 Welcome back. So, we are in the last lecture of this course. So, in the last lecture, we have been discussing we have discussed the electric propulsion systems, electric rocket propulsion we have been discussing. In the last lecture we discussed electrostatic propulsion system. Now, last lecture, I have discussed that three type of primary electric propulsion systems, electrostatic, electro thermal and electro magnetic. We have already discussed the a propellant system which operates by Coulomb force. Today, what we are going to discuss are the other two varieties, that is, electro thermal and electromagnetic propellant system. Electro thermal propellant system, first let us take them up. In this system, an electric heating is used. Primarily, the principle operation is that we heat the propellant using electric power and then accelerate this heated propellant through a nozzle to produce thrust. So, this is an expansion through a nozzle. So, among all these three, this comes close to rocket propulsion because we actually use a converging diverging nozzle to produce the thrust. And then, the electromagnetic forces is a Lorentz force which is created because of the interaction of the electric field and the magnetic field and that accelerates the plasma which is the propellant by the electromagnetic force accelerates that plasma. Now, so today first we will discuss the electro thermal propulsion systems. So, electro thermal, here the electromagnetic fields are used to generate a plasma to increase the temperature of the bulk propellant. So, electromagnetic field or the electric field is not for accelerating but for heating. The primary objective of the electric power is to heat the bulk propellant to high temperature. Now, the thermal energy is imparted to the propellant gas is then converted into kinetic energy by a nozzle of either solid material or magnetic field. Now, magnetic field can also be used to create a virtual converging diverging pattern. Now, a low molecular weight gas typically is a hydrogen, helium or ammonia are preferred propellant. It is a true rocket even though the energy producing the heat comes from external source is not a chemical energy but an electrical energy. Performance of electro thermal systems in terms of specific impulse is modest compared to other electric propulsion system. They fall in the range of 500 to 1000 seconds which is essentially between the chemical rockets and the other electric propulsion systems and we can see that but they are almost double than that the cold gas thrusters or the chemical rockets can provide. In USSR, the electro thermal energies were used since 1971. The Soviet Meteor 3 or Meteor Preroda or Resource O satellite series and the Russian Electro Satellite all of them used this electro thermal engines. Electro thermal system by Aerojet are currently being used on Lockheed Martin A21, 2100 satellites which uses hydrogen as a propellant. So, this is the basic background of electro thermal systems. There are typically two types of electro thermal rockets. One is a arc jet thruster and second is a resistor jet thruster. First let us look at an arc jet thruster. As the name suggests in the arc jet thruster the heating is provided by an electrical arc. So, if the electric arc has to be produced again we need to have a cathode and anode and like a welding machine an arc can be produced. We provide high enough potential difference between the two and electric arc can be produced between the anode and cathode that is the principle. So, here is the schematic picture of an arc jet thruster. Of course, this needs to be insulated. As you can see that the propellant is coming from here into this gap the centre one is the cathode which is typically made of thoriated tungsten and then we have a converging area and this is the anode. Anode is tungsten. So, high voltage is applied between the cathode and anode because of that an electric arc is created here and then the propellant which as I have just mentioned is some low light weight gas passes through this electric arc and because of the high temperature that is produced by this electric arc it gets accelerated and goes to supersonic speed and then it goes through a diverging nozzle creating a very high supersonic speed and then it goes out. As you can see here this is the schematic of an arc jet thruster. So, this device is a simple and reliable low power burst of thrust can be produced such a satellite needs for station keeping it can be produced by this thruster. Typically a non-flammable propellant is heated. So, we do not need we do not have flame typically the changing the we can use if you are using hydrogen which is typically a liquid then that gets gasified when it goes through this arc. So, it converts into gas. So, there is a typically change of state from liquid to gas by an electric arc in a chamber and then the gas goes out of the nozzle throat is accelerated and excelled expelled at reasonably high speed to create the thrust. Arc jet can use electric power from solar cells or batteries also and any variety of propellant can be used. At present hydrogen is the most propellant propellant because it can be used in chemical engine also in the same aircraft. If you are carrying as a this device is for station keeping or for say in a retro rocket or a rural rocket the same propellant system can be taken hydrogen can be used from that because hydrogen is also a chemical propellant. So, that is why this is typically used to provide high thrust capability or to act act as a backup to the arc jet also. Sometimes chemical rockets are also used as backup to the arc jet trusters. So, this is how an arc jet operates. As