 Today we are going to talk about lecture number 36 where we will be discussing two very important and interesting topics. One is laser plasma accelerators and the other one is accelerator driven systems which is also called accelerator driven subcritical reactor systems. Now first one I am going to discuss about laser plasma accelerators. Now we have so far discussed different kind of accelerators for example DC accelerators where maximum gradient of 1 to 2 million volts per meter is achieved or used. Then the improved version of different one is RF accelerators. This could be either room temperature or superconducting time. Now in the case of room temperature RF accelerators, gradients used are of the order of 10 million volts per meter and in the case of superconducting RF accelerators, gradients in the range of 50 to 100 million volts per meter are usable. Now these gradients are not enough if you want to go to very high energies and therefore new technology has to be developed and one of the such technology is a laser plasma accelerator technology where accelerating gradients of 100 to 300 gb per meter are achievable. In fact in experiments 100 giga volts per meter has been measured and has been achieved. Now what is this laser plasma accelerator just to give you some points it involves you apply an high power from terawatt to petawatt ultra short which is of the femtoseconds laser pulse into a plasma that will create the plasma wave. This plasma can be created either by the laser pulse itself or it can be created by some other pulse. So some other pulse suppose the laser this plasma is created then you can inject this ultra short high power laser beam and that will generate a electron pulse beam which is responsible for having the gradients accelerating gradient. Now acceleration gradients of 100 gb per meter have already been achieved and they have been measured in the lab. By injecting electrons properly or some of the electrons from the plasma itself they can be accelerated these electrons can be accelerated to very high energies. Let me just tell you what is the status of this at this moment high energy accelerators for example the I will take examples of two accelerators one is tevatron at Fermilab and that tevatron is a colliding ring where one tv protons interacts with another one tv antiproton and these collagens are studied. This antiproton is denoted by like this so this is p into p bar this is p and antiproton proton antiproton collagens. Another accelerator is a large hadron collider or more popularly known as LSC where seven tv beam collides or interacts with another seven tv proton beam both of them are protons. Of course in this accelerator heavy ions also can be accelerated and they are accelerated to seven tv each. The circumference of this accelerator is about 27 kilometer and these pp collisions take place. They have also planned a future circular collider that is called FCC at Sun for search of new particles and study of the interactions. Circumference of this new accelerator will be 100 kilometer. Cost at this moment is estimated to be about 23 billion tons as superconducting magnets are used. So the energy is 100 tv in center mass and that is the energy which is used in the collisions nuclear reactions or particles. So 100 tv if you take it is 10 power 5 gv and the ultimate goal is to achieve 10 power 19 gv where all forces are expected to unify unification of all the forces will is expected to take place at 10 power 19 gv. So ultimately the technologies and infrastructure has to be developed in such a way that ultimately we should be able to reach to 10 power 19 gv. Now coming back to laser plasma accelerator this plasma based accelerators can support accelerating electric fields many order of magnitude higher than the conventional accelerators. The reason is you have seen as I said in the last slide here that in the RF superconducting accelerators you get let's say maximum 100 mb per meter while in the case of laser plasma accelerators you can get 100 g per meter so that means is 1000 times more. Now this restriction or the limitation in conventional devices come because of dielectric breakdown because of high fields is not able to sustain that and therefore the dielectric breakdown takes place dielectric of because we are using either cavities or waveguides and there when the field becomes very high field ionization takes place and plasma will be formed and we will not be able to go to higher voltages or higher gradients. However in laser plasma accelerators or any plasma accelerators plasma is already broken down therefore there is already plasma is there so there is no such limitation and therefore there is no real limitation on the accelerating gradients. The electric field E z which is a accelerating direction E z is supported by plasma is proportional to the root of electron density so this is the basic thing so gradient is proportional to root n is the electron density electron density the electric fields are created by a driving beam driver beam and that driver beam could be either laser or it could be electron beam also or even the particle beams also and that happens because of due to separation of charges that means in the plasma you know microscopically plasma is neutral that means positive and negative particles are roughly equal and they are totally it is neutral however in this case in laser plasma accelerators there is a separation of electrons from the positive ions and that is what is responsible for generation of electric field. Now let us see that what are the type of things possible these electron plasma waves travel with a phase speed close to the speed of the drive that means