Contents
1 Introduction: The optical nature of a charged particle beam
2.1 Relativistic classical mechanics
2.1.1 Hamilton’s principle of least action
2.1.2 The Hamiltonian function and energy conservation
2.1.3 Mechanical analog of Fermat’s principle
2.2 Exact trajectory equation for a single particle
2.3.2 Liouville’s theorem and brightness conservation
2.4.1 Equation of motion in terms of transverse coordinates and slopes
2.5.1 Exact equations of motion for axially symmetric fields
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