you can see there is a schematic here which is scaled up the propellant is sent through a swiller actually. So, it swills here as you can see here it swills through this. So, a long time it will spend within that and then the direct current of tens or hundreds of mps are passed through the gas between the upstream conical cathode as is shown here. The cathode and the anode a very high current will be passed and this gas is swilling in through this passage. So, then generating a highly constricted arc column that reaches temperatures of several tons and thousands of degrees because of the electric arc that is produced within that and that high temperature will heat up this gas. And anyway increase residence times of time of this gas by allowing it to swill around. So, it is spending lot of time and then it gets heated up it goes to very high temperature. So, as I mentioned here that incoming propellant is usually injected tangentially this then swill around and through this arc it swills expanding in the anode which is also the nozzle as we mentioned the anode is also the nozzle to average velocities of tens of thousands of mps. So, the exit velocity is very high since this arc it operate on a voltage of above 100 volt which is generally higher than the space curve bus voltage dedicated power possessing units are required and then that requires additional mass. So, 100 volt DC power supply is required let me put it this way. So, additional mass the mass of that can be actually more than the mass of the propellant the thruster itself. So, this is what an arc jet is next let us talk about a resistor jet. What is a resistor jet again is an electrical heater an electrical heater is used to heat up the fuel that is what the resistor jet is. So, here thrust is produced by heating a fluid typically a non reactive fluid heat is transferred to the propellant from some solid surface such as the chamber wall or a heater coil. So, heating is usually achieved by sending electricity through a resistor. So, simple electric coil heating nothing else and because of this heating it essentially the propellant the fuel that is used gets converted into gas with taking beyond is boiling temperature then that gas is expelled through a conventional nozzle that is what a resistor jet is. They have been flown in space since 1965 on board air force Vela satellites. However, they become used in commercial applications in 1980 with the launch of first satellite of Intel set 5 program. Nowadays, resistor jet proposition is used for orbit insertion attitude control or d orbit of low earth orbit satellites including satellites in the iridium satellite constellation and they do well in situations where energy is much more plentiful than mass and where proportion efficiently needs to be reasonably high, but low thrust is acceptable. So, proportion efficiency of the systems are very high. So, here is the schematic of a resistor jet. Here the propellant comes in the fuel resistor propellant comes in propellant is passing through this tubes. There is a valve heater here which will heat it then the valve mounting place there is a thermal start thermal standoffs injector plates the propellant is injected here there is a catalyst bed heater after going through all this the propellant is heated enough to get converted into gas. Then this gas is again taken here then it is further heated in this coil. So, the gas is. So, this is a breath sleeve this is a heat shield gas generator breath shield the gas is going here passing through this coils it gets further heated further heated further heated there is a heat exchanger essentially. Then after this is delivered here there is a nozzle converging diverging nozzle going through this. So, many heater a small amount of gas is passed through it gets heated to a very high temperature and then that is essentially exhausted through the converging diverging nozzle. That is the principle of a resistor jet nothing else this devices are very small and compact. Only thing is that lot of insulation is required because so much of heating is taking place. They can be heated to up to 1000 degree Celsius. The temperature the chamber temperature limited by the material of the wall and or heater coil to some 3000 degree or less. So, that is a essentially without chemical heating you are producing about 3000 degree Kelvin temperature. The exhaust velocity even with equilibrated hydrogen is about 10000 meter per second which is essentially factor of 2 or 3 beyond the best chemical rockets best chemical rockets will give about 5000 4800. So, this is double than that. So, specific impulse is higher and the typical resistor jet uses cathodically decomposed hydrogen as its propellant and achieves an exhaust velocity of 3500 meter per second and the thrust of about 0.3 Newton with an efficiency of 80 percent that is a big number when operated at the power level of 750 watt 750 watt is very small. So, 750 watt you are getting that high efficiency. So, that is a good system with that we conclude our discussion on the electro thermal propulsion systems. Next let us talk about electromagnetic propulsion system. As the name suggests in electromagnetic propulsion system the acceleration is primarily provided by electromagnetic fields. So, if ions are accelerated either by Lorentz force or by the effect of electromagnetic field where the electric field is not in the direction of acceleration those devices are called electromagnetic propulsion devices. So, electromagnetic propulsion devices some of the devices are listed here. The electrode rate plasma thruster, the MPD thruster I will discuss which they are pulse inductive thruster, pulse