 So, now what is the limit on the cycle? We have seen recently that focusing of the magnetic field should decrease with it. So, if you want to achieve the vertical focusing magnetic field should decrease with radius that is why we introduce the gradient in the magnetic. However, recall your formula of revolution time. Revolution time increases with increase in number. So, if you want to make revolution time constant gamma by magnetic field this ratio should remain constant. Means as gamma increases we should also increase and as gamma increases particle force outer orbits means orbit with larger radius. So, magnetic field should increase with radius. So, for synchronism we have to have a magnetic field which increases with radius while for focusing we should have a magnetic field which should decrease with radius. So, these are contrary requirements for running the cycle. So, classical cyclotron cannot reach beyond the 2 percent of the rest energy of particle. So, in case of protons classical cyclotron can reach up to only 20 mEV. However, we have heard that cyclotron can reach up to 800 mEV of protons 500 mEV protons or even the 1 GB of the protons energy. How is it possible? We see now. As we know that magnetic field should increase with radius to keep the synchronism. As gamma increases we should increase means with gamma increases we should increase and therefore, with radius magnetic field should increase. This can be obtained using such configuration. Here instead of introducing the gradient field is bearing asymmetry. Magnetic field means in this direction the field is bearing. Here pole caps are closer to each other we say this is the hill and here pole caps are further from each other. So, this is the bearing. In this region magnetic field will be lower in this region magnetic field will be higher. So, where the magnetic field will be higher this region increases with radius. So, effectively magnetic field becomes higher and higher and the order increases. How hills and valley looks like? So if we will go around theta for a constant radius r the pole gap will look like this. So this is the valley and this is the hill. So here the magnetic this is this is the hill. So here the magnetic field is stronger here the magnetic field is weaker. Now how the vertical focusing can be achieved using this? We see this now in a perfect circle if we have v theta here and if we generate v theta the force will be achieved however vertical in the vertical direction. So this kind of configuration cannot give a vertical force or vertical focusing. If there is a angle between the v theta and v theta if there is certain angle then a vertical component of force can be generated using v theta and v theta. So this type of technique is used by introducing the valley and hills. How we can see here? Suppose this is the hill and this is the valley. So at the transition region the magnetic field here it is a strong magnetic field a transition region there will be fringing and there will be fringing means magnetic field has some fringing effect on this v theta. And this fringing effect generates a vertical focus. How this fringing effect generates vertical focusing we will see in detail in later lectures. So this kind of focusing is obtained in this cycle of time. So here instead of perfect circle here the magnetic field will cause a small radius of curvature because it is a strong and here radius of curvature will be larger for the path. So instead of complete circular path it has a collective type of orbit. And here you can see that v theta and v theta has certain angle between them and this leads to vertical focusing. If anyhow we can generate a br means magnetic field in this direction also then vertical focusing can be even stronger. And this can be also done if instead of straight sector we make this spiral sector. In spiral sector we have now b theta as well as br. So these two components make a very strong focusing mechanism available in this cycle from in the vertical. One extreme case may be there that we remove the magnetic field completely from the valley means we make b is equal to 0 in the valley. Means there is no magnet and then there is a strong magnet then there is no magnet then strong magnet then no magnet then strong. This type of cyclotron is known as separated sector cyclotron. And here there is no magnetic element here we can keep RF cavities for particle acceleration. So even a single term many RF cavities can be kept and this type of cyclotron is also known as ring cyclotron. Now if beam reaches up to the certain or desired energy level we have to extract the beam from this cyclotron. How we can extract the beam of the cyclotron? Now you can see that at the outer orbit we can put a deflector. This is an electrostatic deflector means it creates some electric field in the vicinity of this outer orbit. So when particle reaches on this outer orbit with the desired energy this deflector deviates its path from the regular orbit path and it sends outside the orbit. Now here there should be a mechanism for shielding the magnetic field also. And this shielding again produces some fringing at the edges. And this fringing again focuses vertically in the vertical plane. So at the exit of cyclotron we get a vertically focused beam. The another technique for extraction is much simpler when we use the negative ion for acceleration. When negative ion reaches in the outer orbit we can put a very thin carbon foil. So loosely bound electrons stripped out from this ion due to scattering in this carbon stripper foil and these become positive ions. Such a simple case is take the H negative. H negative means hydrogen with an extra electron. When it accelerates and it reaches to carbon stripping foil it becomes probe. Means both of the electrons is lost by the H negative ion due to scattering in this carbon stripping foil and becomes the probe. So same magnetic field which was banding in this direction to the negative ion a proton or positive ion will band off at this. So extraction will take place. This is the picture of the first cyclotron built by the Lorentz and this is the model cyclotron. You can see that this is a separated cyclotron. These are the magnets and here we are the 50 space or no magnetic element. This cyclotron is in the triumph level of Canada. Now how the cyclotron journey started in India? It is very interesting this story. Actually Meghanath Saha who was this famous astrophysicist, he thought that India should start its accelerated program because of this we can go in advances in the nuclear physics research. This was just after the world war 2. You can see that in the early stage these persons thought about how the Indian science can proceed. One of his student Basanti Nar Chaudhary at that time was working with the Lorentz who invented the cyclotron. So with the help of Nar Chaudhary Meghanath Saha got one cyclotron in India. That was in the institute of nuclear physics. Now this institute of nuclear physics has remained as Saha Institute of Nuclear Physics in Kolkata. So that was the first cyclotron ever in India available to the research. Later on Atomic Energy Commission, mainly Dr. Rajaramanna put efforts to make indigenous cyclotron in India because only then accelerated building capacity will be enhanced into the nation and we can make our own accelerators for our own research purposes. And again you can see that this was in the early stage of 70s or later stage of 60s and at that time a K-130 AVF type cyclotron was built in the India at the variable energy cyclotron center in Kolkata. Saha Institute of Nuclear Physics and VECC has common campus and at that time you can think that the magnet weighs about 260 tons. So building such a magnet such a huge magnet with required precision was a challenging job. This challenging job at that time was done by a heavy engineering corporation, Raji. So India at that time had its own cyclotron. Later on a person Harnam Singh Hans also put great efforts. You should read this story in the given references. And he bought a cyclotron for the Chandigarh University from the Rochester University. And now VCC houses a K-500 it is a superconducting cyclotron. If you want to make higher and higher energy for the particles we need higher magnetic field B. You can see in this lecture that T is directly proportional to B. So for reaching up to very high energy we need higher magnetic field. So superconducting magnets can reach to very high magnetic field but superconducting technology is a very challenging technology. We have to keep the magnets at liquid helium temperature. So this is a very very typical technology. Now VCC houses a superconducting cyclotron K-5. This is the biggest cyclotron in our nation and its magnet is 100 tons. So we have 100 tons superconducting magnet in this acceleration. Now also have very large applications in the medical area. It can be used for therapy as well as diagnosis. For diagnosis purpose it can produce various radio elements F-18 in FDG, technician 99. So these are very useful machines in the medical area also. India right now have 19 medical cyclotrons. VCC also has its own medical cyclotron and it is the biggest medical cyclotron in our nation. Again the references are seen as was in the lecture one. So you can go through these references for having the details on cyclotrons. One of the proceeding in certain accelerated school is dedicated to Linux and cyclotron. So you will get very details of cyclotron in that procedure. In next lecture we will see one more accelerated that is magnet.