Introduction to Gyrokinetic Theory

Abstract: Gyrokinetics is a fundamental tool to study turbulence and transport

in magnetized plasmas, such as fusion or astrophysical plasmas. The

exact kinetic modeling of these systems is difficult due to the large

phase space and multiscale nature of the problem. Here, we exploit

the wide separation in spatial and temporal scales in such systems to

construct an adiabatic invariant of motion of single-particle motion,

the magnetic moment. By using the Lie transform, we derive a near-

identity non-canonical transformation that ensures both magnetic mo-

ment conservation and the preservation of the Hamiltonian structure

of the single-particle system. This new set of coordinates describes the

drift motion of particle gyrocenters where the fast cyclotron motion has

effectively been averaged out. With this set of coordinates in hand, we

then construct the gyrokinetic equation, leading to greatly simplified

dynamics and a reduction in the phase space.