 Well, good morning. So, we are inching towards the end of the course. We have already covered in great detail the chemical rockets, the rocket propulsion, the basic principles. Now, only the last topic remaining to be discussed in this course is electric rocket propulsion. So, in the next couple of lectures, we are going to talk about electric propulsion for rockets. Now, first of all, what is electric rocket propulsion? Electric rocket propulsion uses electrical energy to change the velocity of a spacecraft. That is the basic premise of electric propulsion. Now, the work is done in these systems electrically expelling the propellant at very high speed. In the chemical rocket essentially is the conversion of the chemical energy into kinetic energy, but here in this case the conversion to kinetic energy is done electrically. So, electric energy is converted into kinetic energy and the electric thrusters typically offer much higher specific impulse compared to chemical rockets. The reason being that the mass, the velocity produced by these devices are much, much higher compared to the chemical systems. So, because of that the specific impulse is much higher. However, the limitation is the practical availability of power. How much power is available to the system? And due to this practical limitation or the power source constraint, thrust is typically much weaker compared to chemical thrusters by several orders of magnitude. For instance, typical chemical thrusters of a rocket will produce tens and thousands of newtons of thrust whereas, electric system typically will be less than one newton. As we go along we will see that the thrusters produce one say in the range of milli newton or micro newton or at the most way newton. So, that is the major limitation that the magnitude of thrust produced by this devices are much less compared to the chemical rockets. However, these devices have their own advantage and own specific use. For example, Russian satellites have used electric propulsion for decades starting from 1960s. They have been using electric propulsion systems in their satellites for various applications. I will explain what are those applications in which typically the electric propulsion systems are used where the chemical propulsion systems are not very effective. Now, near western U R buildings at spacecrafts or the spacecraft design for deep space applications are starting to use particularly for station keeping. For maintaining the satellite within its course, this small electric propulsion devices are now being used extensively. Unlike rocket engines, many of this type of electric propulsion system do not have rocket nozzles. So, therefore, they in the strictly speaking sense they cannot be considered as rockets. However, some of them do have nozzles. We will talk about them. There is a special category of electric propulsion systems which do have nozzles, but many of them do not have the nozzles. So, therefore, it is not that the through the nozzles you are accelerating it to a high velocity. Essentially the acceleration is primarily because of electric forces or magnetic forces not because of the fluid mechanics acceleration. So, that is why in classical sense probably some of them cannot be classified under rockets, but in general since they are using electrical energy for the production of thrust all of them are classified under electric propulsion systems. So, with this background let us see first why do we need electric propulsion system. Typically it is been now acknowledged over the world that in order to place 1 kilogram of object in earth's orbit you need 9 kilowatt hour of energy to produce to place 1 kg of object in earth's orbit. Now, the maximum available chemical energy which is if you say burning propellant hydrogen and oxygen is 3.7 kilowatt hour per kg per kg of propellant only 3.7 kilowatt hour of energy is available from the maximum possible by burning hydrogen and oxygen. So, you can straight away see that about 2.5 kg or close to about 3 kg of propellant is required to place 1 kg of object in the earth's orbit or may be more because there will be other systems also. So, therefore, this includes a limitation that if you have to put a certain thing in orbit how much propellant you are allowed to use. So, because of this limitation the maximum attainable specific impulse is limited to about 500 seconds for about 480 to 500 for chemical rockets burning hydrogen and oxygen as propellants. So, this limitation is primarily because of how much velocity increment you can get because that depends on your nozzle size. Nozzle size is limited because if you make the nozzle bigger the rocket is going to behavior or the temperature you can get. Now, temperature is also limited by the heating value of the fuel. So, you cannot get much higher temperature than what is physically possible then only thing is that you have to expand it more you have to put a bigger nozzle and that adds to the weight of the structure. So, there is a optimum value which you can choose because of that the specific impulse which essentially is the velocity divided by acceleration due to gravity. So, the velocity increment you can get from a practical chemical system is limited and because of that at the most about 500 second of specific impulse you get. However, if you are using electrical energy now chemical energy has a limitation because to a 1 kg of burning 1 kg of propellant