plasma thruster, helicon double layered thruster and wasimmer. These are the electromagnetic thrusters that are presently in use I will discuss all of them one at a time. First let us look at the electrode less plasma thruster. It was created by Mr. Grigory M. L. S. M. based on technology developed by French Atomic Energy Commission scientist Dr. Richard Geller and Dr. Teran Zio Consoli for high speed plasma beam production. So, the initial aim of the French Atomic Energy scientist were to produce high speed plasma beam which was then modified as a plasma thruster. So, here is how it works propellant is injected at the upstream side of the thruster body. This gaseous propellant is ionized very similar to ion thruster is ionized by one of the following methods. I read the bombarded with electron which has been done in the previous case we have discussed by a hot cathode or by an electron gun steady state electric discharge between two electrodes applying an alternative electric field or electromagnetic waves of various frequency radio frequency. So, this portion is same as the ion thruster that we have discussed. As the ionization stage is subject to a steady magnetic field the ionization process can leverage this situation by using one of the numerous resonance existing in magnetic plasma. So, this ionization state we have a magnetic field around it and that magnetic field and electric field is tuned in such a way that it creates magnetic resonance. So, the resonance can be ion cyclotron resonance, electron cyclotron resonance or lower high bit oscillation. So, the cold and dense so here that plasma is not hot. So, cold plasma is produced here produced by the ionization strain then drips towards the acceleration stage by diffusion across region of higher magnetic field intensity. So, essentially high magnetic field is produced. So, the magnetic field actually is changing in this intensity from one position to another position. In the acceleration state the propellant plasma is accelerated by magnetized funder motive force in an area where both non uniform static magnetic fields and non uniform high frequency rotor magnetic fields are applied simultaneously. So, two fields are applied simultaneously. So, essentially the difference between this and the ion thruster is there it was not converted into plasma just ion. Here in the presence of the magnetic field it gets converted into plasma then the plasma is accelerated by the electromagnetic field. So, that is the difference between that and this one. Next we talk about magneto plasma dynamic thruster. Again similar to the previous case this uses Lorentz force to generate thrust some time also referred as Lorentz force accelerator. In this case a gaseous field is ionized and fed into an acceleration chamber where the magnetic and electric fields are created using a power source. The particles are then propelled by the Lorentz force resulting from the interaction between the current flowing through the plasma and the magnetic field. Then it goes out of the exhaust chamber. Typically the propellant used are xenon, neon, argon, hydrogen, hydrogen and lithium. However, lithium is generally the best preferred propellant for MPD thrusters. This is a schematic of the MPD thruster. So, essentially again it is a similar thing that we have a we take gas, ionize it and then accelerate it using a electromagnetic field. In the previous case in the ion thruster it was only electric field here you have electromagnetic field that is the only difference. So, the concept is similar to an ion thruster. There are different types of MPD thruster typically there are two types. One is in which the electromagnetic field is applied from outside. It is called applied field thruster. Other is it is created by the entire system itself because of the electric field that is there creates the magnetic field. So, that is called the self field. So, applied field thruster have magnetic rings surrounding the exhaust chamber to produce the magnetic field. In the self field thruster you have a cathode extending through the middle of the chamber. So, the presence of the cathode and the charge plasma creates the magnetic field. The applied fields are necessary at lower power levels where self field configuration are typically too weak in the lower power levels. One big problem with the MPD thruster is that the power requirement is on the order of hundreds of kilowatts for optimum performance and that is not available in the current systems because you have to take power from solar energy is not available hundreds of kilowatts are not available. That is what typically so far it has not been used for the intended application. In future they may be used, but not right away. Next let us talk about first inductive thruster. A first inductive thruster or PIT uses perpendicular electric and magnetic field to accelerate a propellant. Once again the concept is similar a nozzle releases a puff of gas which is the ammonia or argon which is pressed across a flat induction coil. Now, it is like the induction cooker induction coil or wire and bank of capacitor release a pulse of electric current lasting certain microsecond or all into the coil generating a radial magnetic field and this induces a circular electric field in the gas ionizing it and causing the ions to revolve in the opposite direction. Because of this motion perpendicular to the magnetic field the ions are accelerated out into the space. So, just try to visualize what is happening that we have a plate on which some gas is put then we are creating a magnetic field by discharging from a capacitor and then because of that a magnetic field is created which