 In earlier lectures we discussed how voltage is generated in DC accelerators, as I mentioned there are three types of DC accelerators, one is Cochroquat-Walton, Wendigraf accelerator, Tendham and Peloton accelerators. In the case of Cochroquat-Walton the voltage is generated by charging and discharging of capacitors. In the case of Wendigraf accelerator and initially in Tendham accelerators the voltage was generated by charging the capacitor formed by the high voltage terminal and the high pressure pressure vessel. In the case of Peloton however the voltage is generated by a much better charging system that is called inductive charging system and although I have discussed this in last lecture but I would like to give some more details of this inductive charging in this lecture also. So here is the details of inductive charging in the case of Peloton. Similarly in the Peloton accelerators you can see that there is no contact of high voltage with the charging systems and there is a Pelot chain which consists of metallic pallets connected by the nylon insulators. So if you want to understand the principle of this inductive charging you can see here suppose there are two cylinders metallic spheres A and B and as they are metallic so positive and negative charges are there on both of them and they are neutral basically. Now you put an electrode here where you can later on apply the voltage. Now if you want to transfer positive charge then you have to apply negative voltage on this inductive system. So what you do is that if you apply negative voltage on this inductor then the charges in this first sphere the positive charge will go to this side and that will be collected here and the negative charge will be repelled because of negative potential and that will be generated that will be collected here in this case. Now if you bring this second sphere which was neutral earlier close to the first one after applying the negative voltage and come in contact with them then because they are metallic spheres so this negative charge this negative charge will be transferred to this and the third stage is that if you remove this second sphere metallic sphere then these two spheres are separated positive charge on the first sphere will be uniformly distributed and the negative charge on the second here. So this will be the condition number three. Now if you ground this second metallic sphere which is the condition number four you can see that you can ground it then this negative charge will go to the ground but still negative voltage is applied to the inductive electrode. So this positive charge will remain on the first sphere and it will be uniformly distributed however there is no charge negative charge on the second sphere is gone to the ground. Now this first sphere which is representing this pallet chain is moving with a sphere while the second sphere is stationary and that is representing this this pulley which is grounded now. So what will happen because this negative voltage is still on when this is moving the positive charge will remain here and the second one second sphere the electrons have moved to the ground. So this first sphere will carry the positive charge and will be taken to the high voltage terminal. Now as I explained in earlier lectures that if you want to transfer this positive charge to the high voltage terminal you have to put extra work because now you are moving this charge against the high voltage and therefore you have to put extra work and that is done by this grounded pulley at the ground so this positive charge goes to this and this is how it will happen this positive charge will go to the high voltage terminal and then in the terminal there is a pickup pulley here and above that there is a suppressor. So this pickup pulley will pick up some charge positive charge and it is connected to the second inductive inductor here you can see is inductive so that means as a consequence of that the second inductor will this inductor will get positively charged slightly positively charged and rest of the charge will go to this pulley here and there is a suppressor which does not allow any sparking because this second inductor this suppressor is connected to a pickup charge here pickup pulley here which is picking up negative charge which is coming in the second one. So there are two pickup pulleys one and two one and two and this is inductor and this is suppressor so there is one more suppressor here because this negative charge is coming down the electric comes in contact with the pulley there really is sparking so in order to suppress that there is a suppressor here and as a consequence of this because of these two suppressors one here in the high voltage and other one here which is applied to around 50 kV and as a consequence of that there is no sparking either at this place or this place due to charge movement and then of course when the charge goes to the terminal is connected to the this high voltage pulley is connected to the high voltage terminal here and the charge is transferred to this high voltage terminal it is initially it is transferred to the inside surface of this but as you know that by this charge cannot remain inside a metallic conductor so it appears outside so this positive charge goes to the high voltage terminal here and this forms this high voltage terminal forms is a capacitor because of this whole thing is put inside a pressure vessel which is grounded in the case of so this forms a capacitor so as per the formula q by c is equal to voltage so voltage on this high voltage terminal will be raised so