- Moreover, fusion reactors will be intrinsically safe, since the losing of the optimum operational parameters will cause the stopping of the fusion reactor.. - Since the needed temperatures for fusion to occur are of the order of hundred millions of degrees the matter will be in plasma state in fusion reactors. - And plasmas are very complex systems to study, especially if they suffer the effect of the confining magnetic field of the device. - e., to the plasmas heated by alpha particles that are born in the fusion reactions. - But ITER will not be the only device relevant for fusion that will be built in the next future. - The long term objective in fusion research modelling is to “build” a numerical tokamak and a numerical stellarator, which implies the full knowledge of the relevant physical phenomena that happens in a fusion device, including plasma physics itself, the properties of plasma waves, and plasma-wall interaction (PWI). - These numerical fusion reactors could help to save a lot of money since all the scenarios and exploitation regimes that can be expected in fusion reactors can be simulated before doing the experiments. - The achievement of this knowledge is a challenging task that needs the understanding of all basic plasma phenomena and of all the physical phenomena that will happen in the reactor. - Especial attention must be paid to the effects of the neutron radiation on the material properties.. - Hence, the most relevant tasks for the fusion modelling can be summarized as: first of all, it is necessary a full understanding of the physically relevant phenomena that will happen in a reactor, inside the plasma but also in the walls and in all the complex systems that will be installed. - In fact, grid activities for fusion research started as a pilot experience in 2004, in the frame of EGEE project [3]. - The remainder of the paper is organised as follows. - Section 3 is devoted to the description of the serial applications that were ported in the beginning of the grid-fusion activities and to their scientific production. - Section 4 is devoted to show the use of genetic algorithms in the grid for fusion research. - Fusion on the grid: the strategy. - The strategy that has been used in order that grid computing is extended in fusion community is to start porting those applications that can be easily gridifyed because of their distributed nature, and still can give physically relevant results. - This is what we call “the demonstration effect”: it was necessary to show that grid computing is useful for the fusion community.. - Beyond considering the extension of the grid use to different types of applications, it is necessary to consider the application of these techniques to different research topics relevant for fusion reactors. - From the core of the reactor to the edge, very different research fields can be identified. - The plasma dynamics can be studied both by fluid and kinetic theories. - The first ones consist of solving continuity-like and conservation equations in the presence of the three-dimensional background magnetic field, while the second consist of studying the properties of the individual plasma particles. - The fluid equations must be solved using finite differences or even finite element techniques, so they are not, in principle, the most appropriated for the grid, while the kinetic approach problems can be easily ported to the grid, as has been done with the application ISDEP [6]. - Plasma heating can be performed experimentally by several methods, but there are two of them that can be modelled by means of grid technologies: electron heating by a microwave beam, which can be simulated by the estimate of a large number of rays as it is performed with the TRUBA code [8], and neutral beam injection (NBI) that can be simulated by means of the Monte Carlo code FAFNER [9]. - The plasma wall interaction and the edge transport can be simulated by means of the use of a Monte Carlo code like EIRENE [10], a widely distributed code for plasma-wall interaction studies, or by a PIC code like BIT1 [11].. - The Magnetohydrodynamic (MHD) equilibrium and stability are also important disciplines since they study the dynamics of the geometry of the magnetic trap. - The main application that estimates the equilibrium is VMEC (Variational Moment Equilibrium Code), which has been also ported to the grid in the frame of the stellarator optimization. - Finally, some material research codes should be considered in order to include the simulation of the reactor structure behaviour in the grid simulations. - The ISDEP (Integrator of Stochastic Differential Equations for Plasmas) code is used to estimate transport properties of fusion devices by following independent particle trajectories in the plasma, according to the well-known movement equations in the guiding centre approximation. - This problem is perfectly suited to the grid, since all the particle trajectories are independent and can be solved separately in the nodes of the computing. - As a first step we solved these equations in the TJ-II stellarator, which has a very complicated geometry, without collisions [12]. - The total distribution function can be obtained at a given position and requires about 1 GB data and 24 h x 512 CPUs. - The use of the grid for these calculations has allowed us to obtain the 3D collisional ion fluxes without any approximation on their diffusive nature or on the orbit size of the trajectories. - This is an excellent example of application to be run on the grid, since all the ions can be run independently and the accuracy of the results can be increased just by adding more calculated ions, distributed initially according to the density and temperature of the background plasma.. - Once the flux structure is known it is possible to develop strategies to minimize the flux and to reduce the possible hot spots in the chamber [13].. - More recently, the problem has been converted in a non-linear one by allowing the background plasma to change by the influence of the test particles [14]. - The non-linear version of the application elapses about 35 times more CPU time than the linear one, but allows the study of the plasma evolution. - This task can be accomplished only due to the grid computing capabilities.. - The microwave beam for plasma heating can be simulated by a bunch of independent rays with different wave numbers. - The microwave beam is simulated by 100-200 rays in the usual situations, where electromagnetic waves are used to heat the plasma. - In these cases about (100-200 rays) x (100- 200 wave numbers) ~10 5 rays can be needed to have a good description of the plasma behaviour. - The TRUBA code has been ported to the grid using the Gridway metascheduler [15] to perform massive ray tracing. - The application that runs on the grid is called MaRaTra (Massive Ray Tracing) [16]. - 3.3 NBI heating: FAFNER2 on the grid. - The collisions will ionize the incoming hot neutrals that will deposit their energy in the plasma.. - FAFNER2 code is the common tool that is used in the. - Every neutral trajectory is estimated in a single CPU of a computing element of the grid and the birth points in the 5D space (3D in real space plus 2D in velocity space) of ions are calculated.. - Figure 3 shows the escape points of the fast particles as coming from FAFNER2 calculations after followed their trajectories using ISDEP. - Escape points of the fast ions as coming