pushes the gas out. So, that is that is what it is. So, you are creating a magnetic field over an inductive field that is why it is called pulse inductive thruster. Unlike an electrostatic ion thruster PIT requires no electrodes because your using just capacitor or inducing coil and its power can be scaled up simply by increasing the number of pulses per second. For one megawatt system it will pulse about 200 times per second, but one megawatt system is a lot. So, that is something that is still not practically available, but this is a concept which probably will soon be taken up for further development. Next we talk about pulse plasma thruster. These are also known as plasma jet engines in general. These devices are the oldest electric propulsion devices. All thrusters are the most widely used, plus plasma thrusters are the oldest devices. They use an electric arc of electric current adjusted to solid propellant similar to arc jet thruster, but arc jet just heats up. Here the heating is such that it creates a plasma and then this plasma is accelerated by an electromagnetic field that is produced. There are two electrodes which produces electromagnetic field and the plasma gets accelerated because of that. So, you can say that it is the combination of conventional plasma thruster and arc jet thruster and the arc essentially is a pulse arc because we will be using some electrodes and capacitors to produce pulses. So, that is why it is called pulse plasma thruster. So, these are very good for attitude control and for main propulsion particularly small size spacecraft which surplus electricity. The problem is that the least efficient electric propulsion system. Efficiency is typically less than 10 percent. At present they are deployed in space vehicles and probes as space does not offer any typically outer space because the thrust produces very small and they can be used for long duration. These are they produce extremely quick and repetitive thrust and because of that they can accelerate the probes in space continuously. Thus it eventually reaches and goes beyond the speed of conventional propulsion system. They will like ramjet it will not be able to start it from 0 because the thrust produces very small but something is moving at high speed. Continuous small push will take it to higher and higher speed that is the idea of the systems. The electric energy required to operate that mechanism is abundantly available by solar energy. So, therefore, we can have solar energy can provide enough energy for operating this pulse plasma thrusters. Let us look at how it works. Here is a schematic of a pulse plasma thruster. We have a Teflon a solid propellant bar on both side of this we have two electrodes and this is connected through a capacitor and a power supply. And there is a spark plug put here. What happens is that when the spark plug is energized it creates a small pool of electrons around it. And because of this electrons and then the capacitor is charged to a because this two electrodes are maintained at a high potential difference in the presence of this electrons and electric arc is produced here. This arc temperature will be very high as we have just discussed earlier and this electric arc is very close to this Teflon. So, because of this high temperature of the electric arc Teflon particles get ablated and in the presence of this arc they get ionized to plasma. So, plasma is created here. Now, these two electrodes essentially make an electric field electromagnetic field. So, in the presence of this electromagnetic field this plasma moves in a particular direction. So, here is the electric schematic. This is the current direction. This is the magnetic field is the capacitive magnetic field is the magnetic field. So, the Lorentz force will move it in this direction. So, because of the presence of Lorentz force the plasma is produced moves in the direction here. So, here is a picture of pulse plasma thruster operating in our lab where plasma is produced and then it moves out from here. There is another picture with multiple pulse plasma thruster firing simultaneously five of them. So, this produces again very small amount of thrust in milli Newton or micro Newton, but the mass ablation rate is also very very small. So, therefore, a small piece of Teflon can go for years that is the biggest advantage of it the mass ablation rate is so small and you can get specific impulse up to 500 or 2000 seconds quite easily by this thrusters. So, because of that they are been very widely used. So, the P P T's have much higher exhaust velocity than chemical propulsion engines. This results in proportionally higher final velocity of the propelled craft. The principle of operation is the electromagnetic acceleration of the propellant via Lorentz force to velocities of the orders of tens of kilometers per second which essentially is almost order of magnitude higher than the chemical engines exhaust velocity. The pulse plasma thruster were the first electric thruster to be deployed in space. They were used for attitude control on Soviet probe zone 2 from parking to earth orbit to march on November 30 1964 and then in zone 3 in 1965. 