you can produce only a fixed amount of chemical energy depending on the heating value of that you cannot produce more than that no matter what you do. Whereas, any amount of electrical energy can be added to any given quantity of mass because electric energy is not related to the amount or mass you are using. So, to a unit mass any amount of electrical energy can be imparted. Now, if that is the case there is a great reduction in mass consumption you can take a very small amount of mass and energize it to a very high level. So, therefore, the amount of mass requirement is much less and it is energize to much higher levels will be moving at a higher velocity. So, specific impulse will be more. So, because of this because we can use very small amount of mass and accelerate it to a very high speed a high specific impulse is attainable. And this energy the electrical energy another advantage of electric propulsion system is that it can be accessed directly from space as solar energy. You can have solar say which can absorb solar radiation and produce solar energy which can be then used for the propulsion. So, you do not have to separately carry a energy source or fuel only thing what you need is something to trap this energy and then use it in the way that we will discuss to produce thrust. So, there will be a conversion of this electrical energy to thrust power, but that is a much economical compared to a chemical energy and not limited by this velocity factors. However, the problem is the amount of power produced by will be much less compared to chemical rockets and why we will discuss that why the amount of power produces less because typically the efficiency of the systems are much lower compared to chemical the efficiency means the energy conversion efficiency is much lower compared to the chemical rockets. So, this kind of brings out the necessity of electric propulsion system to continue with this the exit velocity attainable by a chemical rocket is limited to about 2000 meter per second to about 4800 meter per second. So, now what limits this thing first of all the high combustion temperature if you go to very high temperature as I have discussed earlier the molecules thrust to dissociate and this dissociation reactions are endothermic. So, therefore, the available energy goes down. So, as the temperature goes the goes up the available energy reduces. So, therefore, there is a limit the velocity increment we can go in attain by going to higher combustion temperature at the same time you go to higher temperature the heat losses will be more. So, that also reduces the available energy at the same time. So, first is the high combustion temperature and also the low molecular mass of propellant imposes the limitation on the velocity increment that we can get. So, as I have mentioned previously it is limited by the heat of reaction of the propellant. So, every propellant combination has a specific heat of reaction we cannot get more than that. Now, use of electrical energy on the other hand allows heating of propellant to higher temperature. There is a class of electrical propulsion system I will discuss where which actually directly heats the propellant others may not heat the propellant, but one class directly heats the propellant and there we can go to very high temperature it can be close to 20,000, 30,000 Kelvin very high temperature can be attained by electrical heating and hence if you can get higher temperature we can get higher z velocities. So, by electrical heating or by providing electrical energy we can go to very high z velocities this is one of the major advantage of electric propulsion system. On other thing instead of heating we can also use electrostatic or electromagnetic forces to accelerate the propellants, but in this case they need to be charged. So, we will talk about them. So, electrostatic forces can be used or electromagnetic forces can be used to accelerate charge particles and plasmas to very high velocities and because of this we get always very high values of specific impulse. Bottom line is the electric propulsion system the velocity of exhaust jet is much higher orders of magnitude higher than what is attainable from chemical rockets. So, that is one of the major advantage of electric propulsion systems which provides us with higher specific impulse. Now, let us look at some of the applications of electric propulsion systems. First and foremost is attitude control in outer space when a satellite is moving or a vehicle is moving this typically not much of drag. So, whenever it goes out of the particular attitude you require very small amount of thrust to bring it back. So, that can be done very effectively by this electric propulsion devices. So, one of them is attitude control. Secondly, orbit raising where in any mission actually you go in steps you go to one orbit from there you go to another orbit from there you go to another orbit. Similarly, when you are deorbitating you come from a higher orbit to lower orbit like that. So, this orbit transfer mechanisms or other processes the vehicle itself moving with the very high speed as a small push is good enough to take it out of the orbit and take it to the new orbit. So, again the small amount of thrust is good enough. So, this electric propulsion devices are very effectively can be used for orbit raising. Similarly, translation going from one place to another precision positioning particularly