Approximate integrals of radiofrequency-driven particle motion in a magnetic field

For a particle moving in a non-uniform static magnetic field under the action of a radiofrequency wave, ponderomotive effects result from radiofrequency-driven oscillations nonlinearly coupled with Larmor rotation. Using the Lagrangian and Hamiltonian formalisms, we show how, despite this coupling, two independent integrals of the particle motion are approximately conserved. These are the magnetic moment of free Larmor rotation and the quasi-energy of the guiding center motion parallel to the d.c. magnetic field. Under the assumption of non-resonant interaction of the particle with the radiofrequency field, these integrals represent adiabatic invariants of the particle motion.