First adiabatic invariant of a charged particle modified in a time-dependent magnetic field

The mechanics of the change of the first adiabatic invariant of a nonrelativistic charged particle due to the linear change with time of the spatially-uniform magnetic induction is studied with the aid of an approximate analytic formalism. The same formalism enables one also to undertake an analytic study of the motion of the guiding center of the gyrating particle. The accuracy of the formalism is checked by comparing it with numerical calculations. The results obtained within the formalism are thoroughly compared with a former study of the mechanics of the change of the first adiabatic invariant done by Borovsky and Hansen [Phys. Rev. A 43, 560 (1991)] mainly on the basis of computer simulations. The examined changes of the magnetic field are small compared to the original field and occupy a-time period much longer than one gyroperiod. (C) 1999 American Institute of Physics. [S1070-664X(99)00702-8].