Exact guiding center model in symmetric magnetic fields

We show that magnetic fields with two continuous spatial symmetries possess exact constants of motion that agree with Kruskal's adiabatic invariant series to all orders when the gyroradius is sufficiently small. When paired with a recently developed non-perturbative guiding center model, these invariants lead to exact guiding center models, free of the cyclotron timescale, even for energetic particles with large gyroradii.