where let us say we have to precisely dock vehicle into a space station or something like that precise positioning is very important. So, very small precise amount of thrust is required and that can be provided by this thrusters in a very good controlled manner. Then station keeping which essentially requires attitude control precision positioning, translation everything is station keeping where you maintain the satellite in the certain particular orbit. So, that again requires small amount of thrust which can be provided by this electric propulsion system and transfer of interplanetary vehicles. Typically if you are going for large distance let us say mission to mass or towards the age of the solar system very large distances. In that case many times electric propulsion systems become very very handy because the mass consumption rate is very very small because of that a small amount of propellant will go a long way. So, the life of the life expectancy of this vehicles will be much longer because this missions for interplanetary vehicles essentially are long term missions. So, that in order to continue with the mission you need some propulsion system and that has to work for years. Chemical propellants once they start burning they will burn out very fast and their required flow rate is also much higher, but this systems as we will go along we will see that the mass requirement is very very less because of that a small amount of propellant can last for a long duration. So, therefore, for this long time voyages this is a preferred system for propulsion. Now, let us look at what are the different forces electric forces or electromagnetic forces that actually take part in electric propulsion. There are primary two type of forces one are one is electrostatic force which is also called Coulomb force which is given by this expression f equal to q times e where e is the electric field which is given by k which is a constant q 1 is the charge of that particular point and r is the distance between the two the one by the two charge particles. So, e is the electric field produced by a charge particle located at a particular location and q is the charge of the particle. So, therefore, this is the Coulomb force that is produced because of the presence of two charge particles close to each other. Now, depending on this Coulomb force one particle the lighter particle will move. So, if you produce this force we can move particles. Another type of fort is electromagnetic force also called Lorentz force which is given by f q v b where v is the potential field b is the magnetic field and q is the charge. So, electric field and magnetic field and the charge q is the charge of that particle that produces another force on this particle given by this f Lorentz force. So, again a charge particle is subjected to this force field it will start to move with a particular. Now, this particles is going to see q these are subatomic particles very small particles as we will see there will be photons. So, subatomic particles the mass is very very less. So, even if a small force will produce very high acceleration because force is mass times acceleration. So, mass of this particles are very very less a small force will produce lot of acceleration. So, the particles will be moving at a very high speed and that is the primary idea of any electric propulsion system taking small particles moving them at very high speed. So, next let us talk about what are the different type of electric rockets. They can be classified under three broad categories one are electrostatic propulsion systems which essentially are governed by Coulomb force as I have just discussed. Where we have we produce charge particles by some means we will produce charge particles typically the propellants are treated in such a way that charge particles are produced and then this charge particles are accelerated by electrostatic forces. So, that is essentially at the back of all electrostatic propulsion systems. The other category is electro thermal in electro thermal systems we have a fluid propellant which is heated by electric energy and because of this typically the propellant will be mostly in liquid phase. Because of this heating they get converted into gas and heated to a very high temperature. So, you have a heated gas at a very high temperature then it is expanded through a conventional converging diverging nozzle and because of that very high velocities are produced at the exit. So, since you do not have limitation of chemical energy you can heat it to a very high temperature. So, this is typically there are they can be heated by producing an electric arc which are very strong temperature very high temperature zones or resistive heating by this means you can heat it to a very high temperature and then allow the heated gas to expand through a nozzle. So, this is typically electro thermal propulsion system and the third category is electromagnetic propulsion system where the primary force is the Lorentz force as I have just discussed few minute backs. Here once again we have fluid or plasma as propellant and these are charged. So, and then an electromagnetic force is created around it and the acceleration is produced by the electromagnetic force field. So, in the electrostatic you need only an electric field whereas in electromagnetic you need an electromagnetic field that is a electric field and a magnetic field. So, essentially sometime