this is the inductive charging now the advantage of this inductive charging is that first there is no contact with the high voltage secondly because we are using the metallic pallets and therefore charge will be uniformly distributed and therefore there will not be any non-uniformity of charge and therefore charge will be uniformly transferred to the high voltage terminal and this will lead to a better stability of the voltage that thing is that since it is metallic pallets are metals and therefore there is no formation of links etc and therefore there is no high gradient form on the edge was the case in the in the bad charging here it is uniformly going so much better stability can be achieved in the case of inductive charging and that is what is done in the case of pallet ones and nowadays some of the tandem accelerators are also using this and the difference between tandem and the pallet one was because of charging only so those tandems which are getting converted into pallet ones because of this inductive charging their stability is also improved this details are given in this NEC because these pallet ones are manufactured by NEC national electrostatic corporation USA and you can see that these some details are given here so this is these are the some of the details which I thought I should tell you about in slightly more details now today we are going to discuss lecture number five and which is voltage measurement in its is stabilization now now in earlier lectures I have talked about how the voltage is generated in the case of tandem or Vendigraf or but this has to be measured because and this has to be measured accurately the voltage defines the energy of the particle and energy should be fixed and therefore the voltage also should be fixed because voltage is charged times the energy charge times the voltage charge state times the voltage e and this has to be done properly and if there is any variation in the voltage then they should be stabilized so we have to incorporate a stabilization system also which will correct the any change it will bring back the voltage to the original value if there is any change so the circuit should be such that it establishes the voltage properly so as I mentioned that in DC accelerators which are cockroach Walton Vendigraf tandem or palatons three processes are involved first was voltage generation and that in the case of cockroach Walton it were charging and discharging of the capacitors and the voltage is generated by this formula when Q is the charge transferred to the capacitor that is high voltage then you have to measure the voltage and in early days main source of main method which was used for measurement of voltage was generating voltmeter in the beginning it was not very accurate and therefore it was not really used to measure the voltages and hence not used for the experiments but later on now with the advancement of technology even better GBMs have been built and they also are very accurate ones then the next thing is voltage stabilization and as I said that if there is any change either the voltage is slightly increasing or decreasing it should be correct way so there should be some feedback system and the system which uses feedback is called corona stabilization or the generating voltmeter stabilization system so it has to be corrected and these are the these are some of the systems which are for example this is the cockroach Walton and this is shown in the picture of that cockroach 1 million volt cockroach Walton at Tata Institute of Fundamental Research this is Vendigraf and this is 2 ABV tandem accelerator at BRC which was and then the paletone at TFR so these are some of the accelerating systems accelerators which are DC type and in that one it is necessary that voltage is stabilized and energy is known for very accurate no voltage measurements as I said these done was done earlier with generating voltmeter or we call it GBM and another method which is which can be used but is depends on the various parameters is using current through the resistor chain you can see that the voltage gradient is established through a resistor chain and suppose the total resistances are and I is the current so in the last one you can put in current meter so I is the current total then voltage can be calculated now the accuracy of this voltage will depend on how accurate are the resistances so normally accuracy of the resistances 5 to 10 percent and therefore there will be error in the voltage of that order and therefore we should we should have the very good quality resistances if you want very accurate voltages of course once we know the voltage then we can calculate the energy which is equal to Q times V where Q is the charge and V is the voltage so let me just reiterate that what are the things involved so voltage measurements and in calibration and stabilization is a fundamental problem for precise knowledge of nuclear energy constants which are used for nuclear reaction studies or any any any experiment so this is so what you have to do you see you cannot measure the voltage directly but they are very high voltage several million volts and therefore you have to you have to calibrate it with respect to standard sources and that calibration can have some errors so but you need precise knowledge of energy and for that you have to know the precise knowledge of nuclear energy constants the generating voltmeter has been used to measure the terminal voltage in DC accelerators for very very long time initially it was used even to measure the energy but as I said that that may involve some errors