12 plasma thrusters were flown in 2000 as a flight experiment on earth observer 1 spacecraft as well. They have successfully demonstrated the ability to perform roll control on the spacecraft and also demonstrated the electromagnetic interference from the pulse plasma thruster did not affect other spacecraft systems because the electric electromagnetic field is very short duration. They do not have a long term effect on the other systems of the spacecraft. So, this has been successfully flying for years now. For example, in the zone 2 the first time it was used by the way the in zone the propellant was not teflon. We used some gases whereas, the earth observer 1 spacecraft they used teflon as the propellant. Now, teflon another thing that is I have forgot to mention here is that since as the it starts to work the phase of the propellant gets ablated being consumed. So, then it will start to move away from the spark plug. In order to continuously feed it typically a spring is used at this end. So, the spring will continuously keep on pushing it. So, that the distance between the teflon and the spark plug is maintained. The life limiting component in this is the spark plug which gets eroded. So, if we can replace the spark plug by some other means then the life will be extended. Now, as I was mentioning the zone it actually outlive its life by years few years because of the high because of the pulse plasma thruster was able to operate much longer than it was expected to. So, this is what a pulse plasma thruster is. Next, let us talk about Helicon double layered thruster. This was created by Australian scientist Dr. Christine Charles based on a technology invented by professor Rod Boswell of the Australian National University. This ejects high velocity of ionized gas to provide the thrust to an aircraft. So, once again the basic principle is high velocity ionized gas. As we have been seeing again and again all these devices are doing that only the method of in which we are getting the high velocity is different. So, here in this case what is that done is that the gas is injected into a tubular chamber or the source tube with one open end. Then a radio frequency AC power at 13.5 megahertz is coupled into a specially specially shaped antenna wrapped around this chamber. So, we have an antenna wrapped around a chamber through which the gas is flowing and radio frequency high frequency AC power is supplied to that. The electromagnetic waves emitted by the antenna causes the gas to break down and from the plasma. So, essentially the electromagnetic plasma generation because of this. The antenna then exists a Helicon wave in the plasma excites a Helicon wave in the plasma which further heats the plasma. So, the antenna produces the plasma heats it also. The device is a roughly constant magnetic field in the source tube, but the magnetic field diverges and rapidly decreases in magnitude away from the source region and might be thought of as a kind of magnetic nozzle. So, magnetic field is reducing as it goes away. So, the flow will start to move in this direction. In operation there is a sharp boundary between the high density plasma inside the source region and the low density plasma in the exhaust which is associated with a sharp change in the electric potential. The plasma properties change rapidly across this boundary which is known as a current free electric double layer. The electric potential is much higher inside the source region than in the exhaust and this serves both to confine most of the electrons and also to accelerate the ions away from the source region. So, source region is where the plasma is produced and starts to accelerate then the shape of the magnetic field actually produces the shape of the nozzle which is a virtual nozzle not a real nozzle. So, the flow goes in that direction. Enough electron escapes the source region to ensure that the plasma is in the exhaust is in the neutral overall. So, the electron that is produced here will neutralize the plasma also. So, we do not have a charged plasma. So, here is typically a picture of this operating. The issues like most of the ion propulsion systems this is also an ion propulsion system. The HDLT is a low thrust high specific impulse thruster. It has two main advantages over most other ion thrusters. First of all it creates an accelerating electric field without inserting any unreliable component like high voltage grid into the plasma. In the ion thruster you need the grids. So, this is one of the major advantage and secondly you do not need a neutralizer because it is inherently neutralized. Since there are equal number of electrons and protons emitted. So, it is inherently neutralized. So, you do not need a neutralizer you do not need a grid to accelerate it. So, the antenna itself the magnetic field itself provides everything. So, that is what the biggest advantage of this thruster is. Now, we come to the last one which is variable specific impulse magneto plasma rocket called Vassimar. It uses is also similar to the one we just discussed. It uses radio waves to ionize and heat a propellant and magnetic field to accelerate and the resulting plasma to generate thrust. So, it is very similar to the one we just discussed. The method of heating plasma used in Vassimar was originally developed as a result of research into nuclear fusion. Vassimar is intended to bridge the gap between high thrust low specific impulse propulsion system and low thrust high specific impulse system because it is capable of functioning in both the modes. The Costa Rican scientist and former astronaut Franklin Chang-Diarch created the Vassimar concept. Now, this is let us look at how it works. Here is a schematic diagram of the Vassimar system. Here, first is that we have a converging diverging nozzle for ions and electrons. The propellant which is typically a neutral gas such as argon and xenon is first injected as you can see here into a hollow cylinder surface with electromagnets. So, we have electromagnets here. The gas first is this is surrounded with a antenna where radio frequency is going in. So, the gas is first heated to a cold plasma by a helicon radio frequency antenna