the electric field itself produces a magnetic field and sometime you have separate magnetic field produced. So, these are the various type of reactive rockets. Now, what we are going to do now is we will discuss each type of these rockets and within each of these categories there are various versions depending on various methods of energization. So, we will discuss various type of this. So, today what first we will do is we will focus on electrostatic. So, all our discussion today essentially we focusing on electrostatic propulsion system which uses coulomb force to accelerate particles. In the next lecture we will talk about electrothermal and electromagnetic and that will then cover the entire domain of electric propulsion system. So, start with the electrostatic propulsion systems or electrostatic rockets. Let us see what exactly happens in electrostatic thrusters. The basic principle is that the propellant is electrically charged electrically charged in an ionization chamber and this charged particles are then accelerated to high velocities using an electrostatic field that is the basic principle of operation. So, let us consider that the mass of the charged particle is m, the velocity of the particle which is attained after the acceleration by the electrostatic field is v v sub e q is the charge of the particle and capital v is the electric potential. Then if I look at this equation the kinetic energy attained by this charged particle because of the presence of electric field is half m v e square where v e is this final velocity m is this mass and q is the charge of the particle v is electric potential. So, therefore, this product gives us the total potential energy electric potential energy. So, this is the governing equation from this equation we can simply have phi e and get an expression for the velocity of the charged particle v e. So, that is given by this expression. Now, the force acting on this particle is rate of change of momentum. So, essentially the force is mass flow rate times exit velocity in the classical rocket equation. So, here the mass flow rate m dot essentially is nothing but m which is the mass of single particle times the current divided by charge. So, charge current charge divided by current is the dimensions of time. So, this becomes rate of change of mass. So, therefore, m dot is m i by q where i is the current and q is the charge. So, if I combine all these equations I get an expression for the force which is the Coulomb force produced when a charge particle is subjected to a electrostatic force which is given by f equal to i square root of 2 v m by q where m is the mass of this charge particle q is the charge of the particle v is the potential field and i is the current. Now, if I look at this expression then what I can see is that the force that will be produced will be proportional to current. So, higher the current I get higher force or it is it will be square root of the velocity potential the sorry the electric potential or the voltage across the two cathodes that I will be using. So, if I go to higher voltage I get higher force, but voltage and current product is the power. So, it is power limited right any of them we increase the power requirement is increasing. So, it is limited by power m is the mass of the particle. So, if I use a heavier particle heavier particle I get more thrust and q is the charge. So, lesser charge is better to produce more force. So, this is the expression that we will be working with. Now, as I just mentioned that higher the mass we get higher thrust or higher force or higher thrust produced. So, therefore, typically the propellants which are used for this type of propulsion system have high atomic mass. For example, typically xenon which is atomic mass unit of 132 gram or C C m with a mu of 133 are used these are quite heavy. At the same time we use positive ions not electrons because electrons are very small mass right. So, therefore, the thrust produced will be much less if we are trying to accelerate electrons. So, we use protons which have reasonably higher mass. So, because of that we use the charge particles we want to accelerate will be the protons. So, we accelerate this protons to a high velocity and that is what the principle of operation of electrostatic thrusters are. So, in that case what do we need them to make an electric propulsion system based on electrostatic thrusters. First because all these molecules xenon C C m there will be at equilibrium. So, first we have to energize them and we want to use the protons. So, we have to somehow strip the electrons out of them which can be done by bombarding with electrons right. So, you can bombard this molecules with electrons this will take away some of the electrons out you will be left with charged positively charged protons of this heavier molecules. Then we create an electrostatic force within this electrostatic force this will move right and then they will come out. But, there is a problem if this charge atoms come out it will create its own electric field around it that will have some implication in the space cap applications because it will be charged field completely it may interfere with their communications and all. So, you need to neutralize it also. So, this positive ions atoms which are coming out we need to neutralize it. So, we need again send some electrons to neutralize it. So, that the exhaust finally becomes neutralized. So, that