 Hello everyone, today we are going to start the course on accelerator physics and as has been mentioned in the preamble, this will have three modules, the first module will be on DC accelerators, second on linear accelerators, third one will be cyclic accelerators and there will be a separate lecture on laser plasma accelerators where much higher gradients can be achieved and the total length of the accelerator can be very short. So we will start the first lecture and of course the first question which comes to mind is that why we need accelerators and the main aim of accelerators is to or even the science is to study that what are the building blocks of the matter and their interactions and one of the most important aspect which scientists would like to know is that how the universe originated and how it has happened. For example, one of the theories is Big Bang theory and if you want to create that situation then that can be done in lab using the accelerators. So origin of the universe can be studied using high energy accelerators. Of course when you want to study the matter that means you want to study the properties of nucleus or nucleons like protons and neutrons and subdivided particles. And whose size is very small, in fact if you take the nucleus the sizes of the order of Fermi and one Fermi is 10 to the power minus 15 meter or 10 to the power minus 13 centimeter. So when you are going to use the probe or any particle then the wavelength associated with this should be of this order then only you can study these particles. This is somewhat similar to a microscope to the biologist and the telescope to the astrophysist and there again the wavelength matters and the reason being that the resolution of matter microscopes is proportional to the wavelength and that depends that is inversely proportional to the momentum and you know that momentum is proportional to E or rather root E then higher the energy smaller will be the wavelength and high resolution can be achieved. This is demonstrated here in this one that higher the momentum that means shorter the wavelength so you can have a better resolution. Sometimes even low mass particles can be used for creating a very heavy particles who are having masses very large and that is because of Einstein's equation where energy and matter are equivalent and this is shown by this equation E is equal to mc square and m is nothing but is the mass of the particle which is gamma times m naught and m naught is the rest mass and c is the velocity of light. So when the particle energy increases is mass also increases and therefore at higher velocity higher energies the mass of that particle increases and you will be able to create much heavier particles and that is shown here that if beta which is v by c is of the order of let us say 0.99 then the gamma is 7 which means that particle has become 7 times heavier than the particles at rest and if it is let us say 0.999 then it will become 2000 and that precisely the reason why we are able to create very heavy particles using the light particles at higher energies. So let us see what is an accelerator accelerator is an instrument which increases the kinetic energy of the charged particles it could be electrons or it could be protons or even heavy ions so different kind of accelerators will increase the energy is kinetic energy basically of different kind of particles but at low energy the kinetic energy is which we know is half mv square and at this low energy the mass of the particle will be m naught rest mass and which will not be so gamma will be 1. High energy of course the mass also increases as per this which I have already discussed where mass of the particle is given by this equation where beta is v by c so if let us say v the velocity of the particle is equal to c then this becomes almost like infinity that is m naught is equal to m is equal to m naught under root 1 minus beta square so if you put beta is equal to 1 then this this factor becomes 0 and therefore m becomes infinity very large as compared to the rest mass now that is why at high energies at 6.5 TeV in a proton proton collision collision at large head on collider Higgs bosons which are also called God particles were produced and the mass of the Higgs boson is around 125 GeV and you you might be wondering that how a 125 GeV particle can be produced when rest mass of the proton colliding with proton that means each is roughly about 1 GeV actually it is 935 mvv so let us say it is 1 GeV and two 1 GeV particles when they collide with each other interact with each other they produce a Higgs boson of a 125 GeV and that is all because of this increase in the mass because of increase in the velocity so that's the reason now let us see how how these accelerators was what are the basics involved in it the kinetic energy of the particle is half mv square as I mentioned earlier but in the layman's language an accelerator means suppose I have two electrodes one is grounded and the other is having a voltage of V and if a particle let's say electron is injected then the energy gained by the time it reaches the second electrode is eV e is the charge of the particle and V is the voltage difference it is not necessary that it should be grounded but the voltage difference has to be V so if it is V1 here it can be V2 and the difference V2 minus V1 has to be V now the various units used here what has happened that since it is positively charged electron will be attracted because of coulomb attraction and if suppose you inject positive charge then it will not get accelerated then the V has to be minus V so for attraction or it can be even the you can have V here and grounded this one and then you inject positive charge and then it will be accelerated to the same energy because of coulomb repulsion now the different units which are used are listed here for your convenience and they are kev which is the one kev is 1000 electron volts and one mv is 1000 kev that means 1 million electron volts and so on and today if you see high energy particles in tv ranges are also available and for example the large hedon collider where the maximum as per the design the 7 tev proton will be colliding with 7 tev another proton so the center of mass energy in that case will be 7 plus 7 is equal to 14 tev because particles are coming from opposite direction now if you compare that as compared to the rest masses the rest mass of the electron is only 0.5 mv 511 kev proton is 531 mv Newton is slightly heavier is 938 mv and of course when we talk