 You can see here in the diagram which or the circuit which you is mentioned here and in the Cockroach-Walton accelerator you can see that a rectifier or a multiplier produces a high voltage applied to the accelerating column and that accelerated column is used for accelerating the particles. Now what is this Cockroach-Walton accelerator? In a simple voltage, it is a simple voltage multiplied where AC voltage charges the capacitors. Now you have seen that when we discussed about the two plates there we were applying a battery or a voltage source which was DC. Now here that DC voltage is replaced by AC voltage source and that will be responsible for going to much high voltage because once you are using a DC voltage the capacitor can be charged only to that voltage. While in this case they use the AC source AC voltage and then by using several units the much higher voltages could be used. So these they charge the capacitors and these two people Cockroach and Walton they basically built a multiplier voltage multiplier and that was connected to two column section and that is accelerating tube and the many experiments were done. In fact these two scientists they performed the first artificial splitting of nucleus atom in 1932 and for this what they did was that they accelerated proton beam to about 600 to 700 keV and they bombarded lithium-7 and they found that it gets converted into two helium nuclei. So you can say this was the first experiment of splitting the nucleus using accelerated beam. As I mentioned earlier that before that all the experiments were done using alpha particles of the radioactive ion sources. So this was the first experiment done using artificially accelerated beams and where the nucleus was split in this case for example lithium-7 is split with the bombardment of proton and two helium nuclei were produced. In fact at that moment it was such an exciting experiment that they got Nobel Prize in physics in 1951 for this splitting of atoms nucleus. So you can see here just to give you the configuration that there is a transformer here where AC voltage is applied and across this you get a voltage which is V is equal to V0 sine omega t. So this has AC voltage has a frequency of omega and it is a sinusoidal beam. So this is the one and in subsequent lecture subsequent transparency you say that how the system works. So basically it is a network of capacitors and diodes and diodes are used see when you are using a DC voltage source you could use the resistance but here because the voltage is also going to negative and therefore you cannot use the resistance for charging the capacitor because otherwise the current will flow in the reverse direction if AC voltage is used then in one cycle half cycle it will flow it will charge and in the other half cycle it will discharge so you will not get any voltage that is why in this case you have to use diodes and I have already talked about the characteristics of the diode because it functions and forward wise and the reverse wise. So these are two circuits for example in the first one is a single stage here you can see here this is a source which is an AC voltage AC source and if A for example is positive in this case positive then this diode which is D1 will be forward wise and there will be current flowing in this circuit and as a consequence of that this or condenser will be charged to a maximum voltage of V0 while when it becomes negative then you see when this is negative then this will be reverse wise so this will not conduct then this circuit will be active because this is negative and this is positive and then this will be charged and that will be it will be charged to two V0 because one is this is V0 plus the voltage here so you can see that this is a circuit which is which can also be shown here in the negative for example this will not be charged this because this will not be active so it will be charged this will be charged through this circuit because this is now forward diode this is reverse and this is forward so this circuit which will be using here for charging is here and this C2 will be charged to two V0 V0 is the maximum or DP voltage of this AC signal which you are giving here so you can the same thing is explained here that during the positive half cycle that is this the point age is positive and the first diode D1 is conducting that is forward diode and C1 will be charged through diode D1 to V0 in the second case when the voltage is negative then D1 is reverse wise but D2 is forward wise so then circuit follows is here so you will get same thing is explained here and I have already told you that in the case of in the case when this is not BC voltage then you cannot use the resistance because in the case of resistance there is nothing like forward or reverse wise and therefore if in the positive positive positive and this is positive let's say this is charged or it is raised to the voltage and when the polarity changes then this will be discharged and there will not be any voltage across this this is also shown here the same thing which I have all so this basically was the so what the cockroach Walton did was that instead of having just one unit this is shown here this is one unit of multiplier and what one unit or one stage is having two capacitors and two diodes while if you want to go to higher voltages then you can keep adding these stages and of course you can't go infinitely because then there will be other problems so this is how the cockroach Walton works and you can see here that this is a basically a three stage so one stage one two three so like this it will be three times voltage and each capacitor is two V naught so it will be six times of that V naught so this is how it works now in this case you can see that there is a capacitor of capacitance value C and the capacitance value calculation of capacitance value is very important and there and for two parallel plates it is given as epsilon zero a upon D is the area of the plates and D is the distance between them and epsilon naught is the permittivity of air so this is the relation of capacitance for two