is the basic principle on which this will be working. So, let us see now the different type of thrusters. One thruster is electrostatic ion thruster. So, here ions are produced which are accelerated. So, this concept was first demonstrated by Ernst Stullinger and developed in practice by Kaufman at NASA Lewis. The concept is exactly what I discussed right now here is the schematic of it. You can see that this is a chamber this is a electrically insulated chamber propellants atoms are injected into this chamber as you can see this green ones are the neutral propellant atoms which are injected into this chambers. And these are then we have an electron gun in between this electron gun fires electrons into it. These electrons collide with this neutral atoms and strip the electrons away leaving it leaving the protons which are positively charged outside. So, therefore, typically what we are having is that the propellant atoms are injected in the discharge chamber and these are ionized by electing bombardment forming a plasma. Now, this method can be carried out in several ways. One method I have shown here is electron gun it can be done in various ways. For example, the electrons are emitted from a hollow cathode which is electron gun and accelerated on their way to the anode this is the anode positive anode. So, the first grid you can see here is the anode I will come to that again detail or they can be accelerated by an oscillating electric field induced by a magnetic field. You can have magnets which will induce the electric field. So, that will also allow a directional directed movement of this charged particles. And typically the radio frequency ion thrusters use this type of thing where radio frequency waves are created which will essentially a magnet over a magnetic coil which results in safe sustaining discharge and omits any cathode requirement that is also possible or you can have microwave heating which will also strip the electrons and produce protons. So, essentially the basic idea is to produce this protons first. Second is to accelerate this protons. So, by the way this device which was a electrostatic ion thruster was successfully used in deep space one probe. The first mission to fly an interplanetary trajectory using electric propulsion as the primary propulsion device. So, it has been successfully tried also. So, this is the schematic as we see here. Now, let us see how it works in practice. So, this is the operation the positively charged ions move towards the extraction system essentially which are the 2 grids 2 or 3 grids. So, you can see here these are the grids. One of them is positively charged and there is a negative grid. What a positive grid or there is negative grid and we have holes in between. Now, the once the air entered the plasma sheet at a through this grid holes it will pass through. And now, so we have a positively charged ion it passes through the positively charged it gets accelerated further accelerated. And after this acceleration, so after that the second skin is you can see there is a negative grid. So, there is a potential difference between the 2. So, this charged ion now gets accelerated because of this potential difference based on the Coulomb force we have just discussed. So, there is a electric potential that is created because of that there is a massive acceleration of this particles. So, once they pass through this electric field they get accelerated to a very high velocity. And the negative voltage of the accelerator grids prevents the electrons of the beam plasma outside the thruster to come back in because of the negative at the exit. So, it will not is like works like a valve it will not allow the things to come from outside to inside. And now this entire thing the particles that are coming are out are charged positively charged. So, there is a separate cathode space outside as you can see here this one this one is a separately placed cathode which sends electrons to neutralize this ion beam. So, the ion beam is coming out which is positively charged it is neutralized means by this electron coming out of this electron ion or cathode and this is called neutralized that. So, finally, what we have is a neutralized exhaust. So, this is the entire operation as you can see it is fairly simple, but it has its own limitations. First of all it is limited by the power that we can produce. And secondly this electrons are the life limiting devices always because they get contaminated they get burned etcetera. And because of the high potential difference that we are creating. So, and also the thrust produce is not very large, but in practice they can operate for days and years this is one of the thing that they can operate for long durations without much of problem. Now, the next type of thruster I am going to talk about is colloid ion thruster. This is also an ion thruster, but the difference is in the previous start thruster the propellant was gaseous. In this one we have liquid as the propellant and liquid droplets are charged. So, what we have is charged liquid droplets. So, this were first proposed in 1960s and then alternative to normal ion charges. This is closely related to electro spray ionization and other hydrodynamic spraying process where a liquid is sprays spread into a atmosphere of the high potential field that liquid gets charged. And then that charged liquid particles or liquid droplets move out of the system. So, charged