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A canonical 8-dimensional formalism for classical spin-orbit motion in storage rings

I. A new pair of canonical spin variables

  • Theoretical Physics
  • Published:
Zeitschrift für Physik C Particles and Fields

Abstract

In this paper we present a classical symplectic treatment of linear and nonlinear spin-orbit motion for storage rings using a fully coupled eight-dimensional formalism which generalizes earlier investigations of coupled synchro-betatron oscillations [1, 2] by introducing two new real canonical spin variables which behave, in a small-angle limit, like those already used in linearised spin theory. Thus in addition to the usualx−z−s couplings, both the spin to orbit and orbit to spin coupling are described canonically. Since the spin Hamiltonian can be expanded in a Taylor series in canonical variables, the formalism is convenient for use in 8-dimensional symplectic tracking calculations with the help, for example, of Lie algebra or differential algebra [3, 4], for the study of chaotic spin motion, for construction of spin normal forms and for studying the effect of Stern-Gerlach forces [5].

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  1. Deutsches Elektronen-Synchrotron DESY, D-22603, Hamburg, Germany

    D. P. Barber, K. Heinemann & G. Ripken

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  1. D. P. Barber
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  2. K. Heinemann
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  3. G. Ripken
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Barber, D.P., Heinemann, K. & Ripken, G. A canonical 8-dimensional formalism for classical spin-orbit motion in storage rings. Z. Phys. C - Particles and Fields 64, 117–142 (1994). https://doi.org/10.1007/BF01557243

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