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Stationary self-consistent distributions for a charged particle beam in the longitudinal magnetic field

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Abstract

A review of analytical solutions of the Vlasov equation for a beam of charged particles is given. These results are analyzed on the basis of a unified approach developed by the authors. In the context of this method, a space of integrals of motion is introduced in which the integrals of motion of particles are considered as coordinates. In this case, specifying a self-consistent distribution is reduced to defining a distribution density in this space. This approach allows us to simplify the construction and analysis of different self-consistent distributions. In particular, it is possible, in some cases, to derive new solutions by considering linear combinations of well-known solutions. This approach also makes it possible in many cases to give a visual geometric representation of self-consistent distributions in the space of integrals of motion.

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  1. St. Petersburg State University, St. Petersburg, 199034, Russia

    O. I. Drivotin & D. A. Ovsyannikov

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Original Russian Text © O.I. Drivotin, D.A. Ovsyannikov, 2016, published in Fizika Elementarnykh Chastits i Atomnogo Yadra, 2016, Vol. 47, No. 5.

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Drivotin, O.I., Ovsyannikov, D.A. Stationary self-consistent distributions for a charged particle beam in the longitudinal magnetic field. Phys. Part. Nuclei 47, 884–913 (2016). https://doi.org/10.1134/S1063779616050038

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