On nonlinear dynamics of a sheet electron beam

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

“…In the nonlinear case some additional assumptions should be made. For this aim, the modified one-dimensional invariant should be used (Barminova 2014), which allows us to study beams with both strong and weak nonlinearity. In figure 2 the case of a weak self-field nonlinearity, caused by the deviation of the charge distribution from uniformity, is illustrated.…”

“…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). Such models may be useful to study the laser-plasma interactions too (Bertrand et al 2005).…”