and therefore that voltage nowadays the voltage measured using the GBM is used only to get an idea about the voltage plus to avoid the corona discharges and things like what are the breakdowns so but this has been used for very long time and even today it is used very effectively and therefore I will give little more details of that GBM how it functions at how accurately it can be used and therefore I would like to talk about the working principle of this GBM because it that is popular even today although some better methods are available like you can calculate the energy through nuclear reactions resonances and threshold and neutron experiments and things like that but this is still very useful it gives fairly accurate although in the beginning there were more errors but now with the advancement of technology GBMs good quality GBMs giving accurate value of voltages have been built and therefore is fairly good voltage value can be taken from that can be achieved so in GBM what happens static charge is induced on an insulated matter plate or we call it wave mounted on the outer vessel as I said that the outer vessel together the high voltage terminal forms the capacitor so this and outer vessel is grounded so the GBM is mounted on the outer vessel or we call it pressure vessel and that is surrounding the high voltage terminal the magnitude now once you have high voltage here and there is a vein here definitely there will be an electric field and there will be an induced charge so the magnitude of this induced charge it determined by the electric field established by the high voltage terminal on the way so this the last one is there are several ways and the last one is grounded just before that it is insulated and voltage the charge is collected on that and that is rectified and we measure the current and then the voltage is measured through that so high voltage terminal on the way so this is magnitude of induced charge on that one it determines and charge induced depends on what is the electric field and electric field depends on the voltage so you get voltage value from this current which you are measuring the due to charge collected on that one and insulated well rotates at this now how this is how this is happening will be explained so there is a insulated way which rotates at the constant speed behind a grounded shield shaped so that the veil is covered during the half of its travel so what you happen suppose you take the two wings this is fixed and this is rotating so let's say these are these are slots so when these slots are matching with the slot in the stationary one then there will be electric field seen by the another vein which is behind it behind both of them now as and since this is rotating so as soon as it goes out of the face then there will not be any electric field seen by this plate so that is what is happening so this is rotating so depending upon what is the speed there will be charge collected so you can see here that there are four electrodes which are shown here you can see here first one is this is the source of corresponding to this and where we want to measure the voltage so this is like high voltage terminal now you see high voltage terminal is not touching any of them so the gvm is a system which is not none of the components are touching the high voltage so this is a electrode this is a vein or equivalent to high voltage source then there is a rotor which is this one and then there is a stator and there are fixed electrodes so you can see here this is a rotor stator and this is a face so this actually opening is almost all very close to it but it's not touching this out so there is a shaft here is passing through this and it is it is rotating this rotor is rotating this rotor and this is by a synchronous motor because speed has to be fixed and it has to match because it has to go out in it has to be in phase rotor has to be in phase with the stator and out of phase so in the phase means that it is electrically received and when it is out of phase it's blocked and therefore they will not be electric so these are metallic this sort of thing with slots so this is the high voltage source there's no slot here this has slots this is identical slots and this is rotating and this is fixed and this is a fixed electrode which is which we mount on the now one good part of it is that there is no physical contact between the high voltage and rest of the circuit that's the beauty of it so it's like induction and synchronous motor is used shaft holding rotor disc only no how the voltage measurement is done now let us try to analyze it so we know that q is equal to Cv that means charge induced on that is proportional to the voltage because the electric field is proportional to the voltage distance etc and therefore charge induced on the plate or the disc is proportional to the voltage which you are you want to measure so charge is the is q is the charge is stored in a capacitor of capacitance C and v is the voltage developed across that high voltage term now as I said that a rotor is rotating so that means the C on the capacitance value will keep changing and it since it is rotated by a synchronous motor so this C can be assumed to be varying in a certain manner so there will be fixed value plus there will be let's say sinusoidal component added to this so C is varying with time then the current passing through the capacitor is given by i is equal to dq by dt and q is nothing but q is nothing but c into v and therefore it becomes v into dc by dt plus c into dv by dt so now so this is the current which will flow based