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Comment on "Electrostatic and magnetic transport of energetic ions in turbulent plasmas".

In a recent Letter [1], Hauff et al. state [see also Eq. (3) therein] without proof that the condition for the validity of orbit averaging is that the orbital time of the equilibrium periodic motion is shorter than the time for the perpendicular drift across a turbulence eddy by either the turbulence E B drift or the equilibrium magnetic drift. The authors further state that the equilibrium magnetic drift dominates over the perturbed E B drift in the high energy limit and that the orbit averaging is invalid since the perpendicular magnetic drift time is shorter than the equilibrium orbital time. This time-scale separation between the equilibrium drift across the eddy and the equilibrium periodic motion is identical to the spatial-scale separation between the turbulence eddy size ( c) and the guiding center orbit size ( r), as is plainly expressed in Eq. (4) of Ref. [1], which is independent of the turbulence intensity. This claim of a spatial-scale separation between equilibrium and perturbed fields is of both fundamental and practical significance. Fundamentally, the claim implies that the orbit-averaged theory is valid only if c > r. This claim contradicts the textbook [2–4] notion that the time-scale separation between equilibrium and perturbed motions is the only requirement for the validity of the wellestablished orbit-averaged theory [5–7] in plasma physics. Practically, the requirement of the spatial-scale separation leads to an energy scaling in Ref. [1] different from that of the orbit-averaged theory [6–8] for the turbulent transport of energetic trapped particles. In this Comment, we present a canonical perturbation theory to demonstrate that orbit averaging is valid for arbitrary radial eddy size. The orbit-averaged theory (averaging over the canonical angle variable) strictly follows from the existence of an adiabatic invariant (canonical action variable). The gyrokinetic quasilinear theory with orbit averaging for low-frequency electrostatic turbulence in an axisymmetric system has been rigorously derived [6]. Here we apply the general theory of Ref. [6] to the diffusivity for deeply trapped particles in a tokamak: