the thing is that in case of neutrons as I am harping again and again, lots of radiation it comes out from the reactor or the target and the desirable thermal or cold neutrons with which we want to do the experiments are always accompanied by a lot of undesirable fast neutrons and gamma rays and we need to cut them down. Then we need to cut down the neutrons because if I have neutrons which is not so harmful to health but it can be harmful so far as the experiment is concerned because it will increase the background in the experimental law. The beam needs to be tailored properly even before it reaches a monochromotor and also be tailored after the monochromotor before it reaches a sample. So before it a beam reaches the monochromotor at the center of the monochromotor drum which I showed you earlier I will show you later also. In-pile collimeters are used to cut down and tailor met the beam. It filters the beam path beam so that unwanted and undesirable components of the beam can be removed. So now we are here so let me say this is the beam path the core is somewhere here where the meter and there is a large monochromotor drum it's a drum because it needs to be rotated and the center there is a monochromotor. Monochromotor means it reflects the neutron beam and chooses the monochromotic wavelength because in a scattering we need a direction and energy defined. So but before it reaches the monochromotor inside the beam also inside the beam path because this beam lines are around 100 millimeter I mentioned to you earlier or 300 millimeter diameter. So it's a large beam path you can keep them open also if required we should have the facility to close down the beam because sometimes you might have to go approach this path and this is directly open to the reactor core and very heavy radiations can come so you should have some way of cutting down the beam. So all these come inside the beam path the inner gate and what is known as in-pile collimators. So and also after you have removed the harmful radiation we also need to filter the filters in the beam path to take out the undesirable components of neutron. So moreover neutron flux being low so we need to have a large beam size unlike this is the biggest difference I can tell you physically for example when you are working in a synchrotron source the synchrotron radiation which is coming from an accelerating electron beam is highly what should I say highly directional few micron size beams come out and of course it needs to be monochromatized but you can compare this with a neutron flux of 10 to power 14 neutrons per centimeter square per second in the core it has come down to 10 to power 8 or 10 to power 7 neutrons per centimeter square per second at the beam whole mouth and then we normally in neutrons in general we can make it a rule of thumb but we will be using a large beam as large as 5 centimeter by 5 centimeter. So the neutron beam is first cut down using an in-pile collimator in the beam path that means in-pile the name itself indicates that it is inside the pile that means it is inside the biological shielding and inserted in the biological shielding so that we take out only that part of the beam that size of beam which is desirable rest all we try to cut down right inside the beam tube. So this collimator is made with neutron absorbing materials it can be paraffin wood and gamma absorbing materials like lead encased in steel or even steel itself with a large opening large opening because we need to have at least 5 centimeter by 5 centimeter beams in a reactor typical it can be slightly smaller in a reactor the higher flux but it can be of the other centimeter square and there is a shutter in the beam path to close the beam. So I show a schematic of a beam line so far I have showed you the beam line just as an opening rather a hole going all the way up to the core but now in details I show you that this beam has got an inner gate this inner gate can be closed when wished so that the beam does not come out and we can approach the experimental spaces there is a collimator this is an in-pile collimator that orange color and then there is an outer gate that means right at the beam hole mouth we have a gate that also can be closed there is a shutter for that and then we have something called a sample manipulator I don't want to get into that and detector this is taken for a neutron imaging beam so this part you need not bother but I just want you to concentrate on the beam geometry that the beam comes out through this we have inner gate we have got a collimator and you have got an outer gate so the in-pile collimator is somewhat as I showed you in this case here actually it it is like a cone actually you can even use a conical in-pile filter as I show you here this schematic but basically often we don't do like this because the easy to make cylindrical objects and it is at the in-pile collimator may look as I show you here and often so Newton we often use Newton filters inside the beam line filter materials are something which will remove gamma rays from the neutron path because gamma rays are extremely harmful for human health and we need to cut them down to allowable level before we start even teller in the beam so we can use gamma absorbers but at the same time these absorbers should be such that they allow the desirable neutrons to pass through so how do we have this dual nature that means it will allow me to take out the thermal neutron at the same time absorb the gamma rays so we use single crystals silicon single crystals of bismuth or even sapphire the because why single crystals because because if I put a filter in the beam path now there is neutron which is trying to pass through and there's gamma ray which is going to pass through now if the absorption coefficient is sigma for gamma I can write it as e to the power minus mu linear absorption coefficient and T so it's a linear absorption coefficient and the thickness observation that is apart from there's something called a built-up factor because this is true for pinhole geometry this is not a pinhole geometry along with that the neutron is going to pass through now in case of single crystals thing is that that means I can say if these are the planes let us say it might have planes oriented in this direction but only these planes are there so if that happens then from the neutron beam possibly some lambda will be scattered out by this filter but others will not get brag scattered will not get brag scattered scattered and we'll pass through what happens in case of powder if I have a powder one then for the same geometry in case of a powder one I can have beams oriented like these like these maybe like these we have all possible orientations in the beam path and lot of neutrons lots of neutrons of neutrons neutrons will be scattered out that is undesirable we want to do that job using a monochromatic sometimes we also use filters I'll come to that we don't want that that's why mostly we use single crystal filters single crystal and to stop gamma rays we know high-z materials are desirable so we use bismuth single crystals we can know silicon single crystals we can also use alumina for fast neutrons so alumina this is sapphire so these are the single crystal filters that we use even and I can tell you that in some energies the transmissions they have been measured can be as good as 80% with the fast neutron and gamma rays down by several order magnitude lower so the desirable thermal neutron and fast neutrons sorry fast neutrons and gamma rays