similar to the helicon system we just discussed. It is converted into a cold plasma. It is also known as coupler which bombards the gas with electro-magnetic waves stripping electrons of the gas at the argon and xenon we are using and leaving plasma consisting of ions and loose electrons which is now continuing down this step. Now, by varying the amount of energy dedicated to this radio frequency heating and the amount of propellant delivered to the plasma generation, the Vassimar is capable of either generating low thrust high specific impulse or high thrust low specific impulse. Both are possible. Now, the second phase which is shown here is a strong electromagnet position to compress now this ionized plasma in a similar fashion like a converging diverging nozzle. So, in the previous case in the in the HDLT you had one radio one antenna with one electro-magnetic field. So, naturally it was getting weaker and producing this virtual nozzle, but here you have two of them separately one is to produce the plasma other is to give the shape. So, you have much more control over it and can be compressed much more the access can be compressed much more, but this compression is magnetic compression. So, the second phase is a electro-magnetic position electro-magnets position to compress the ionized plasma in a similar fashion like a converging diverging nozzle which compresses gas in traditional rocket engine. The second coupler known as the ion cyclotron heating section emits electro-magnetic waves in resonance with the orbits of ions and electrons as this travel through the engine. This resonance of the waves and plasma is achieved through a reduction of magnetic field in this portion of the engine which slows down the orbital motion of the plasma particles. This section further heats the plasma to temperature upwards to 1 million Kelvin 200 times the temperatures of sun surface. So, it is a electro-magnetic heating to that temperature very high temperature and after that there is a final diverging section which contains a steadily expanding magnetic field which forces the ions and electrons into a steadily lengthening spiral orbits in order to eject from the engine as you can see here. This comes parallel to the engine axis and the speed as high as 50,000 meter per second can be attained. So, essentially what is being done here is you have electro-magnetic heating first of you create plasma then electro-magnetic heating of that plasma and then electro-magnetic forcing of the plasma by creating a varying electro-magnetic field which works like and converging diverging nozzle and accelerating this to a high velocity field. So, everything is essentially done by electro-magnets you do not have physical boundaries doing it. So, essentially what you need is a very good insulation so that the magnetic field is insulated and as you can see there are two radio frequency generators, RF generators used one for the cold plasma production other for the hot plasma heating and the acceleration part. So, this is what a Vassimar is the benefits is R of the Vassimar system is it does not use electrodes instead it magnetically shields plasma from most of the hardware parts thus eliminating electro erosion which is a major source of problem for ion engines. Electro erosion is a major source of problem compared to traditional rocket engines with very complex plumbing this does not require any valve and neither actuators not turbo pumps. So, eliminates all moving parts from is design and because of that it maximizes the long term durability of the system because you do not have turbo pumps you do not have valves you do not have actuators. However, the problems are first of all interaction with strong magnetic field and thermal management first let us talk about the thermal management. A relatively large power at which the Vassimar operates generates a lot of waste heat because the temperatures are going to be very high right I mentioned about 1 million Kelvin. So, lost of waste heat is generated which needs to be channeled away without creating a thermal overload and undue thermal stress on the material used the material can melt because of the high temperature is created. So, the thermal management becomes an issue and secondly the magnetic field that is generated require powerful super conducting electromagnets which are employed to contain the hot plasma generate Tesla range magnetic fields which are very high magnetic field. They can present problem with other onboard devices and also can produce unwarranted torque by interacting with the magnetosphere. So, these are the two major issues with Vassimar system, if used properly this system can have has potential to work both as a high thrust low specific impulse and low thrust high specific impulse system that is a major advantage. So, it will be a universal system. So, with this we come to our discussion. So, first I would like to once again thank the references from which I have taken the material Dr. Ramurth's book then NASA's web page Wikipedia Google and this personal web page naka rocket tree dot net which provided me the material for this part of the course. So, let me just summarize what we have discussed in this course. We started off with type of rockets rocket equations the space dynamics then the rocket performance then the multistaging then the rocket performance in the chemical rocket performance then combustion then nozzle design after that we talked about solid propellant rockets liquid propellant rockets and then couple of lectures on electric propulsion system. So, I think we have fairly covered the entire gamut of rocket propulsion and we will just stop it here. Thank you.