Non-linear gyrokinetic theory of magnetoplasmas

A crucial issue in relativistic plasma, particularly relevant in the astrophysical context, is the description of highly magnetized plasmas based on a covariant formulation of gyrokinetic dynamics. An interesting case in question is that in which the background electric field (produced either by the same plasma of by other sources) results suitably small (or vanishing) with respect to the magnetic field, while at the same time short-wavelength EM perturbations can be present. The purpose of this work is to extend the relativistic gyrokinetic theory developed by Beklemishev \textit{et al.} [1999-2005] to include, in particular, also the treatment of such a case. We intend to show that this requires the development of a perturbative expansion involving simultaneously both the particle 4-position vector and the corresponding \textit{4-velocity vector}. For this purpose a synchronous form of the relativistic Hamilton variational principle is adopted.