  A two-fold analysis of electromagnetic core tokamak instabilities in the
framework of the gyrokinetic theory is presented. First principle theoretical
foundations of the gyrokinetic theory are used to explain and justify the
numerical results obtained with the global electromagnetic particle-in-cell
code Orb5 whose model is derived from the Lagrangian formalism. The energy
conservation law corresponding to the Orb5 model is derived from the Noether
theorem and implemented in the code as a diagnostics for energy balance and
conservation verification. An additional Noether theorem based diagnostics is
implemented in order to analyse destabilising mechanisms for the electrostatic
and the electromagnetic Ion Temperature Gradient (ITG) instabilities in the
core region of the tokamak. The transition towards the Kinetic Ballooning Modes
(KBM) at high electromagnetic $\beta$ is also investigated.
