Numerical Paraxial Approximation for Highly Relativistic Beams

F. Assous (Israel)

Keywords

Modelling and Simulation Methods, paraxial approxima tion, numerical schemes

Abstract

The numerical modelling in plasma physics as well as in microwave devices or accelarator technology, requires to develop methods for solving the time-dependent Vlasov Maxwell problem. Eventhough the numerical approxima tion of this complex system of equations is necessary in a number of cases, it leads however to very expensive com putations. For this reason, simpler models have been devel oped in many situations. Hence, when dealing with charged particle beams, it is often fruitful to exploit the paraxial property, i.e the property that the particles of the beam re main close to an optical axis. In a previous paper, such a model was developed and mathematically analyzed. We present here the resulting axisymmetric model, in case of highly relativistic beams. Then, numerical schemes are constructed and results to illustrate the ef´Čüciency of the model are presented.

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