Nonlinear relativistic gyrokinetic Vlasov-Maxwell equations

A set of self-consistent nonlinear gyrokinetic equations is derived for relativistic charged particles in a general nonuniform magnetized plasma. Full electromagnetic-field fluctuations are considered with spatial and temporal scales given by the low-frequency gyrokinetic ordering. Self-consistency is obtained by combining the nonlinear relativistic gyrokinetic Vlasov equation with the low-frequency Maxwell equations in which charge densities and current densities are expressed in terms of moments of the gyrokinetic Vlasov distribution. For these self-consistent gyrokinetic equations, a low-frequency energy conservation law is also derived.