Conservation of Magnetic Moment

Abstract

An approximate method for describing the motion of charged particles in a magnetic field as a combination of cyclotron gyration and drift motion is called the adiabatic or drift approximation. In the adiabatic approximation certain quantities can be assumed to be conserved. These quantities are called adiabatic invariants. One of these is the angular momentum Mvr. The angular momentum of the cyclotron gyration is obtained if we substitute the cyclotron radius rc for r:

$$Mv{r_c} = \frac{{M{v^2}}}{{{\omega _c}}} = \frac{{{M^2}{v^2}}}{{Ze\,B}}.$$