Higher-Order Perturbations

  • Helmut Wiedemann


The rules of linear beam dynamics allow the design of beam transport systems with virtually any desired beam characteristics. Whether such characteristics actually can be achieved depends greatly on our ability or lack thereof to control the source and magnitude of perturbations. Only the lowest-order perturbation terms were discussed in [4.1] in the realm of linear, paraxial beam dynamics. With the continued sophistication of accelerator design and increased demand on beam quality it becomes more and more important to also consider higher-order magnetic field perturbations as well as kinematic perturbation terms.


Beam Line Linear Collider Perturbation Term Dispersion Function Beam Emittance 
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  1. 4.1
    H. Wiedemann: Particle Accelerator Physics I (Springer, Berlin, Heidelberg 1993)Google Scholar
  2. 4.2
    SLAC-LINEAR-COLLIDER. Conceptual Design Report, SLAC- 229 (1981)Google Scholar
  3. 4.3
    G.E. Fischer: Ground Motion and its Effects in Accelerator Design, ed. by M. Month, M. Dienes, AIP Conf. Proc., Vol.153 (American Institute of Physics, New York 1987)Google Scholar
  4. 4.4
    N. Vogt-Nielsen: Expansions of the characteristic exponents and the Floquet solutions for the linear homogeneous second order differential equation with periodic coefficients. Int. Note, MURA/NVN/3 (1956)Google Scholar
  5. 4.5
    H. Wiedemann: Chromaticity correction in large storage rings. Int. Note PEP- 220, SLAC (1976)Google Scholar
  6. 4.6
    P.L. Morton: Derivation of nonlinear chromaticity by higher-order “smooth approximation”. Int. Note PEP-221, SLAC (1976)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • Helmut Wiedemann
    • 1
  1. 1.Applied Physics Department and Synchrotron Radiation LaboratoryStanford UniversityStanfordUSA

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