Short waves and cyclotron losses in the relativistic gyrokinetic theory
  Radiation damping of the motion of charged particles in relativistic, optically thin plasmas is described within the framework of the covariant gyrokinetic theory. It involves description of the collisionless single-particle dynamics as well as the Vlasov and Maxwell equations both written in the covariant formulation. The damping causes corrections to the phase-space trajectory of the particle, as well as to the form of the kinetic equation itself, due to the failure of conditions of the Liouville theorem. Both effects result independent of the gyrophase, which is retained as an ignorable variable. In addition, the applicability range of the covariant gyrokinetic theory is extended to describe short-wavelength perturbations with the background of zero parallel electric field. The presented theory is suitable for description of magnetized, relativistic, collisionless plasmas in the context of astrophysical or laboratory problems. Non-uniquenes of the gyrokinetic representation and consequences thereof are discussed. 
A.Beklemishev (Budker Inst.of Nucl.Phys., Novosibirsk) and   M.Tessarotto (Trieste U. and CMFD, Trieste)