Particle Description of the Magnetosphere

Abstract

It is more than merely a therapeutic exercise to realize that everything that happens to a charged particle moving in an electromagnetic field is given by the basic equation of motion

$$ {\rm\bf F}={{\rm d\bf p}\over {\rm d}t}=Ze\Big({{\rm\bf v}\over c}\times {\rm curl{\bf A}}-{1\over c}{\partial{\bf A}\over \partial t}-{\rm grad}\ U\Big).$$

((1))

Here F is the force acting on the particle of charge Ze that moves with velocity v and momentum p in the electromagnetic field determined by the vector potential A and scalar potential U. The first term on the right in (1) serves only to deflect the particle without changing its energy, while the remaining terms are due to the electric field and can change both the direction of motion and the energy of the particle. Regardless of the complexity of the description of charged particle motion, one must always be able to identify what happens within the framework of the above fundamental equation.