laser and laser it moves almost at the velocity of light and therefore when these electrons also move with that high energy electrons can be accelerated so if the plasma density is of this order that means 10 per 19 per cc then it can support the field of about 300 g e per meter more than roughly thousand times as I have just now explained it than the more than thousand times greater than the radio frequency per even with the superconducting structures. Now I loudly think that if suppose that you can get I do not know I do not know whether it is possible how difficult it is the electron density of 10 or 20 per cc then the field can be in tv per meter in distance so that means in tv energy you can get in one meter structure itself and that will be a fantastic thing but there will be a lot of difficulties in getting this plasma density of 10 or 20 per cc so this basically when you get these kind of high energies what it translates it translates that the size of the accelerator will be reduced considerably see for example what was hundreds of meters will become only a few meters and when the length of the accelerator reduces considerably then the cost also will come down because the building has to be very small infrastructure has to be very so cost also will reduce so these are two advantages then the size of the accelerator also comes down as a consequence of that the cost also cost reduction is there but to explain that how this works just a few remarks about how this laser plasma accelerators in laser plasma accelerators a short laser pulse of the order of femtosecond excites a wake of plasma oscillations and as a consequence of that the radiation pressure of this short intense laser beam pushes plasma electrons forward and aside separating electrons from the positively charged ions creating a positive positively charged column this also can be explained that there is a powder voltage force which pushes electrons away from the axis and generates a charge separation between ions and influence that this is what is responsible for this is where the density of the electrons in plasma will come into picture of course there will be a restoring force also and that will initiate a local density oscillations this is demonstrated here in this figure which I have taken from this reference that at the center of this axis there are no electrons and since the positive ions they are much heavier almost 2000 times heavier than electrons they move very slowly so there will be a separation of ions from the electrons so ions all the electrons will be generated will be collected here or it will be all around so there will be a gradient accelerating gradient will be formed which could be of the order of 100 to 300 right now maybe at some stage it will increase and those electrons if they match phase wise with the wave then they will be accelerated to very high energies so this is I've already explained that plasma accelerators use wave fields generated by plasma density electron plasma density waves so this is most important now what kind of things when I'm talking about that 100 to 300 giga oh giga volt per meter what are the conditions involved in it so let's see as I explained earlier that the gradient is at is proportional to root of electron density now suppose the density is 10 power 19 electrons per cc and you are able to separate one percent of this then one percent means the density is of this order and that will amount to an electric field of 0.3 GB per meter however if your system is such that you are able to have the density per termination of almost 100 percent that means there are no electrons in the center then the gradients correspond to about this and as I mentioned that if it goes to about 10 to 20 per cc then you will get it into almost like TV per meter range so most important of this to summarize this whole thing the most important of this whole process is generation of charge separation that means you are separating electrons from the positive charge so there is a separation of charge between ions and electrons now depending upon how this process takes place the plasma accelerators are categorized into several categories and some of them are mentioned so how this electron plasma wave is formed so suppose this plasma wave is formed by electron plasma wave is formed by an electron bunch then those kind of accelerators are called plasma wave field acceleration however if that is done using a laser beam so a laser beam or laser pulse in introduced from outside to form an electron plasma wave ultimately it is the plasma wave which is responsible for acceleration of electrons so if that is formed because of laser beam or laser pulse then it is called laser wave field acceleration now it is also possible that we inject two laser beams and with different frequencies and then they interact and a beat wave is formed and that baby also can give acceleration that kind of accelerators or the acceleration is called laser beat wave acceleration in this case the electron plasma wave arises based on different frequency generation of two laser beams two laser pulses here two lasers are required now there is another category which is even more efficient they are the formation of an electron plasma beam effectively electron plasma wave is required and that is achieved formation of this is achieved by a laser pulse modulated by stimulated Raman forward is getting instability and here the much higher gradients are possible and that kind of accelerators are called cell modulated laser wave field acceleration so these are some of the categorization these are some of the types of accelerators which are now the first laser plasma accelerator this concept