An examination of the first adiabatic invariant for particles in time-dependent magnetic fields

Summary form only given, as follows. The mechanics of first-adiabatic-invariant conservation (and nonconservation) was investigated theoretically and by means of test-particle computer simulations. In a time-changing magnetic induction, it is found that adiabatic invariants can be broken even though the magnetic induction changes by only a small amount during one gyroperiod and even though the electromagnetic fields change only by small amounts over a gyroradius. For a linear-ramp magnetic induction, the change in the adiabatic invariant Δμ=μ_final-μ_initial was calculated as a function of the change in the induction ΔB and the time Δt over which that change occurs. For a group of particles all having the same initial value of μ and the same guiding center, expressions for the ensemble average and the standard deviation were obtained. The linear magnetic-induction ramp was compared with other forms of ramps, including the familiar hyperbolic-tangent ramp. The nonconservation of μ can lead to velocity-space diffusion for the particles of a plasma in a fluctuating magnetic field