from FAFNER2 calculations after following their trajectories using ISDEP.. - Therefore, it can be necessary to use a standard tool to estimate the transport in a way in which the electric field can be calculated self-consistently. - This can be done using the standard neoclassical transport code DKES (Drift Kinetic Equation Solver), which is very common among the stellarator community. - DKES estimates the mono-energetic transport coefficients, valid for a single particle of given energy, which must be convoluted with the Maxwellian distribution function of the particles (ions and electrons) in order to obtain the final coefficients for all the plasma species. - Every mono-energetic coefficient must be estimated on a single node of the grid. - Once a large number of values are obtained for different plasma parameters (namely electric potential and collisionality) the final transport coefficients can be estimated. - The density and temperature gradients are ingredients to obtain the fluxes and, from the latter, the electric field can be calculated. - The use of the grid for running DKES code allows us to obtain a well calculated monoenergetic coefficients as a function of the input parameters, thus allowing a more precise estimation of the matrix of coefficients.. - Stellarators are steady state devices and are free from disruptions, which are the main caveats of the tokamak configuration. - Nevertheless, the problem is that there is not a unique stellarator configuration that can be proposed as a candidate for the reactor. - The optimization can be performed numerically by variation of the magnetic field parameters. - The outermost magnetic surface can be described by about 120 Fourier modes. - The optimization criteria can be:. - Metaheuristics can be used to select the optimum configuration for given target functions.. - As a first step, we minimise the drift velocity of the particles, which in principle would imply the improvement of the confinement of the device. - All the population elements are chosen by using a tournament selection of a size of two and the worst one of the pair is randomly crossed with values of the best individual.. - With crossover operator this can be easily done with the proper initial random generation. - The first execution of the genetic algorithm generates a random population of 1,000 individuals where the initial values of every parameter are into some predefined values for each of them.. - Overview of a GA on the grid.. - Once the equilibrium for the configurations has been obtained, the algorithm selects the different individuals of the population by pairs, using a tournament selection method, and performs a crossover replacing the chromosomes of the worst element, i.e., the one with higher value for the fitness function, and inserting the new element instead of the selected one.. - This function assures some level of convergence in the values of chromosomes, even though this is only noticed after a long number of generations, as well as a large diversity of the population. - The mutation using the standard deviation value could be used too, but with that approach the dispersion of the population would become higher. - Figure 4 shows a GA running in the grid.. - Like for GAs, in this case all the control over the execution of the fitness functions, in fact, all the logic needed to carry out this algorithm, is executed in the User Interface, while the fitness function, which is the time demanding process, is executed in the different Worker Nodes of the grid infrastructure.. - The main advantage of porting this application to the grid is the capability of exploring a wide extension of the parameter space, which happens to be huge for this problem. - The usual optimization applications has the disadvantage of exploring a limited zone of the parameter space, so a local optimum is reached, while the parameter exploration performed here allows one to explore a wider parameter range and, probably, to find different locally optimal configurations.. - These applications are highly time consuming because of the large number of simulation particles and the phase space grid cells . - which could be needed in the simulation. - Traditional PIC module: solver of the Maxwell equations.. - During a PIC simulation the trajectory of all particles is followed, which requires the solution of the equations of motion for each of them. - This code is important to simulate the interaction of the plasma with some critical points of fusion devices, specially the divertor at the bottom of a vacuum vessel of a fusion reactor: its function is to protect the walls from the strong plasma fluxes and to exhaust the escaping power. - We have successfully ported to the grid the serial version of this application. - Time evolution of inwards (LHS) and outwards (RHS) particle fluxes (in arbitrary units) as functions of time, estimated on the grid.. - In order to obtain relevant physical results we decided to carry out a parameter scan of the input file. - Several different parameters can be explored like scrape-off layer width or the impurity species that are under consideration. - The code provides the time evolution of several quantities, estimated in the inner and outer walls. - The use of the grid for this application allows to explore a huge number of input parameters, which will provide an extensive study of the plasma-wall interaction depending of those parameters.. - These ones can be cyclic, linear or more complex and can include applications that run on different infrastructures. - Ideally, both types of large scale computing platforms must be available in order that the suitable architecture can be used for the application to run since both parallel and serial applications are needed in fusion, as has been discussed above. - As it has been described above, FAFNER estimates the birth point of fast ions in the 5D phase space (3D in real space plus 2D in velocity space). - These birth points can be taken as starting positions for running ISDEP and this exactly what we have done. - Figure 3 shows the distribution of hit points on the vacuum vessel of the TJ-II stellarator. - A very fruitful and flexible way to build workflows is to take the transport equations of the plasma. - The right hand side of this equation is can be given by function as complex as ne could imagine that need to be estimated numerically on HPC or on the grid. - For instance, this evolution equation can be solved by the transport code ASTRA (Authomatic System for Transport Analysis), where a complex heat diffusivity that must be estimated on an HPC using MPI has been introduced. - An example of the plasma evolution estimated using this workflow can be seen in Figure 7. - The range of problems solved and the techniques used have been increased from the first use of the grid for fusion. - Besides the large variety of grid applications, it is remarkable the wide range of problems solved using the grid. - Moreover, the present work shows the capability of grid techniques for helping to reach the full simulation of the numerical reactor, helping to the traditional HPC applications. - of the 2005 EGEE Conference. - of the 4 th EGEE/OGF User Forum. - Guasp and M.Liniers: “The Complex FAFNER/EIRENE at Ciemat: Scripts and file structure”. - Castejón, et al.“Calculated evolution of the Electron Bernstein Wave heating deposition profile under NBI conditions in TJ-II plasmas”.