was given by Tajima and Dawson and in that was published in physical review letters here and it's a short paper but very good paper and this was theoretical paper theoretical concept was given by these two scientists later on a system was built in the lab by Chandrasekhar Joshi and colleagues and they accelerated the particles electrons using this laser plasma accelerator to high energies in the GEV per meter gradients after that several labs have started working and for example Laurence Berkeley national laboratory they have one GEV over 3.3 centimeter that means it is a gradient is of the order of so it's roughly 30 so gradient is of the order of 30 GEV per meter similarly slack the Stanford laboratory linear Stanford linear accelerator center they injected 40 GEV electrons into the laser plasma accelerators and they accelerated this to 82 GEV adding 42 GEV energy to the electron over a length of only about 85 centimeters now if this energy had to be achieved in slack itself it will corresponds to about 65 meters so you can say that is almost like thousand times reduction in the length itself so this is a very good technique and very good excellent now the challenges which are involved here is improved performance of laser systems and in this one the laser beam quality reliability and stability have to be improved and perhaps the average power also that means right now we were using only femtosecond pulse width maybe that is because of this the average power is very small so average power also has to be increased if you want to have higher acceleration so these are some of the things which we have to improve and of course this is very important right now people have developed terawatt or even petawatt lasers and they have been is thinking of developing even higher power accelerators so you can see that there are various labs which are using terawatts some people have been developing petawatt and also now people have started talking about exawatt lasers so once this is available the gradients of much higher values will be available another thing which we have to develop is to develop the external injection because right now suppose when you are picking up some of the electrodes which are there in the system and accelerating them they the current will be very small so you should be able to develop an external injection system scheme to increase the energy of the electrodes as well as quality of the beam also will improve further and the density will go up so higher currents can be achieved if you are if you can master the technique of external injection scheme then there is a also thinking that if you want to do all this is it possible to have a multi-stage of acceleration not just one but you can assemble for example in the RF accelerators we have different cavities they are so particle accelerated by one system or further accelerated by another system like this there are several systems so can we have can we have a multi-stage accelerations and of course there will be a lot of technical difficulties but one should think about it so multi stages of acceleration to compensate for laser damping and electron defacing in the plasma because phasing of match phase matching of these electrons to the wakes will be extremely important for further acceleration of the beam so these are two things which we have to we have to master and we have to improve it and if that is done so three things will happen one is that we will be able to get higher energies second thing is that we will be able to get much higher currents and then we will have a quality of the beam will also increase will improve further and these all these things so we we achieve them the these accelerators of good quality beams will be possible so this is laser plasma accelerators so these plasma accelerators are showing a great promise and they were giving lot of importance by the best journals like nature physical regulators and Scientific American and you can see that they published it on the front page now in India also we have started working on in this field for example a system has been developed has been developed in the RRCAD and the diagram is shown here where a 10 terawatt 45 femtosecond pulse from the laser is made to interact with the gas which forms the plasma and a mono energetic beam was accelerated was energy beam was obtained you can see here on the the parameters of that mono energetic beam are given here the electron energy was about 50 mbv energy is spared of about 5 percent beam divergence 4 milliliter and one charge was of the order of 10 picocoulomb they have also further improved the system and recently sometime back the accelerated electron beam of up to 1 gb with a broad spectrum has been obtained with a peak of 500 mbv and here again the 10 terawatt laser with the 10 hertz was used so they have gone up to and the further improvements are being done to increase the energy and to make it a very sharp peak this has been taken from this uh uh invited talk by Anand Murthy from RRCAD there is another system developed at Tata Institute of Fundamental Research Mumbai and they have developed a laser plasma accelerators system to get high energy multiple charge state ion beams and then converted them into a neutral beam for their studies and some typical results is the they showed that it's a neutral argon beam of mbv energy with intense laser has been accelerated and this is shown here and they were interested in studying the neutral beams and that is why first they accelerated to high energy and then they convert into uh neutral beams so these are two accelerators which have been developed in India and used and now I will be talking about the second part