liquid droplets are produced by an electro spray process and then this charged droplets are accelerated by a static electric field. The liquid used for this applications have low or typically low volatility ionic liquids. This devices have high efficiency, high thrust density and high specific impulse. It provides for very fine attitude control and efficient acceleration of small space craft over long periods of time. That is why primary application of this thruster. The problems with the colloid ion thruster is that the thrust produce is very low of the order of micronutants. And the values of droplet mass per unit charge that could be generated with the technology that was available in 1960s were so large that they led to voltages of 10 to 100 kilo volt for typically about 1000 second of specific impulse. So, you can see that the voltage requirement was very, very high. And because of this high voltage requirement it created very difficult insulation and packaging problems. And that is what made this device quite unattractive. At the same time the droplet generators were usually composed of arrays of large number of individual capillaries. And each of them will produce thrust in the range of 1 micronutant. So, we need many, many of this devices to produce some appreciable amount of thrust. So, for the machine at which they are supposed to be used this was not practical. However, at present there is a renewed interest in this technology because of some newer technology that emerged already. First of all at present we are thinking about mineralization of mineralization of spacecraft. We are thinking about small satellite clusters. So, we are thinking about producing very small nano satellites or micro satellites. And for this small satellites the very small thrust emitter can become a very useful thing because they are very high efficiency light weight. So, because of this they will allow design of both fine controllability and high performance. So, because of this emphasis on the miniature spacecraft there is a renewed focus on this type of thruster. At the same time the electro space science has made a massive progress in the past few years, past few decades rather. Typically this collards have been used in the extraction of charged biological micro molecules from liquid samples. And this was done electrically and for detailed mass spectroscopy. So, there has been lot of advancement in this. Similarly, there has been advancement in printed technology, in jet printed technology, which sometime uses this essentially spray electric spray devices. And because of that the technology has matured enough to produce good quality droplet spray charged particles. And that is why there is now a renewed interest because it is now possible to operate this devices within 1 to 5 kilo volt that is within our doable range. So, therefore, now there is a renewed interest in this type of thruster. Now, one essential advantage of this collard engines for small thrust level is that there is no gas phase ionization. This is a big improvement you do not have to ionize a gas. And the problem is that because of this ionization requirement, if you have to make smaller thrusters from the conventional gas phase electrostatic thrusters the charge density becomes so much that it becomes very difficult to handle. So, because of that not only charge density the heat fluxes will be very high. So, because of that there is a size limitation, we cannot make the conventional electric thrusters smaller than a particular size because of the other issues. Whereas, this device is works best to the smaller size. So, that is why it is the best choice for the smaller spacecraft. And in this colloidal case the charging mechanisms essentially variation of field ionization on the surface of a liquid. So, small size typically enhances the efficiency of this system. So, where small size reduces the efficiency of other systems for this type of system the small size enhances the efficiency that is the major advantage. So, therefore, they will be the choice for the future electric propulsion systems for smaller spacecrafts. Now, I just mentioned one thing that the field ionization. So, there is a new concept field emission electric propulsion system which actually based on field ionization of liquid metal. So, here in this system this is a schematic given here we have a emitter electric field is provided here this through a small sheet liquid metal is passed through and this is the accelerator. So, this two will be maintained at a potential difference as you can see. And because of this electromagnetic field this will move at a high speed that is the very simple process. So, we have charged metal accelerated by a electrostatic field. So, it is based on field ionization of liquid metal subsequent acceleration of ions by strong electric field. This also form of an ion thruster, but it is using liquid metal either cesium or idium, indium or rubidium as the propellant. Again this consist of an emitter and an accelerator electrode very much like an ion thruster only thing is that propellant is different. The potential difference between the two cathodes or the two electrodes will be in the range of about 10 kilo volt. And this generates a strong electric field at the tip of the metal surface. And this inter play of the electric force and the surface tension generates surface instabilities which give rise to Taylor cone on