  The main idea of Gyrokinetic dynamical reduction consists in systematical
removing of fastest scale of motion (the gyro motion) from plasma's dynamics,
resulting in a considerable model simplification and gain of computing time.
  Gyrokinetic Maxwell-Vlasov system is broadly implemented in nowadays
numerical experiments for modeling strongly magnetized plasma (both laboratory
and astrophysical). Different versions of reduced set of equations exist
depending on the construction of the Gyrokinetic reduction procedure and
approximations assumed while their derivation.
  The purpose of this paper is to explicitly show the connection between the
general second order gyrokinetic Maxwell-Vlasov system issued from the Modern
Gyrokinetic theory derivation and the model currently implemented in global
electromagnetic Particle in Cell code ORB5.
  Strictly necessary information about the Modern Gyrokinetic formalism is
given together with the consistent derivation of the gyrokinetic Maxwell-Vlasov
equations from the first principle of dynamics. Variational formulation of
dynamics is also used for simultaneously obtaining the corresponding exact
energy conservation law. The result of that explicit derivation is used for
verification of the energy conservation diagnostics currently implemented in
ORB5 code.
  This work subscribes into the context of codes verification project VeriGyro
currently run in IPP Max Planck Institut in collaboration with others European
institutions.
