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@PHDTHESIS{Valetov:844677,
      author       = {Valetov, Eremey},
      othercontributors = {Berz, Martin and Senichev, Yury},
      title        = {{F}ield {M}odeling, {S}ymplectic {T}racking, and {S}pin
                      {D}ecoherence for {EDM} and {M}uon $g\textrm{-}2$
                      {L}attices},
      school       = {Michigan State University},
      type         = {Dissertation},
      publisher    = {ProQuest Dissertation Publishing},
      reportid     = {FZJ-2018-02062, FERMILAB-THESIS-2017-21. 1647076},
      pages        = {348 pages : figures, tables, listings},
      year         = {2017},
      note         = {Copyright 2017 Eremey Vladimirovich Valetov; Dissertation,
                      Michigan State University, 2017},
      abstract     = {While the first particle accelerators were electrostatic
                      machines, and several electrostatic storage rings were
                      subsequently commissioned and operated, electrostatic
                      storage rings pose a number of challenges. Unlike motion in
                      the magnetic field, where particle energy remains constant,
                      particle energy generally changes in electrostatic elements.
                      Conservation of energy in an electrostatic element is, in
                      practice, only approximate, and it requires careful and
                      accurate design, manufacturing, installation, and
                      operational use. Electrostatic deflectors require relatively
                      high electrostatic fields, tend to introduce nonlinear
                      aberrations of all orders, and are more challenging to
                      manufacture than homogeneous magnetic dipoles. Accordingly,
                      magnetic storage rings are overwhelmingly prevalent.The
                      search for electric dipole moments (EDMs) of fundamental
                      particles is of key importance in the study of C and CP
                      violations and their sources. C and CP violations are part
                      of the Sakharov conditions that explain the
                      matter–antimatter asymmetry in the universe. Determining
                      the source of CP violations would provide valuable empirical
                      insight for beyond-Standard-Model physics. EDMs of
                      fundamental particles have not to this date been
                      experimentally observed. The search for fundamental particle
                      EDMs has narrowed the target search region; however, an EDM
                      signal is yet to be discovered.In 2008, Brookhaven National
                      Laboratory (BNL) had proposed the frozen spin (FS) concept
                      for the search of a deuteron EDM. The FS concept envisions
                      launching deuterons through a storage ring with combined
                      electrostatic and magnetic fields. The electrostatic and
                      magnetic fields are in a proportion that would, without an
                      EDM, freeze the deuteron's spin along its momentum as the
                      deuteron moves around the lattice. The radial electrostatic
                      field would result in a torque on the spin vector,
                      proportional to a deuteron EDM, rotating the spin vector out
                      of the midplane.The principle of an anomalous magnetic
                      dipole moment (MDM) measurement using a storage ring, shared
                      by BNL's completed E821 Experiment and the ongoing E989
                      Experiment operated by Fermi National Accelerator Laboratory
                      (FNAL), requires injecting muons into a magnetic ring at the
                      so-called magic momentum. The magic momentum, as defined in
                      this context, would freeze the muon's spin vector along its
                      momentum if the anomalous MDM was zero. The spin precession
                      in the horizontal plane relative to the momentum is
                      proportional to the anomalous MDM.Storage rings for
                      measurement of EDM and anomalous MDM present a new frontier
                      in tracking code accuracy requirements. For accurate
                      tracking of storage rings with electrostatic particle
                      optical elements, it is necessary to model the fringe fields
                      of such elements accurately, in particular, because not
                      doing so provides a mechanism for energy conservation
                      violation. However, the previous research on fringe fields
                      tended to focus on magnetic rather than electrostatic
                      particle optical elements. We will study and model the
                      fringe fields of several electrostatic deflectors. Field
                      falloffs of electrostatic deflectors are slower than
                      exponential, and Enge functions are not suitable for
                      accurate modeling of these falloffs. We will propose an
                      alternative function to model field falloffs of
                      electrostatic deflectors. We will use conformal mapping
                      methods to obtain the main field of the Muon g-2 storage
                      ring high voltage quadrupole, and we will calculate its
                      fringe field and effective field boundary (EFB) using
                      Fourier analysis.Furthermore, we will study tracking of
                      storage rings with electrostatic elements using map methods.
                      We will find that, for simultaneous symplecticity and energy
                      conservation, it is only necessary to enforce symplecticity
                      in COSY INFINITY. We will model and track several benchmark
                      lattices – an electrostatic spherical deflector, a
                      homogeneous magnetic dipole, and a proton EDM lattice – in
                      COSY INFINITY and MSURK89, our in-house eighth order
                      Runge–Kutta–Verner tracking code. Finally, we will
                      investigate spin decoherence and systematic errors in FS and
                      quasi-frozen spin (QFS) lattices. Spin decoherence effects
                      are similar in FS and QFS lattices, and spin decoherence in
                      said lattices often remains in the same range over time,
                      indicating the feasibility of EDM measurement using FS and
                      QFS lattices.},
      cin          = {IKP-4},
      cid          = {I:(DE-Juel1)IKP-4-20111104},
      pnm          = {631 - Accelerator R $\&$ D (POF3-631) / 574 - Theory,
                      modelling and simulation (POF3-574) / 511 - Computational
                      Science and Mathematical Methods (POF3-511) / srEDM - Search
                      for electric dipole moments using storage rings (694340)},
      pid          = {G:(DE-HGF)POF3-631 / G:(DE-HGF)POF3-574 /
                      G:(DE-HGF)POF3-511 / G:(EU-Grant)694340},
      experiment   = {EXP:(DE-Juel1)JEDI-20170712},
      typ          = {PUB:(DE-HGF)29 / PUB:(DE-HGF)11},
      url          = {https://juser.fz-juelich.de/record/844677},
}