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An Emission Model for the Particle-in-Cell Method

Technische Universität
Publication Date
  • Computer Science
  • Mathematics


The thesis ‘An Emission Model for the Particle-in-Cell Method‘, presents a comprehensive approach in simulating electron emission from a given electron source of any material type and geometrical shape. The model presented in this work is simple and computationally efficient. The shortcomings of the popular methods are circumvented and efficiency greatly enhanced in solving complex emission problems, which otherwise have remained un-addressed. In the beginning, the Theory of Electron Emission and the governing relations to model thermionic, field and photo emission are presented. The importance of having accurate field solutions on an arbitrary shaped emission surface is discussed. In this regard the Conformal Finite Integration Technique and its relevance in emission model is highlighted. The interaction of charged particles with external fields and the resulting dynamics is studied using the Particle-in-Cell method. A brief overview of this method and the time integration schemes of the particle equations of motion are presented. A vital component of the emission model is the initialization of the particle positions on the emitter. The initialization depends on the type of emission, the geometrical shape of the emitter and the initial conditions. To meet the requirements of any real time problem, we developed a Geometric Modeling tool that uses Constrained Delaunay Triangulation to generate a problem specific surface mesh necessary for initializing particles. In all practical problems, there is a limit to the current that can be drawn from the emitter. The limits can be classified as Space Charge Limited and Temperature Limited. The analytical solution to the space charge limited emission can be obtained using the 1D Child’s law. For practical problems, the Virtual Cathode method is widely used to obtain a 3D numerical solution of the Child’s law. There are obvious disadvantages in using this method which are highlighted. As an alternative, a Charge Conservation method is developed and its efficiency over the Virtual Cathode method is demonstrated. Finally the emission model is tested extensively in the case of planar, spherical and circular cylindrical diodes and a comparative study between the Virtual Cathode and Charge Conservation methods is presented. As an application problem, simulation of a Traveling Wave Tube Amplifier is performed at the end of the dissertation and the results are found to be in good agreement with the experiment.

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