Coordinate System and Hamiltonian for a Circular Accelerator

  • Gennady StupakovEmail author
  • Gregory Penn
Part of the Graduate Texts in Physics book series (GTP)


In this chapter, we derive the Hamiltonian for a particle moving in a circular accelerator. Our derivation uses several simplifying assumptions. First, we assume that there is no electrostatic field, \(\phi = 0\), and the magnetic field does not vary with time. Second, the magnetic field is arranged in such a way that there is a closed reference (or nominal) orbit for a particle with a nominal momentum \(p_0\)—this is achieved by a proper design of the magnetic lattice of the ring. We will also assume that this reference orbit is a plane curve lying in the horizontal plane. Our goal is to describe the motion in the vicinity of this reference orbit of particles having energies (or, equivalently, momenta) that can slightly deviate from the nominal one.


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© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.SLAC National Accelerator LaboratoryStanford UniversityMenlo ParkUSA
  2. 2.Lawrence Berkeley National LaboratoryBerkeleyUSA

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