about it we know the Einstein equation which I have discussed earlier e is equal to mc square so energy this kinetic energy can be converted into mass these are some of the other units which are other parameters which are listed here for example charge of the proton which is equal to charge of the electron is 1.6 into 10 power minus 19 coulombs now as per this I showed you that there are two electrodes is it necessary that we should have only two electrodes or can we divide this into several and in fact there there is a advantage that if you divide this into several pieces and you have instead of total v across two electrodes we can have data v1 v2 v3 etc you can divide into and there is a advantage of it but if the total voltage difference is v then the kinetic energy will remain same but then the there is a advantage which is by law is is that you can you will be able to get higher voltage voltage across that for example if you have let's say two electrodes here and this is ground and this is v and this is let's say is 1 meter 1 meter and it is it is able to extend a voltage of v as compared to this now what happens that if you divide this into two portions then in in principle this should be v by 2 but it happens that because of passion's law once that it is able to extend more than v by 2 so therefore in accelerating tubes which are used in the accelerators normally we divide that into several pieces and which you see in subsequent lecture that if you do this then there are several advantages and one advantage is that the voltage which you can hold on this really higher than v but it will be much more than that. Now coming back to the accelerators what are the different components which you should understand is one of one of the thing is that we want to accelerate the particles therefore they should be produced so there should be ion production and that means for doing that there has to be ion source or it could be sources also there may be more than one sources in the in the in the accelerator and then in the case of DC accelerators you have to generate the voltage so there has to be a voltage generator and then as per this as I said that there has to be a voltage gradient and that not only helps in getting the higher voltages but also in focusing so acceleration has to be done and large gradient will help in attaining higher voltages now normally in any accelerator the ions coming from the ion source are de-focusing time they are not they will have certain diversion and therefore before getting into the accelerator they have to be focused and therefore they have to be focusing systems then at each stage we should have a beam diagnostic systems because we should know whether it is de-focusing focusing or what is the current and we have to monitor them and not only we should monitor but also we should control them so we have to have monitoring and control systems then we should also have the energy measurement devices and control also and we should be having analysis systems for that that means when you have accelerated using the accelerator we should be able to measure that what is the energy and if suppose energy is slightly different we should be able to control it and correct it that means we have to have a feedback system so analysis has to be done and there will be lecture on this portion RTV TEM is of course that this beam should be utilized and therefore there has to be an experimental system here which is shown here and that could be a scattering chamber or which is housing lot of detectors and things like that so a typical layout of that accelerator is given here which is you can see different components so you can see that beam handling components are not only immediately after ion source but also after the beam is accelerated that means at the high energy side of this because that as I said that beam is diverging right from ion source as well as from the most of the time from accelerated beam from the accelerator also and therefore it has to be done now this accelerators based on the different criteria different parameters are divided into three to four categories and the simplest category and the most earlier developed category was DC accelerators but the problem there is that you can get voltage gradients of not more than 1 to 2 million volts per meter and therefore they could be used only to accelerate particles for low energies then this was improved and new technology came and RF technology was invoked and the accelerators based on that RF technology is called RF accelerators which could be linear accelerator if the particle is moving in the linear path then they are called linear accelerators or it could be cyclic if they are moving almost they are moving as well as getting accelerated in the circle or close to circle then they are called cyclic accelerators they could also be these accelerators could also be room temperature that means the structures are working at room temperature or they could be lower to the temperature superconducting temperature so the structures are superconducting and the voltage gradients which could be achieved in these two different structures are different for example in the case of room temperature these gradients are less than about 5 million volts per meter 5 to 10 maximum while in the case of superconducting it could be 50 to 100 in that range maximum 200 so these are the things now this also will not be enough if you want to accelerate the particles to higher energy and therefore some other kind of technology has to come in and one technology which has broken all these barriers is called laser plasma accelerators where gradients accelerating gradients of 100 to 300 gb per meter are possible in fact the gradients up to 100 gb per meter has been measured and have been achieved and measured so if you compare this you see that if suppose I have a dc accelerator which is 1 million volt per meter type of gradient then if you are having a you want to design an accelerator which will accelerate the particles to 1 pv then it will be almost like 1000 kilometer long because the gradient is very small and if it is a 1 million volt per meter then it is about 1 million mv and therefore the length will be almost like 1000 kilometer which is impossible this inconvenient and therefore it will not be possible to get so you have to find the technologies new technology where the gradients are and if the gradients of this type are available then you can see that even 100 gb 100 to 200 gb energy particles can be achieved in 