Titlebook: Classical Mechanics and Electromagnetism in Accelerator Physics; Gennady Stupakov,Gregory Penn Textbook 2018 Springer International Publis

Madrigal

The Basic Formulation of Mechanics: Lagrangian and Hamiltonian Equations of Motionuations of motion and discuss the transition from Lagrange’s to Hamilton’s equations. We write down the Lagrangian and Hamiltonian for a charged particle in an electromagnetic field, and introduce the Poisson bracket.

GIST

极少

Action-Angle Variables for Betatron Oscillationsthe action remains constant and the angle increases linearly with time. With minor modifications, the same transformation can be applied to the Hamiltonian (.) that describes betatron oscillations in an accelerator. This yields an invariant of the motion and is also a useful starting point for analyzing more complicated dynamics.

endoscopy

Magnetic Field and Energy Errors, the particle energy in the beam deviates from the reference energy for which the ideal closed orbit is designed. It is important to understand what new effects the non-ideal magnetic fields introduce to the particle motion. In this chapter, we study how the dipole and quadrupole field errors as well as small energy deviations affect the orbits.

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Ardent

Gennady Stupakov,Gregory PennProvides a well-organized broad introduction based on the author‘s extensive research and teaching experience.Develops in-depth understanding of fundamental concepts of electromagnetic radiation.Intro

Ballerina

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Myofibrils

collagen