Gyrokinetic

Gyrokinetic theory is a reduced kinetic description of magnetized plasmas that averages over the fast gyration of charged particles around magnetic field lines. By removing the rapid cyclotron motion, it focuses on slower dynamics such as turbulence and transport, while retaining essential kinetic effects like finite Larmor radius and wave–particle interactions. The theory reduces the full six-dimensional phase space to five dimensions by introducing guiding-center coordinates, with the distribution function depending on the guiding-center position, the parallel velocity, and the magnetic moment; the gyrophase is averaged out. This leads to the gyrokinetic equation, a form of the Vlasov equation for the gyrocenter distribution, coupled to Maxwell's equations through charge and current densities. Gyrokinetic simulations can be electrostatic or electromagnetic, linear or nonlinear, and often employ delta-f or full-f formulations. Gyrokinetics is widely used in fusion plasma research to study microinstabilities such as ITG, TEM, and KBM, and the resulting turbulent transport that limits confinement in devices like tokamaks and stellarators. The framework is implemented in multiple numerical codes (for example, GENE, GS2, GYRO, GKW) and supports both axisymmetric and three-dimensional magnetic configurations. It relies on scale separations: strong magnetic field, fluctuations with frequencies well below the cyclotron frequency, and perpendicular wavelengths on the order of the ion Larmor radius. Limitations include its reliance on strong magnetic field and well-separated scales; near magnetic reconnection regions or ultra-fast phenomena, full kinetic or hybrid models may be required. Gyrokinetics remains a central tool in theoretical and computational plasma physics for understanding confinement and transport.