  The exact energy and angular-momentum conservation laws are derived by
Noether method for the Hamiltonian and symplectic representations of the
gauge-free electromagnetic gyrokinetic Vlasov-Maxwell equations. These
gyrokinetic equations, which are solely expressed in terms of electromagnetic
fields, describe the low-frequency turbulent fluctuations that perturb a
time-independent toroidally-axisymmetric magnetized plasma. The explicit proofs
presented here provide a complete picture of the transfer of energy and angular
momentum between the gyrocenters and the perturbed electromagnetic fields, in
which the crucial roles played by gyrocenter polarization and magnetization
effects are highlighted. In addition to yielding an exact angular-momentum
conservation law, the gyrokinetic Noether equation yields an exact momentum
transport equation, which might be useful in more general equilibrium magnetic
geometries.
