On Validity of Gyrokinetic Theory

We study the validity of gyrokinetic theory by examining the destruction of magnetic moment adiabatic invariant in the presence of fluctuations. Contrary to common assertions, it is shown for the first time that the gyrokinetic theory rests not only on the magnetic moment conservation, but also on the fact that the particle dynamics constitutes a boundary layer problem. For low frequency fluctuations, there exists a quantitative, frequency independent threshold below which the adiabaticity is preserved, allowing thereby the general validity of gyrokinetic theory. The adiabaticity threshold in the high frequency regime, however, depends sensitively on frequency, which questions the generalization of gyrokinetic equation to arbitrary frequencies. Further analyses suggest that it is not feasible to construct a reduced kinetic equation based on superadiabaticity.