Chapter 2
Geometrical optics
Geometrical optics of charged particle beams begins with relativistic classical mechanics, specifically, the motion of a charged
particle in the presence of external electric and magnetic fields.
The fields exert an instantaneous resultant force on the particle,
which determines the path of motion. Mathematically, the solution
consists of finding the three-vectors for position x and velocity v
at any time t, given initial values at time zero, taking account of
the influence of the fields.
Having found a prescription for solving a general particle trajectory, we can then apply this to families of trajectories. This permits
us to delineate the geometrical optical properties of a beam of particles. We begin with a review of relativistic classical mechanics,
focusing only on those specific topics which will lead directly to
geometrical optics.
19
Geometrical optics
Geometrical optics of charged particle beams begins with relativistic classical mechanics, specifically, the motion of a charged
particle in the presence of external electric and magnetic fields.
The fields exert an instantaneous resultant force on the particle,
which determines the path of motion. Mathematically, the solution
consists of finding the three-vectors for position x and velocity v
at any time t, given initial values at time zero, taking account of
the influence of the fields.
Having found a prescription for solving a general particle trajectory, we can then apply this to families of trajectories. This permits
us to delineate the geometrical optical properties of a beam of particles. We begin with a review of relativistic classical mechanics,
focusing only on those specific topics which will lead directly to
geometrical optics.
19