on these these two values now in the case of dc accelerator the voltage has to be fixed so and the variation is very little and ideally we will like to see that the voltage is constant so if the voltage is constant then dv by dt the time variation of this is equal to zero so for the sake of analysis we can put dv by dt is equal to zero although it will not be zero it will have a very small number because that is what we want to stabilize it so but to the first approximation to the first order it will be d by dt will be zero now let us say if c varies as c0 that is a constant value plus cm sin omega t and here this variation this addition to this is because it's rotating and it's both when the whenever slots are matching then the there will be a variation in it so that means c varies and like this now there if this is the how this capacitance is varying then the current can be written as current is equal to v into d by dt of c0 plus cm sin omega t now cm is the peak value of this and when you when you differentiate it since c0 is constant we are taking that that's the constant value and over and above there is a variation and that variation is shown by this so that means d by dt of this c0 will be zero and therefore the i will be equal to v into cm which is a maximum value of that into omega cos omega t and this you can write as im that is a maximum so this becomes im maximum current cos omega t so this becomes the im that is the maximum value is a peak current and omega is the angular frequency radian per second and it is given by here and n is the rpm of the motor synchronous motor which is which we are using now if you see then the rms current which we measure is nothing but im divided by root 2 and therefore im will be root 2 times irms and that is this im is shown to be here so this is im so that means v the voltage which you are trying to measure is nothing but root 2 times irms into cm into omega or you can say that here the voltage is proportional to irms and that rms value of that voltage we are measuring through a meter or something but once it is proportional that means see ultimately what you are doing is you are measuring the current and which is a root mean square value of the current and that is proportional to the that is v is proportional to that means you have to calibrate it you have to calibrate these values with known sources and these known sources will depend this calibration constant will depend on several parameters like geometry of the voltage source and etc many more parameters and hence the proportionally constant may not be very accurate and you cannot so normally when you are calibrating it you normally calibrate at lower voltages and try to extrapolate it to the high voltage because ultimately you are measuring the high voltages and the constant obtained at low voltage may not be very accurate or will not be usable at high voltages so this has to be taken into account the alternating electrostatic voltage induced in the vein is amplified and rectified its magnitude is a measure of the terminal potential but calibration with known sources is required and that is what may involve some errors so if this method geometry plays a very important role the geometry of the system limits the precision of the calibration constant on the calculation of the capacitance so there may be some error in the calculation of the capacitance itself because geometry of the high voltage terminal may be slightly different or may you have to and the electric field also what I mean is that support the geometry is let's say normally as I showed that high voltage terminally let's say like this this is a cylinder and here we are using the gvm gvm and the electric field from this let's say this is a very small portion now elect which is used for this taking the charge then the electric field coming from different places will be different and therefore this may add to some errors also the if the geometry in some cases it may be cylinder hemisphere or in some cases it may be cylinders or even combination of that and therefore you have to be very careful when you are using those constants which are which are used for measuring the voltage so geometry has to be properly defined and finding in finding the calculations of capacitance at the constants and here the most serious limitation is the distortion of electric fields as I explained us now due to corona discharge from the terminal see we are handling now high voltages so there will always be some corona formation so once there is a corona formation there will be distortion in the electric field and this electric field may vary slightly and that electric field is responsible for inducing the charge so once there is a variation or in the electric field itself then there will be a variation in the charge induced and hence the current which we are measuring and so this may add to some errors voltage scale is usually calibrated calibrated against some other standard potentials normally at lower voltages this I have I have repeatedly said that your calibrations are normally then at lower voltages and you are trying to extrapolate it to see for example suppose you take a dc accelerator with 10 million volts or 20 million volts then you can't measure this this very accurately you can measure the they will be generating voltmeter because their distance also really large but there will be some errors involved in it so we have to be very very careful and therefore some other good method has to be has to be used to to find the energies of the particle which we are going to use in the experiments