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Concept# Particle-in-cell

Summary

In plasma physics, the particle-in-cell (PIC) method refers to a technique used to solve a certain class of partial differential equations. In this method, individual particles (or fluid elements) in a Lagrangian frame are tracked in continuous phase space, whereas moments of the distribution such as densities and currents are computed simultaneously on Eulerian (stationary) mesh points.
PIC methods were already in use as early as 1955,
even before the first Fortran compilers were available. The method gained popularity for plasma simulation in the late 1950s and early 1960s by Buneman, Dawson, Hockney, Birdsall, Morse and others. In plasma physics applications, the method amounts to following the trajectories of charged particles in self-consistent electromagnetic (or electrostatic) fields computed on a fixed mesh.
Technical aspects
For many types of problems, the classical PIC method invented by Buneman, Dawson, Hockney, Birdsall, Morse and others is relatively intu

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The ring cyclotron of the Paul Scherrer Institute (PSI) accelerates an intense proton beam from 72MeV up to 590MeV. This happens in four cavities of very high quality factor, oscillating in the fundamental mode. The beam can excite parasitic oscillation modes (HOMs), because of its time structure. Measurements showed that their field can leak out into the vacuum chamber. Until now, there is no tool available to predict the potentially harmful effect of these HOMs onto the beam operation of the cyclotron. It is foreseeable that these effects might play a role if even higher beam currents have to be accelerated. This dissertation therefore deals with the numerical analysis and measurement of beam-cavity interactions. First calculations for a single cavity, interacting with a proton bunch were performed with MAFIA's eigenmode- (E3), time domain- (T3) and particle-in-cell (TS3) solvers. However, the structured grid and the limited computing performance of MAFIA make realistic simulations impossible. A simplified computation method is developed in this dissertation since a self-consistent simulation is impossible on today's computers: The parallel eigensolver Omega3P of the Stanford Linear Accelerator Center (SLAC) allowed us to calculate eigenmodes of the entire ring cyclotron for the first time ever. The rf fields are expanded onto a superposition of these modes and the excitation is calculated in frequency domain. Trajectories of the particles in the static magnetic field, superposed with the space charge fields and the beam excited HOMs, are then simulated. However, the quantitative accuracy of this model is still limited. On the one hand, because of the simplification in the geometry of the simulated rf structure, which otherwise would lead to a problem size going beyond the available computing resources. On the other hand, because it is not yet possible to simulate strongly absorbing boundaries more accurately. The simulation results confirm that up to proton beam currents of 2mA, corresponding to the routinely accelerated beam intensities, only a small deformation of the charge distribution appears. This thesis leads to a new simulation tool for further studies of intensity increases in high power cyclotrons.