plates where the medium is air while if you are using some other medium then it is gets multiplied by epsilon r where epsilon r is a relative permittivity of the medium and that you can see that it by putting for example in the case of we have done it suppose you put and close this system into SF6 which has higher dielectric constant you can go to higher voltages so this is how the DC DC coctop Walton type DC accelerator works and I will further explain because you have to understand it that how the charging and discharging takes place so these are some of the things you can see that this is set of capacitors and the diodes so you take that first one if suppose AC voltage is applied which is V naught sin omega t so first one is positive let us say this is A and this is B which is shown here now if A is negative this point is negative with respect to this ground so this ground then this diode will be forward biased and for charging the current will flow through the path which is shown here in red so in the first positive first half of the cycle this will be active and this capacitor will be charged in the next half cycle this see earlier this one negative now it becomes positive so when it is positive then this will not conduct and so this will take this becomes positive and this becomes negative and therefore in the second half which is negative cycle then this current will flow through this cycle so this condenser will be charged this capacitor will be charged to be twice of V naught and that is because the see this is charged in the first one to V naught and to this will be added as far as the voltage at this point is concerned so this plus the voltage across this will be V naught plus V naught sin omega t and therefore since the voltage across this this is V naught plus V naught sin omega t so this capacitor will be charged to 2 V naught which is a maximum value of this like this you can keep adding units so this is called one stage similarly next will be this stage and so on and each stage will give a voltage of 2 V naught and suppose you have 10 stages then you will have 2 into m into V naught so you can up to then the problem of that voltage voltage breakdown will come and you cannot go infinitely so now you are connecting this because ultimate aim your aim is to accelerate the particles so you connect you connect an accelerating tube here for example with an ion source and that ion source you enclosed in a high voltage terminal and that is connected to this and then you have several electrodes and then you connect these ones here and the particles will be accelerated and current will flow when current is flowing there will be a drain this will be a drain on the high voltage and therefore the voltage will slightly come down depending upon how much voltage is drop across this because when the current is passing through the accelerating tube so that is equivalent to a voltage drop that is shown here as a delta V so the total V the voltage will not be 2 and V naught but it will be reduced by a delta V and of course in this one the enter because we are using different systems and there is always some variation and there will be little bit uncertainty in the voltage and that is called this delta V here so that actually defines the beam resolution so and that is a random and that is a function of several for example breakdown voltages and several factors are taking care of this and this V the delta V which is a drop will depend upon how many stages you are using and this is the empirical relation and it is 1 by fc f is the frequency of the ac voltage which you are input ac voltage and c is the capacitor capacitance of the entire system so you can see that if you want to have a very small drop delta V then the frequency and the capacitance has to be very large as large as possible and of course you should also have if number of stages also should be small then only delta V will be small now all these things are contradictory because if you have less number of stages then obviously the total voltage will be less and if you have high c then the as you have seen in the second lecture that if the capacitance value is large then the charging of the capacitor takes longer time and therefore you have to have a smaller c if you want to have very fast but if you have a smaller c here then the delta V which is uncertainty in the voltage will be large and therefore you have to optimize this equation to in terms of all the three parameters that is f frequency capacitance value c and the number of stages and of course you have to also see that voltage drop is also minimized because as I said in the preample the you would like to have the voltage as fixed as possible a constant will and that again is given by this so that also says now you or see that whatever for delta V you need it a smaller number of here also you should have a small number of is number of stages if you want to have on ripple is as low as possible and so both of them show that and f f and c have to be large and number of stages have to be small if you want to have both these things as small as possible and that's somehow contradicts the requirements and therefore you have to find an optimal value of all the three parameters so while you are you are designing the pockford valton type of accelerator that you have to keep optimized all these parameters so in order to keep voltage drop and ripple is small one should choose the frequency f and the capacitance value c as large as possible and limit the number of stages to and to number of stages and to as small as possible and that will not be in that is in contradiction with the high voltages you want to have there is another parameter which you have to be very careful while designing these accelerators see that electric field at the surface of the electrodes should be kept in such a way that corona discharges are not taking place otherwise not only the voltage will come down that will be another load that will voltage will come down but also this uncertainty in the voltage and the fluctuation in the voltage there will also be luck and