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@INPROCEEDINGS{Hoffstaetter:309979,
      author       = {Hoffstaetter, G. H. and Dumas, H. S. and Ellison, J. A.},
      title        = {{A}diabatic {I}nvariants for {S}pin-{O}rbit {M}otion},
      reportid     = {PUBDB-2016-04120, DESY-M-02-01S},
      pages        = {332-334},
      year         = {2002},
      abstract     = {It has been predicted and found experimentally that the
                      polarization direction of particles on the closed orbit can
                      be manipulated, without a noticeable reduction of
                      polarization, by a slow variation of magnetic fields. This
                      feature has been used to avoid imperfection resonances where
                      thespin precession frequency is close to a multiple of the
                      circulation frequency. We report here on a proof that
                      relates this property to an adiabatic invariant of spin
                      motion. The proof is relatively simple since only two
                      frequencies, the spin rotation frequency and the
                      particle’s rotation frequency on the closed orbit, are
                      involved. The invariant spin field describes a periodic
                      polarization state of a beam’s phase space distribution.
                      This invariant spin field leads to a very useful
                      parametrization of coupled spin and orbit dynamics. We also
                      report on a proof showing that the invariant spin field
                      gives rise to an adiabatic invariant of spin-orbit motion.
                      The proof is now much more complicated since the orbital
                      frequencies are involved. Due to this adiabatic invariance,
                      the spin field of a polarized beam follows slow changes of
                      the accelerator’s invariant spin field that can occur
                      during a slow acceleration cycle. This feature is essential
                      when high-order spin orbit resonances are crossed since it
                      allows a reduced degree of polarization at the resonance
                      condition to recover, to a large degree, after the resonance
                      has been crossed.},
      month         = {Jun},
      date          = {2002-06-03},
      organization  = {The 8th European Particle Accelerator
                       Conference, Paris (France), 3 Jun 2002
                       - 7 Jun 2002},
      keywords     = {talk: Paris 2002/06/03 (INSPIRE) / synchrotron: polarized
                      beam (INSPIRE) / polarization: resonance (INSPIRE) / spin:
                      orbit (INSPIRE) / invariance: adiabatic (INSPIRE) /
                      differential equations: perturbation theory (INSPIRE)},
      cin          = {M(-2012)},
      cid          = {$I:(DE-H253)M_-2012_-20130307$},
      pnm          = {Facility (machine) HERA (POF1-HERA-20130405)},
      pid          = {G:(DE-H253)POF1-HERA-20130405},
      experiment   = {EXP:(DE-H253)HERA(machine)-20150101},
      typ          = {PUB:(DE-HGF)29 / PUB:(DE-HGF)8},
      doi          = {10.3204/PUBDB-2016-04120},
      url          = {https://bib-pubdb1.desy.de/record/309979},
}