  In fusion plasmas the strong magnetic field allows the fast gyro-motion to be
systematically removed from the description of the dynamics, resulting in a
considerable model simplification and gain of computational time. Nowadays, the
gyrokinetic (GK) codes play a major role in the understanding of the
development and the saturation of turbulence and in the prediction of the
subsequent transport. Naturally, these codes require thorough verification and
validation.
  Here we present a new and generic theoretical framework and specific
numerical applications to test the faithfulness of the implemented models to
theory and to verify the domain of applicability of existing GK codes. For a
sound verification process, the underlying theoretical GK model and the
numerical scheme must be considered at the same time, which has rarely been
done and therefore makes this approach pioneering. At the analytical level, the
main novelty consists in using advanced mathematical tools such as variational
formulation of dynamics for systematization of basic GK code's equations to
access the limits of their applicability. The verification of numerical scheme
is proposed via the benchmark effort.
  In this work, specific examples of code verification are presented for two GK
codes: the multi-species electromagnetic ORB5 (PIC) and the radially global
version of GENE (Eulerian). The proposed methodology can be applied to any
existing GK code. We establish a hierarchy of reduced GK Vlasov-Maxwell
equations implemented in the ORB5 and GENE codes using the Lagrangian
variational formulation. At the computational level, detailed verifications of
global electromagnetic test cases developed from the CYCLONE Base Case are
considered, including a parametric $\beta$-scan covering the transition from
ITG to KBM and the spectral properties at the nominal $\beta$ value.