therefore the sharp edges should be avoided so that corona formation does not take place the electric field is proportional to one by function of r r is the radius of that sharp surface so if it is a very sharp surface the electric field will be very large as a consequence of high electric field the voltage breakdown will take place so you can see here it is mentioned that electric field is equal to be the voltage divided by r but it is basically a function of r so if r is very small that means if it is a sharp point then the electric field will be very large and the breakdown will happen and the corona formation will be taking place so all the sharp surfaces should be avoided for open air accelerators the electric field should not exceed is apparently it is shown it is measured that they should not exceed more than 3 million volts per meter and as a consequence of that if you want to do all this then you cannot exceed 1.5 million volts in the case of cockroach valton so that is why as I mentioned earlier that the maximum voltage which could be achieved in the case of a cockroach valton type of accelerator was from 1.25 to 1.5 million volts now when you are using this cockroach valton type of accelerators for acceleration of charged particles then the accelerating tube should have ultra high vacuum because otherwise when the particles are accelerated and they move inside the accelerating tube and the vacuum is not good then there will be a lot of collisions and there will be not only there will be loss of energy but there uncertainty in the energy will also so a high vacuum is needed to minimize the electrons generated from the collisions of of ions with the residual gas because if the vacuum is not good there will be a lot of residual gas in the accelerating tube in some accelerators electron suppressors are used to avoid these things permanent mandates are also used in accelerating tube to reflect those electrons which are generated because of collisions and therefore they they don't get multiplied and the load is decreased and the breakdown also will be avoided so these are some of the some of the precautions which we have to take in all the tc accelerators now this slide I have shown you earlier that even the cockroach valton type of accelerators were very useful in many for many applications and two applications which were very very efficiently done to that one was a dt reaction and otherwise dt reaction and the q values of these reactions they both of them produce neutrons and in fact even today the second one is used for generating mono energetic neutrons of 14 mvv because the second second reaction has a q value of 17.6 mvv and depending upon the masses for example the kinetic energy will be shared between the the products for example here if the d is falling on prism is going to million four plus newton and the kinetic energy you can say that from the kinematics you can say the energy of the newton will be four by five times and that will be about 14 so it is 14 mvv newtons are produced through this reaction and the from the first one d plus d you get two mvv newtons so these these two reactions are very popular and even the cockroach valton type of accelerator was very useful in this now these cockroach valton accelerators are still used as pre-injector for the large accelerator facilities in fact till almost like 80s they were the only ones which were used as a pre-injector of course in the around that time another accelerator was developed this is a rfq radio frequency quadruple and now all the cockroach valton accelerators have been replaced by that but till that time for several decades it was the unique accelerator which was used as pre-injector even in the hundreds of gv accelerator facilities and they were very useful they are very rugged they are perfect and not only in as a pre-injector but they have also been used for several applications which are listed here and which you can see that some of them important ones and since the energies were less than about 1.5 and maybe they could only be used for applications in solid state atomic and solid state physics experiments ion beam modifications of materials atomic physics and now this 14 mvv newtons have been used for doing demo experiments in accelerator difference of critical reactor systems and they are very useful and they are generating lot of data now the advantages of this cockroach valton type of accelerator is that as you have seen that only capacitors and diodes are used and using these two simple components electronics components you can step up the low voltages to high voltages depending upon how many stages is used so that is one advantage so you are using only two kind of components capacitors and diodes this elements the requirement of the heavy core for example here you are using a transformer and simple transformer and bulk of the insulator and the potting is required that you can eliminate voltage across each stage of the cascade is equal to twice the peak value of the ac voltage voltage in the half wave rectifier and advantage of sub sub this is this becomes advantage because it is capacitor is charged to the peak voltage another advantage is that it needs very cost effective components and it is very easy to insulate them so it the whole system is very cheap one can also tap the output from various stages suppose if you are having a big cockroach valton and you don't want to use it you can tap the voltage from any place and you can use it one big advantage even today is that high average current we said dc voltage multiplied so high average current can be obtained in this case so these are some of the advantages and of course the disadvantage as i said was that the maximum voltage is limited to about 1.5 million volts and therefore the breakdown of the insulate insulations have to be avoided and if you want to do that you cannot go to very high voltages so these are some of the disadvantage so if you want to go to higher voltages then you cannot use this up to 1 to 1.5 there is no problem they are one of the very good accelerators and thank you very much