Adiabatic motion in a charged particle trap

Synopsis The adiabatic invariants associated with the motion of charged particles, trapped in electromagnetic fields with rotational and reflection symmetry, have been studied using classical methods based on the Hamilton-Jacobi equation. It has been shown that results, valid for trapping in purely magnetic configurations, may be applied in the analysis of electromagnetic charged particle traps, provided that suitably modified expressions are used for the angular frequencies in the various dynamical modes. Attention is drawn to circumstances in which the adiabatic conditions may be violated because of cancellation of electric and magnetic terms in the equations.