Boundary of the adiabatic motion of a charged particle in a dipole magnetic field

The motion of a charged particle in a dipole magnetic field is considered using a quasi-adiabatic model in which the particle guiding center trajectory is approximated by the central trajectory, i.e., a trajectory that passes through the center of the dipole. A study is made of the breakdown of adiabaticity in the particle motion as the adiabaticity parameter chi (the ratio of the Larmor radius to the radius of the magnetic field line curvature in the equatorial plane) increases. Initially, for chi greater than or equal to 0.01, the magnetic moment mu of a charged particle undergoes reversible fluctuations, which can be eliminated by subtracting the particle drift velocity. For chi greater than or equal to 0.1, the magnetic moment mu undergoes irreversible fluctuations, which grow exponentially with chi. Numerical integration of the equations of motion shows that, during the motion of a particle from the equatorial plane to the mirror point and back to the equator in a coordinate system related to the central trajectory, the analogue of the magnetic moment mu is conserved. In the equatorial plane, this analogue undergoes a jump. The long-term particle dynamics is described in a discrete manner, by approximating the Poincare mapping. The existence of the regions of steady and stochastic particle motion is established, and the boundary between these regions is determined. The position of this boundary depends not only on the adiabaticity parameter chi but also on the pitch angle. The calculated boundary is found to agree well with that obtained previously by using the model of a resonant interaction between particle oscillations associated with different degrees of freedom. (C) 2002 MAIK "Nauka/Interperiodica".