Dynamics of a three-dimensional charged particle dense bunch

Abstract

The behavior of a uniform charged particle bunch is studied. External and own bunch fields are taken into account. Two-dimensional and three-dimensional self-consistent problems are considered. The equations for bunch radii are obtained in the case of the bunch formed as a rotation ellipsoid. The model is proposed for the bunch with zero longitudinal emittance.

One-dimensional self-consistent kinetic models as Vlasov equation solutions

“…The linear equation for the independent beam particle oscillation has two independent integrals, whose combination or bilinear integral (or quadratic form with respect to the particle coordinates and velocities in the most general case) may be used as an invariant and be included into the distribution function. Similar invariants are developed for two-dimensional and three-dimensional configurations of the charged particle beams, one can see, for example, Yarkovoi (1966), Chikhachev (1984), Barminova & Chikhachev (1991), Danilov et al (2003) and Barminova & Chikhachev (2013). For some physical tasks the application of a 1-D approximation simplifies the analysis, so a one-dimensional model appears to be more useful, for instance, when considering the problem of wide flow propagation in plasma diodes and ion diodes (Barminova & Chikhachev 2012), or the propagation of the ribbon beams born in the terrestrial magnetosphere or in the laboratory while extracted from the ion and plasma sources with the slit geometry of extractors (Barminova 2014).…”