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Modèle particulaire 2D et 3D sur GPU pour plasma froid magnétisé : Application à un filtre magnétique

Abstract : The PIC MCC (Particle-In-Cell Monte-Carlo Collision) method is a very powerful tool to study plasmas (we focus here on low temperature plasmas) since it can provide the space and time evolution of the charged particle velocity distribution functions under the effect of self-consistent fields and collisions. In an electrostatic problem, the method consists of following the trajectories of a representative number of charged particles, electrons and ions, in phase space, and to describe the collective interaction of the particles by solving Poisson's equation as the particles move. In a low temperature plasma, the trajectories in phase space are determined by the self-consistent electric field and by collisions with neutral atoms or molecules and, for large enough plasma densities, by collisions between charged particles. The computational cost of the method is very high in terms of CPU and memory resources, especially when multidimensional conditions must be taken into account and when steady state regimes are studied. This is because of the constraints (at least in explicit PIC simulations) on the time step (smaller than a fraction of the plasma period and inverse of the electron gyro frequency), on the grid spacing (on the order of the Debye length), and on the number of particles per Debye length in the simulation (larger than a few tens). The PIC MCC algorithm can be parallelized on CPU clusters (the treatment of particle trajectories is easy to parallelize, but the parallelization of Poisson's equation is less straightforward). The emergence of GPGPU (General Purpose computing on Graphics Processing Unit) in scientific computing opens the way to low cost massively parallel simulations by using the large number of processors of a graphic card to perform elementary calculations (e.g. computation of electron trajectories) in parallel. A number of numerical tools for GPU computing have been developed in the last 10 years. Furthermore, NVIDIA developed a programming environment called CUDA (Compute Unified Device Architecture, [1]) that allows to create efficient GPU codes. PIC modeling using GPU or a combination of GPU and CPU has been reported by several authors, however PIC models with Monte Carlo Collisions on GPU is an expanding area. To the best of our knowledge this work first reports results using a full GPU based implementation of 2D PIC-MCC model focused on low temperature magnetized plasma. Tracking of particles in PIC simulations involving no creation or loss of charged particles (e.g. periodic boundary conditions, no ionization) is straightforward. However, we need special reordering strategy when charged particle creation or loss is taken into account (e.g. ionization, absorption, attachment etc.). This thesis highlights the strategies which can be used in GPU PIC-MCC models to overcome the difficulties with particle reordering during particle creation and loss. The aim of this work is to propose PIC MCC algorithms to be implemented on GPU, to measure the efficiency of these algorithms (parallelization) and compare them with calculations on a single CPU, and to illustrate the method with an example of plasma simulation in a low temperature magnetized plasma. Our purpose is to describe the detailed features of the CUDA code that has been developed and to give an overview of the possibilities and constraints of programming a PIC MCC algorithm on a GPU, and to provide an estimate of the gain in computation time that can be obtained with respect to a standard CPU simulation. The discussion is focused on 2D simulations. The method we have developed has however already been implemented for 3D problems. The manuscript is organized as follows. Chapter I gives a state of art of CPU and GPU architectures and an overview of GPU computing and of the CUDA environment. The basic principles of PIC MCC simulations are presented in chapter II. Our implementation of the PIC MCC algorithms (particle position updating, charge density assignment, Poisson solver, field interpolation, Monte Carlo collisions, generation of Maxwellian distributions of particles) is described also in this chapter. Chapter III presents simulation results for the example of a low temperature magnetized plasma under conditions similar to those of a negative ion source for neutral beam injection in fusion plasmas. We discuss in the chapter II the computation times of different parts of the simulation and the total computation time as a function of parameters such as the number of particles or the number of grid cells. In the Chapter III, we discuss about the physics of a magnetic filter for the negative ion sources and a theoretical analysis of the electronic transport through the magnetic barrier is shown. Finally, 3D simulations are used to compare results with 2D simulations, but a more detailed analysis still have to be done !
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Jonathan Claustre. Modèle particulaire 2D et 3D sur GPU pour plasma froid magnétisé : Application à un filtre magnétique. Plasmas. Université Paul Sabatier - Toulouse III, 2012. Français. ⟨tel-00796690⟩

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