 Today, we will have this lecture number 4, where we will be discussing Vendigraph Exilator, Tendon and Peritone Exilators. You saw that in earlier lecture that in Cogtrope-Walton type of exilators was open air type and therefore the maximum voltage that could be achieved was in the range of 1.25 to 1.5 million volts. Vendigraph is an improved version of that, that means if you put that whole system inside a tank and fill it with the high insulating gas which has a dielectric constant higher than the air, then it will go to higher voltage, the breakdowns will be much less. So this basically this principle was used by R.J. Vendigraph and in 1949 he developed an accelerator called Vendigraph Exilator. In Vendigraph Exilators a high potential difference is built and maintained on a conducting surface by the continuous transfer of positive static charges from a moving insulating belt. Now the material of this insulating belt in the beginning was nylon or the rubber and the surface on which this charge is transferred is called high voltage dome or high voltage terminal. Now this shown here this is the high voltage dome and this is the pressure vessel and this pressure vessel is filled with a high dielectric constant gas. For example in the beginning it was filled with the nitrogen plus carbon dioxide gas at much higher pressure sometimes 250 psi or so. As a consequence of that the dielectric constant around this high voltage terminal was increased and the breakdowns were avoided, corona formations were avoided. Now how this the voltage generator is different from Cocteau-Walton is that this here the charging of this capacitor takes place by transferring the charge through the belt this is shown here and how that takes place that takes place that suppose you have a comb which has lot of sharp points and you apply a positive voltage here then this belt is running over to this one inside the high voltage terminal and other one is grounded. Then because of this sharp point there will be high field and as a consequence of that this gas in this region will be ionized and positive and negative charged particles will be ions will be formed and positive ions will be attracted by the grounded pulley and then we start between these two there is a belt running at high speed so as soon as this positive ions they try to start moving towards this they will be collected by this belt and there will be transferred to this and inside this high voltage terminal that there is a similar system which takes away the charge to the high voltage terminal and it is going to the inside of this and since by electromagnetic this whole thing is a equipotential surface or volume and there could charge cannot stay here then the charge goes outside. So basically this high voltage terminal along with this grounded pressure vessel forms a capacitor which is charged a charges transferred by this and then this voltage will be raised to this so this is a high voltage terminal. Now if you install an ion source here and put a evacuated accelerating tube then these ions will be accelerated because of Coulomb repulsion. So as I mentioned in earlier lecture that you have to have several electrostatic or equipotential surfaces that means there has to be a gradient here and that gradient has to be generated or has to be maintained through a series of resistances here so these are resistances. So suppose V is the voltage and total resistance is R then there will be current passing through this resistor chain and that will be V is equal to IR then there are so that means this is a current again passing through this so this has to be equal to this but in addition to this there are several other leakages but for example there is a corona formation here and that is intentionally done to or voltage stabilization so that also has to be taken. So different components of this Vendigraf accelerator are pressure vessel, high voltage terminal, the insulating valve is either nylon or the or the or the hover and then it is a high voltage column section which maintains the potential gradient. The R of course is if there are air number of resistances put will be multiplied by R which is normally it is all R knots are equal it is R total R is equal to N into R. Other components of this are the charge carrying dome this is charge carrying dome then there is a ion source here which generates positive ions here and when they are extracted towards this accelerating cube they are accelerated because of this potential gradient. So these are the gradient resistors the accelerating cube and then of course once the beam is coming out of the accelerator you would like to know the exact energy and that is done by analyzing the energy using an analyzing magnet a proper magnetic field is put into that and that will tell you the exact energy of course always there will be some variation in the voltage and that has to be corrected. Most of the time in the beginning this Vendigraph accelerators were used for nuclear resonances studies nuclear structure where there is a requirement to have a fixed energy with minimum amount of variation and therefore there should be some mechanism that if because of several paths leakage paths there is a fluctuation with the voltage terminal voltage that should be automatically corrected and that is done by giving a feedback through the slits here you can see there are two slits opening is only one or two millimeter and through which the exact energy particles will go so if they are the energy changes because of change in the voltage particle will fall either on A or B depending upon the energy is increased or decreased so if it is falling on A that means the energy is low if it is falling then B that means energy has increased energy is directly proportional to the voltage that means there is a variation and that has to be corrected and by putting a feedback from these slit resistances to a system which is here is called corona feedback system the voltage of this terminal high voltage terminal can be stabilized and in vending graph accelerators it has been possible to stabilize the voltage to 1 to 2 kV in the tens of million volts now you would like to ask a question that high voltage is at high voltage terminal is at high voltage and you are taking the charge from the ground potential so how the ground potential charge will be able to enter inside the high voltage and wage it to further voltage well which is at high voltage so it is against the principle so can we do that and that is demonstrated in this slide that yes we can do it and that is demonstrated suppose you have two spheres A and B and suppose A and B are at the same voltage then that means they are charged equally so VA is equal to VB then if you connect them then there will not be any flow of charge because both of them are exactly at the same now second situation is suppose A is at higher potential than the B and then if you connect then what will happen it will happen that if A VA is greater than VB and we connect them then charge will flow from A to B charge will flow from A to B till the voltage is become equal third possibility is that VA is less than VB and if you connect them then charge will flow from B to A from higher potential today but you like to think that can we transfer the charge from B to A where that means from lower voltage lower potential to higher potential in principle it is not possible but under certain conditions it will be possible that if you spend some energy in carrying this charge to the high voltage and you overcome the difficulties then this charge can be transferred answer is of course yes you can do it it is possible and you have to spend energy and take a sphere wave one of the wages that is sphere B inside A and then if you just take that B inside that that means now the A is much bigger as compared to this and you take this inside B and touch it to A this is having lot of charge if you touch it and this for taking this you have a span energy there you will find that this