the liquid surface. And at sufficiently high values of the applied field ions get extracted from the cone by the field evaporation which are accelerated then to very high velocities. The typically the velocity can be in the range of about 100 kilometer per second or more. So, we can see that it is orders of magnitude higher than what a chemical rocket will produce. So, this there is another problem here you also need a neutralizer because this will be charged. So, you need a neutralizer to neutralize the charged particles. So, separate neutralizer is used and however, the thrust produce is very low due to very small thrust are primarily used for micro radian or micro neutral attitude control of space craft. Typically the thrust produce will be in the micro Newton or milli Newton range the specific impulse can which can be achieved by this devices at close to 10,000 seconds with extremely high power efficiency where the thrust will be ranging from 1 kilo few micro Newton to few milli Newton. But this is a major advantage specific impulse is so high. So, this is again device which is now being tried out for various applications. So, this is the now with this we come to the most widely used electrostatic reposition system which is Hall effect thruster. This is the Hall thruster again the principle is same we produce some electrons and then move accelerate them. So, Hall thruster trap is not electrons the ions or the charged particles let me just simplify it. So, Hall thruster also requires some charged particles then accelerate them. So, Hall thrusters trap electrons in a magnetic field and then use the electrons to ionize the propellant which is then efficiently accelerate the ions to produce thrust. Unlike an ion thruster where the propellant is bombarded by electrons to produce the charge here the electrons are trapped in a magnetic field and then that is used to ionize the propellant. So, there is a basic difference between it this operates on variety of propellants the most common propellants are xenon other propellants of interest are krypton argon bismuth iodine magnesium and zinc. This devices can accelerate their exhaust to speeds between 10 to 80 kilometer per second. So, specific impulse up to 8000 seconds can be achieved by these devices. Most model however available model or walking model operate between 15 to 30 kilometer per second speed range or about 3000 second specific impulse. The thrust produced by Hall thruster varies over a range depending on the power level. Typically a device operating at 1.35 kilowatt produces about 83 milli Newton of thrust high power models are available which can produce up to 3 Newton. Power levels up to 100 kilowatt have been demonstrated by xenon Hall thrusters. So, these are the basics what has been achieved by Hall thrusters. Let us see how they work. So, as I mentioned the Hall thrusters are very much similar to ion thrusters. So, here is a schematic of a Hall thruster. Here this is the anode or the gas distributor where the propellant is stored and charged and we have a magnetic coil outer magnetic coil. So, between these two the electric field is created. So, electric potential between 150 to 800 volt is applied between the anode and the cathode. The central spike that is here forms one pole of electromagnet and we have an annular surrounding it annular space around it in the other pole of the electromagnet is the other pole of the electromagnet with the radial magnetic field in between. So, we have a magnetic field in between these two. The propellant which is like a xenon gas as is shown here is fed through the anode which has numerous small holes you need to act as the gas distributor. So, it is like a spray. So, anode has very many small holes through which the spray the gas is coming out. As the neutral xenon atoms diffuse into the channel of the thruster they are ionized by the collision with high energy circulating electrons in the anode. Now, the xenon ions are then accelerated by this electric field between the anode and the cathode as is shown here. And for then because of this electric field they move at a high speed for discharge voltage of 300 volt the anode ions will reach speed of about 15 kilometers per second. So, this is typically what they do. However, after coming out of this as you can see here after coming out of this thruster the ions pull an equal number of electrons with them. So, we have a cathode neutralizer the ions pull this electrons and then neutralize it here. So, finally what we get the thrust is neutralized by the electrons pulled by the cathode from the cathode. Now, this is typically what is a Hall effect thruster is the radial magnetic field is designed to be strong enough to substantially deflect the low mass electrons, but not the high mass protons. So, the magnetic field should just take away the electrons not the protons. So, that is how it has to be designed. And the majority of electrons are thus stuck orbiting in the region of high magnetic field. So, the electrons essentially keep on orbiting this field. And because of this orbiting electrons an electromagnetic field is created right it is given by E cross B. So, because of this orbiting electrons here electromagnetic field is created and this electromagnetic field actually produces the acceleration this effect is called Hall thruster. That is why this thrusters are called Hall thruster. So, this is how as you can see the radial