BREAKING OF THE 1ST ADIABATIC INVARIANTS OF CHARGED-PARTICLES IN TIME-DEPENDENT MAGNETIC-FIELDS - COMPUTER-SIMULATIONS AND THEORY

The mechanics of the first adiabatic invariant-mu of nonrelativistic charged particles in time-dependent magnetic inductions B(t) are studied by means of computer simulations and analytic theory. Linear-ramp magnetic-induction profiles B = B0 + (DELTA-B/DELTA-t)t are utilized, as well as hyperbolic-tangent ramps and sine half-wave ramps. The change in mu that results from an induction change DELTA-B that occurs over a time DELTA-t is quantified for all values of DELTA-B and DELTA-t, as well as for all values of the particle position. It is found that the cases fall into two categories with very different mu-behavior: cases in which the change in the magnetic induction occurs over a time DELTA-t that is exactly equal to an integer number of gyroperiods (textbook case) or cases in which the change in the induction occurs over a time DELTA-t that is not equal to an integer number of gyroperiods (more general case). In both categories-mu is an adiabatic invariant, although the conservation of mu is much poorer in the latter category. It is pointed out that, in addition to the well-known constraints on DELTA-B and DELTA-t there is a constraint on the particle's initial position in the magnetic field if the change in the adiabatic invariant is to be kept small.