charge which was there on B that will be transferred to A because it it will suppose it is transferred to inside surface and as per the electromagnetic you cannot hold the charge there because it's a equipotential surface and therefore it will be transferred to outside surface so that is it and this is the principle of Vendigraf accelerator you have seen it here that charge is taken and that extra energy is spent by this motion of the pulley so there is a motor here which drives this pulley so you are spending energy and this spending energy will take care of transferring this charge which is going there inside the high voltage terminal and as more and more charge is transferred the terminal will be raised to higher and higher in this case at a reasonable pressure the Vendigraf accelerators up to about 10 to 15 million volts was possible because in the Vendigraf in the initial stages nitrogen 80 percent and carbon dioxide 20 percent was used as insulating gas and more than 10 to 12 million volts this insulating media was not able to hold and therefore most of the Vendigraf were built in less than the 15 million volts most of them were about 10 million volts up to 10 million volts so in this case in the Vendigraf the ion source is put inside the high voltage terminal and the ions are extracted and now you see that ion source when you are producing ions it needs some power and there is no power there in the terminal so that power has to be generated in order to create these ions and that power basically is generated by the motion of the pulley which is here and that power is given to the ion source and since these belt is running at a certain speed and therefore a fixed amount of power is generated which is available for producing the ions and as a consequence of that the ions of proteins protons and alpha particles were only generated there heavy ions could not be generated of course later on technology improved and it was possible to generate positive ions of heavy elements and some Vendigrafs have been able to accelerate heavy ions also so these are the some of the so most of the initial stage Vendigrafs were able to accelerate protons and alpha particles that means H e plus in fact that power was not enough to even generate H e plus plus because helium has two electrons so in principle you can remove both the electrons but that power was not enough to do that so only H e plus was generated and therefore the energy which could be obtained through Vendigraf accelerators maximum energy was to be into the charge it was simply charged so it is suppose it is a 5.5 million volt the energy will be 5.5 mbv it could not be 11 because doubly helium or alpha particles could not be produced so I said that this is the this is what is done that you strain energy at lower pulley grounded pulley and that drives the belt with the charge and that charge is able to go inside the high voltage terminal because of that energy span now this charge you have transferred so effectively this is again the charge is transferred to a capacitor and in the earlier lecture we have seen that we have two plates and they are connected to a battery or the voltage source then the parallel plates will be developing voltage in the case of Vendigraf there are either it can be just a hemisphere or it could be you can see that this is nothing but a hemisphere this one so it could be either a hemisphere or it could be even a combination of a cylinder plus hemisphere so the capacitance has to be calculated accordingly then there is a another improved version of that that is a tandem accelerator and in the tandem accelerator it is a simple coaxial cylinder this is the this is the pressure vessel this is the high voltage terminal so this forms a capacitor so there is a system which transfer the charge to this capacitor and the high voltage is generated so these are mainly three types of systems are used systems are available and they form the capacitors which are charged charge is transferred and as a consequence of that so as a consequence of that the voltage so this this system was used in copper hot water this is used in the Vendigraf accelerator and this is used for tandem or the peritone and of course the how the charge is transferred that will define whether it is a tandem or it is a peritone so I have already explained this that in the case of Vendigraf generator following the components are there that one is a motor driven belt made of rubber or the nylon or any insulating material which is suitable and that moves between two pulleys you can see that these are two pulleys here and here this pulley is grounded and this is the belt and this is called com com is the having sharp surfaces and the high voltage is applied on this belt this belt is electrically charged by a brush this is called brush or com of metallics also there is a they have sharp points so high electric field will be generated even for a smaller voltage and there will be ionization the charge is carried by the belt to the high voltage terminal that means the charge is carried by this belt to the high voltage terminal at the terminal the charge is transferred from the belt to the terminal by a second brush or the com of the metallic surface here so as I said that is just reverse of that it will transfer to the inside surface and since charge cannot remain there so it appears outside and this electric charge they get collected on the terminal external surface of the terminal and the high voltage is generated now depending upon the geometry the capacitors values this is called capacitance they are defined for one or two geometries they are defined for example terminal voltage is a function of diameter of the terminal see if it is a small one then less charge can be termed if it is much bigger and the capacitance value is given by here so if you put these constants into then it is as a function of r that means the radius of radius of this and this is given here so if you take that r is the radius of the terminal electrode if air is used as insulating material then for a value of r that means resistance of about one meter will have that means you put one meter here and it will have 111 picofrat but if you have fully is a spherical terminal of radius r1 and it is enclosed in a grounded concentric cell of radius 2 which is the case in the Vandegra is a high pressure also high pressure vessel is another electrode so if you take this here then the capacitance value is given by this so you can see that this becomes but just by putting value of r1 and r2 you can get the c value calculated and then depending upon charge which you are transferring here using this equation you can get the voltage raised to that now so you see the when you are transferring the charge how much charge you have to transfer you have seen earlier that if you keep transferring the charge then the d by dt could be very large and that will be a safety issue and therefore you have to calculate the transferring of the charge which is equivalent to current so you can say that it is equivalent to i charge and that should be balanced by different different loadings which are there on the accelerator for example you can see here that there are different loads on that terminal so this i belt which is the i belt has to be equal to mainly one is that i beam is coming down which you want to exhalate and let us say that is the that is the current is i beam and of course as i mentioned that the corona has to be there constant corona current and which has to be modulated by the feedback from the on the slits and that is equivalent to i corona and of course the continuously to maintain the gradient you have to have the i rested so these three which are the three main component there may be a few more but they are all very small and therefore this i belt that means the amount of charge which you have to transfer using the belt has to be such that it is equivalent to or it compensate these three currents so at least at least it should be equal to that