Cole Stephens, IFS, UT-Austin

"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 moment 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.