1 meter itself so if you take go to let's say 1 tv then in that case it will be only about 10 meter distance but of course there are technological difficulties in that but you see the whole accelerator with this kind of gradient will be of the order of 10 meter only now so these accelerators they not only have been categorized on the basis of energies and the type of structures we use but also on what kind of voltages are applied to accelerate the particles for example in the case of dc accelerators in this category come the cocco valton vendigraph accelerators tandem accelerators peloton and dynamite on where all the dc voltage is used and in dc voltages most of the time or rather all the time the ions are passed through only once therefore the they are there is a energy limitation and we cannot go to very high energy but of course they have other advantages and that is that the energy resolution is very high and therefore if you want to study the resonance kind of nuclear reactions particularly nuclear spectroscopy then they are the best accelerators and they are still very popular everywhere in the world where the more accurate measurements have to be done there the dc accelerators are used particularly nowadays the peloton in the case of rf accelerators they are linear or we call them linux and there is a one accelerator called rfq radio frequency quarter pole rfq which actually has sort of revolutionized the whole thing and this does all the three functions of focusing bunching and acceleration together as a consequence of that the beam transmission can go up to even 100 percent but mostly more than 90 percent that in this category are cyclotones synchro cyclotones isopronous cyclotones and synchrotones and colliding rings because in colliding rings you are able to get the central mass energy which is sum of e1 plus e2 that means e1 is the energy of this particle and e2 is this then they when they come together from opposite direction the central mass energy will be e1 plus e2 which is not the case in the case of when fixed target is there and the particle is in fact if the fixed target experiments are there then the energy required for doing the same thing is very very very high which is not achievable and as I mentioned that this laser plasma accelerators which are still in rdmd stage voltage gradients of 100 to 300 gv per meter are possible in fact up to 100 gv per meter has been uh have been measured even but they they they have been measured over a very short length and therefore the total energy which could be achieved in this case is uh uh limited and therefore the lot of rnd has to be done to to go to very high energies let's say in tv or of course then you will like to know at some stage that what is the energy what is the ultimate goal of it so these were two categories there is a third category which defines the accelerators and most of the time we call them low energy accelerators if the accelerators are in the range of 100 kv to 100 mv then we call them low energy x in fact there are almost like 30 to 40 thousand accelerators operating in the world and they are their energy range is a few kv to few kv's and therefore the accelerators which are in the range of 100 kv to 100 mv we call them low energy accelerators then we call them medium energy accelerators if the energy is in the range of 100 mv to few gv earlier they were called high energy accelerators but now with the progress of the accelerators we call them medium energy accelerators and high energy accelerators is few gv to tv regions now because that that kind of accelerators are also possible therefore high energy accelerators are able to provide beams of tv energies then we have accelerators for electrons then for proton accelerators and also the heavy ion accelerators now just to give you an idea that what kind of things are available at this man and cost is one thing which defines that how big accelerator you can make because in some cases it can be several billion dollars and size also defines because the whole thing has to be aligned within micron so you can keep encouraging even if you are not worried about cost you can keep increasing the length but the entire structure has to be aligned within microns and that becomes very difficult so they become very large and for example if you take LSE which is a large head down collider then the circumference is 27 kilometers and some is also planning to build one the future accelerator this is called FCC future cyclic accelerators or future circular accelerators and the circumference of that will be almost like 100 kilometers cost of course will be several billion dollars these are some parameters of that FCC are given here and that is a future accelerator at SARM which has been planned in fact SARM council has approved the to make the studies for that it has been accepted in April 2020 and the studies feasible studies have started with that and one of the aims of that will be to search the new particles see it was in the LSE already we have we have discovered the Higgs boson and therefore in these heavy and this high energy particle high energy accelerators we would like to see whether some more particles can be discovered and then what are the interactions among these for example one of the aim of this is to study the Higgs-Higgs boson interaction how they interact with each other and of course and this is at this moment the cost estimated is 23 billion dollars and it will use superconducting magnets and energy central mass energy will be for head ones it will be about under TV now this will have three options one is that there will be head on collisions studies like proton proton or proton heavy ions other one will be electron and positron collisions as well as was the case in the former LEP lab large electron positron collider larger and then it will also have an option to study proton electron collisions now just to give you an idea about that what is possible in the present large head on collider is that in large head on collider two proton beams each of seven seven TV will collide and as I said that suppose it is a circular one the one proton is coming from this side and that is seven TV and another proton is coming from this side which is again seven TV and let us say this is this is the nuclear or the experimental area then these two protons which are seven TV each with the will have interaction and the central mass energy which is e1 plus e2 will be 14 TV can be this is a 14 TV so that is the that is the parameters of this