Systematic approximations for magnetized transit-time interactions

A systematic procedure is given for generating analytic approximations to the wave-particle energy transfer in magnetized transit-time interactions. The procedure can be applied to any wave-packet field structure, and yields especially simple results in the physically important limits of (i) small and large Larmor radius and (ii) small and large values of the ratio of the wave frequency to the cyclotron frequency. In many applications, the approximations developed here are the only viable means of calculating the wave—particle energy transfer, because the exact analytic theory and numerical test-particle calculations are too demanding computationally.