will be cut down and 80% of the thermal neutrons will pass through so we'll have a rather clean beam beam after the filter I just show you some of the things which have proposed this is a proposed beam in a Dalat reactor Vietnam so here they have talked about a silicon single crystal filter in their beam path this is an imaging beam path and this so in the beam path they put bismuth to remove gamma rays I just show you the transmission these are all published ones you can see that especially for silicon single crystal for various thicknesses 5 10 20 centimeters but the fact that some energies at some energies at the center of this plot the transmission is as large as almost 72 80% the sum energy the transmission is very large similarly for sapphire you can see the transmission for longer wavelength neutron is large it is almost 80% but for short wavelength neutrons it is very low so sapphire can cut down the fast neutrons at the same time it can allow the thermal neutrons preferably to pass through and they are routinely used as filters in neutron beam experiments silicon single crystal bismuth single crystal and sapphire sometimes we can also use the same property of Bragg scattering for some of the powder crystals powder crystals comprise of many crystallites small crystallites so in case of beryllium I am just showing you the schematic plot you can see that the transmission drastically the cross section drastically falls beyond four angstrom and below four angstrom there is a very large cross section this is scattering cross section basically it goes to Bragg through Bragg scattering so what I mean to say that when I use beryllium powder powder 2d sin theta equal to n lambda so you have if you have a beam then you have all possible orientations of around the beam of various various orientations of planes so lots of lambda will be thrown out because of Bragg scattering Bragg scattering is very strong so it will throw out the wavelengths by Bragg scattering but once you know because 2d sin theta n lambda that means sin theta is let me just say first order lambda by 2d so when lambda becomes larger than the largest 2d in the system they don't get scattered anymore because then it becomes greater than one sin theta can be greater than one ninety degree so you don't have these wavelengths lambda greater than lambda cutoff cutoff they will not be cut off by this powder beryllium and we can use the filtered beam for further use in us experiments if the experiments demand long wavelength electron so let me consolidate by saying that we normally use single crystals for thermal neutron filtering that means not thermal neutron filtering rather to filter out gamma rays and fast neutrons from thermal neutrons with a high Z single crystal but sometimes if you want to cut down the thermal neutrons and enhance the whole neutrons for some experiments we can also use beryllium as a filter so similarly some people have also measured the iron cutoff you can see in iron the cutoff wavelength increases slightly iron in case of iron it goes to four angstrom and more so if you use want to use some wavelength which is greater than six any of these filters even if you go to seven angstrom and more you can use a powder Bismuth filter but the fact we must remember that in the maxolium that is coming from the reactor neutrons of longer wavelength are fewer before we use this kind of filters it is preferable or it is desirable that we have a cold neutron source in place in our reactor and in that beam path we can use a filter I'll use an example later where a beryllium oxide filter was used and a pseudo monochromatic beam was used for small angle neutron scattering in Dhruva so now question of collimation of the beam in neutron scattering we need as I told you a relatively large beam of typical centimeter square but this if I keep a 5 centimeter by 5 centimeter beam open then you can see that the divergence will be given by the simple geometrical value of delta x by L will be the divergence of the beam if the delta x is the opening of a collimator now if you have a collimator with 5 centimeter opening 5 centimeter by 5 centimeter opening and one meter length the divergence is about 3 degrees and that is too large because of the fact that if I do an experiment even if a diffraction experiment first order then delta d by d is a sum of delta theta by theta and delta lambda by lambda the easiest approximation okay and then delta theta by theta if it is 3 degrees this is of no use for a diffraction experiment so we so we have a competing interest we need a large beam but we need a smaller divergence how to satisfy these two so this is what is done by a solar collimator so it makes a compromise between resolution and beam size how this is a typical design of a solar collimator so now I will just explain to you a solar collimator has got a rectangular cross section usually the neutron beams are always rectangular in our experiments and if it is a horizontal geometry that I am using for scattering experiment then the resolution is dictated by the resolution in the horizontal plane and in the vertical plane we can play we don't have any resolution requirement if my delta theta by theta is dictated by the horizontal resolution so now the solar collimator has a rectangular cross section and interspersed with a strong neutron absorbing material so this is the collimator this size is the desirable size I can say 2 2 3 centimeters this height may be of the order of 10 centimeters but I can interspersed this thing with narrow so I have made this collimator using these narrow slits so it is this so now the beam size is dictated by the width and height of the collimator which is in centimeters height in centimeters and the collimation is given by delta x which I have defined here which is the distance between two of such absorbing material so this absorbing material is run all throughout the length of the collimator and actually the beam divergence is dictated by the delta x which I showed here in this diagram and the separating foils are actually foils or materials are made from gadolinium or cadmium and we have to take lots of pain to keep them straight stretched so that this beam path does not get closed in the length so typically 300 to 500 centimeter length and this is called a solar collimator so a solar collimator with the delta x of around 1 millimeter I said 1 millimeter it can be even less and 500 millimeter length you can easily estimate the delta x by delta x by L it can give me a collimation of 6 to 7 half minutes 6 to 7 half minutes of diverges is very much commensurate with the delta lambda by lambda of few percent in a mosaic crystal and they are matching with each other and that is the best situation for a diffraction experiment so this is a solar collimator and I explain to you the solar collimator actually adds makes a makes a gain by reducing the beam size width wise at the same time allows the beam to be large so this is a game game situation for the neutron scattering experiment and solar collimators are used in almost all beam parts where you are using a monochromatic beam I am just showing you some photographs of this solar collimators of this company JJ x-ray and you can see this is how they look like and this solar collimators is routinely used in the neutral beam part they come after the monochromatic drum and before the sample and this can reduce the dive angular divergence of the beam to few half minutes at the same time providing a large beam for use in our experiment