 Today we will be talking about DC accelerators. Initially I will summarize what I have talked about in earlier two lectures before starting these details of DC accelerators. So I will first give the introduction to the DC accelerators and today I will be talking about one of that that is Cochrane-Walton type of accelerators and we will go into details of other ones. Now this you have seen again these are various kind of accelerators DC accelerators mainly and you can see that basic equation which I talked about was that if we transfer the charge Q on a capacitor C then the voltage generated is V and that is the basic equation which is used in all the DC accelerators and how this charge is transferred and what kind of capacitor is formed with what value of capacitance it will define the type of accelerators. So you can see at the first one here is the two plates and voltage is applied through a battery here which has a let's say the voltage V then depending upon what is the type of voltage for example here this will be negative and this will be positive. So if we inject the charge with the positive quality then it will be attracted by this grounded electrode and it will be accelerated to the energy of Q times V where Q is the charge and V is the voltage difference between two plates. Now you will see that this this DC voltage battery cannot be used in the Cocktor-Walton type of accelerators which you will see later this is only in the plate two plates type of capacitor it can be used for charging the system. Now you can see here various accelerators which have been developed over the over the time first one is a one million volt Cocktor-Walton type of accelerator at Tata Institute of Fundamental Research. It was installed and operated during late 50s or early 60s you can see Dr. Romi Bhava at the time of commissioning of these accelerators in somewhere in middle of 50s. Later on the high energy Vendicraft accelerator was set up at BARC and the voltage was 5.5 million volt and this was commissioned in 1962 and then we built one tandem accelerator two MVB tandem accelerator where much higher energies are available can be obtained because of because you can inject negatively charged heavy ions also in this one and this was built and it achieved 2.1 million volts and it was very well used for various experiments. After that this 5.5 Vendicraft was upgraded was converted into a folded tandem ion accelerator and this is called FOTIA with a 6 million volts on the terminal while the terminal voltage in the case of Vendicraft was 5.5 and we could get it 6 million volt because insulating gas used in the tank in the case of FOTIA was SF6. Then it was failed that these accelerators big accelerator should be set up and as a consequence of that another accelerator which is the is a 14 million volt paletton was set up at TFR and that has been functioning for last 20 25 years now and this is the status of these DC accelerators here and you can see that the kinetic energy depends upon the charge which is N times E and is the charge state so in the case of heavy ions the charge state can be higher and therefore with the same voltage you can you can get the much higher energies. Now you can see that kinetic energy is Q times V in the units of MVV if voltage is in million volts and Q is the charge state. Now this you have seen earlier this is just to demonstrate to demonstrate one point that here the accelerator as I said earlier was is a device which is which increases the which increases the kinetic energy of the charge particle here since the electrostatic voltage is used and therefore the energy kinetic energy is Qv this is also equal to half MV square so this is kinetic energy defined by and then these these are the units which are used and depending upon what are the wavelengths for example these energies are used in various fields for example in the case of molecular and atomic physics the energies which are sufficient to study the structure as a try is in electron volts or at the most kev and kev and energies are also used to study atomic physics while in the case of nuclear physics you need MVV energies or in some cases the gv in the range of gv energies so nuclear physics and particle physics at particle physics you need higher in gv range and of course the TV ranges are used for particle physics now the point which I want to bring out here is you have seen that there are two electrodes here and a voltage v voltage difference of v is applied to this and then the particle is accelerated now I will ask a question whether this is a most optimum configuration or there is a some way to improve it and you can see here this is one of the this is a tandem accelerator and this has two column sections that is why it is called tandem vending graph accelerator and this is the high voltage terminal you can see that there are several electrodes here for example there are almost like 50 electrodes and why those 50 electrodes are required and that is because this is a high voltage let's say it is v and this is grounded here so that voltage difference is divided into 50 portions and why it is necessary to do that and is it is it an optimum way to do it or is it required that question one would like to ask and that question comes from from the fact that you have seen it here that you can divide that into several segments like v can be a sum of dv1 dv2 and you can see here that that voltage of v to that ground is divided by equipotential surfaces in many many and there is a advantage to that but of course some of these all differences is equal to v that is the total difference now there will be disadvantage if you have only two electrodes and the voltage difference is v because then there will be the sum problem and will not be and that I will be discussing about so in this lecture I will mention about dc accelerators and there are barely three to four type of accelerators which are used and one is better than the other one previous one the first one which was built in the beginning in 1927 or 28 was a cockroach valton type of accelerator that is basically a multiplier that is a voltage generator and then Vendigraf accelerator then the improved version of Vendigraf was a tandem and that improved version of tandem was a peloton now you see that there is when you are dealing with these accelerators one aspect which you should know is safety aspect and that you can see here on the right hand side that as we mentioned that the voltage is equal to q by c that is charged divide by c it's like basically it is a capacitor which is charged and if you just differentiate it then it becomes dv by dt is equal to dq by dt divide by c and dq by dt that is the rate of charge transfer is equivalent to the current and therefore it is i divided by c if suppose i the current which is flowing through the device which is responsible for charging the capacitor is let's say 1 milli ampere of the order of 1 milli ampere and the capacitance values about 100 pico farad these are some typical values for the accelerator then you will see that d by dt that the rate of rate of increase of the voltage is about 10 million volts per second