magnetic field and the acceleration electric field. And because of that finally the particles will move out. So, Hall thrusters as I have just mentioned they are very efficient first of all the collisions with other particles and walls as well as plasma instabilities allow some of the electrons to leave the magnetic field and drift toward the anode that reduces some of the efficiencies. So, about 20 to 30 percent of the discharge current is electron current which does not produce any thrust. Other 70 to 80 percent that is quite a high number of the current is in the ions. Because of this the thrust efficiency is very very high. Let us just look at this paragraph here because the majority of electrons are trapped in the Hall current. They have a long residence time because they are circulating remember rotating in the radial direction. So, they are present a lot of time within that so because of the long residence time inside the thruster they are able to ionize almost all the propellants. So, therefore, the mass utilization of propellant the xenon is 90 to 99 percent that is a very high ionization. And because of the high mass efficiency the mass utilization of the thruster is about 90 percent the discharge current efficiency is about 70 percent. So, overall thruster efficiency will be about 63 percent that is pretty high efficiency 63 percent thruster efficiency. So, even with improved design efficiencies as I have 75 percent has been achieved by this thrusters. Compared to chemical rockets the thrust is very small as as as I have been just saying because the particle masses are small very very small. The order of about 83 milli Newton for a typical 300 volt system 1 kilo watt system. And but it can be increased, but they are limited by the power available with the on board the aircraft or on board the spacecraft. And because of the availability of power the thrust produce is limited the efficiency is limited the specific impulse is limited. However, they operate at high specific impulse as we have just mentioned one particular advantage of the whole thruster as compared to the gridded ion thruster we had discussed is that the generation and acceleration of ion takes place in a quasi neutral plasma. And so there is no space charged space charge that is a saturated current limitation on the thrust density. This allows much smaller thrusters compared to the gridded ion thruster because in the gridded ion thruster let me go back this is the gridded ion thruster the charge is created here. So, if you make a small the charge density becomes so much that the if losses will be much higher whereas, that problem is not there in this device. So, because this continuously flowing out as you can see it is continuously flowing out. So, because of this advantage the there is no it is not this allows much smaller thruster compared to the gridded ion thrusters. Another advantage is that this thruster can use a wider variety of propellant it can be even oxygen can be used not need not be xenon wider variety of propellants can be used although something which is easily ionized needed at the cathode, but in the anode even higher a lot of propellant different type of propellants can be used. So, these are the different types of advantages of hull thrusters. Now, some of the applications I will have listed out about the hull thruster they have been flying in space since December 1971 in the Soviet SPT 50 on the meteor satellite. Then over 240 thrusters have flown in space since that time with 100 percent success rate. So, this perhaps the most widely used electric propulsion system is hull thruster. They are now routinely flown on commercial geocommunication satellites where they are used for orbit insertion and station keeping. The first hull thrusters to fly on a western satellite was a Russian D 55 built by TSNI MASH on the NRO STEX spacecraft which was launched in October 1998. The solar electric propulsion system of European space energy smart one spacecraft uses a hull thruster which is a SNECMA PPS 1350 G hull thruster. This was this technology demonstration mission that orbited the moon. This use of this thruster starting on September 2003 was the first use of hull thruster outside of geosynchronous orbit. So, see that it has gone to moon unlike most hull thruster propulsion systems used in commercial application the hull thruster on smart one could be throttled over a range of power specific impulse and thrust. So, that is at the present as I was just I just mentioned that the hull thrusters are most widely used electric propulsion systems particularly in geosynchronous orbit satellites where typically used for station keeping or orbit insertion over has been used for a while now and will be used in future as well. So, with that I come to an end on the discussion on electrostatic propulsion systems. So, I would like to thank the sources from which I have got this material first of all the book on rocket propulsion by professor Ramurthy. Then the NASA website Wikipedia, Google then one this paper on by Maracuse et al experimental performance of field emission micro thrusters from which at least one of the topic has been taken. So, I would like to thank all these references. So, with this I stop the discussion on electrostatic propulsion system. In the next class we will discuss the electric heating electro thermal that is electro thermal and electromagnetic propulsion systems. Thank you.