and if in one second any terminal is raised to 10 million volts this will definitely give a safety issue and therefore one has to be very careful and of course when you are writing this equation we are assuming that there is no charge leakage and that is why the entire charge which you are transferring is getting into the capacitor and that will generate that will create a safety issue and of course when he assumed that there is no charge leakage this is ideal situation there will always be a charge leakage and in fact if there is a charge leakage it is not bad it is good because it will help you in reducing this d by dt that means rate of change of voltage on the on the terminal and it will become slightly slower and that will be that will become as a consequence of that that will become slightly safer so it is good that there is always some charge leakage and sometimes the charge leakage is actually introduced so that the voltage does not rise so rapidly that it gives a safety issue and as I mentioned that the first problem was the whether just two electrodes are enough to get the high voltage or or we should divide that into smaller and a smaller voltage gradients or voltages and that comes from a from a law which is called Parsons law and that Parsons law says that if it is shown here this is summary of this one here this here the Parsons law was studied Parsons effect was studied for several gases and several geometry then you can see a particular geometry then you can see that when you plot the breakdown voltage as a function of pressure into distance between two electrodes so this is I am talking about when you take two plates and you charge them voltages so at what voltage it will it will spark and that will limit the voltage to which it can go so you can see that on either side suppose the system is having a constant pressure a particular posture you can then you can say that the breakdown voltage is proportional to the distance between them so you can see that if the d is smaller or d then the it can go the voltage breakdown voltage can go much higher and every rise is very sharp you can see here it's very sharp that means if you instead of having only two electrodes you divide into several several equipotential surfaces then the total sum dv1 dv2 and all that will be higher and as a consequence of that the total voltage which you can achieve on the terminal can be higher than the case where only two electrodes work here so that is regarding voltages another problem will come when the see the ion beam coming from the ion source is diverging and if there are only two electrodes there is nothing there will be nothing to guide the beam diverging beam and there will be nothing to focus it and therefore if you have several electrodes the equipotential surfaces will be formed in such a way and the force which guides them which focuses them is perpendicular to that the equipotential surface therefore the focusing will be better and the beam will not be allowed to diverge too much and we will get a much higher intensity in the case of now this passion's law which normally is a basic equation a basic law which tells that how much voltage you can reach it was done empirically it was discovered in 1889 and this still guides of course this has been modified because those experiments were valid in a limited range of p and d and for parallel plates only these measurements were done and of course that time the technology was not so much advanced and now the technology is much better and you can get the much better polishing much sharp sharp points can be removed and therefore you can your voltage breakdown voltage can be much higher in today's things where manufacturing can be done better much better now this is the law they they gave at that time which is a function of the breakdown voltage is a function of several things particularly the pressure and the distance between them and of course this there's a constant called secondary electron emission coefficient that also comes so this is quite complicated equation which is a empirical relation which still holds to some give to give an order of magnitude the breakdown voltages and of course it doesn't give the accurate one because of the technological advancement and much better manufacturing is possible and so this is still valid there is another the measurements which were done by a scientist and that is called kilpatrick limit kilpatrick limit basically gives mainly it was done for RF accelerators but it is valid for is equally valid for DC accelerators and it gives the breakdown voltage maximum in the accelerators in given by the kilpatrick limit so from that you can calculate that at what voltage the surface will spark or corona will be formation and above that criteria above that kilpatrick limit the voltage breakdown will take place and some sort of plasma or you can say corona will be formed and there will be tremendous amount of leakage and the voltage will not go up so that also gives an idea about how much voltage you can go in that kind of structures so DC accelerators also have limitations on the on the achievable beam energy because beam energy is proportional to the to the voltage due to high voltage breakdown effects and in the case of in the case of DC accelerators mainly the electric fields are limited to about 1 to 2 m e per meter so that defines that to what energies you can accelerate the particles in the in the DC accelerators now these accelerators as I mentioned started somewhere in middle of 20s 1920s first cockroach world will cock out walton type accelerator was built in 1948 or so but before that lot of experiments were done using the alpha particles and rather for particularly with his colleagues did several experiments with alpha particle beams which were emitted by decay of radioactive sources and in fact he got the Nobel prize rather for got the Nobel prize for discovery of proton in 1904 90 08 where we bombarded alpha particle coming from radioactive source on a nitrogen 14 and then he got proton plus oxygen 17 so this proton was sort of discovered he did several experiments using this alpha particles coming from the radioactive sources but the problem here was that the energy of this alpha particles from coming from the old radioactive sources was limited to about 8 mvb and there were several nuclei where these studies cannot be done because of coulomb coulomb barrier and therefore it was felt he himself felt that there is a need to accelerate charged particles to much higher energy so that we can overcome the coulomb barrier between the projectile and target and nuclear nuclear studies can be done so this was the history before 1920s or middle of 1920s where on the suggestion of rudder force and other scientists cockroach and walton they first made a voltage multiplier in fact in the first attempt they doubled the voltage to about 20 to 25 k eb and that was the beginning of this so now I will be discussing little bit about the their system and that is called cock or walton accelerators and you will see that they could not be raised to very high energies because of limitations of the multipliers